Structural Transformation and Comparative. Advantage: The Implications for Small Open. Economies

Transcription

1 Structural Transformation and Comparative Advantage: The Implications for Small Open Economies Jin-Hyuk Kim Unjung Whang y Abstract International data from past decades reveal that agricultural productivity, as measured by value added per worker, relative to manufacturing is negatively correlated with changes in labor share in manufacturing. Further, a measure of revealed comparative advantage in agriculture is negatively associated with the growth rate of employment in manufacturing sector. Motivated by these ndings we construct and calibrate a simple two-sector growth model, similar to Matsuyama (992), where there is learningby-doing in manufacturing whose output can be used as an intermediate input in the agricultural production. A quantitative analysis of the calibrated model economy shows that small di erences in a country s comparative advantage and speed of learning-bydoing can account for a large variation in structural transformation of small open Department of Economics, University of Colorado at Boulder. jinhyuk.kim@colorado.edu. y Department of Economics, University of Colorado at Boulder. un.whang@colorado.edu.

2 economies. JEL Classi cations F43, O, O4 Keywords: structural change; comparative advantage; economic growth 2

3 Introduction There has been an extensive literature on the role of agriculture in economic development. A number of authors have argued that increases in agricultural productivity are essential for industrialization and takeo in the early stages of development (e.g., Johnston and Mellor 96; Fei and Ranis 964; Chenery and Syrquin 975; Johnston and Kilby 975; Hayami and Ruttan 985; Timmer 988), on which there seems to be a high degree of consensus. The importance of agricultural productivity in determining the starting date of structural transformation the decline of agricultural employment and production shift towards a manufacturing economy was quantitatively analyzed by Gollin et al. (2007), where the agricultural productivity that is one- fth of that of the benchmark economy can delay a country s industrialization by roughly 250 years. Nevertheless, there is much less consensus on how observed sectoral (i.e., agricultural vs. nonagricultural) di erences can be explained across countries. For instance, Restuccia et al. (2008) showed that poor countries are much less productive in agriculture than in nonagriculture compared to rich countries. This implies that there is a positive link between agricultural productivity and industrialization. However, as pointed out by Matsuyama (992), the relationship between agricultural productivity and industrialization could be negative in open economies. This is because low agricultural productivity could imply a comparative advantage in nonagricultural sector such as manufacturing. Using a twosector, endogenous growth model with one mobile factor, Matsuyama showed a negative link between agricultural productivity and economic growth. This argument was based on historical evidence produced by Mokyr (976) on Belgium and the Netherlands and Field (978) and Wright (979) on New England and the South, respectively. 3

4 In this paper we quantitatively investigate the importance of relative productivities, hence a country s comparative advantage, in explaining di erent trajectories of structural transformation across countries. Our model builds on and tries to combine two streams of literature. One is the literature on learning-by-doing in the context of trade and growth (e.g., Krugman 987; Boldrin and Scheinkman 988; Lucas 988; Matsuyama 992; Wong and Yip 999), where having a comparative advantage in high-learning goods will lead to higher-than-average growth intensifying the initial pattern of comparative advantage. The other is the literature on economic growth that explicitly takes into the account the role of agricultural sector (see, e.g., Echevarria 997, 2008; Laitner 2000; Kongsamut et al. 200; Gollin et al. 2004, 2007; Restuccia et al. 2008). 2 To be more precise, we consider a simple, two-sector model with one factor of production (labor) as in Lucas (Section 5) and Matsuyama. Instead of assuming that both agriculture and manufacturing sectors are subject to learning-by-doing, only manufacturing total factor productivity (TFP) grows with the scale of production. Following the latter literature mentioned above, agricultural sector can be modernized by using manufacturing output as an intermediate input to its production. Due to tractability reasons we do not model capital accumulation in our small open economy. However, by showing that our simple model can explain economically meaningful di erences in a country s course of structural transformation, we believe our analysis helps understand the relationship between agriculture and growth in more realistic open economy settings. In the next section, we present cross-sectional evidence that there is a negative rela- 2 This literature focused on what is called the "food problem," an observation that, until countries make scienti c advances to reliably meet their subsistence needs, they are unable to begin the process of modern economic growth (Schultz 953). 4

