Brazilian Ethanol: A Gift or Threat to the Environment? (Preliminary and Incomplete - Please Do Not Cite)

Transcription

1 Brazilian Ethanol: A Gift or Threat to the Environment? (Preliminary and Incomplete - Please Do Not Cite) Sriniketh Nagavarapu Department of Economics and Center for Environmental Studies Brown University ssn@brown.edu August 28, 2009 Abstract The Brazilian government has been pushing for changes to the United States extensive barriers to ethanol imports. However, removing these barriers would present a crucial environmental tradeoff. On the one hand, replacing US consumers use of petroleum and corn-based ethanol with Brazilian sugarcane-based ethanol could have a large positive impact on carbon emissions. On the other hand, this additional ethanol would require an expansion in sugarcane production that could lead to greater deforestation and other environmentally harmful land clearing in Brazil. This paper addresses this tradeoff by answering the question: Would freely importing Brazilian ethanol into the US lead to enough land clearing to offset the environmental benefits of greater ethanol use? To answer this question, I develop and estimate an empirical general equilibrium model of Brazil s regional agricultural markets. I estimate the model using rich household survey data, region-level data on production and land use, and data on the prices of key goods. I then use the estimates to simulate the effects of a change in US import barriers, where I examine the sensitivity of the results to alternative assumptions about the level of international ethanol prices after the policy change. Reassuringly, I predict that if the US could freely absorb Brazilian ethanol at a price 12% above the baseline, Brazil would supply 12.4 billion gallons of ethanol to the US with a decline of only 37 million acres of non-agricultural land. However, if the price rose 15%, Brazil would supply approximately 21 billion gallons to the US, and the additional 8.7 billion gallons of exports would require a large additional decline of 86 million acres, with a large share coming in the regions containing the Amazon Rainforest. Whether or not the US importing Brazilian ethanol is ultimately good or bad for the environment will turn on the exact nature of US and international demand in the future, as well as on the Brazilian government s ability to direct the above acreage declines away from the most environmentally important land. I owe a large debt to Thomas MaCurdy, John Pencavel, and Jayanta Bhattacharya for their advice, support, and encouragement. I am also grateful to Luigi Pistaferri and Aprajit Mahajan for their guidance. I benefited greatly from conversations with Orazio Attanasio, Nick Bloom, Marcus Edvall, Andrew Foster, Zephyr Frank, Giacomo De Giorgi, Gopi Shah Goda, Caroline Hoxby, Lovell Jarvis, Seema Jayachandran, Colleen Manchester, Naercio Menezes- Filho, Pedro Miranda, Jonathan Meer, Marc Muendler, Kevin Mumford, Gerald Nelson, Frank Wolak, attendees of Stanford s Applications Seminar, and members of Stanford s Labor Reading Group. Suggestions received in seminars at Brown University, RAND, the USDA, Mathetmatica Policy Research, and the AEA annual meetings are greatly appreciated. For their immense help with acquiring data used here, I thank Steven Helfand, Frank McIntyre, Marcia Moraes, and the staff at Fundacao Getulio Vargas. I appreciate the financial support provided by SIEPR for data acquisition and by the Taube/SIEPR dissertation fellowship. Remaining errors are, of course, my own. 1

2 1 Introduction Amid growing economic, security, and environmental concerns related to oil usage, the United States has shown interest in greater use of ethanol. The 2007 energy bill passed by the United States Congress requires that the total amount of transportation fuels used in the US contain at least a minimum level of renewable fuels in each of the next 14 years. For instance, renewables must constitute 11.1 billion gallons of total transportation fuel in 2009, 15.2 billion gallons by 2012, and 36 billion gallons by While bio-diesel may play a role in the coming years, this renewable fuel mandate will be fulfilled primarily through the use of ethanol. Brazil. No country is in a better position to take advantage of this surging interest in ethanol than Brazil s sugarcane-based ethanol has three important advantages over US corn-based ethanol. First, beginning in the 1970s, Brazil spent a substantial amount of government resources to develop infrastructure for ethanol production and distribution. Second, Brazil s natural endowments are conducive to growing sugarcane at low cost. Third, sugarcane can be converted into ethanol with a smaller energy input than that needed for corn. Brazil is the most cost- and energy-efficient producer of ethanol in the world, and the country has vast potential for expanding sugarcane cultivation further. Brazil would be a natural source of ethanol for the United States, except for one fact: The US protects its own, less efficient ethanol producers with a 2.5% ad valorem tariff and a 54 cent per gallon duty on imports. These recently extended measures have come under increasing criticism by the Brazilian government. In fact, the government has aggressively pitched freer markets for its ethanol as a potential win-win. Increased opportunities for ethanol export could help spur further economic development in Brazil. Meanwhile, the rest of the world would gain a significant environmental benefit as fossil fuels are displaced with a cost-competitive renewable alternative. 2 Nevertheless, more open markets for Brazilian ethanol generate uncertain implications for the environment in Brazil and elsewhere. There is a crucial tradeoff. On the one hand, Brazil s sugarcane-based ethanol is a renewable, lower-carbon alternative to petroleum and US corn-based ethanol. Replacing US consumers use of petroleum and corn-based ethanol with Brazilian ethanol could therefore have a large positive impact on carbon emissions. On the other hand, this additional sugarcane-based ethanol has to be produced somewhere in Brazil. In particular, the expansion in sugarcane production required to produce more ethanol could lead to greater deforestation and other environmentally harmful land clearing. This paper addresses this tradeoff by answering the research question: Would freely importing Brazilian ethanol into the US lead to enough land clearing to offset the environmental benefits of greater ethanol use? To answer this question, it is necessary to determine how responsive Brazilian ethanol production is to the opening of the market, and how much land will be brought into agriculture as sugarcane cultivation increases to support the greater ethanol production. Crucially, it is not suffi- 1 The Energy Independence and Security Act of 2007 became Public Law on December 19, The relevant portion of the law is Title II, Subtitle A, Section For instance, see Our Biofuels Partnership, by President Luiz Inacio Lula da Silva, in the March 30, 2007 edition of the Washington Post (page A17). 2

3 cient to simply examine ethanol and sugarcane production in isolation. As the US ethanol market opens, sugarcane prices will increase in each region of Brazil. Sugarcane supply in each region will respond to this change in prices. But precisely how much it will respond depends on a large number of factors. For instance, the appropriateness for sugarcane production of land not currently used for sugarcane will help determine the response on the extensive margin. On the other hand, the substitutability between labor and land will determine how feasible it is to cultivate existing land more intensively. This substitutability, along with the elasticity of labor supply to the sugarcane sectors, will have consequences for wages and the amount of labor used in sugarcane and other sectors, which will in turn impact sugarcane supply. Preferences for other goods and the ability to import these goods to satisfy domestic demand will also play a role. In summary, answering the question above involves the consideration of the intimate but complicated links between land use decisions, labor markets, and product markets. In view of this, in this paper I develop and estimate a general equilibrium model of regional agricultural markets in Brazil. The model consists of the intermediate good of sugarcane and five final goods ethanol, sugar, a non-sugarcane agricultural good, a non-agricultural good, and capital. Producers of these goods compete over the inputs of land, labor, capital, and sugarcane, with their input choices dependent on input prices and the relevant production functions. Heterogeneity enters the picture in two important ways. First, in each region, parcels of land have heterogeneous quality in the three possible uses of sugarcane, other agriculture, and non-agriculture. I derive the aggregate supply of sugarcane and other agriculture in each region by aggregating over the production of these heterogeneous parcels of land, which are individually being allocated to their highest profit use. Second, consumers have heterogeneous non-labor income and heterogeneous preferences for working in the various region/sector combinations, where the possible sectors in each region are sugarcane, other agriculture, and non-agriculture. I derive the aggregate supply of labor hours to each region/sector and the aggregate demand for each product by aggregating over these heterogeneous individuals. The resulting upward-sloping supply curves to sugarcane for land and labor are the most fundamental parts of the model; they capture the linkages between sugarcane production and the rest of the economy. Using data from the period, I estimate all parameters of the model using maximum likelihood methods. For the structural estimation, I bring together rich cross-sectional survey data, state-level information on production and land use, national income accounts data, and information on the prices of sugarcane and other goods. As described below, the use of the individual-level survey data aids in securing identification of the labor supply parameters. Despite the simultaneous use of individual-level and aggregate data, my methodology imposes constraints that ensure the logical consistency and coherence of the overall empirical model. I then use these parameters to perform simulation exercises in which I assess the consequences of changes in US policies regarding ethanol imports. I represent the change in US policy in a very simple way, as making international demand for Brazilian ethanol perfectly elastic at a price higher than the initial equilibrium price. 3 I include results from simulations of three alternative policy 3 The exact nature of the simulations will be discussed further below, but the form of the model requires the simulations to make assumptions about the movement of world sugar prices as well. 3

4 regimes, which set world ethanol prices at 10%, 12%, and 15% above the 2005 equilibrium price. I choose these numbers to keep the price of ethanol competitive with gasoline, while providing a range of possible consequences. When simulating the effect of opening up the international market for ethanol, I find that in all three regimes, a significant amount of ethanol could be produced for export. The increase in exports of ethanol is supported by a shift of sugarcane from sugar to ethanol production, as well as a growth in the total amount of land used for sugarcane in each region. Depending on the regime considered, exports are predicted to increase to 5.5, 12.4, or 21.2 billion gallons (in the 10%,12%, and 15% regimes, respectively). To provide an idea of how large these numbers are, consider that total ethanol production in the US in 2007 was 6.5 billion gallons. With 13 billion gallons of ethanol, the US could have used ten percent ethanol blends in all of its gasoline consumption in The 21.2 billion gallons from the 15% regime would satisfy almost the entire 2016 requirement for renewable fuels in the 2007 energy bill. Consequently, Brazil could provide enough ethanol to have a significant impact on the use of renewables in the US. However, we are equally interested in the impact of this increased supply on deforestation and other harmful land clearing. Here, the results are mixed. In interpreting them, it is important to keep in mind that all the regions in the model contain environmentally sensitive land of one sort or another. But from a carbon capture point of view, the Mato Grosso region is the most significant, since it is the region in the model that contains the largest amount of the Amazon Rainforest. 5 The increase in total agricultural land in the 10% and 12% regimes is moderate enough to think that significant environmental damage could be averted. For instance, moving from the baseline to the 12% regime increases exports by about 12 billion gallons, and leads to a predicted decline in non-agricultural land of only 37 million acres. Moving from there to the 15% regime induces an additional 8.7 billion gallons of exports, but requires a further predicted decline of a large 86 million acres. A large share of this decline comes in the Mato Grosso region. The regions are very broadly defined in the model, so it could be the case that even in this latter situation, the decreases in non-agricultural land do not come from deforestation, but rather from relatively unimportant areas. To understand the extent to which the carbon sink of forested land is lost would require more detailed, disaggregated analysis in the future. Nevertheless, from the results presented here, we can still make two conclusions: First, Brazil can supply up to 13 billion gallons of ethanol to the US without a large risk of significant deforestation or environmental damage; and second, supplying a much larger magnitude on the order of the complete renewable fuel mandates for 2016 and beyond could pose extreme risks in particular parts of Brazil. This paper complements recent work by Elobeid and Tokgoz (2008) and Nelson and Robertson (2008). 6 The former paper addresses the response of ethanol production in the US and Brazil to potential changes in U.S. trade policies by using a detailed model of ethanol demand and supply in the US, Brazil, and the rest of the world. Their model is then paired with an existing partial 4 Most vehicles in the US cannot run entirely on ethanol. For the source of these numbers, see the Department of Energy ar-ticle at http : //apps1.eere.energy.gov/news/news detail.cfm/news id = The exact regional classifications are described more completely in Chapter 2. 6 For other studies of the sugar and sugarcane industries, see Barros, de V. Cavalcanti, Dias, and Magalhaes (2005) and Moraes (2007), which focus on consequences for worker wages. 4

5 equilibrium model of agriculture in world markets. Nelson and Robertson (2008) examine the environmental impact in Brazil of greater incentives for bio-fuel production. These authors goals are broader than mine, in that they aim to simulate the effect of increasing maize and sugarcane prices on the expansion of total agricultural land, and then quantify the potential effects of this expansion on bio-diversity and carbon sequestration. They use detailed data on land-use for a recent year, as well as linked agro-climatic and socio-economic data, to estimate a non-linear model of the probability that parcels of land are used for particular purposes. 7 predict massive expansions in total agricultural land. Using this model, they I have a different focus and approach from these useful studies. In contrast to Elobeid and Tokgoz (2008), I instead focus on the details of agricultural production and land changes within Brazil. In doing so, as opposed to Nelson and Robertson (2008), I explicitly model linkages between land use decisions and labor markets. More generally, I use an estimable general equilibrium model. 8 This necessitates major simplifications in the modeling of trade policy and depiction of land quality relative to the previous studies. In exchange, the empirical general equilibrium model allows for a better understanding of the role of the labor market and results in parameters that emerge from the use of multiple years of data, rather than calibration. In this way, this paper is in the spirit of Foster and Rosenzweig (2003), who use a general equilibrium framework to examine empirically the relationship between agricultural production and deforestation in India. 9 They find evidence consistent with increased income leading to greater demand for wood, and hence more land devoted to forests. Here, I allow for migration (relatively unimportant in the Indian context) and estimate the general equilibrium model directly. not distinguish between the demand for forest products versus the demand for non-sugarcane agricultural goods, or the use of land for forest versus non-sugarcane agriculture. is most important to know how much land is left out of production entirely. I do In Brazil, it The most recent Agricultural Census suggests that the large majority of privately owned natural forest land in Brazil is used for uses other than sustainable wood products, including the grazing of animals and growing of particular crops. Meanwhile, planted forests may have a very different biological composition than virgin land, and therefore be less acceptable from an environmental point of view. To the extent that privately managed production on forest land is environmentally sustainable and non-invasive, my results over-state the threat to environmentally sensitive areas. The remainder of the paper proceeds as follows. Section 2 provides an overview of sugarcane and ethanol production in Brazil. It begins by briefly describing the sugarcane and ethanol industries, and then illustrates differences across regions in production levels, land usage, and wages. Section 3 develops the general equilibrium model. The sub-sections describe the various components of 7 For details on methods, see Nelson and Geoghegan (2002). For studies using broadly similar methods, see Pfaff (1999) and Pfaff and et al. (2007). 8 There are also studies of agricultural trade liberalization in Brazil that have used computational general equilibrium models. See de Souza Ferreira Filho and Horridge (2005) and Bussolo, Lay, and van der Mensbrugghe (2004). For an interesting blend of the CGE approach with use of household survey data in a different country, see Ravallion (2004). 9 Some empirical work on deforestation looks at another sort of detail, namely the management of forests by communities in developing countries (see, for example, Edmonds (2002), Alix-Garcia (2008), and Alix-Garcia (2007)). 5