5 tionship between agricultural productivity (relative to manufacturing) and changes in the manufacturing sector s employment share, which is consistent with the theoretical prediction by Matsuyama (992). However, we also show that there is no cross sectional relationship between agricultural productivity and the manufacturing sector s employment growth rate. To further motivate our study, we construct an index of revealed comparative advantage (RCA) in agriculture relative to manufacturing, as proposed by Balassa (965), and show that there is in fact a negative relationship between RCA in agriculture and the manufacturing sector s employment growth rate, where the opposite relationship holds between RCA in manufacturing and its employment. In Section 3, we present our model, discuss conditions for industrialization to begin in a subsistence economy, and then characterize the equilibrium and the time path of a small open economy s share of employment in manufacturing sector, which depends on the growth rate of world labor share in manufacturing, the labor elasticity of output in manufacturing, and the speed of learning-by-doing in manufacturing. In Section 4, we calibrate our model to match the US and the UK data on agriculture s employment shares. The calibrated model accounts fairly well for the long-run patterns of structural transformation, such as the evolution of agriculture s share of total output in the US and the UK. Using the 50 largest countries labor share data from 96 to 2003, we then proceed to quantitatively analyze the e ect of comparative advantage on small open economies. Our numerical experiments show, for instance, that a mere four percent comparative advantage in manufacturing leads to a factor di erence of three in agriculture s employment share, and about 4 percent increase in aggregate output relative to the world by the end of sample period. Further, a ve percent increase in learning-by-doing can account for a factor di er- 5

6 ence of three in agriculture s employment share, and about 8 percent increase in aggregate output during the sample period, while it has little e ect in a closed economy. Finally, our paper is related to a set of previous contributions that quantitatively analyze the e ects of trade in industrialization using data from individual countries (e.g., Echevarria 995; Stokey 200; Teignier 202), where productivity growth or technological changes are exogenous. The paper in this literature closest to our analysis is Teignier (202). Teignier calibrates a neoclassical growth model to data from the U.S., the U.K., and especially South Korea to estimate the impact agricultural trade policies had on welfare. Our basic approach is similar except in our model manufacturing productivity grows endogenously and there is no capital accumulation. The di erence is that we focus on the quantitative e ects of comparative advantage on structural transformation while the above mentioned papers compare free trade with autarky. 2 Empirical Support As discussed earlier, the conventional view is that improvements in agricultural productivity allow resources to ow out of agriculture to nonagricultural sectors ("manufacturing"). 3 Therefore, there is a positive relationship between agricultural productivity and employment share in manufacturing. In an open economy, as Matsuyama (992) has argued, this relationship could be reversed if high productivity in agriculture implies a country s comparative 3 In this paper, we focus on comparative advantage in agriculture and manufactured goods abstracting from non-tradable service goods. Yi and Zhang (20) analyze structural change in an open economy model with three sectors, where the manufacturing employment share exhibits a hump-shaped pattern as a country develops (see also Ngai and Pissarides 2007; Buera and Kaboski 2009). Our view is that the learning-bydoing model in this paper captures well a country s structural transformation in the medium run, not in the long run. 6