6 the model and how these components come together. A final sub-section discusses limitations of the model. Section 4 describes the the sources of data, as well as how the raw data is used to construct empirical analogues to quantities in the model. Section 5 takes the model to the data. It begins by testing a few of the implications of the model and describing the structural estimation approach in detail. It goes on to cover the estimation results. Section 6 describes the policy simulations. The first section details the assumptions and methods behind the simulations, and the second section shows results from the simulations. These results answer the research questions posed above. Section 7 concludes. 2 The Sugarcane and Ethanol Industries in Brazil This section describes aspects of the sugarcane and ethanol industries that are essential to understanding the debate behind the research question and formulating the model. Specifically, in the first section, I briefly examine regional differences in production to illustrate the arguments of those in favor of greater production of Brazilian ethanol, as well as the arguments of those who are concerned about this prospect. In the second section, I discuss key features of the industries that the model should be able to capture. I refer to tables and figures that rely on a wide variety of data sources, and I leave the description of these data sources to Chapter Regional Patterns of Production and the Ethanol Debate Figure 3 is a map of Brazil, where I have divided states into eight regions. This is the regional classification that I will use in the remainder of the paper. I choose to group states together into regions based primarily on geographical proximity, but also consider anecdotal evidence about the integration of labor markets. The states composing these regions are: Parana, Santa Catarina, and Rio Grande do Sul (region 1); Sao Paulo (region 2); Minas Gerais, Rio de Janeiro, and Espirito Santo (region 3); Bahia and Sergipe (region 4); Mato Grosso, Mato Grosso do Sul, Goias, Tocantins, and the Federal District (region 5); Pernambuco, Alagoas, Paraiba, and Rio Grande do Norte (region 6); and Maranhao, Piaui, and Ceara (region 7). 10 In the analysis, I do not include the remaining states of Brazil, which all come from the sparsely populated North Census region of Brazil. This is unfortunate, given that the majority of the Amazon Rainforest is located in this region. However, household survey data do not contain representative information on the rural parts of these states for years before In determining the number of regions, I strike a balance between, on the one hand, using so few regions that important heterogeneity within regions is neglected and, on the other hand, using so many regions that the PNAD does not contain a reasonably large number of sugarcane workers in some regions. I sometimes refer to region 5 as the Center-West, even though Tocantins is technically a part of the North census region, and not the Center-West. I do so because Tocantins was once connected to Goias. 11 The North Census region is a small, though non-trivial, part of the economy. In a recent year, about 5% of GDP was produced in the North. Using the PNAD data described below, I find that in 2005, approximately 6.3% of the over-15 population lives in the North, and approximately 6.6% of over-15 workers are located in the North. To assess the importance of omitting the North for this analysis, it would be more helpful to look at migration rates into the North over the period. However, doing this in a complete fashion is again only possible after

7 For later reference, Table 1 displays the states composing each region. The second column provides the shorthand reference that I use to refer to each region in future tables. The table also shows how each of my regions come together to form the government-defined Census regions. To avoid confusion, whenever I use the term region in the paper, I am referring to my definition of the seven regions and not the Census definition. Table 1: Composition of Regions Region Number Shorthand Reference States Census Region 1 Parana Parana South Santa Catarina Rio Grande do Sul 2 Sao Paulo Sao Paulo Southeast 3 Minas Minas Gerais Southeast Rio de Janeiro Espirito Santo 4 Bahia Bahia Northeast Sergipe 5 Mato Grosso Mato Grosso Center-West Mato Grosso do Sul Goias Tocantins Federal District 6 Pernambuco Pernambuco Northeast Alagoas Paraiba Rio Grande do Norte 7 Maranhao Maranhao Northeast Piaui Ceara Note: The Federal District and Tocantins are not officially part of the Center-West Census region Regional Environmental Concerns Before discussing the regional pattern of sugarcane cultivation in Brazil, it is useful to describe the location of the most environmentally sensitive areas. The areas of primary environmental concern 7

8 are the Amazon Rainforest, the Atlantic Rainforest, and the Cerrado. 12 While many observers identify the carbon storage potential of the forested areas as the reason to protect them, it is also the case that all three areas contain a substantial amount of bio-diversity. Figure 4 shows the location of the Amazon and Atlantic Rainforests, outlined in black. The Brazilian portion of the Amazon covers the North Census region almost entirely. While the Legal Amazon includes the entirety of the states of Mato Grosso, Tocantins, and Maranhao (as depicted in the figure), the actual rainforest exists in only a portion of these states. Of these states, Mato Grosso is the most important, containing a substantial amount of rainforest still. The Atlantic Rainforest exists today only as a thin strip along Brazil s eastern coast, running from Rio Grande do Norte, down through Sao Paulo, and into the southernmost parts of Brazil. Anecdotally, government regulations concerning the Atlantic Rainforest are more effective than those concerning the Amazon. The original area of the savannas known as the Cerrado lie primarily in Mato Grosso, Mato Grosso do Sul, Tocantins, and Goias, though the area also covers the edges of neighboring states. Large swathes of this area are already under agricultural use (to a large extent, pasture), and there is concern about further expansion. This is especially true given that such small portions of the Cerrado are legally protected by the government Regional Pattern of Production With this context in mind, we can examine the regional pattern of production and better understand the debate over ethanol production in Brazil. One line of argument points to the current distribution of sugarcane across Brazil as evidence suggesting that a sugarcane expansion would have limited effects on the Amazon or the Cerrado. The current distribution reflects differing soil qualities, weather patterns, and other characteristics across regions, which together provide an advantage to current sugarcane-growing regions in any future expansion. The current pattern of production is illustrated in Figures 1 and 2 and Table 2. The first figure divides the hectares of cultivated land in sub-state administrative areas into eight quantiles, and depicts areas in higher quantiles with darker colors. The second figure instead classifies the administrative areas into eight bins of equal size. Both figures depict data from While the first figure shows the areas with the highest relative amounts of sugarcane production, the second figure makes clear that the majority of sugarcane in Brazil still comes from Sao Paulo in the Southeast. Table 2 puts numbers on these patterns. The table shows land allocations and production quantities in 2005 for all seven regions used in the analysis. Except for the sugarcane-growing states of Pernambuco and Alagoas (in the Pernambuco region), the South-Southeast portion of the country dominates sugarcane production. 13 This distribution of sugarcane production across Brazil suggests that any future sugarcane expansion might take place primarily in Sao Paulo, Pernambuco, and possibly other states in the South-Southeast. 12 The Pantanal, in Mato Grosso and Mato Grosso do Sul, is another ecologically rich area, but the threats to these wetlands do not come from agricultural expansion. 13 The differences in sugarcane production across regions translate naturally into differences in ethanol and sugar production. Table 3 displays differences across regions in ethanol and sugar production, as well as the value of that production. 8

9 The counter-argument to this point is that technological changes and other pressures can quickly lead to changing patterns of cultivation. This view gains support in an examination of the regional trends over time. First, to put the regional trends into context, it is helpful to first look at trends in the prices of sugarcane, sugar, and ethanol. Figures 5 and 6 illustrate the changes over time in these prices. Movement in the absolute level of prices appears in Figure 5, while the latter figure depicts the price of each good relative to its level in The petroleum price is provided for the sake of comparison. In order to think about the economic incentives for allocation of land across uses, one should also consider movements in prices of non-sugarcane agriculture. Figure 7 compares changes in the relative price of sugarcane to the relative price of other agriculture, using 1990 as the base year in both cases. How did sugarcane land allocations and production levels change in each region over this time? Consider Figures 8 and 9, which show the relative sugarcane land share over time for each region, taking the base year for each region as Since the total land area of each region is fairly constant over time, these figures could also be interpreted as depicting movements in the relative sugarcane land acreage over time. The top panel shows the trends for the four regions in the Center-South, and the bottom panel refers to the regions in the Northeast. In all the regions, sugarcane land grows over the period, though data for the Mato Grosso region are not available in this period. Since 1990, the picture is very different. In the Center-South, all regions except Minas Gerais show growth since 1990, while no regions in the Northeast show growth since The strongest relative growth is in Mato Grosso, where new seed varieties made sugarcane production possible in the Center-West soils. The introduction of new distilleries will also have played an important role. 15 In summary, these figures tell a very different story from the crosssectional distributions for 2005 and 2007, and suggest that growth in sugarcane cultivation may not be confined to Sao Paulo and Pernambuco. The movements over time and the cross-sectional distributions of regional sugarcane production are each consistent with one line of argument in the ethanol debate in Brazil. In reality, the patterns in all the tables and figures above are the result of a complicated set of interactions. The model in this paper is a vehicle to disentangle the various forces at work and predict the response to an opening of the international market to Brazilian ethanol. 2.2 Important Features of the Sugarcane and Ethanol Industries The most important features of the industries, and ones that are reflected in the model below, are: Demand for sugarcane comes almost completely from ethanol and sugar mills. Sugarcane is essentially an intermediate good, in that the vast majority is used for ethanol and sugar 14 Note that this is the share of land cultivated with sugarcane. It is not the share of land planted with sugarcane. Examination of the data suggests that there is a very close correspondence between the amount cultivated and the amount planted in almost all regions and periods, though this could be the result of poor data rather than actual fact. 15 The patterns in these figures resemble the patterns in Figures 10 and 11, which illustrate the movement in relative production over time for each region, again taking 1990 as the base year. 9

10 production. 16 In some cases, sugar and ethanol are produced in distinct facilities by distinct producers; in others, a single producer can produce both goods. 17 In total, there are more than 300 distilleries capable of producing ethanol in Brazil, with new projects appearing at a rapid pace. Land is very heterogeneous in effectiveness for sugarcane production. Two different parcels of land may be the same size, but have very different appropriateness for sugarcane production. Four factors in particular help to determine the appropriateness of a given parcel: precipitation; soil make-up; gradient; and distance to the nearest mill. The first two are selfexplanatory. The gradient of the land is important because flatter land is easier to harvest, either with manual harvesting or if the capital is available mechanical harvesting. 18 Labor productivity varies markedly across regions. The household survey data, in combination with the data on sugarcane production, reveal substantial regional differences in labor productivity. Table 4 shows median hours of work and estimated total number of workers in 2005 in each sector/region combination. By comparing this with the production totals in Table 2, one sees that the Center-South regions have a strikingly higher level of production per hour of labor. Sao Paulo and Mato Grosso generally show the highest labor productivities. To the extent that wages are competitively determined, differences in sugarcane wages across regions will reflect differences in the marginal product of labor. Table 5 shows median wages in sugarcane, and indicates that the marginal product of labor is also higher in the Center-South. 19 Sugarcane work generally comes with a wage premium. Table 5 illustrates that sugarcane wages in 2005 were generally higher than wages in other agriculture. This is not confined to Figures 12 and 13 depict the evolution of median hourly wages in sugarcane, other agriculture and non-agriculture in each of the seven regions. For many of the regions, there is a persistent gap between sugarcane wages and other agricultural wages; in fact, sugarcane wages sometimes approach the level of non-agricultural wages In a recent year, for example, approximately 10% of harvested sugarcane went to a use other than ethanol and sugar. Such uses include chemical-based products, plastics, etc. 17 There is a limit to this flexibility, however. Anecdotally, most of these dual activity mills can move their ethanol production share between a range such as 45% to 55%. 18 The majority of production shifted from the Northeast to the Center-South of Brazil by the 1950s, partly because of the advantage of flatter lands. Productivity differences must have also played a role. Nunberg (1986) provides a detailed description of this shift over time, as well as an analysis of Brazilian sugarcane policies before the 1980s. 19 All wages are in 2000 Reais, and the Real/US Dollar exchange rate was approximately 1.84 Reais per US Dollar at the time. 20 In Mincer regressions not shown here, I examine the role of crop-specific wage premia for agricultural workers. I regress the logarithm of wages on controls for year, age, education, literacy, and gender, as well as on dummy variables for major agricultural activities (e.g., sugarcane, coffee, cocoa, livestock, etc.). I find large wage premia in sugarcane. This finding is not driven by the fact that the household survey takes place during the sugarcane harvest. Using data from the 2000 Census, which takes place at a different time period, I find the same feature. 10

11 3 Model I cover the key aspects of the model here, and then describe the model in more detail in the sections below. To begin with, the model is static. The economy contains seven regions, detailed in Table 1 and depicted visually in Figure 3. These constitute the seven regional markets. Wages differ across these markets, but I assume that all other prices are national. In each region, firms produce one of five goods: sugarcane, another agricultural good (which I will call other agriculture ), ethanol, sugar, and a composite consumption good. Sugarcane is an intermediate good that is purchased only by ethanol producers or sugar producers. Ethanol, sugar, the other agricultural good, and the composite consumption good are all final goods, either consumed by individuals in the Brazilian economy or exported. In the following sections, I discuss each of the model s components separately in order to clearly delineate the assumptions behind each one. In the first section, I derive expressions for aggregate labor supply and product demand from an aggregation over individual utility-maximizing decisions about work and consumption. In the second section, I set out expressions for government demand for the final goods. In the third section, I derive expressions for aggregate supply and labor demand in the sugarcane and other agriculture sectors from an aggregation over individual parcels profitmaximizing decisions. In the fourth and fifth sections, I describe ethanol and sugar production, as well as production of the composite good. The sixth section provides the assumptions about the international market before and after a change in US ethanol policy. The seventh section defines equilibrium in this economy, and briefly discusses existence and uniqueness of equilibrium. The final section presents a number of features of the ethanol and sugar industries that the model is not able to capture; future research could investigate the implications of these omissions. 3.1 Aggregate Labor Supply and Product Demand In this section, I begin by setting out the individual utility maximization problem that underlies all individual choices in the model. The set-up is mostly conventional. Individuals have preferences defined over leisure, the composite consumption good, ethanol, sugar, the other agricultural good, and capital. They consume out of their non-labor income and labor income. Their non-labor income is the value of their capital endowment, plus profits received from land used in agricultural production, plus net transfers from the government. Nevertheless, two elements of this set-up deserve further note here. The first point regards the treatment of capital. Having individuals value holding capital is unconventional. However, in a static setting it is important to make an assumption of this sort. Otherwise, individuals would consume all their income and the national income accounts would be grossly violated. I treat capital analogously to labor; each individual has a capital endowment and chooses to rent some of it out and hold the remainder. 21 For convenience, we can think of this as individuals holding goods for future consumption. The capital rental rate determines how much of the capital endowment the individual rents out and how much the individual holds for future consumption. The second 21 This is the approach taken in a recent paper by Bovenberg, Goulder, and Jacobsen (2006), which uses a one-period general equilibrium model to assess the consequences of particular environmental policies. 11

12 point involves agricultural profits. The quality of the individual s land in different uses determines the specific use of an individual s land, and the return that she obtains on this activity. Land use decisions are described more completely in the third section of this chapter, and are assumed to be completely separable from work decisions. The second sub-section makes distributional assumptions about individual heterogeneity, and then uses these to aggregate over individuals. This yields expressions for aggregate labor supply to each region and sector, as well as aggregate product demand. These aggregate quantities are items I will ultimately use in estimation Individual-Level Utility Maximization In period t, individual i chooses consumption levels, whether or not to work and if she works a region-sector combination s, and hours of work. 22 The individual s choices happen simultaneously, in a static setting with no uncertainty. I use a Stone-Geary utility function because it simplifies aggregation (see, e.g., Deaton and Muellbauer (1983) and Blundell and MaCurdy (2007)). The individual s maximization problem is given by: max lit, y it,j it 1(j it = s)[βln(l it ψ hs ) + ln(c it ) + κ st + η ist ] s subject to c it = (y eit ) γet (y sit ) γst (y ait ) γat (y oit ) γot (y kit ) γ kt and w jit l it + p ot y oit + p 2t y at + p et y eit + p st y sit + r t y kit = w jit T + r t Kit + π it τ it l it T l it 0 y zit 0 z There are several choices here. The region-sector choice is denoted by j it and leisure is l it. Meanwhile, y o,y a,y e,y s, and y k are the amount of the composite good, the other agricultural good, ethanol, sugar, and capital that the individual consumes. These choices are made subject to a constraint involving the following quantities. The price of good x is given by p xt, with r t denoting the capital price and p 2t denoting the price for the other agricultural good. The wage that the individual faces in the chosen market-sector is given by w jit, and this wage is common across all individuals. 23 The time endowment is T, and the capital 22 The vast majority of workers in Brazil report working in only one occupation. In calculations from the PNAD data described later, I find that in 2005, the reported share of all workers with hours in a second job is less than 5%, and less than 9% for self-described employers. These numbers are higher and have an increasing trend over time for agricultural workers. However, even for employers in agriculture, the percentage does not increase past about 15%. In principle, unemployment in region 1 could be treated separately from unemployment in region 2, and so on; however, I do not make this distinction here. 23 In practice, I use the median wage in a sector/region as the wage for that sector/region. 12

13 endowment is K it ; the time endowment is common across individuals but the capital endowment is not. Land profits appear as π it and net taxes are τ it. For convenience, denote total non-labor income as M it, with M it = r t Kit + π it τ it. The remaining facet of the maximization problem is the set of items describing preferences. To begin with, the additive term κ st gives preferences for a particular region-sector combination s that are common across individuals. I parameterize κ st as κ st = κ s + ϕ st. The ϕ st terms are region-sector-year specific shocks to preferences. Heterogeneous preferences for a region-sector combination arise in η ist. Unemployment is also a sector, denoted with s = 0, and I treat it analogously to region-sector combinations for work (subject to the additional assumptions below). The other important part of preferences consists of the items governing the marginal utilities of consumption and leisure. I allow the threshold parameters ψ hs to differ by sector, with the value for the unemployed state being identical to the sugarcane value. This allows the marginal utility of leisure to vary by sector of work. I further assume that the share parameters β, γ ot, γ et, γ st, γ at, and γ kt are common across individuals, with β + i γ it = 1. I allow the γ parameters to vary by year, subject to year-specific shocks. In particular, I use the parameterization γ it = exp(a i +δ it ) (1 β) 1+ j exp(a j+δ jt ), where the δ are year-specific shocks to preferences and a o = δ o = 0 is a normalization. Together with the condition that 0 < β < 1, this parameterization ensures that the γ parameters remain in the unit interval. In order to make the aggregation of the next sub-section as transparent as possible, I set out expressions for the optimal hours choice, optimal consumption choices, and associated indirect utility function V ist for each sector-market combination s. Given a choice of s, for workers these are: h ist = (1 β)(t ψ hs ) β M it w st y iot = y iat = y iet = y ist = y ikt = γ ot p ot (1 β) (w sth ist + M it ) γ at p 2t (1 β) (w sth ist + M it ) γ et p et (1 β) (w sth ist + M it ) γ st p st (1 β) (w sth ist + M it ) γ kt r t (1 β) (w sth ist + M it ) V ist = log[w 1 β st (T ψ h ) + w β st M it] + ln[β β ] + W t + κ st + η ist 13

14 and for non-workers these are: h i0t = 0 y iot = y iat = y iet = y ist = y ikt = γ ot p ot (1 β) M it γ at p 2t (1 β) M it γ et p et (1 β) M it γ st p st (1 β) M it γ kt r t (1 β) M it V i0t = log[(t ψ h ) β ( M it 1 β )1 β ] + W t + κ 0t + η i0t where W t is a function of the share parameters and national-level prices, as follows: W t = b γ bt log( γ bt p bt ) + γ kt log( γ kt r t ) As a final note, a potential complication in this model concerns those who declare themselves as employers, self-employed, or non-remunerated family workers. I treat these individuals analogously to wage laborers. Employers and the self-employed work in their chosen sector for the same wage as other hired laborers in that sector, and profits from their enterprises accrue to them as non-labor income. A producer (employer or self-employed) is indifferent as to whether a unit of labor comes from a household member or someone outside of the household, and can hire as much as she wishes. At the same time, a member of a farm household is indifferent between and entirely capable of working inside the household or outside the household. These assumptions ensure that producers maximize profits independently of their work decisions Aggregation Over Individuals Ultimately, I need to obtain expressions for aggregate labor supply to each region-sector and aggregate product demand for each final good. While the aggregate product demands do not require it, I must make assumptions about individual heterogeneity to derive the aggregate labor supply expressions from the individual-level optimal choices above. After noting these assumptions, I write expressions for the aggregate product demands and labor supplies. 24 On this point, the model is related to a traditional household maximization problem in which separation between the household-operated firm and consumption decisions allows for a two-stage maximization process in which firm profits are maximized independently of other household characteristics (See Bardhan and Udry (1999)). Fixed costs to working outside the household, or other labor market frictions, could call this assumption into question. Calculations based on the PNAD data for households with someone working in agriculture suggest that a fair number of agricultural households overcome whatever cost there is. After 1992, between 20 and 25% of households contain both a self-employed person/employer, as well as a hired laborer. 14

15 The first set of assumptions involves heterogeneity in non-labor income. I assume non-labor income is given by M it = e θ it+µ it, where both θ it and µ it represent individual heterogeneity. now make distributional assumptions on the θ parameters. I assume that the distribution of θ is a discrete distribution over two points. Denote these points in year t as (θ 1t, θ 2t ), and define π m = P r(θ = θ m ) for m = 1, 2. Note that π m is not time-varying. Finally, assume µ it N(0, σ 2 ), and is independent of the θ i. 25 Before continuing, I add here that it is imperative that total nonlabor income equal the integral over individual non-labor income in each year to ensure coherence of the model. This necessitates a method of shifting the θ parameters in each year to match the nonlabor income for that year. For this purpose, define θ it = θ i + log( M t / M 2005 ), with log( M t / M 2005 ) as a shifting factor for period t and the constant parameters θ 1 and θ 2 reflecting 2005 non-labor income. This ensures that the aggregation is consistent with economy-wide non-labor income. The second set of assumptions involves heterogeneity in preferences. I assume η ist T ype I Extreme V alue, and is distributed independently of µ,θ 1, and θ 2. I normalize the unemployment preference shocks ϕ 0t to be zero for all t. However, I make distributional assumptions on the time-constant portion of unemployment preferences, κ 0. two values, either κ 01 = 0 or κ 02 = κ 0 > 0. Specifically, I assume that κ 0t can actually take one of This discrete random variable which indicates some preference to be unemployed separate from that captured by the direct value of leisure is distributed independently of all other individual-level random variables, except θ 1 and θ 2. Let d 1 h = P r(κ 0i = 0 θ i = θ 1 ) and d 1 l = P r(κ 0i = 0 θ i = θ 2 ), with d 2. = 1 d I am now in a position to set out the expression for aggregate labor supply to a particular region/sector. (For a more complete derivation of this expression, see the Appendix.) In order to be compatible with the notation for other parts of the economy described below, instead of using s to denote a particular region-sector combination, use the pair (r, j), where r represents the region and j represents the sector. Let f(x) be the probability density function of the random vector x. Let N t be the total number of individuals in period t. Based on the expressions above, we can write period t aggregate labor supply in region-sector combination r, j as: [ ] L S jrt = N t π m [(1 β)(t ψ hj ) β e θmt+µ ]P r(j, r θ mt, µ)f(µ)dµ m w jrt Therefore, an increase in labor supply to r, j can come from an increase in the exogenous number of individuals, an increase in the share of individuals in r, j conditional on non-labor income, or an increase in hours among workers. Let S 1 be the set of region-sector combinations (excepting unemployment) for which optimal hours of work are positive. Then the terms in the final expressions 25 This follows the approach of Heckman and Singer (1984). This method has been widely used in the labor literature, with just two notable examples being Mroz (1999) and Eckstein and Wolpin (1999). 26 These choices regarding the flexible distribution of preferences for unemployment were made after preliminary estimation showed that a simpler model fit the data very poorly. I 15

16 above are (with the time subscripts implicit): f(µ) = P r(j, r θ m, µ) = z 1 σ 2π e 1 2 ( µ σ )2 d z θm if r, j S 1 e κ jr β β [w 1 β jr (T ψ hj ) + w β jr eθm+µ ] e κ 0z (T ψh0 ) β ( eθm+µ 1 β )1 β + k,p S e κ kpβ 1 β [w 1 β kp (T ψ hp) + w β kp eθm+µ ] = 0 if r, j / S 1 The (much simpler) expressions for aggregate product demands are: Yot D γ o = w jrt L S jrt + M t p ot (1 β) r,j Y D at = Y D et = Y D st = Y D kt = γ a w jrt L S jrt + M t p at (1 β) r,j γ e w jrt L S jrt + M t p et (1 β) r,j γ s w jrt L S jrt + M t p st (1 β) r,j γ k w jrt L S jrt + M t r t (1 β) r,j Government Demand I assume that the government takes in net tax revenue of τ t, and then spends this intake on the composite good, the other agriculture good, ethanol, and sugar in the same proportions that individuals do. Importantly, the government does not consume capital in the model. Therefore, the consumption shares from above have to be normalized, and the summations below are over all non-capital final goods only: Y G ot = Y G at = Y G et = Y G st = Y G kt = 0 γ o p ot j γ j γ a p at j γ j γ e p et j γ j γ s p st j γ j The scaling of the consumption shares ensures that the government s budget balances This is a simplification for the sake of the model, but in reality the government s budget does not actually balance. I briefly return to this in Chapter 4. τ t τ t τ t τ t 16

17 3.2 Aggregate Agricultural Supply and Land Use This section describes the portion of the model covering agricultural production and land use. Land owners use their land for sugarcane production, agricultural production, or non-agriculture. 28 Land is used for sugarcane or other agriculture only if the profit from that use exceeds a threshold. This threshold indexes two characteristics that are monotonically and positively related to the quality of untouched forest land: one, the expected penalty imposed by the government for developing the land; and two, the cost of preparing the land for use in agricultural production. That is, the government will be more likely to penalize the development of the most environmentally important forest areas. These areas are also likely to have the largest cost of development. 29 This set of assumptions poses three potential obstacles, which can be overcome with additional assumptions. First, if the government actually fines an agricultural producer, I assume that this fine is simply returned to individuals in lump-sum fashion, so that net transfers from the government are unaffected. Second, any fixed costs paid to prepare land for production are assumed to be a transfer from agricultural producers to other individuals in the economy. This leaves total nonlabor income unchanged. Third, if the land under question is public land or lacks any ownership, I assume that the same considerations apply. Potential owners of the land weigh agricultural profits against the threshold to determine whether or not to infringe on the public land or unowned land. At the outset, it is important to note that the production functions on each parcel of land will take a very particular form. Specifically, the only inputs to agricultural production in the model are labor and effective land units. The term effective land units refers to the quality of a parcel of land in a particular use. 30 In sugarcane production, for example, quality differences arise through differences in distance from the closest mill or distillery, availability of irrigation, weather, and land gradient. At the same time, capital does not enter agricultural production, nor do inputs such as fertilizer. This choice relates to data constraints, since information on capital usage and other 28 Only a small percentage of land operators rent their land, so focusing on use by owners is superficially an advantage (See Valdes and Mistiaen (2003)). In actuality, though, the model here is isomorphic to a model in which parcels of land are rented out to constant returns to scale producers in each agricultural sector. 29 It is important to note two ways in which this approach to non-agricultural land use is not fully satisfactory. First, a (relatively small) portion of land is used for industrial development or residential housing in urban areas. The current framework does not represent this adequately. Second, landowners sometimes hold land purely for speculative or savings purposes, and do not use it in agriculture for this reason. Assuncao argues convincingly that savings during times of uncertainty can be a significant motive for a large number of landowners in Brazil. See, e.g., Assuncao (2006). de Rezende (2002) and Helfand and de Rezende (2004) also point to the role of the macro economy in determining the evolution of land prices over time, as investors responded to changing risk structures. Such motives cannot be taken into account in the necessarily simplified model here. 30 My approach is closely related to the approach used in Timmins (2006). There, land owners in Brazil allocate land to various uses depending on heterogeneous value of each parcel in each use. The notion of effective land units is exactly analogous to a Roy model framework for labor supply decisions, in which a single person can provide a different number of effective labor units in different sectors. For a classic discussion, see for instance Heckman and Sedlacek (1985). 17

18 inputs in agriculture is only available during agricultural census years. For this reason, differences in land quality or labor productivity parameters across regions will in part reflect differences in usage of other inputs. In the first sub-section below, I describe the profit maximization problem on any individual parcel of land, and in the second sub-section I use distributional assumptions on the parcel-specific heterogeneity to aggregate over the parcels in any region. This yields expressions for aggregate product supply and aggregate labor demand. Since I do not have data on the allocation of individual parcels of land, I rely entirely on these aggregate expressions in the estimation Parcel-Level Profit Maximization To determine the use to which a parcel of land is allocated, the profits from the two agricultural endeavors - sugarcane (j = 1) and other agriculture (j = 2) - are compared to the threshold discussed above. Let j = 3 denote the non-agricultural use. The parcel is used for j if and only if: π jrt > π krt for k j where π jrt = max Lsrt e κ jrt [p jt y jrt (L jrt ; u jrt ) w jrt L jrt ] forj = 1, 2 π 3rt = e λ 3rt+u 3rt In the above expressions, L jrt indicates the amount of annual labor hours used on the parcel of land, u jrt describes parcel-specific heterogeneous effectiveness in use j (described more completely below) and y jrt gives the amount of annual output on the parcel. The exact form of the production function appears below. The output price and wage in the region are given by p jt and w jrt. The vector (κ 1rt, κ 2rt ) can be viewed as frictions in the agricultural output market; those who farm land lose a portion of the profits due to frictions. 31 This does not pose a problem for the framework here as long as agricultural profits resulting from land allocation decisions accrue to some individual in the economy. For the profit-maximizing decision, I assume the production function for sugarcane and other agriculture on a parcel of land takes a CES form with effective land units of the parcel and labor as inputs. The effective units of the parcel in use j are e λ jrt+u jrt, where λ jrt is a region-time-specific indicator of land quality that is common across all parcels in region r and u jrt is the portion of land quality that is heterogeneous across parcels. I assume that the production function takes the following CES form: y jrt (L jrt ; u jrt ) = z jrt ((1 α jrt )(e λ jrt+u jrt ) ρ j + α jrt L ρ j jrt )1/ρ j for j = 1, 2 31 Another way to interpret these parameters is as optimization error. That is, people allocating land incorrectly perceive the return they can get for it. Regardless, from a practical point of view, without the vector of κ s, the model imposes too tight a relationship between shares of land and production. The production parameters govern both the share of land and production in each of the two activities, sugarcane and other agriculture. This imposes a situation of over-identification that can lead to a very poor fit. 18