7 advantage in agriculture, which keeps the agricultural labor share from falling. Below, we present a partial support for the latter prediction. That is, without any control variables, there is a signi cantly negative relationship between relative productivity (hence, comparative advantage) in agriculture and changes in labor share in manufacturing sector. Figure plots agricultural productivity relative to manufacturing, measured as the ratio of value-added per worker, against changes in labor share in manufacturing using data from the World Development Indicators (WDI) and the World Resources Institute (WRI), respectively. 4 The value-added data is only available from 980 to 2000 while the labor share data from WRI span a longer period, There are 39 countries in each subpanel of Figure, where the slope coe cients are for the period ; for ; for ; and for All the coe cients are signi cantly di erent from zero at less than one percent level. Though this is by no means de nitive evidence, it does suggest that Matsuyama s prediction appears valid at least for the sample period. An important question that has been neglected by previous studies is whether the e ect of relative productivities (or comparative advantages) is a one shot gain (i.e., a level e ect) or a permanent change in the growth rate (i.e., a growth e ect). When we plotted the sample countries agricultural productivity (relative to manufacturing) against growth rate of labor share in manufacturing, the previous negative relationship disappeared. In Figure 2, the slope coe cients are for the period ; for ; for ; and for None of these coe cients were statistically signi cant at conventional levels. Therefore, agricultural productivity does not seem to have a longer 4 Agricultural labor as a percentage of the total labor force is calculated by dividing the number of agricultural workers by the total number of workers in the labor force. 7

8 lasting e ect on a country s structural changes, an observation consistent with Gollin et al. s (2007) analysis. In this paper, however, we focus on the case of comparative advantage. Although relative productivity is one of the determining factors of a country s comparative advantage, the value-added productivity measures do not alone determine it in our model because manufacturing output can be used as an intermediate input to agricultural production. Hence, we resort to a more direct measure of a country s comparative advantage. Balassa s (965) index measures revealed comparative advantage from international comparisons of exports data. Although Balassa s approach do not reveal sources of comparative advantage, the index has been extensively used in empirical papers. We construct Balassa s index of revealed comparative advantage for 42 countries for which data are complete for the period as follows: RCA j i = ( EXP j i EXP i ) ( EXP j W EXP W ) for j = A; M, where j = A stands for agricultural and M for manufacturing sector, as de ned by the SITC framework. Here, EXP j i is country i s export value of sector j goods, and EXP i is country i s total export value. Similarly, EXP j W is the value of the world s export in sector j, and EXP W is the value of the world s total export trade, where the world consists of 53 countries for which export data are available in the UN Comtrade database for every ve-year period between 965 and When we match these data up with labor shares in agriculture and manufacturing, the sample size reduced to 42 countries. Figure 3 plots the index of revealed comparative advantage (RCA) in manufacturing 8

9 against the rate of growth of labor share in manufacturing. In each subpanel of Figure 3, there is a clear, positive correlation which is also supported by formal statistical tests. That is, all the slope coe cients are signi cantly di erent from zero at less than one percent level. As a robustness check we also plotted in Figure 4 the RCA index in agriculture against the rate of growth of labor share in manufacturing. This time there is a clear, negative correlation between the two variables, where all the slope coe cients are statistically signi cant at less than one percent level. Although there may be some unobserved (or uncontrolledfor) factor that is responsible for these relationships, the results from this exercise provide some suggestive evidence that the law of comparative advantage plays an important role in explaining a country s structural transformation in the second half of the twentieth century. 3 A Theoretical Model In this section we present the basic structure of the model, which is a variant of Matsuyama s (992) model and characterize the equilibrium path under closed and open economy conditions. 3. Basic Structure The economy has two sectors, agriculture and manufacturing, in which competitive rms produce output according to Cobb-Douglas technologies. Speci cally, the agricultural sector has two types of technologies for producing goods, which we refer as traditional and modern. The agricultural sector with the traditional technology produces output using land and labor while the modern agricultural technology uses intermediate inputs, such as chemical 9