19 where z jrt = e φ jrt is a scale or TFP term and ρ j < 1. We now have enough information to write down the profit-maximizing choices on each parcel of land. 32 Dropping the time subscripts for convenience, the optimal product supply and labor demand for the parcel, as well as the optimal profits, are given for j = 1, 2 by: y jr (u jr ) = z jr (1 α jr ) 1 ρ j (w jr ) 1 1 ρ j 1 ρ [(w jr ) j (α jr ) 1 1 ρ j (p j z jr ) L jr (u jr ) = (α jr p j z jr ) 1 1 ρ j (1 α jr ) 1 ρ j 1 ρ [(w jr ) j (α jr ) 1 1 ρ j (p j z jr ) πjr(u jr ) = e κ jr p j w jr z jr (1 α jr ) 1 ρ j 1 ρ [(w jr ) j (α jr ) 1 1 ρ j (p j z jr ) ρ j ρ j ρ j ρ j ] 1 ρ j 1 ρ j e λ jr+u jr ρ j ] 1 ρ j 1 ρ j e λ jr+u jr ρ j ] ρj 1 ρ j 1 ρ j e λ jr+u jr Finally, there are two identification issues that require normalizations in the model. First, it is not possible to separately identify z jrt (= e φ jrt ), α jrt, and λ jrt. 33 Since the levels of the α jrt are arbitrary, I set them to the region-specific means of the share of labor costs in total revenue over the ten year period (2000 excluded). This facilitates the interpretation of ρ 1 and ρ 2, in that values close to zero correspond with Cobb-Douglas production, with share α jrt. 34 Second, observing agricultural production levels will help to identify λ 1rt and λ 2rt. However, there is no way to disentangle λ 3rt, κ 1rt, and κ 2rt. Consequently, I simply set κ 1rt = 0. Thus, κ 2rt = κ rt captures the relative tendency to put land into non-sugarcane agricultural use, regardless of the level of profits received directly by producers Aggregation Over Parcels By using assumptions for the distribution of land quality in each region, I now derive expressions for aggregate product supply and aggregate labor demand in each agricultural sector, in each region. Assume that u jrt for j=1,2,3, are mutually independent and take the Type I extreme value distribution with parameter γ r. That is, the probability density function of u jrt is given by u jrt 1 γr e e γr. 35 γ r e ujrt Using these assumptions, I integrate over the parcels of land allocated to each use in order to derive the share of land devoted to producing each good (S jrt ), total effective units of land in each 32 There is an important implicit assumption behind the expressions: wages and prices are assumed to take values such that it is profitable to have non-zero land area devoted to sugarcane or other agriculture. This is true in the data, but the approach ignores the possibility of zero land area in the simulations of equilibria under alternative policy environments 33 To see this, consider a vector (ρ 1, z 1, α 1, λ 1) that satisfies the product supply and labor demand equations for sugarcane in a particular region and year. If z 1 = ( α 1 α 1 ) 1/ρ 1 z 1 and e λ 1 = ( α 1 1 α 1 α 1 1 α 1 ) 1/ρ 1 e λ 1 for some α 1 in (0, 1), then the vector (ρ 1, z 1, α 1, λ 1) also satisfies the system Here, the elasticity of substitution is given by 1 ρ j, with values of 0, 1, and infinite representing, respectively, Leontief, Cobb-Douglas, and perfectly substitutable production. 35 Timmins (2006) assumes use-specific land values are linear in heterogeneous errors that take the extreme value distribution. One might think that land values could be negative in some uses if there are fixed costs to production in those uses. However, in the setup here, heterogeneous errors across parcels enter through an exponential function, and it is important for interpretation that effective land units always remain positive. 19

20 good (A jrt ), total labor demand in each sector (L D jrt ), and total supply of each good (Y S jrt ). For convenience, define πjrt c such that π jrt (u jrt) = πjrt c eu jrt. Let c jrt = ln(πjrt c ) and let A rt be the total amount of land in region r at time t. Let Γ(.) denote the gamma function, as opposed to the gamma density. 36 Also, we have κ 3rt = 0. Then for k, p j, the allocated land share and the total effective land units are: S jrt = c jrt e γr 3 i=1 e c irt γr A jrt = A rte λ jrt (S jrt ) 1 γr Γ(1 γ r ) A more complete derivation of these expressions appears in the Appendix. Note the implicit restriction that γ r (0, 1). 37 This expression corroborates the intuition that the marginal impact on effective land units of increasing the land share slightly is diminishing in the land share. Finally, from the expression for A jrt and the parcel-level labor demands and product supplies above, it is easy to see that aggregate labor demand and aggregate product supply in each sector for all regions r are: L D 1rt = (α 1rp 1tz 1rt) 1 ρ 1 (1 α 1r) 1 A e λ 1rt (S 1rt) 1 γr Γ(1 γ r) L D 1 2rt = (α 2rp atz 2rt) 1 ρ 2 (1 α 2r) 1 A e λ 2rt (S 2rt) 1 γr Γ(1 γ r) 1 ρ 1 [ ρ 2 [ (w 1rt) ρ 1 1 ρ 1 (α 1r) (w 2rt) ρ 2 1 ρ 2 (α 2r) ] 1 1 ρ 1 (p 1tz 1rt) ρ 1 1 ρ 1 ρ 1 1 ] 1 1 ρ 2 (p atz 2rt) ρ 1 2 ρ 1 ρ 2 2 and Y S 1rt = z 1rt(1 α 1r) 1 [ 1 ρ 1 (w 1rt) 1 ρ 1 A e λ 1rt (S 1rt) 1 γr Γ(1 γ r) Y S 2rt = z 2rt(1 α 2r) 1 [ 1 ρ 2 (w 2rt) 1 ρ 2 A e λ 2rt (S 2rt) 1 γr Γ(1 γ r) (w 1rt) ρ 1 1 ρ 1 (α 1r) (w 2rt) ρ 2 1 ρ 2 (α 2r) ] 1 1 ρ 1 (p 1tz 1rt) ρ 1 1 ρ 1 ρ 1 1 ] 1 1 ρ 2 (p atz 2rt) ρ 1 2 ρ 1 ρ 2 2 Finally, for use in estimation, I need to parameterize λ jrt for j = 1, 2, 3, φ 1rt, φ 2rt, and κ 2rt. Assume that for each j, λ jrt takes the following form: λ jrt = λ 0 jr + ν jrt for j = 1, 2, 3 where ν jrt is a shock to land quality that is common to all parcels of land in the given region. Set φ jrt = φ 0 jr + ɛ jrt for j = 1, 2, where ɛ 1rt and ɛ 2rt are shocks to production. Finally, let κ 2rt = κ 2r + ν krt, with ν krt a shock to the tendency to allocate land to other agriculture. 36 That is, Γ(x) = 0 t x 1 e t dt, and the function is defined for x (0, ). 37 In the structural estimation below, I impose γ r = γ for all r. Preliminary estimation results suggested that the region-specific values are close to each other. 20

21 3.3 Ethanol and Sugar Production and Input Demand I assume production of ethanol and sugar is constant returns to scale, taking capital and sugarcane as inputs. 38 In the production of sugar and ethanol, substitution possibilities between sugarcane and other inputs are extremely limited; a producer cannot easily economize on sugarcane by using more of other inputs. Therefore, I use Leontief production functions: Y srt = min {α st Y 1srt, β s K srt } Y ert = min {α et Y 1ert, β et K ert } where Y 1jrt and K jrt are the amounts of sugarcane and capital demanded by producers of good j, where j = s for sugar and j = e for ethanol. Note that the production functions are common across all regions. The α st, α et, and β et are allowed to vary over time. Specifically, assume that α st = e αs+ɛst, α et = e αe+ɛet, and β et = e βe+ɛ ebt where ɛ st, ɛ et, and ɛ ebt are shocks to production. Because of the constant returns to scale assumption, the supply of ethanol and sugar at any given set of prices is indeterminate. However, cost minimization implies that the input demands are related to the product supplies as follows, for all regions r: Kert D = Y ert S β et Ksrt D = Y srt S β s Y1ert D = Y ert S Y D α et srt α st 1srt = Y S 3.4 Composite Good Production and Input Demand I assume that production of the composite good is Cobb-Douglas, taking capital and labor as inputs. The share parameters potentially differ across regions. Formally, the production function for each region r is: Y ort = z ort L βort ort K1 βort ort Here, I assume z ort and β ort are both stochastic. In particular, z ort = e φort with φ ort = φ or + ɛ p ort, and β ort = 1 1+e βor+ɛb ort. The terms ɛ p ort and ɛb ort are region-year-specific shocks. The constant returns to scale assumption implies that composite good supply in any region is indeterminate. However, cost minimization implies that the input demands are related to the 38 Due to the industry definitions in the PNAD, it is not possible to clearly identify those who work in the ethanol and sugar industries prior to production functions. Owing in part to this limitation, I omit labor from the ethanol and sugar 21

22 product supplies as follows, for all regions r: ( ) (1 Kort D βort )w βort 3rt Yort S = β ort r t z ort L D p ot Yort S ort = β ort w 3rt 3.5 International Market Since the focus of the paper is not the international market for ethanol or other products, I model the interaction between Brazil and the rest of the world in a very simple way. All final goods can be exported and imported. Net exports of the other agriculture good, ethanol, sugar, and the composite good are denoted by Y X at, Y X et, Y X st, and Y X ot, respectively. I assume that the prices of the other agricultural good, the composite good, and sugar are all determined outside of Brazil. This assumption is least controversial for the case of agriculture. Brazil s trade barriers in agriculture fell markedly in the early 1990s. Helfand (2003) illustrates how domestic agricultural prices move more closely with international prices after the reforms. However, the assumptions are much more controversial for the composite good and sugar. In the model, capital can move easily out of composite good production since this good can be freely imported. But the composite good in part represents services, which in reality are not tradeable. If the model were to take into account these non-tradeables and non-tradeables production were to use capital then capital could not move as much into ethanol production in response to greater opportunities for ethanol exports. The assumption is also controversial in the case of sugar. Brazil is a major player on the world sugar market, in terms of share of world exports. However, Brazil s share of world production is smaller. In the 2005/06 marketing year, data from the Foreign Agricultural Service (FAS) of the USDA show that of the 144,860 thousand metric tons of sugar produced in the world, 26,850 thousand metric tons were produced in Brazil, approximately 18.5%. 39 Brazil s influence on the world sugar price somewhat. This will at least reduce Finally, I need to specify the form of trade barriers for ethanol. For ethanol, the US is by far the largest potential market for Brazilian output. Currently, the US protects its own ethanol producers with a $0.54 per gallon duty on imports and a 2.5% ad valorem tariff. To avoid modeling US ethanol demand, I take a stylized approach: I represent the current policy situation as one in which Brazil faces downward-sloping domestic demand for ethanol, but also faces L-shaped international demand. That is, international demand for ethanol is perfectly inelastic at low quantities, and perfectly elastic once the price gets low enough to overcome the effect of barriers to trade. This price level at which international demand becomes elastic is assumed to be lower than the equilibrium 39 See FAS data for the November 2007 World Production, Supply, and Distribution Report, available at tables.pdf 22

23 price level before policy changes are made. In the baseline, then, ethanol prices in Brazil are determined entirely by Brazilian demand. For the purposes of answering the research question with policy simulations, I need to decide how to represent a change in US policy. Removing US import barriers to ethanol is assumed to increase the price at which Brazilian ethanol becomes competitive with US ethanol. The perfectly elastic portion of international demand moves upwards, to a point higher than the price in the baseline equilibrium. That is, in the alternative simulation of no barriers, the ethanol price is set internationally and ethanol quantities are determined by total (Brazilian plus international) demand. In the simulations, I consider three cases: in the first, ethanol demand becomes elastic at a price 10% greater than the price in 2005; in the second and third, ethanol demand becomes elastic at a price 12% and 15% greater than the baseline. The choice of these numbers is designed to give a range of possible policy consequences, while at the same time keeping ethanol reasonably competitive with petroleum. This discussion of the international market covers the last component of the model. As a final note, as will be stated formally in the definition of equilibrium in the next section, I close the model by assuming that the value of total net exports is zero. 3.6 Equilibrium In this section, I begin by defining the market equilibrium in the model. All quantities appearing below in the definition of the equilibrium have been defined previously in the relevant section above. The second sub-section comments briefly on the existence and uniqueness of equilibrium in this model Definition The only exogenous variables in the baseline case are: prices of sugar, the other agricultural good, and the composite good; net exports of ethanol; total population; total capital stock; and the total amount of land in each region. All other variables are determined endogenously within the model, based on the exogenous variables, the parameters, and the values of the shocks. In the alternative case of lowered trade barriers, I assume the price of ethanol is exogenous and net exports of ethanol become endogenous. Keeping this in mind, an equilibrium in this economy involves the following conditions: Agricultural Goods r [Y1ert D + Y1srt] D = r Y D at + Y G at = r Y S 1rt Y2rt S Yat X 23

24 Non-agricultural Goods Y D ot + Y G ot = r Y D st + Y G st = r Y D et + Y G et = r Yort S Yot X Ysrt S Yst X Yert S Yet X Capital and Labor Y D kt + r (K D ort + K D ert + K D srt) = K t L D jrt = L S jrt forj = 1, 2, 3 r Zero-profit Conditions p ot z ort = ( w3rt β ort p et = p 1t + r t α et β et p st = p 1t + r t α st β st ) βort ( rt 1 β ort ) 1 βort r Trade Balance and Budget Constraints p ot Y X ot + p et Y X et + p st Y X st + p 2t Y X at = 0 p ot Y D ot + p et Y D et + p st Y D st + p 2t Y D 2t + r t Y D kt = r,j p ot Y G ot + p et Y G et + p st Y G st + p 2t Y G 2t = τ t w jrt L S jrt + M t where total non-labor income is given by M t = r t Kt + r [p 2tY S 2rt w 2rtL D 2rt +p 1tY S 1rt w 1rtL D 1rt ] τ t Existence and Uniqueness There are two natural questions at this stage: Must an equilibrium exist in this economy for any draw of the production shocks and any set of exogenous variables? And if an equilibrium exists, is it unique? First, consider the existence question. The production side of the economy is quite conventional. The production of the non-agricultural goods is constant returns to scale, and poses no special difficulties. Examination of the model also reveals that it is isomorphic to a model in which aggregate agricultural production is constant returns to scale in aggregate effective land units and aggregate labor, and the representative firms rent effective land units from landowners. Therefore, the production side of the economy may not by itself pose problems for existence. 24

25 The unconventional aspects of the economy arise in three ways: non-convex individual preferences, land supply, and the trade environment (in combination with the restrictive production functions and hence zero profit conditions for ethanol and sugar). Any one individual s preferences are non-convex because of the choice of region and sector. This creates obstacles to conventional proofs of existence, though the presence of individual heterogeneity may actually impose sufficient discipline on the aggregate net labor demand expressions (see Mas-Colell, Whinston, and Green (1995) for an example of how heterogeneity can be exploited to sidestep obstacles posed by non-convex preferences). But such arguments are not sufficient to preserve existence here. To informally see why, consider the baseline case where net exports of ethanol are exogenous. Suppose net exports take a very large value while the production shocks in sugarcane production are negative and very large in magnitude. The need to produce ethanol would then require a high sugarcane price. If this price is high enough, the zero-profit condition in sugar would be violated by any positive value for the capital rental rate. In the simulations below, existence is further hampered by the fact that I search for equilibria with strictly positive land shares, production quantities, and wages in all regions. 40 The second issue is whether an equilibrium is unique if it exists. Again, the lack of convex preferences may be a significant obstacle to applying the common conditions for uniqueness in a closed economy (see Mas-Colell, Whinston, and Green (1995)). The implicit function theorem allows us to say something about local uniqueness, however. The method of estimation ensures that, given the parameter estimates and in the vicinity of the production and preference shocks for a given year of data, the endogenous variables are a one-to-one function of the shocks. This guarantees existence and uniqueness in an open set around the realized shocks. I say more about this point in the section on estimation below. While this is comforting, it does not guarantee uniqueness at points farther away from the realized production shocks of a given year. Moreover, it does not guarantee uniqueness for all possible values of the parameters, or all possible combinations of the exogenous variables and shocks Features Not Captured in the Model There are aspects of the sugarcane industry that are much more difficult to capture in a general equilibrium model of this nature. These aspects are the following: Ethanol distilleries and sugar mills often produce sugarcane in addition to purchasing it from others. The sugarcane industry consists of two basic types of producers: the independent cane growers and the millers. The largest growers of sugarcane are often the millers themselves, which is a natural arrangement owing to the fact that harvested sugarcane must be 40 I impose these restrictions not only because these are the most plausible equilibria. It also simplifies the process of simulation, since the equations from maximum likelihood estimation can be used directly to form the non-linear system, and these equations rely on positive quantities in certain variables. 25