10 fertilizers and harvesting equipment, that are produced in the manufacturing sector (see Gollin et al. 2007). To be precise, agricultural output using the traditional technology is given by Y a t = AF (L; N a t ) = AL (N a t ), where L is land (normalized to one) and N a is the fraction of total labor employed in the agricultural sector. A represents agricultural TFP parameter that is a ected by several factors such as government policy, institutions, and climate. We assume, without serious loss of generality, that A is constant, which we will normalize in our calibration. In this paper we focus on the e ect of comparative advantage between otherwise identical small open economies. As we will see below, it is necessary for the economy to start using modern agricultural technology in order to begin industrialization and trade. Hence, for the most part of this paper, we will consider the modern agricultural technology, where we substitute land with intermediate input, X t, so output is given by Y a t = AF (X t ; N a t ) = AX t (N a t ). Following Lucas (988) and Matsuyama (992), for simplicity s sake, the manufacturing sector produces output using only labor. Although it would be more realistic to incorporate capital accumulation in this model, we do not pursue this here. The production function in the manufacturing sector is given by Y m t = M t F (K; N m t ) = M t K (N m t ), 0

11 where K is capital (normalized to one), M t represents knowledge capital, which is predetermined but endogenous. Knowledge capital accumulates as a by-product of manufacturing production, speci cally, _M t = Y m t so that _M t =M t = (N m t ), where is the (countryspeci c) parameter that re ects the speed of learning-by-doing process. 5 Therefore, the engine of growth in this economy is learning-by-doing in the manufacturing sector, and this e ect is external to the individual rms so that each manufacturing rm treats M t as given when making production decisions. We assume that one unit of manufacturing output is required to produce = units of X. Under competitive factor and output markets, is the price of intermediate inputs relative to manufactured goods (see Restuccia et al. 2008). Hence, the representative farmer s and the rm s maximization problems are respectively given by max X t;n a t p t AXt (Nt a ) X t w a;t Nt a, and max N m t M t (N m t ) w m;t N m t, where p t is the price of agricultural goods relative to manufactured goods, which is the numeraire good, is the price of intermediate goods, and w a;t ; w m;t are the agricultural and 5 For instance, the productivity e ects of learning-by-doing can be in uenced by government policies on human capital investment that impact learning on the job site.

12 manufacturing sector wages. Using the optimality condition, we have w m;t = M t (N m t ) () w a;t = Ap t X t (N a t ) (2) = ( )Ap t X t (N a t ). (3) On the demand side, there is an in nitely-lived representative consumer, who inelastically supply one unit of labor in each period. Labor is perfectly mobile across sectors within a country (but immobile across countries), and factor market clearing condition ensures Nt a + Nt m =. Thus, from now on, we denote Nt m = N t and Nt a = N t. To account for the secular decline in agriculture s share of economic activity, we assume a functional form for preferences of the Stone-Geary variety, where the income elasticity of demand for agricultural goods is less than unity while the income elasticity for manufactured goods is greater than unity. 6 Speci cally, the representative consumer s per-period utility is given by U(c a t ; c m t ) = c a t if c a t c = log(c a t c) + log c m t + c if c a t > c, where c a t and c m t denote individual consumption of agricultural and manufactured goods at time t, c > 0 is a subsistence level of food consumption, and 2 (0; ) is a relative weight 6 The observation that the slope of the Engel curve for agricultural goods is less than unity is a wellestablished empirical regularity both in cross sections of countries and in time-series data (see, e.g., Bils and Klenow 998; Kongsamut et al. 200). 2

13 on food consumption. Since there is no storage technology and all consumers are identical, intertemporal consumption smoothing is not possible, so the representative consumer maximizes the discounted stream of utility, P t=0 t U(c a t ; c m t ), subject to the usual budget constraint, where 2 (0; ) is the discount factor. 7 The optimality condition for the representative consumer is straightforward. When c a t c, individuals only consume food. When c a t > c, the representative consumer rst allocates p t c amount of income (which we denote by I) to meet the subsistence consumption of food, and then allocates the remaining income to both goods proportional to their weights in the utility function, that is, c a t = c + p t ( + ) (I c m t = + (I p tc). p tc) Hence, assuming that the consumer has enough income to purchase more than c unit of food, the optimality condition is given by c a t = c + p t c m t. (4) 3.2 Subsistence Economy In this subsection, we brie y discuss how a country starts the development process in our model and can produce in excess of subsistence needs. There are two possibilities for allo- 7 As is common in this literature, we ignore the problem that the instantaneous utility is lowered when c a t increases from c to a slightly higher number. 3

14 cating labor force across sectors in the subsistence economy. One possibility is that farmers produce agricultural goods using the traditional technology. Since consumers derive no utility from consuming manufactured goods in this state, there is no labor allocation in the manufacturing sector. The other possibility is that farmers produce agricultural goods using the modern technology, in which case there will be some labor allocation in the manufacturing sector; however, all manufactured goods will be used as intermediate inputs to agricultural production. Hence, a subsistence economy will optimally adopt the modern technology if and only if the consumer s lifetime utility from using the modern agricultural technology is greater than that from not using it. This holds if ( ) + ( M 0 ( ) ) +, (5) the derivation of which is relegated to the Appendix. 8 The above condition implies that if the initial value of manufacturing productivity, M 0, is su ciently large even though a country s initial agricultural productivity falls short of the subsistence level, then labor will immediately ow out of agriculture before even agricultural production rises above the subsistence level. To be precise, the labor allocation during this gestation period will be constant, Nt m =Nt a = ( )=, while food consumption level increases gradually as M t grows over time. Once food consumption reaches the subsistence 8 This makes the conservative assumption that the learning-by-doing parameter is su ciently small, so that the lifetime utility from using the modern agricultural technology will not go to in nity. If is large enough so that + ( ( )+, then this su ces to use the modern agricultural technology under subsistence conditions. 4

15 level, consumers begin to consume manufactured goods and additional labor will ow out of agriculture into manufacturing sector. Of course, if the above inequality is not satis ed, then labor may be entirely devoted to the traditional agricultural sector, and we need an exogenous increase in either agricultural productivity or manufacturing productivity to start the industrialization process. In particular, as in the conventional arguments, if the increase in agricultural productivity can pull the economy out of subsistence level, this su ces to start industrialization process. However, in light of the empirical evidence suggested above, initial manufacturing productivity seems to play an important role in explaining recent development experiences, where learning-by-doing is an important feature of manufacturing production. 3.3 Closed Economy In what follows, we focus on the equilibrium path after a country begins structural transformation moving beyond the subsistence level. Here, we focus on the case in which agricultural production uses the modern technology, so the representative consumer consumes both agricultural and manufactured goods. Since the economy is closed, the following market clearing conditions hold. c a t = Y a t = AX t ( N t ) c m t = Y m t X t = M t N t X t. Combining these conditions with equation (4) yields 5

16 AXt ( N t ) = c + M t N t p t X t. (6) On the other hand, the no-arbitrage condition in the competitive labor market holds in each period (i.e., w m;t = w a;t for all t). From () and (2), it follows that M t (N t ) = Ap t X t ( N t ). (7) Hence, equations (3), (6), and (7) may now be solved for the three unknowns fx t ; p t ; N t g. From (3) and (7), we have p t = A X t = M ( ) t N t (8) M t N t ( N t ). (9) Substituting (6) with (8) and (9) yields ( N t )N ( )( ) t (+( )) ( )( )+ N t = c A M t. Note that the left-hand side of equation (0) is strictly decreasing in N t, and the righthand side is a positive number. Further, the left-hand side tends to in nity as N t approaches zero, and it is negative at N t =. Since M t on the right-hand side grows over time at the rate N t, equation (0) has a unique solution in N t 2 (0; ), which depends on the parameter values of the model, fa; c; ; ; ; g, and the learning-by-doing technology, which governs the evolution of manufacturing productivity M t. Since _ M t =M t = (M t+ M t )=M t = N t, (0) 6