26 transported to factories very quickly. 41 Until 1997, the Brazilian government intervened strongly in the market. The Instituto do Acucar e do Alcool (IAA) operated a system of quotas and price controls for sugarcane, sugar, and ethanol over a period of 60 years. For sugarcane, IAA production quotas specified the amount of sugarcane that mills had to purchase from independent growers. Over the 1980s, quotas for sugar production also worked to limit the production of sugarcane by larger enterprises. 42 In addition to quotas, the IAA set prices. Over the 1980s, the agency reduced sugarcane prices dramatically, which is reflected in the price data discussed above. As time went on, the system of quotas and administered prices came under increasing pressure. 43 In 1990, the IAA was abolished and sugar exports were privatized. In 1995, sugar quotas were ended, and from , prices for sugar, ethanol, and sugarcane were liberalized. Since 1999, sugarcane prices have been determined in essentially a free market. The large number of independent growers, as many as 60,000 by some measures, assures a fair degree of competition. There is regional heterogeneity in sugarcane, ethanol, and sugar prices. Price differences across regions persist because of different growing seasons for sugarcane, government policy, and transportation costs. In some months of the year, ethanol comes primarily from the Center-South, while in others it comes from the Northeast, in accordance with the differing harvesting periods. Regarding government action, special allocation of sugar export quota to the Northeast and subsidies to sugarcane producers in the Northeast also lead to differences. 44 Finally, sugarcane is a locally marketed good, since transportation over long distances is infeasible for biological reasons. Despite all this, examination of the region-level data reveals that the price of sugarcane moves in similar ways over time in all states. The model does not deal with any of the three complications noted here. For the sake of simplicity, ethanol and sugar producers are assumed to procure sugarcane in a competitive market, and the prices of all three goods involved ethanol, sugar, and sugarcane are assumed to be identical across regions. The results in this paper should be interpreted cautiously in light of these limitations. 41 For basic details on the preparation and milling of harvested cane, the website of the Sao Paulo cooperative COPERSUCAR is a useful source ( 42 However, the increasing emphasis on alcohol production, which was not constrained by quotas in the same way, provided a growing outlet for excess sugarcane. Ethanol quotas instead took the form of levels of domestic production that a mill/distillery had to meet before exporting. Sugar exports also fell under government control. 43 For a brief listing of major events in government policy, see notes by I.C. Macedo of Unicamp on the website for Cane Resources Network of South Africa, For greater detail, see Barros and Moraes (2002), Lopes and Lopes (1998), and Borrell, Bianco, and Bale (1994). 44 Unfortunately, I do not have time series data on the size of the government subsidies. While there are some data on region-specific prices for ethanol and sugar (see these data do not use consistent definitions across regions and are available for the Northeast only for 2001 onwards. 26

27 4 Data I utilize data from a large array of government and non-government sources. Here, I describe the primary data sources briefly. For further details on the data and on construction of variables used in the analysis, please see the Appendix. I rely primarily on five sets of data: first, labor force data from the Pesquisa Nacional por Amostra de Domicilios (PNAD); second, data for agricultural production amounts and land allocations from the Producao Agricola Municipal (PAM), the Producao Pecuaria Municipal (PPM), the Agricultural Censuses, and regional income accounts; third, data on output and input prices from Fundacao Getulio Vargas (FGV); fourth, data on ethanol and sugar production; and fifth, data on other non-agricultural production, capital investment, net exports, and government spending from the regional and national income accounts. I describe these sources of data in separate sub-sections. 4.1 Labor Force Data (PNAD) The PNAD is a cross-sectional representative household survey collected by the Brazilian government s statistical group IBGE. I will use PNAD data from 1981 through 2005 for all but three years. 45 On average, the PNAD surveys roughly 100,000 households each year, which corresponds to more than 300,000 people. The only region of the country not represented fully in the PNAD sample is the North Census region. 46 This will prevent me from addressing the sugarcane markets in the Northern portion of the country. The PNAD has information on several aspects of employment. I use the following information for each member of a household: whether or not the member is employed (with September being the reference month); if she is employed, then her monthly income and usual weekly work hours from her primary job; the sector of her primary job, with sector being narrowly defined enough to allow for the identification of specific crops; and whether the individual is hired labor, a nonremunerated family worker, self-employed, or an employer. The advantage of such large samples is that there are a considerable number of survey respondents working in any particular crop. In order to construct aggregate hours worked in a particular region/sector, I multiply weekly hours by 52 and take the weighted sum over all individuals in that region/sector, using the PNAD-provided survey weights In 1991 and 2000, the PNAD was not conducted because those were national demographic census years. In 1994, the PNAD was not conducted due to other constraints. Although I have the national census data for 1991 and 2000, these were conducted at different times of year from the PNAD, making comparisons difficult in the agricultural sector. 46 The rural parts of the six states in the North region are not represented through In the 2004 and 2005 data, this deficiency has been remedied, and the PNAD is now nationally representative. 47 If 52 is the incorrect factor to multiply weekly hours by, then in general all the estimates shown here will be affected. I do not analyze the sensitivity of the estimates to this choice in this paper. For region of work, there are a limited number of cases in which the survey respondent was not present in the current state as of the last week of September (the reference month). In these cases, I simply drop the respondent. 27

28 4.2 Agricultural Production and Land Use (PAM, PPM, Forest Values, Agricultural Censuses, Regional Income Accounts) The analysis below requires an estimate of the total value of production in, and total amount of land devoted to, the two agricultural sectors in every region and year. I use four sources of data to construct information on production and land allocations: the PAM, the PPM, the IBGE data on forest production values, the Agricultural Censuses, and the regional income accounts. The PAM is a valuable resource that has certain deficiencies, and I use the latter four sources to supplement the information from the PAM. To be specific, the PAM provides annual information on total production and total area harvested for major crops in each state. Data are available for all permanent and temporary crops in the time period, and for the most important crops in the period. 48 Sugarcane is covered in all years. Moreover, there are data on the acreage planted and the acreage harvested for sugarcane. These numbers are quite close together, and I use the acreage harvested. The PAM does not capture four types of land uses: pasture land; land temporarily at rest; forest land; and land used for minor crops (a problem in the period). To address this problem, I use data from the 1980, 1985, 1995, and Agricultural Censuses, which contain information on pasture, forests, and all other agricultural land (at rest or otherwise). I also use annual data on cattle herd sizes from Producao Pecuaria Municipal (PPM), and IBGE data on the total value of forest production. Using these data sources and the PAM data, I use simple regression equations and extrapolation procedures to project total agricultural area in the years of my analysis period. These projections are important, and I provide more detail on them in the Appendix. Finally, the PAM data I have do not provide the total value of agricultural production for all years. For this purpose, I use regional income accounts information for the period. The value of agricultural production from the income accounts includes the value of forest production, though this is a small percentage of the total. To construct the value of other agricultural production, I use the sugarcane price data described below and sugarcane production information to calculate total value of sugarcane production, and then subtract that from the value of total agricultural production. 4.3 Output and Input Prices (FGV) The price data come from FGV, a foundation that compiles a large number of price indexes for Brazil. I use the FGV data sources to construct prices for sugarcane, other agriculture, ethanol, sugar, petroleum, capital, and the composite non-agricultural good. Sugarcane and petroleum information appears as absolute prices in the raw data, whereas the prices for the other goods must 48 The quality of the data varies over time, generally being better near agricultural census years. I obtained the data from SIDRA, an online database operated by the Brazilian government. The earlier PAM data come from IPEA, an institute affiliated with the government, with a website at 28

29 be constructed using FGV price indexes. In the case of the composite non-agricultural good, I construct a price index by using changes in relative prices of all other goods, the overall consumer price index, and the shares of all other goods in the consumption basket. The simpler set of data involve absolute prices. The FGV has monthly time series on prices received for detailed agricultural product categories, by state. 49 I obtain the sugarcane prices this way. I convert petroleum prices from their US dollar values to Reais using exchange rate data from the Banco Central do Brasil. In the case of price indexes, I use different procedures depending on the good. Whenever possible, I construct a series on absolute price levels by benchmarking the index to outside data for a particular year. I use this procedure for ethanol and sugar prices. For the remaining goods, there are no natural units. Accordingly, I create an artificial unit by benchmarking a particular year to a value of Ethanol and Sugar Production I use data on the amount of sugar and ethanol produced in each state and year from the Brazilian government. These data span the time period. Unfortunately, these data are for local harvesting years, rather than calendar years. I impute a measure of the ethanol and sugar quantities for calendar year t by taking a weighted average of the surrounding harvest years, where the weights differ between the Northeast regions and the Center-South regions. 50 The data on sugar and ethanol production also contain the amount of sugarcane crushed by mills and distilleries in each harvest year. In this paper, I use data on harvested sugarcane, rather than crushed sugarcane. There are discrepancies between the total amount of sugarcane crushed in a region and the total amount harvested, with the total amount produced being larger in every case besides one region-year observation. This should be expected: Sugarcane will be lost during transportation and initial processing, and a small amount of sugarcane is used for purposes other than ethanol and sugar. Here, as noted in Chapter 2, I assume that all sugarcane goes into the production of either ethanol or sugar. 4.5 Other Data Finally, I require data on total regional production, national capital investment, government spending, and net exports (overall, agricultural goods, ethanol, and sugar). For this purpose, I use national and regional income accounts data from IBGE, and data on imports and exports from Brazil s Secretaria de Comercio Exterior (SECEX). In the following section, I discuss the use of these data to construct empirical analogues to quantities in the model. 49 These data are collected using farm surveys in the relevant geographical regions. 50 The harvest year definition runs from May to April in the Center-South, and from September to August in the Northeast. The heaviest periods of the harvest are located in a few months within those periods. 29

30 5 Empirical Analysis In this section, I start by examining some assumptions in the model with a preliminary look at the data. In the second sub-section I describe my structural estimation approach. Details on an alternative estimation approach one that has certain advantages to the one used here appear in the Appendix. The third sub-section provides estimates of the model s parameters. 5.1 Examination of the Model s Assumptions The model contains a wide variety of assumptions. In the case of the agricultural component of the model, these assumptions yield a few testable implications. Here, I examine three of the most significant: CES production functions for sugarcane and other agriculture Parcel-specific heterogeneity takes a Type I Extreme Value distribution History-independent level of land quality in both agricultural uses I examine testable implications of each of these assumptions one-by-one. For each of these assumptions, rejection of the null hypotheses tested below is not definitive. Rejection could mean that the assumption is incorrect, or could mean that another, linked part of the model is incorrect. Still, the tests indicate aspects of the model that should be re-visited in the future CES Production Functions From the assumptions of the model, and using the innocuous normalization that the α parameters equal 1 2, one can derive the following equation for labor productivity for each sector i: ( ) Y S log ir L D = 1 log(2) ρ i φ ir + 1 log(w ir ) 1 log(p i ) + ɛ 1r ir 1 ρ i 1 ρ i 1 ρ i 1 ρ i Therefore, the model implies that the wage and price effects should be of equal magnitude and opposite sign. Tables 6 and 7 present results from regression estimates of this equation for sugarcane and other agriculture, respectively. The tables are structured analogously. The first three columns present estimates of the equations without imposing the equality of the wage and price effects. I can use these results to conduct a simple Wald test of the constraint on the wage and price coefficients. The next three columns use the ratio of wages to prices as a regressor, implicitly imposing the constraint. Turning to the sugarcane regressions first, the first column shows OLS estimates of the equation. However, both the wage and the price are endogenous according to the model. This suggests estimating the equations with instrumental variables. The second and third columns instrument for the wage and price using the instruments indicated in the table. Both columns suffer from potential issues with weak instruments, though the excluded instruments enter significantly in 30

31 most cases. The third column contains a negative coefficient on wages, which is inconsistent with the model. Still, this is statistically insignificantly different from zero. I test the null that the sum of the wage and price coefficients is zero. I fail to reject this is the case in the second and third columns, and in results not shown here, I also fail to reject when using petroleum and sugar prices as instruments. The size of the coefficients in the second column are consistent with an elasticity of substitution smaller than For the sake of comparison, the next set of three columns show the results when the constraint is imposed. Next, I turn to the labor productivity regressions for other agriculture, in Table 7. The Brazilian government altered the definition of work between the pre- and post-1992 PNAD surveys. Before 1992, subsistence workers or non-remunerated workers who worked fewer than 15 hours per week were not counted as working in the survey. After 1992, all these individuals were counted as working. This is not likely to affect the measurement of labor hours in sugarcane because sugarcane workers are predominantly hired laborers. However, this has a substantial effect in the case of other agricultural labor prior to Comparing total labor hours in other agriculture before 1992 and after 1992 is therefore not possible. Because of the problem with the pre-1992 PNAD definitions, I use only the post-1992 observations for other agriculture. Again, the first and fourth columns show the OLS results, while the remaining columns instrument for the endogenous regressors. In this case, the price is not endogenous by assumption. The instruments for the second and third columns both enter significantly, though there is a weak instrument concern again. The wage variable has the expected positive sign in both cases, and the magnitudes suggest an elasticity of substitution greater than one. One can reject the null that the sum of the price and wage effects is zero for both sets of IV estimates. While I show the results that impose the constraint for the sake of completeness, it appears that there is more reason to question the form of the production function in the case of other agriculture. Therefore, the estimates of the sugarcane equation are not inconsistent with the CES production function assumption, though the fact that some coefficients take an unexpected sign may still cause some concern. On the other hand, I reject the null hypothesis of wage and price effects of equal magnitude for the the other agriculture equation. This suggests considering more complicated production functions in the future Distribution of Parcel-Specific Heterogeneity The next assumption I consider is the assumption of Type I errors in land quality. This assumption implies that the ratio of the sugarcane land share to the non-agricultural land share is not affected directly by the price or wage in other agriculture. To test this, I use a first-order Taylor approximation to the model s expression of this ratio. This gives an equation for the log of the 51 The magnitude of the wage and price coefficients are both above 1 in the (omitted) regression with petroleum and sugar prices as instruments, though with large standard errors. More will be said about the elasticity of substitution for sugarcane and other agriculture in the structural estimation below. 31

32 ratio between the sugarcane and non-agricultural land shares as follows: ( ) S1r log β 0r + β 1r log(w 1r ) + β 2r log(p 1 ) + ɛ s S 3r where the asterisk in the error term indicates that this error does not have a strict interpretation as a structural error from the model, but instead incorporates approximation error as well. To test the Type I error assumption, I test whether or not the characteristics of other agriculture enter the equation above. The first four columns of Table 8 address this issue by including the price and wage in other agriculture in the regressions. The first two columns do not include interactions with the Northeast dummy, while the second two columns do include these interactions. 52 OLS should produce inconsistent estimates of these equations because wages and prices are correlated with the shocks to total factor productivity and land quality that appear in the error terms. Therefore, I show IV estimates using the logs of the total number of individuals, the petroleum price, and the sugar price as instruments. Where necessary, I interact the instruments with a dummy for the Northeast. In all four columns, the price of other agriculture enters positively and significantly. It is difficult to know whether this is because of the linear approximation I am using or because the Type I assumption is incorrect. In the structural estimation, I proceed with the Type I error assumption. But it is important to investigate this issue and consider a more complicated class of models in the future History-independent Land Quality Finally, I turn to the issue of land quality being independent of the history of land allocations. This implies there is no inertia in land allocations, which is an especially strong assumption for sugarcane. I test this by allowing the land quality term to include a lagged sugarcane land share in the model for land shares above. The fifth and sixth columns of Table 8 show the relevant results. Under the assumption of no serial correlation in error terms, there is no need to instrument for the lagged log sugarcane share. Both the OLS and IV estimates yield positive coefficients that are statistically different from both zero and one. This is worrying, in that it suggests a non-stationary process. In results not shown here, I further explore this issue. The result is sensitive to the instruments and sample used. An IV regression using petroleum price and total population as instruments yielded a small and insignificant effect of the lagged share. However, the estimates in this regression are in general very imprecise. In regards to the sensitivity to the sample, OLS regressions on samples restricting the years to 1990 and beyond, as well as 1995 and beyond, show much smaller 52 Small sample sizes prevent me from having the coefficients be fully region-specific, so I instead allow them to differ between the Center-South regions and the Northeast regions. The constant terms in this equations reflect, in part, the total factor productivity and land quality parameters. These may potentially change over time, so I include a time trend in the analysis. 32