17 M t = M 0 Q t = ( + N ) for t. Therefore, the labor share in manufacturing in each period t after industrialization can be written as N t = v [M t (M 0 ; ; ); A; c; ; ; ; ]. The function v exhibits standard features that explain a country s structural transformation. For instance, holding other factors constant, a higher initial manufacturing productivity, M 0, increases the labor s share in manufacturing because of the learning-by-doing e ect. A higher agricultural productivity, A, increases the manufacturing labor share because it substitute for the labor demand in agriculture. Relatedly, the labor s share in manufacturing is negatively related to, the conversion ratio of manufacturing output to intermediate inputs, and c, the subsistence level of food consumption. Thus, a technological progress in the intermediate-input production, through lower, can push labor into the manufacturing sector. A successful development strategy can also be found in the speed of learning-by-doing in the manufacturing sector, where a country with more e cient learning technology,, can experience rapid industrialization in which labor ows to the manufacturing sector in a relatively short period of time. If we assume that knowledge spillovers across countries occur over time (even without trade), then the country that starts industrialization process later on tends to have a higher value of because it can save some cost of learning. As we will show in our calibration, a relatively small di erence in can lead to a large di erence in a country s structural transformation, especially in an open economy setting, which we turn to next. 7

18 3.4 Open Economy Consider a small open economy, called home, which is the country described above, while the rest of the world has the same preferences and production functions as home and its variables are labeled by an asterisk ( ). The two countries di er only by agricultural productivity, A, initial knowledge capital in manufacturing, M 0, and conversion ratio for the intermediate inputs,. Labor is immobile across countries, and there is no borrowing and lending across countries. Finally, it is assumed that learning-by-doing e ects do not spill over across countries. Suppose that these countries are allowed to trade with each other. In the absence of international capital market, the world economy evolves just as we described in the previous subsection. Consumers maximize their instantaneous utility, and rms in each sector maximize pro t in the competitive factor and output markets. In particular, if we denote the world (relative) prices of agricultural goods and intermediate inputs by p t and, respectively, then the following rst-order conditions hold. M t (N t ) = A p t X t ( N t ) () = ( )A p t X t ( N t ). (2) Given the properties of the production functions, trading partners will not completely specialize. Then, under the assumption of free trade the home country s labor share in manufacturing sector is determined by the two equations above together with (3) and (7). 8

19 Speci cally, combining () and (7) yields M t AX t N t ( N t ) = Mt A X t N t ( N t ). (3) From (2) and (3), we have X t Xt A = A N t N t. (4) Finally, combining (3) and (4) yields Nt N t A = A M t M t. (5) Suppose at time t the home country opens up to trade. Notice that the home country has a comparative advantage in manufacturing if and only if M t AX t > M t A X t. From equation (3), we conclude that N t T N t if and only if M t AX t M t T A X t, that is, the labor s share in manufacturing sector must be greater for the home country than that for the rest of the world, if the home country has a comparative advantage in manufactured goods. From the free trading equilibrium condition (5), we nd the time 9

20 path of the labor share in the home country by di erentiating (5) with respect to time. _N t N t = _ N t N t = _ N t N t + _M t M t _M t M t + (N t N t ).! (6) Thus, in a small open economy, the growth rate of labor share in manufacturing sector depends on the growth rate of the world s labor share in manufacturing and comparative (dis)advantage in manufacturing. The labor share in manufacturing in the home country will increase at a faster rate than that in the rest of the world if its initial labor share in manufacturing is larger than that in the world (i.e., N t > Nt ), hence, a comparative advantage in manufacturing. The e ect of comparative advantage depends on the speed of learningby-doing,, and the labor elasticity of output in manufacturing,, (which is assumed to be identical across countries). In particular, if and are su ciently large, then the country that has a comparative advantage in agriculture can experience de-industrialization (i.e., _N t =N t < 0) as put forth by Matsuyama (992). Another di erence from the closed economy models such as the one analyzed by Restuccia et al. (2008) is that in this paper import tari s have no implications for small open economies structural transformation. Speci cally, the home country s time path of the labor share in manufacturing (i.e., equation (6) above) is una ected by ad valorem tari s on agricultural and intermediate good imports. That is, suppose p t = p t ( + ) and = ( + 2 ), where s represent the domestic tari rates. It can be easily shown that the di erential equation in (6) remains the same as long as the tari rates are held constant across time. Intuitively, this occurs because the optimal allocation of labor in a small open economy is determined by 20