33 coefficients. Below, for simplicity, I estimate the structural model without allowing for any lagged terms or dynamics. This issues is worth exploring further in the future, however. 5.2 Maximum Likelihood Estimation In this section, I describe the details of the estimation procedure. A large body of work by Dale Jorgenson, as well as studies such as Fair and Parke (1980), also pursue estimation of large-scale macroeconomic models. The work here differs in its derivation of aggregates from underlying heterogeneity of individual preferences and land quality, as well as its use of individual-level data to aid in identification. In this way, this paper is closely related to the relatively recent work on dynamic general equilibrium models with individual labor supply and human capital decisions (see seminal papers such as Heckman, Lochner, and Taber (1998) and Lee and Wolpin (2006)). This paper restricts itself to a static setting in order to allow for a more detailed exploration of crossregion patterns and deal with data limitations. In exchange for having a much simpler setting, I am able to incorporate an intensive margin of hours of work, give an economic role to all shocks, and use an estimation approach that guarantees all equilibrium relationships hold. In contrast to most work on empirical general equilibrium models, I use maximum likelihood instead of SMM or GMM methods. The first sub-section provides a rationale for using the MLE approach, along with a description of advantages and disadvantages. The second sub-section goes on to make distributional assumptions and list the parameters to be estimated. The third and final sub-section describes my MLE approach in detail Rationale for Using MLE In the past, authors have noted problems with estimating GE models with maximum likelihood, and have therefore turned to alternative estimation methods (See, e.g., Heckman, Lochner, and Taber (1998),Lee and Wolpin (2006)). However, I pursue the MLE approach instead for four reasons. First, maximum likelihood ensures that all the constraints implied by the equilibrium system are accounted for. It would be possible to implement all these constraints in a more agnostic method of moments approach, but it would require a great deal of caution. Second, using GMM and SMM does not address the more fundamental economic problem of existence and uniqueness of equilibria. Consider the SMM approach, for example. This approach guarantees that at all the error draws used in the calculation of the moments, one has an equilibrium. However, this does not guarantee existence and uniqueness in the neighborhood of the actually realized error draws. Third, for the simulations I need to know what distribution to draw the errors from. At this point, even with GMM and SMM, I would be forced to make stringent distributional assumptions. Fourth, and finally, MLE dictates exactly what moments to use, while GMM and SMM would force me to choose moments somewhat arbitrarily. To be sure, in small samples and with the concern noted above it is difficult to know if the MLE moments are any better than the GMM/SMM moments I could choose; however, MLE does provide a clear guide to the choice of moments. 33

34 To be sure, MLE has its own obstacles. 53 For instance, the small number of observations force me to make stringent assumptions about the independence of unobservables to secure identification. In a linear FIML model without constraints on the contemporaneous correlation of the error terms, identification is impossible if the number of observations is smaller than the sum of the number of endogenous and exogenous variables in the model (see Sargan (1975)). Independence assumptions help substantially. Another problem is that there is no guarantee that a solution to the equilibrium system exists (i.e., that every possible combination of the error terms allowed by the normality assumptions below has an equilibrium for the endogenous variables associated with it). Third, even if a solution exists, there is no guarantee that it must be unique for every possible combination of the error terms allowed by the distributional assumptions. (For a brief discussion of these issues, see for instance Amemiya (1985)). Therefore, the normality assumptions do not capture restrictions on the possible distribution of the error terms that are implicit in the model. Keeping these limitations in mind, I describe my MLE approach below Distributional Assumptions and Parameters to be Estimated Here, I lay out distributional assumptions and clearly state the parameters to be estimated. I assume that all stochastic errors in the economy are normally distributed, independent of one another. Each group of agricultural land quality and TFP shocks shares a common variance; for instance, all regional shocks to land quality in sugarcane have the same variance, etc. 54 In particular, ν irt N(0, σνi) 2 for i = 1, 2, 3 ν krt N(0, σνkr 2 ) ɛ irt N(0, σɛi) 2 for i = 1, 2 ɛ eit N(0, σɛei) 2 for i = 1, 2 ɛ st N(0, σɛs) 2 ɛ i ort N(0, σɛ 2 oir) for i = p, b δ it N(0, σδ 2 i ) for i = e, s, 2, k ϕ jrt N(z jr, σϕjr) 2 53 One of the earliest applications of non-linear FIML to a large equilibrium system was in Fair and Parke (1980), where the authors compared this approach to estimates from non-linear 3SLS and 2SLS. See also Fair and Taylor (1983). 54 I allow the variance of shocks to vary by region for those shocks that are associated with the most cleanly identified parameters. The shocks to labor shares in composite good production, for instance, are allowed to be region-specific. This is because, as will be clear below, the maximum likelihood estimate of the associated parameter will simply be the mean of a certain transformation of the relevant quantities. The estimate of the variance of the associated shock is simply the average of the squared deviations from the mean. 34

35 This leaves us with 174 parameters to estimate: (1) Four parameters governing marginal utilities of consumption, a e, a s, a 2, and a k ; (2) 21 land quality parameters λ 0 jr, for j = 1, 2, 3 and all regions; (3) Seven land allocation friction parameters, κ 2r ; (4) One land quality distribution parameter γ, where I assume γ r = γ for all r; (5) Seven TFP parameters in sugarcane, φ 0 1r ; (6) Two CES parameters ρ in sugarcane and other agriculture; (7) Seven TFP parameters in other agriculture, φ 0 2r ; (8) Seven labor share parameters in composite good production, β or; (9) Seven TFP parameters in composite good production, φ or ; (10) Four parameters governing ethanol and sugar production, α j and β j, for j = e, s; (11) 21 means of the shocks to labor supply, z jr ; 55 (12) 21 parameters governing the consumer preference for region-sector, κ jr ; (13) Three parameters indicating the propensity to be unemployed, p 0, d 1 h, and d 1 l ; (14) Four parameters giving the properties of the non-labor income distribution, π 1, θ 1, θ 2, and σ; (15) Four parameters controlling the preference for leisure, β, ψ h1, ψ h2, and ψ h3 ; (16) 33 parameters governing the variance of shocks on the production side of the economy; and (17) 21 parameters governing the variance of shocks to preferences. Crucially, it is the independence assumptions that give us the leverage necessary to identify such a large number of parameters from so few observations. Without stringent independence assumptions on the errors, identification would not be possible Implementation of MLE Finally, I describe the implementation of my maximum likelihood approach. Estimation of the model will actually require maximizing two likelihood functions. One likelihood function deals with the individual-level data, while the other deals with the aggregate data. This is necessary because I would not be able to identify the labor supply parameters using the aggregate data alone. Theoretical identification of the labor supply parameters using only the aggregate data, if even possible, would rely heavily on the non-linearities of the labor supply functions. Given the small sample size (only 10 observations on the entire economy), identification using only the aggregate data would be practically impossible regardless. Therefore, I proceed with a two-step estimation procedure. First, I estimate the labor supply parameters using the individual-based likelihood function. Second, I maximize the likelihood function that comes from writing down the density of ( V 1, V 2 ). In doing so, I replace the labor supply parameters in this likelihood function with estimates from the first step. Below, I describe various approximations used as I ensure coherence between the individual-level estimates and the aggregate estimates. While I do not pursue it here, there is an alternative approach to estimation that can avoid the separation of the individual estimation from the aggregate estimation. The procedure turns on the fact that we can write an analytical expression for the conditional density f( V 1t ψ 2t ). One could then use the following procedure: 1) Choose a trial parameter vector of the non-preference shifter 55 Note that in the complete model, these are not separately identified from the κ jr. These items will play a role in the linearized version of the model pursued below, however. 35

36 parameters; 2) Use the non-linear constraints to solve for the preference shifters κ jrt ; 3) Use GMM and the κ jrt to estimate the κ jr ; 4) Substitute the values of κ jrt into the two likelihood functions (one individual-level likelihood function and one aggregate likelihood function composed of the conditional densities); 5) Find the values of all non-preference shifter parameters that maximizes a weighted sum of these two likelihood functions. This procedure is related to the Micro-BLP approach, presented in Berry, Levinsohn, and Pakes (2004) (for the original BLP approach, see Berry (1994) and Berry, Levinsohn, and Pakes (1995)). Unlike in the Micro-BLP case, there is no clear guarantee that one can find a parameter vector such that all the non-linear constraints are satisified; 56 even if one had this guarantee, there are significant computational difficulties. I instead pursue the two-step estimation method. Likelihood of Individual Labor Supply Decisions For each individual, we potentially observe four choices: whether or not they work, the region of work, the sector of work, and hours. The last three are observed only for those individuals who work. To assure coherence of the individual and aggregate models, the likelihood function conditions on the vector of region-sector wages w jr and national-level non-labor income M t. Let d it = 1 if individual i works, and equal zero otherwise. The likelihood function is: L = t N t i=1 [L it (d it = 1, h ijrt, s it = (r, j) w jr, M t )] d it [P r(d it = 0 w jr, M t )] 1 d it where h ijrt is the hours choice and s it is the region-sector choice, with s it taking a value (r, j), for r = 1,..., 7 and j = 1, 2, 3. Given the functional form and distributional assumptions from the model section above, for workers we have L it(d it = 1, h ijrt, s it = (r, j) w jr, M t) = P (d it = 1, s it = (r, j) h ijrt, w jr, M t)f(h ijrt w jr, M t) where, leaving the conditioning implicit and dropping some subscripts, we have: P (d = 1, s = (r, j) h) = P r(κ 4z h) eκ jr β β 1 [w 1 β jr (T ψ h h)] D(z) z [ ] 1 β D(z) = e κ 4z (T ψ h ) β w jr β(1 β) [(1 β)(t ψ h) h] [ ] + e κpk β β w β pk (T ψ h)(w pk w jr) + wjrw β pk (T ψ h h) β p,k S 1 ( ( ) ] ) 1 f(h) = σ exp 1 wjr 2 [ln [(1 β)(t ψ 2σ 2 β h) h] θ m π m 2π (1 β)(t ψ h ) h m 56 One can show that under certain conditions on the non-preference shifter parameters, the non-linear system will have a unique solution. But it is not clear that these conditions will always hold. 36

37 For non-workers, the likelihood contribution is given instead by: P r(d = 0) = z d(z m)π m m K = e κ 4z (T ψ h ) β ( eθm+µ 1 β )1 β + e κ 4 (T ψ h ) β ( eθm+µ 1 β )1 β f(µ)dµ K e κpk β β [w 1 β pk p,k S 1 (T ψ h) + w β pk eθm+µ ] I take two steps to ensure the coherence of the individual-level estimates with the aggregate economy. First, constraints on the non-labor income parameters in the likelihood function ensure that in any given year, the expected value of non-labor income will equal per-capita non-labor income in the aggregate data. Second, I constrain the ϕ preference shifters to approximately ensure that, for any given region-sector-year, the analytical expression for aggregate labor supply to any regionsector combination is equal to aggregate labor hours in that region-sector in the data. In practice, I use a linearized version of the constraints. I solve for the ϕ jrt as a linear function of labor hours, wages, and non-labor income using the linear approximation to labor supply, and substitute these expressions for ϕ jrt into the likelihood function. I maximize the resulting likelihood function using two other approximations for computational purposes. The probability of being unemployed is an integral over non-labor income. I numerically approximate this integral using Gauss-Hermite quadrature with 20 nodes (See, e.g., Judd (1998)). The other issue is that, in dealing with labor supply, it is important to take into account the fact that for certain values of non-labor income, the probability of being in particular region/sector combinations is zero (due to the zero hours constraint). This leads to a discontinuity in the likelihood function. To smooth the likelihood function, I multiply the value of being in each region-sector by Φ(h/sd), where h gives desired hours of work and sd is a small, fixed constant. I use sd = 0.1, and this causes Φ(h/sd) to be close to 1 when h > 0, and close to zero when h < 0. Likelihood Function for Aggregate Quantities Denote the entire vector of endogenous variables in the economy in period t as V t = ( V 1, V 2 ) and the entire vector of errors as ψ = ( ψ 1, ψ 2 ). Let the notation Z r = (Z 1, Z 2,...) represent the vector of variables Z for all seven regions, and leave the subscripts t implicit. Let V 1 = ( Y 1r, Y 2r, S 1r, S 2r, Y or, Y e, M, p 1, p e, Ys X, Y2 X, K D, w 1r, w 2r, w 3r ) V 2 = ( L 1r, L 2r, L 3r ) ψ 1 = ( ɛ 1r, ν 1r, ɛ 2r, ν 2r, ν 3r, ν kr, ɛ b or, ɛ p or, ɛ s, ɛ e1, ɛ e2, δ 2, δ e, δ s, δ k ) ψ 2 = ( ϕ 1r, ϕ 2r, ϕ 3r ) Note that the length of V 1 and ψ 1 are both 63, while the length of both V 2 and ψ 2 are

38 The joint density of V t is: f( V 1t, V 2t ) = g( ψ 1t ( V 1t, V 2t ), ψ 2t ( V 1t, V 2t ))det = g( ψ 1t ( V 1t, V 2t ))g( ψ 2t ( V 1t, V 2t ))det ) ( ψ1 ψ 1 V 1 V 2 ψ 2 ψ 2 V 1 V 2 ( ψ1 ψ 1 V 1 V 2 ψ 2 ψ 2 V 1 V 2 ) since ψ 1 and ψ 2 are independent. In fact, the errors within the vectors ψ 1 and ψ 2 are independent as well, which breaks apart this density even further. The next step in constructing the likelihood function involves finding expressions for the error vectors ψ 1 and ψ 2 in terms of the endogenous variables. These expressions can then be substituted into the densities above in the change of variables formula. There are convenient expressions for ψ 1 : ɛ 1rt = ρ1 1 ln( Y1rt ) + 1 ln( 2w1rt ) φ 1r ρ 1 L 1rt ρ 1 p 1t ν 1rt = Y 1rt ln( A rt(s 1rt) 1 γr Γ(1 γ ) ρ1 1 r) ɛ 2rt = ρ2 1 ln( Y2rt ) + 1 ln( 2w2rt ) φ 2r ρ 2 L 2rt ρ 2 p 2t ν 2rt = Y 2rt ln( A rt(s 2rt) 1 γr Γ(1 γ ) ρ2 1 r) ν 3rt = γ rln(1 S 1rt S 2rt) ln(s 1rt) + ln ν krt = ln( S2rt p1ty1rt w1rtl1rt ) + ln( ) κ r S 1rt p 2tY 2rt w 2rtL 2rt ρ 1 ρ 2 ( ) p1tβ s ɛ st = ln ln(α s) p stβ s r t ( p 1tβ sy et ɛ e1t = ln ( ɛ e2t = ln ln( Y1rt L 1rt ) + 1 ρ 1 ln( ln( Y2rt ) + 1 ln( L 2rt ρ 2 ( p1ty 1rt w 1rtL 1rt A rtγ(1 γ r) β s(p 1t r Y1rt pstyst) + rtyst r tβ sy et ) ln(α e) β s(p ety et + p sty st p 1t r Y1rt) rtyst ɛ b ort = ln (p oty ort w 3rtL 3rt) ln(w 3rtL 3rt) β or [ ] ɛ p ort = log( rt p oty ort ) + log p ot p oty ort w 3rtL 3rt [ ] + w3rtl3rt potyort w3rtl3rt log( ) φ or p oty ort r tl 3rt δ at = ln ( ( δ et = ln ( δ st = ln ( δ kt = ln ln p 2t( r Y2rt Y X X p ot r Yort + p2ty2t 2t ) + pety et X p et(y et Y X X p ot r Yort + p2ty2t et ) + pety et X p st(y st Y X X p ot r Yort + p2ty2t r tkt D X p ot r Yort + p2ty2t ( pot r Yort + p2t r p ot r Yort + p2t r st ) + pety et X + pety X et + p sty X st + p sty X st + p sty X st + p sty X st p1ty1rt w1rtl1rt ) λ 1r w 1rtY 1rt p2ty2rt w2rtl2rt w 2rtY 2rt ) ) λ 3r ) ln(β e) a 2 ) a e ) a s ) Y2rt + petyet + pstyst τt Y2rt + petyet + pstyst ) a k ) λ 2r 38