21 the world prices, which are taken as given. Hence, a protective trade policy does not a ect structural transformation. 4 Numerical Experiments In this section we calibrate the model economy to the UK and the US labor share data and quantify the potential importance of comparative advantage and learning-by-doing in a small open economy. 4. Closed Economy The length of a time period is set to one year. Without loss of generality, the values of A, M 0, and are normalized to one for the benchmark economies. The subsistence level of food consumption, c, is normalized to one so that A = c, which means that if the agricultural sector uses the traditional technology it will produce exactly the subsistence needs of the population. The parameter determines the expenditure share as well as the long-run share of employment in agriculture. Following Gollin et al. (2004), we set = 0:003. Next, we choose the value of to match the intermediate-input-to-output ratio in agriculture. The data from the U.S. Department of Commerce s (975) Historical Statistics suggest that this ratio is 0:39, so we set = 0:6. Accounting for intangible capital investment, we set the labor share parameter in manufacturing equal to 0:5. 9 Finally, we set the value of such that the model matches the evolution of agricul- 9 Corrado et al. (2009) estimate that the average investment in intangible capital was around 5% of the output during Gollin et al. (2007) also set the (physical and intangible) capital share paramter equal to 0:5, which is higher than the conventional one-third level. 2

22 ture s employment share as accurately as possible. That is, given some data on employment shares, we calculate annual time series by cubic interpolation, and then choose the value of that minimizes the sum of squares of the distance between the data and the model s prediction during the time period when the labor s share in agriculture decreases from 70 to 20 percent. Admittedly, this may appear to be somewhat arbitrary but re ects a balance between power considerations and a desire to focus on the rapid industrialization period. Thus, = arg min P t2ft:0:2s [S t0:7g t Nt a ] 2, where S t is the labor share data and Nt a is the value generated by the model. The employment as well as output shares data are taken from Kuznets (966) and International Historical Statistics (Mitchell 992, 993). 0 First, we calibrate the model to UK data on labor s share in agriculture. The parameter is estimated as 0:050. By construction, the calibrated model matches the data very well. Figure 5 displays the estimated data on agricultural labor share from 775 to 995 together with the time path predicted by the model. Given the parametrization chosen, the calibration assumes that the rst year in which labor started owing out of agriculture is approximately 700, which is in line with Gollin et al. s (2007) estimate. The model performs fairly well in replicating the long-run pattern of agriculture s share of output even though the model was not calibrated to explicitly match this data. Figure 6 shows the output share of agriculture. Despite its parsimonious structure, the model appears to provide a good description of agriculture s share of labor and output in the UK data. Next, we calibrate the model to US data on labor s share in agriculture. Following the same procedure as above, the parameter is estimated as 0:062, which is greater than the 0 In the data, manufacturing sector includes mining, public utilities, transportation, and communications. Services are not included in calculation. 22