39 where r t = 1 Kt [M t + τ t ] (p 1t Y 1rt w 1rt L 1rt + p 2t Y 2rt w 2rt L 2rt ) p st Y st = w jrt L jrt + M t + τ t p et Y et p ot Y ort p 2t Y 2rt r t Kt D j r r r Unfortunately, there are not analogous, simple analytical expressions for ψ 2. Instead, recalling that the elements of ψ 1 will appear in the preference shifters κ, we have: [ ] L S jrt = N t π m [(1 β)(t ψ hj ) β e θmt+µ ]P r(j, r θ mt, µ)f(µ)dµ m w jrt where f(µ) = P r(j, r θ m, µ) = z 1 σ 2π e 1 2 ( µ σ )2 d z θm if r, j S 1 e κ jr β β [w 1 β jr (T ψ hj ) + w β jr eθm+µ ] e κ 0z (T ψh0 ) β ( eθm+µ 1 β )1 β + k,p S e κ kpβ 1 β [w 1 β kp (T ψ hp) + w β kp eθm+µ ] = 0 if r, j / S 1 Analogously to the case of individual-level estimation, I linearize the labor supply functions to write linear expressions for aggregate labor hours as a function of wages, non-labor income, and the shocks ϕ jrt. As noted above, the z jr are not separately identified in the complete model. The linearization allows us to obtain estimates of the z jr, but it is difficult to know what these estimates mean; for instance, the estimates will in part simply reflect the approximation error. 57 I make two additional simplifications motivated by preliminary estimation. First, I discretize the parameter space of the land quality variance parameters γ. 58 For the estimates below, I constrain γ to be identical across regions, and perform a grid search to locate a maximum of the likelihood function. Second, and more importantly, I placed upper bounds on the value of ρ 1 and ρ 2. Such a bound proved necessary because the maximum value of the likelihood function was actually achieved at values of 1 for both parameters. This seems highly implausible, based on a consideration of the economics behind these parameters; perfect substitutability in any agricultural sector is clearly unlikely. Given this consideration, as well as the fact that imposing constraints from economic theory is especially important with such small samples and limited variation, I chose to impose upper bounds. I use 0.6 as an upper bound, where the choice was informed by the range of values seen in the simple regression results from estimates of the labor productivity equations above. 57 The estimates of z jr are of relatively small magnitudes, which provides some comfort; however, this does not speak fully to the concern here. 58 Preliminary estimation attempts allowed this parameter to be continuous and vary by region. Due possibly to practical constraints on identification with the given data, optimization algorithms failed to locate a local maximum, though each region s values of γ at the termination of algorithms were close to one another, and quite close to the estimate presented below. 39

40 5.3 Estimates of the Model A final change to the estimation procedure described above concerns the likelihood function used for the individual-level data. In the expression for those who choose to work, P r(κ 4z h) appears. This is the probability that the individual has a particular value for the unemployment preference shifter, conditional on hours of work. In estimation, I use the simpler unconditional probability P r(κ 4z ). The implications of this for the estimates are uncertain. With these caveats in mind, Tables 9-12 show the estimates of the model. Standard errors are not shown here. While asymptotic standard errors would be meaningful for the estimates of the labor supply parameters which rely on a large number of individual-level observations from the PNAD data they would be potentially very misleading for the production parameter estimates. These latter parameters are estimated from only 10 years of data, necessitating small sample corrections that are not pursued here. To begin with, Table 9 display estimates of all the parameters affecting labor supply, except for the region-sector preference shifters. The estimation was performed using 168 as the total number of possible hours one could work; that is, the estimation was performed on a weekly basis, rather than an annual basis. Therefore, the estimates of the ψ hi parameters give the threshold level of leisure for one week, and the estimates of the non-labor income distribution parameters refer to non-labor income for one week. 59 The first column of the table addresses preferences for leisure. The estimates there suggest that workers in other agriculture or non-agriculture obtain a slightly higher marginal utility of leisure than workers in sugarcane, and have a slightly higher requirement for leisure. The second column speaks to the propensity to be unemployed and the income of the unemployed. The estimate of κ 4, in combination with the estimates of the region-sector preference shifters in the following table, suggest that the data are consistent with the population being divided into two groups, one of people who always work, and one of people who almost never work. The estimate of d 1 l means that, conditional on being a low permanent income person (i.e., having θ = θ 2 ), that person is always in the work force. Conditional on being a high income person, the probability of being in the work force is about The third column of the table described the non-labor income distribution further. The unconditional probability of being the high type of non-labor income is Based on the estimate of θ 2, there are then about 25% of people who are estimated to have essentially zero non-labor income. Given limited access to land and other assets in Brazil, this seems entirely reasonable. Table 10 presents the remaining non time-varying parameters determining labor supply choices. The table contains estimates of the region-sector preference shifters. While a full understanding of preferences for region-sector would require seeing the estimates of the ϕ jrt and their means, the 59 This choice does not produce any consistency problems when it comes to the aggregate data; weekly labor supply is simply multiplied by 52 to form annual labor supply where necessary. At the same time, using weekly hours helped computationally. 40

41 estimates in Table 10 begin to suggest a few points: The sugarcane sector is much less desirable than the other sectors; non-agriculture tends to be the most preferred sector within any region; and the first three regions which form the South and Southeast of the country tend to be the most desirable to work in. Estimates of the parameters common to all regions and using the aggregate data appear in Table 11. The fact that the ρ parameters both hit their upper bounds suggest a high degree of substitutability between effective land units and labor. This is surprising in at least sugarcane, and I looked extensively at portions of the parameter space where ρ 1 < 0. This region of the parameter space yielded lower values of the likelihood function, though I have not attempted formal tests to see if the differences are statistically significant. Moreover, policy simulations using values of ρ 1 that were negative led to unreasonable conclusions; in particular, they showed unreasonably large increases in median sugarcane land allocations with almost negligible increases in the median value of total sugarcane production. These results are available upon request, but they suggest that the positive values of ρ 1 are more likely. Considering the degree to which the labor hours needed can vary with land type for example, harvesting sugarcane on the hilly landscapes in areas of the Northeast may involve many more hours of labor per amount harvested than harvesting sugarcane in Sao Paulo perhaps the degree of substitutability between effective land units and labor hours should not be so surprising. Moreover, flatter landscapes permit mechanization; in areas like Sao Paulo, a small though not insignificant share of the harvest is mechanized. Next, I turn to the remaining parameters in Table 11. The value of γ is at the upper bound of the discretized parameter space that I considered. This indicates a large amount of variance in land quality within each region. The remaining parameters in the first column describe the variance to shocks to agricultural land or productivity. The second column deals with ethanol and sugar production. The estimates of α e and α s suggest that each metric ton of sugarcane can produce slightly more cubic meters of ethanol than metric tons of sugar. The estimates of β e and β s imply that ethanol requires much more capital than sugar. This result is reasonable qualitatively, but the magnitude of the difference is disconcerting. The estimates appear to be relatively insensitive to allowing the values of ρ 1,ρ 2, and γ to differ, but this warrants exploration into more flexible production functions in the future. Finally, the estimates in the third column relate to aggregate consumption, and show that people on average spend their budget shares in highest to lowest order on capital, the other agricultural good, ethanol, and sugar. The variance estimates suggest that substantial volatility in budget shares comes from the shocks to the sugar parameter, though one must remember that these shocks result in changing budget shares for all goods because of the functional form assumptions used here. Table 12 shows the estimates of the remaining parameters, which vary by region. One must be very cautious in comparing the agricultural parameters across regions because of the normalizations made above. The first two rows show that the Center-South of Brazil holds large advantages in TFP over the Northeast (Bahia, Pernambuco, and Maranhao) in both sugarcane and other 41

42 agriculture. That is, conditional on the same number of labor hours, same amount of effective land units, and same values of α jr, one parcel yields more output in the Center-South than in the Northeast regions. The third row, for λ 1r, shows that Sao Paulo and Pernambuco have the highest estimates for sugarcane land quality, while Mato Grosso has the lowest. Similarly to the case of TFP, differences in these parameters across regions are difficult to interpret in terms of land yields because of regional differences in the values of the normalized α 1r. However, going back to the definition of total effective land units in each sector from Chapter 3, it is clear that higher values of λ 1r correspond to a higher ratio of effective land units in sugarcane to total hectares in sugarcane. Moreover, one can show that the derivative of sugarcane output divided by sugarcane land with respect to α 1r is negative. This means that if a high labor share region like Bahia has a lower estimate of λ 1r, then holding land shares and wages constant across regions, Bahia will have a lower sugarcane yield than the comparison region. Similar statements can be made in regards to λ 2r. The estimates of κ suggest that Parana and Sao Paulo have a bias toward sugarcane land, while Mato Grosso in particular has a bias toward other agricultural land. Moving on to the remaining parameters in the table, the estimates of φ or imply that Pernambuco and Maranhao s composite good sectors have low relative total factor productivity, and the estimates of β or show that these two regions also tend to have the highest labor shares in composite good production. Finally, the estimates of the z jr parameters confirm the suggestion of the region-sector preference shifter estimates from above that sugarcane is a highly undesirable sector, conditional on constant wages across sectors. Nevertheless, the large negative estimates in nonagriculture especially in Sao Paulo should make us wary about the other tentative conclusions from the region-sector preference shifter estimates. For all of the parameter estimates, it is difficult to provide intuitive interpretations. For that reason, I avoid further discussion of the estimates and move to the simulations that use these parameter estimates. 6 Simulations The primary goal of this paper is to use the estimates to simulate the effect of changes in international ethanol policies on Brazil. In order to do so, I use the parameter estimates to form the system of nonlinear equations implied by the equilibrium conditions, the system identical to that used in FIML estimation. I first solve the nonlinear system in the baseline case, where international demand for sugar and ethanol is treated as inelastic and the price of ethanol is determined domestically. Then I simulate three alternative environments. In the first, international demand for ethanol becomes perfectly elastic at a world price that is 10% higher than the price in the baseline. In the second and third, demand again becomes elastic, but now at a world price that is 12% and 15% higher than the baseline price. For reasons discussed below, the simulations increase the world sugar price by the same percentage as the world ethanol price. The first section discusses details behind the method of simulation, and compares the 2005 data with baseline simulations of 42

43 the model. The second section covers the results of the simulations of alternative trade regimes. 6.1 Simulation Methods In running the baseline simulations, I need to make several choices. In what follows, I list the key choices, along with a short description of each: Baseline year. Simulating the model first requires making a choice of which year s exogenous variables to use. As a reminder, the exogenous variables are: the total number of individuals, the world sugar price, the world agricultural price, the world composite good price, the level of ethanol exports, the total amount of land available in each region, the total capital stock, and the level of government taxes/spending. I choose to use the most recent values in my data, from Number of draws. The structural model has stochastic elements. One simulated equilibrium involves drawing one vector of error terms from the normal distributions in Chapter 5, and then solving the system of equilibrium equations for the endogenous variables. Since any resulting vector of endogenous variables is random, it is important to have multiple realizations of this vector to ascertain something about the characteristics of the distribution. This necessitates multiple draws of the vector of error terms, with the equilibrium system solved at each draw. I make 300 such draws. Fixing particular error terms. There is no guarantee that a unique equilibrium exists for any given draw. Initial experimentation with the simulations suggested that it would be very difficult to find equilibria if I were to draw all 84 error terms. However, as noted above, FIML guarantees the existence of a unique equilibrium in the neighborhood of the 2005 values for the error terms. Therefore, loosely speaking, the more error terms that are fixed at their 2005 values, the better the chance of finding an equilibrium. With this in mind, I fix the error terms for composite good production, ethanol and sugar production, and aggregate good consumption. I take error draws for all the agricultural parameters and all the labor supply region-sector preference parameters. Restrictions on equilibria. I confine myself to equilibria that have strictly positive land shares for all uses in all regions, strictly positive wages bounded above by the value of 6 Reais, strictly positive quantities of production for all goods in all regions, and strictly positive agricultural profits in both sugarcane and other agriculture in all regions. Summary measure. Each simulated equilibrium yields one possible realization of the endogenous variables. It is therefore necessary to have some measure that can summarize the results of a large number of simulations. Because of concerns about the sensitivity of the mean 43

44 to outliers, I use the median as a summary measure below. 60 Importantly, this method of summarizing the outcomes means that equilibrium constraints will not in general hold across the medians presented in the tables below. For instance, the median sugarcane land share across simulated equilibria, plus the median other agriculture land share, plus the median non-agriculture land share will not in general sum to 1. However, within any one simulated equilibrium, the three land shares will sum to one in a region, and all other equilibrium constraints will hold as well. 6.2 Baseline Simulations I now turn to the results of the baseline simulations. Of the 300 sets of simulated draws of the error terms, 253 resulted in equilibria. Tables 13 and 14 compare the median outcomes from the baseline set of 300 simulations with the actual 2005 data. In doing these comparisons, it is important to keep in mind that there is no reason to think that the ideal model would have median outcomes that replicate the 2005 data. My intention here is only to show that the median outcomes are reasonable in magnitude, where their reasonableness is suggested by their closeness to the actual 2005 outcomes. Table 13 illustrates that key aggregate quantities in the 2005 data are quite close to the median of these aggregates from the baseline simulations. As expected, the most comparable aggregates involve endogenous variables that are primarily determined from equations that hold the error draws fixed at 2005 values. For example, note the closeness of the median composite good production and rental rate to the 2005 analogues. However, even the median sugarcane and other agricultural production amounts which should be more affected by the stochastic elements of the system are fairly close to the 2005 values. The next table, Table 14 looks at the medians of regional outcomes from the baseline simulations. In particular, the table examines land shares and wages in sugarcane, other agriculture, and nonagriculture. The actual 2005 outcomes appear under the columns labeled 2005, while the medians of the baseline simulations appear under the column Base. Note that the other agriculture land shares are almost identical to three digits, and the other agriculture wages differ by only small amounts. The largest discrepancies between the 2005 and median baseline values are for sugarcane land shares and wages. This should be expected, given that land quality and TFP in sugarcane have higher estimated variances than their other agriculture counterparts (see 11). Of particular note is that the Mato Grosso land share is higher than what is seen in the data in most years. As we will see below, this leads to a higher number of median acres in sugarcane production across Brazil than the actual 2005 value. Still, most sugarcane values from the baseline simulations appear reasonably close to their 2005 counterparts. 60 Conceivably, one would also be interested in other aspects of the distribution of simulated outcomes, such as the variance or 75th percentile. Depending on how risk averse one is, a policy choice could be made on the basis of a higher percentile or lower percentile. 44

45 A comparison of variables not shown in these tables also reveals a fairly close correspondence between the median of the baseline simulations and the 2005 data. I next use the model to simulate the effect of expanding ethanol export opportunities on median outcomes, with the primary outcomes of interest being ethanol production, sugarcane production, and declines in non-agricultural areas. 6.3 Simulations of Alternative Policy Regimes The primary goal of this paper is to determine whether a removal of US barriers to ethanol imports would lead to enough deforestation in Brazil to offset the positive environmental impacts of the Brazilian ethanol that could be exported. That is, how large would the increase in the supply of Brazilian ethanol to the US be relative to the increase in land clearing of environmentally sensitive areas? This section answers this question. I represent the removal of US barriers in the simple way noted in Chapter 3. I consider the following policy changes in the simulations: The international (essentially US) demand for ethanol becomes perfectly elastic at a price 10%, 12%, and 15% above the 2005 price, while the world sugar price increases by the same percentage as the ethanol price in each of the three cases. 61 A sharp increase in the ethanol price amid falling trade barriers could certainly lead to increased sugar prices, as sugarcane in Brazil and elsewhere could be diverted to the production of ethanol. Nevertheless, in the third sub-section, I address concerns about this assumption. Are these price increases for ethanol reasonable? As a point of reference, the 2005 price of ethanol in the data is about US$1.77 per gallon. Considering that the energy equivalent of 1 gallon of ethanol is around 0.7 gallons of petroleum (see Wolak (2007)), the cost of an amount of ethanol equivalent to one gallon of petroleum in 2005 is $2.53. It is hard to know how this price relates to the hypothetical price at the pump in the US, since the ethanol price in my data are derived from the export price of ethanol. Still, this suggests that the 10%, 12%, and 15% price increases on the 2005 level could keep ethanol competitive with petroleum in times of relatively high petroleum prices. As a final note, for each of the three alternative policy environments, I take 300 draws of the error vector, try to find an equilibrium for each draw, and then calculate the median of outcomes over all the equilibria. In particular, for all the alternatives, I use the same draws of 300 vectors that were used in the baseline simulations. Equilibria were found in 269, 254, and 249 of the error draws for the 10%, 12% and 15% alternatives, respectively. The simulation results broadly suggest that Brazil could supply the US with a significant amount of ethanol without posing an extreme risk to forested areas and other environmentally sensitive parts 61 Importantly, I do not consider any endogenous changes in Brazilian government policy, producer productivity, or land quality in response to the policy change. For instance, Hay (2001) and Muendler (2002) find that in Brazilian manufacturing, productivity tended to improve as firms faced increased competition due to changes in the tariff structure. 45

46 of the country. Below, I make this statement precise. The discussion relies on the median values of key variables over all the equilibria that appear in Tables The medians of the baselines simulations appear in rows or columns denotes Base, while the medians for the simulations with an x% change in ethanol/sugar prices appear in the rows or columns denoted x%, for x = 10, 12, 15. Note that the medians from the baseline simulations rather than the actual 2005 data serve as the proper points of comparison with the medians from the alternative regime simulations Ethanol Production and Exports Increase Substantially The comparison between the medians for the baseline and the alternative regimes reveals that all three alternatives lead to a substantial increase in ethanol production and exports. Table 15 displays the medians of key aggregate quantities under each policy environment. The initial movement from the baseline to the 10% regime leads to a massive increase in the median amount of ethanol produced. The median production increases from 4.1 to 8.9 billion gallons, allowing exports of ethanol to jump from a baseline level of 684 million gallons to 5.5 billion gallons. To gauge the size of this number, note that in 2007, total US production of ethanol was 6.5 billion gallons. The projected increases are much larger for the 12% and 15% regimes. Median ethanol production and exports are predicted to jump to 15.9 billion and 12.4 billion gallons, respectively, in the 12% regime. An export total of 12.4 billion gallons would make a sizeable impact on the US fuel mix. As noted in the introduction, with 13 billion gallons of ethanol the US could have used ten percent ethanol blends in all of its 2007 gasoline consumption. In the 15% regime, median ethanol exports move to 21.2 billion gallons, which by itself falls just short of the 2016 renewable fuels mandate in the 2007 US energy bill. These predictions suggest that Brazil could have a significant impact on the shift to low-carbon fuels in the US Less Sugar and More Sugarcane Enable Greater Ethanol Exports This substantial increase in ethanol exports comes from the movement of sugarcane away from sugar production and into ethanol production, as well as an increase in total sugarcane production. The third column of Table 15 illustrates the decline in sugar production. Median sugar production falls from 27.8 million metric tons (MT) in the baseline to 19.5 million MT in the 10% regime and essentially zero in the 12% and 15% regimes. Correspondingly, median net exports of sugar also fall dramatically, as seen in the seventh column of the table. The fact that median net exports are slightly higher than median sugar production should not be disconcerting, since one must remember that these two values do not come from the same equilibrium. 62 One must keep in mind that these results assume nothing is changing in terms of domestic ethanol consumption within Brazil; if domestic preferences for ethanol increased at the same time as the policy change (because of increased purchases of flex fuel vehicles, for instance) one would expect significant implications for the amount of ethanol exported. 46

47 The increase in ethanol exports also comes from an increase in total sugarcane production. The first column of Table 15 shows that sugarcane production jumps from a median of 355 million MT in the baseline to 392, 424 and 478 million MT in the 10%, 12%, and 15% regimes. In principle, these increases could come through intensified cultivation of existing sugarcane land. Alternatively, they could come through extensive changes in land allocated to sugarcane. The results in Table 16 suggest that the production increases actually come through the latter channel. This table shows the millions of acres allocated to each use under each regime, for all seven regions. In moving from the baseline simulations to the 10% regime, median sugarcane acreages increase in every region. In terms of absolute number of acres, the largest changes occur in Mato Grosso, followed by Sao Paulo. The increases in Mato Grosso despite the low land quality in sugarcane, and the strong preference not to work in sugarcane there are helped along by the low land quality in other agriculture, the high TFP levels in sugarcane, and the high degree of substitutability between effective land units and labor. As we next move to the 12% and 15% regimes, the sugarcane land allocation changes in all the regions are massive, with particularly large absolute changes in Mato Grosso, Minas Gerais, and Maranhao. Interestingly, these large shifts of land to sugarcane occur even as median aggregate sugarcane production increases by a relatively small amount. The high variance of land quality and low mean levels of land quality in many regions implies that the marginal land coming into play is relatively ineffective in sugarcane production. Moreover, as we will see below, labor hours per acre in sugarcane appears to drop as sugarcane production expands, putting further downward pressure on yields Consequences for Land Clearing are Non-Linear Given that Table 15 shows median values of other agricultural production to be stable or increasing across regimes, and that sugarcane land expands greatly across regimes, the natural concern is that all these changes are happening at the expense of a great deal of non-agricultural land. However, the picture is a bit more subtle than this. The sugarcane expansion is accompanied by a decrease in at least some land for other agriculture in many regions. The net result is that a large expansion of ethanol exports happens at the expense of relatively little non-agricultural land in the 10% and 12% regimes, but the marginal increase in exports from a shift to the 15% regime comes at the expense of a large amount of non-agricultural land. Again, Table 16 shows the relevant results. By looking at the second and third panel, for other agriculture and non-agriculture median land use respectively, it is clear that the sugarcane expansion is being absorbed to some extent by decreases in other agricultural land in all regimes. For instance, looking again at Mato Grosso, median sugarcane land increases about 20 million acres from the baseline to the 12% regime. At the same time, median other agricultural land falls by about 10 million acres under this policy change, as does non-agricultural land. The degree to which other agricultural land absorbs the sugarcane expansion varies across regions, ranging from 47

48 very strong decreases in Parana and Sao Paulo to apparent increases across regimes in Maranhao. An increase in other agricultural labor hours (see below), and perhaps a shift of other agricultural production across areas, keeps total other agricultural production from falling. What are the ultimate implications of the sugarcane expansions and accompanying changes in other agricultural land for non-agricultural land clearing? To make the size of non-agricultural land clearing concrete, it is useful to think about the quantity of non-agricultural land traded off for a quantity of ethanol exports. The 12$ regime leads to an increase in ethanol exports from the baseline of about 12 billion gallons, while moving from the 12% regime to the 15% regime leads to a further increase of 8.7 billion gallons (for a total increase of about 21 billion gallons relative to the baseline). The first 12 billion gallons of additional ethanol exports come at a median cost of 37 million acres of non-agricultural land over all of Brazil. This is large (an area about the size of New York), but seemingly manageable if it is distributed across the country. However, the next 8.7 billion gallons of exports come at a median cost of an additional 86 million acres, which should cause great concern. The situation is especially worrisome in Mato Grosso and Maranhao, two regions containing at least portions of the Amazon Rainforest. The first 12 billion gallons of ethanol exports come at a cost of 10 million acres of non-agricultural land in Mato Grosso, and 9 million acres in Maranhao. The next 9 billion gallons of exports come at a further cost of 29 million acres and 24 million acres in Mato Grosso and Maranhao, respectively. This dramatic non-linearity in land clearing with respect to exports suggests that there could be a substantial amount of ethanol exported without causing concern, but that moving to very high levels could pose a serious environmental risk Labor Supply Plays a Role Labor supply to the agricultural sectors plays an important role in the results seen above. Tables 17 and 18 describe the changes in median wages and median annual labor hours across the regimes. Two points emerge from these tables. First, the ability to substitute labor for land in other agriculture facilitates decreases in other agricultural land area (by facilitating more intensive agriculture). Movements in median other agricultural labor hours help to stabilize other agricultural production levels across regimes, even as land allocations to the sector fall. This is most apparent in the move from the baseline to the 15% regime. This is also true for particular regions in the 10% and 12% regimes. 63 In practice, this means more intensive cultivation of each acre. One way in which this could be achieved in practice is by switching from pasture to high value export crops, for instance. As we would expect, Table 17 shows a corresponding increase in the other agricultural wage relative to the non-agricultural wage across regimes, necessary to draw in labor. 63 Note that this is likely not the whole story in the 10% and 12% regimes, since some regions do not show labor hour increases. There may be a composition effect, wherein the land being brought out of other agriculture was relatively unproductive, so that total production does not fall much. There could also be a re-allocation of other agricultural production across regions. 48

49 The second point in the tables is that sugarcane production uses dramatically less labor per acre in the alternative regimes, likely because of inelastic labor supply to the sugarcane sector. Table 18 shows that relative to land allocations, median annual labor hours in sugarcane increase by a relatively small amount. 64 Therefore, as we move from the baseline to the various regimes, median hours per median number of acres fall sharply. In practice, this could be facilitated by less intensive harvesting of each acre, or use of more land suitable for mechanical harvesting, or a combination of both. The amount by which labor hours per acre fall appears to be so large that this may warrant further refinement of the model. But the central point is that labor supply to sugarcane is inelastic and sugarcane producers can economize on labor by choosing more land and more appropriate land Caveats The results present a compelling story. Still, it may be possible that the inflexibility in production and trade relationships for ethanol and sugar influences the results in important ways. One issue is that one may think that the flooding of the ethanol market with Brazilian ethanol would help dampen the price increase; given this, 15% may be too large a price increase to expect, though it is difficult to say without a more complete model of international ethanol demand. Another issue is that the zero-profit conditions impose a tight relationship between the prices of ethanol, sugar, sugarcane, and capital. Once the ethanol price becomes internationally determined, the two zero-profit conditions completely determine the price of sugarcane and capital. The tight relationship imposed by the zero-profit conditions has two implications. First, it necessitates strong assumptions on the joint movement of sugar and ethanol prices. One can show that an increase in the ethanol price that holds the sugar price constant must have an opposite effect on the sugarcane price from an increase in the sugar price that holds the ethanol price constant. Given the estimates, an increase in the ethanol price holding the sugar price constant will actually decrease the sugarcane price in our case. It is this fact that necessitates the assumption of increasing sugar prices along with increasing ethanol prices. 65 The other implication of the tight relationship in these prices is that the increase in ethanol and sugar prices causes the capital price to rise, which causes wages in the composite good sectors to fall through the composite good zero-profit conditions. Indeed, median wages in non-agriculture fall monotonically as one moves across regimes in the third panel of Table 17. The falling wages in non-agriculture allow the sugarcane and other agriculture sectors to draw in more labor hours without sizable increases in the absolute level of wages in those sectors. This is critical because it helps keep sugarcane and other agriculture profitable on land parcels that would otherwise not be profitable. These considerations suggest that making ethanol and sugar production more flexible 64 Again, as in other agriculture, median sugarcane wages increase relative to non-agricultural wages to draw in labor. 65 The zero-profit conditions guarantee that after the policy change, an increase of x% in the ethanol and sugar price leads to exactly an increase of x% in the sugarcane price. 49

50 could have important effects on the simulation results. 7 Conclusion The quest for alternative sources of energy in the US has led to greater interest in ethanol and other bio-fuels. This interest has crystallized into stringent renewable fuel mandates in the 2007 energy bill. Under that law, renewables must constitute steadily increasing amounts of total US transportation fuel each year, with a requirement of 36 billion gallons by As bio-fuels requirements increase, corn-based ethanol has so far been the primary bio-fuel source and corn producers have been the primary beneficiaries. Under current policies, the only serious technological alternatives to corn-based ethanol may still be years away from being cost effective. Of course, current policies could change. The US protects its ethanol producers with significant import restrictions. The Brazilian government has been pushing with no success to lift them. By allowing free entry of Brazil s lower-cost sugarcane-based ethanol, the US government could make it easier to move the US transportation fuel mix away from petroleum and avoid the economic side effects of the current reliance on corn in the process. However, there is a crucial tradeoff for the environment involved. Freeing the US ethanol market could have substantial environmental benefits, as the lower cost of ethanol could encourage movement away from petroleum and, equally importantly, the net carbon savings of sugarcanebased ethanol are several times greater than corn-based ethanol. On the other hand, the sugarcane necessary to produce ethanol has to be produced somewhere in Brazil. What carbon could be saved by shifting energy consumption of vehicles to ethanol could be quickly lost through deforestation of the Amazon or Atlantic Rainforests. Moreover, deforestation and clearing of other environmentally sensitive areas could have important effects on bio-diversity and eco-system functioning. This paper addresses this tradeoff by answering the question: Would freely importing Brazilian ethanol into the US lead to enough land clearing to offset the environmental benefits of using larger quantities of more energy efficient ethanol? In short, I find that Brazil could increase ethanol exports sharply in response to a removal of US import restrictions. The cost in terms of land clearing could be manageable until exports reach a very high level, at which point there would be a strong risk of destructive land clearing. More concretely, the results indicate that an additional 12 billion gallons of ethanol exports could come at a median cost of only 37 million acres of non-agricultural land. However, if the international ethanol price were higher, Brazil would export more and the next 9 billion gallons of exports would require an additional decline of approximately 86 million acres. In absolute terms, the greatest damage would occur in the Mato Grosso region, the region of the model that includes the Amazon Rainforest. Of course, the model defines regions very broadly. For instance, my Mato Grosso region contains the very large states of Mato Grosso, Mato Grosso do Sul, Goias, and Tocantins. Consequently, a predicted decline in non-agricultural land in the Mato Grosso region may not necessarily come 50

51 from the Amazon, just as a predicted decline in Parana may not come from the Atlantic Rainforest. Importantly, in the event of a US policy change, exactly where such a decline comes from will to a large extent be under the control of the Brazilian government in the coming years. This is not only because of decisions over the enforcement of forest regulations. A number of other decisions could also influence exactly where land is cleared in an ethanol boom. For instance, permitting a new distillery to be constructed in Parana but not Mato Grosso will increase the appropriateness of land for sugarcane production in Parana and, potentially, keep pressure off Mato Grosso. Determining the consequences of such policy choices within Brazil is not so straightforward, due to the possibility of simply displacing other agricultural producers to Mato Grosso. More generally, to determine the effects of such policy choices will require an adequate consideration of the linkages between land use decisions, labor markets and product markets. This is exactly the value of the framework developed in this paper; and while I used the framework to address a stylized change in US trade policy, it has the potential to serve as a foundation for more detailed policy analysis in the future. 51

52 A Tables and Figures Figure 1: Sugarcane Cultivation Area, Eight Quantiles in 2007 Figure 2: Sugarcane Cultivation Area, Eight Equal-Sized Intervals in

53 Environmentally Sensitive Areas Figure 3: Regional Classification p Figure 4: Amazon and Atlantic Rainforests Sriniketh Nagavarapu Brazilian Ethanol 53