23 in the U.K. Figure 7 shows the estimated labor share in agriculture in the U.S. from 800 to 2000 and the model s prediction. The model predicts that the transition during which labor share in agriculture drops from 70 to 20 percent in the U.S. occurs between approximately 860 and 940, while the same structural change occurs in the calibrated UK economy between 765 to 878. Hence, the model can explain the fact that the US economy experienced structural changes in a shorter period than the UK economy did. Figure 8 displays the agriculture s output share in the US data and in the calibrated economy. The model t is not perfect in this dimension but captures the general trend reasonably well. 4.2 Open Economy We now use the model to examine the implications for small open economies, where we focus on the e ect of comparative advantage and learning-by-doing. In what follows, we aggregate the 50 largest countries labor share data over the period and use it as representing the world economy. Each country s labor share data is taken from the World Resources Institute (WRI). During this period, the agricultural labor share of the world economy decreased from 60 to 42 percent. Given the world s labor share in agriculture, the equilibrium path of a small open economy s agricultural labor share is determined by equation (6) above. Figure 9 displays a series of numerical experiments where the home country di ers from the rest of the world by only the initial value of manufacturing labor share. In what follows, we set = 0:055 and M0 = M 0 = 4. The world s learning-by-doing parameter value is taken between the above two estimates for the US and the UK. The initial manufacturing productivity in 960 for both home and the world re ects the equilibrium path of the benchmark closed economy, so that M 0 is the implied productivity when the agriculture s labor share is 0:6. 23

24 Figure 9 shows that comparative advantage alone can explain a large variation in the secular decline in agriculture s labor share. That is, holding constant the parameter values across countries, a small (in the range of one to four percent) di erence in a country s initial comparative advantage implies a dramatically di erent time trend of agriculture s labor share for a small open economy. Speci cally, if a country has an initial, four percent comparative advantage in manufacturing relative to the world, then its employment share in agriculture will fall from 0:60 to 0:3 between 96 and In contrast, a county with a small comparative disadvantage in manufacturing can experience slowdown and even deindustrialization. Next, we quantify the e ect of learning-by-doing under open economy conditions. That is, the home country s initial labor share in manufacturing is assumed to be the same as that for the rest of the world (i.e., N 0 = N0 ), but its learning technology can be di erent from the world s. Notice that in this case the equilibrium path of the home country s agricultural labor share changes from above, where the new di erential equation is given by _ N t =N t = _ N t =N t + (N t N t )=( ). Figure 0 shows that a small (around ve percent) increase in the speed of learning-by-doing can explain just as much variation in secular decline of agriculture s employment share in the absence of any initial comparative advantage in manufacturing. To be fair, however, this result is in part due to the dynamics of the small open economy. To assess the e ect of learning-by-doing in a closed economy, we simulate an arti cial economy whose parameter values are the same as those discussed earlier except that varies between 0:052 and 0:058. Figure displays the time path of this benchmark closed economy s labor share in agriculture. A once-and-for-all increase in from 0:055 to 0:058 makes 24

25 only a minor di erence to the agriculture s share of employment in a closed economy, whereas in Figure 0 the same change leads to a factor di erence of three in 40 years. Therefore, learning-by-doing alone cannot explain as much variation in a country s structural transformation. We close this section by discussing the model s implications for economic growth and relative productivities for small open economies. Figure 2 and Figure 3 display the total output of the home country for the respective cases considered above. 2 The model predicts that the small open economy s output grows almost vefold between 96 and 2003 with an average annual growth rate of four percent. However, di erences in comparative advantage or learning technologies only make about 5 percent di erences in total output by the end of the sample period. Hence, the model does not capture well the large output gap between the rich and the poor countries, which might be due to the lack of capital accumulation in the model. Figure 4 and Figure 5 display the ratio of manufacturing output per worker relative to agricultural output per worker employed in each sector of the small open economy. Figure 4 shows that a comparative advantage in manufacturing has a level e ect on the relative productivity; however, it has little e ect over time. On the other hand, Figure 5 shows that an increase in learning-by-doing parameter has some growth e ect on relative manufacturing productivity, but the magnitude of this e ect is negligible compared to the e ect of comparative advantage. These ndings seem consistent with the observation that nonagricultural productivity relative to agricultural productivity is stable over time for some countries like 2 A country s total output (GDP) is measured as p t Y a t X t + Y m t. 25

26 the US and UK. 3 5 Conclusion Traditional explanations of the structural transformation rely on a couple of mechanisms, such as an income elasticity of the demand for agricultural goods less than one and faster total factor productivity growth in agriculture relative to other sectors of the economy. Our results partly con rm this conventional wisdom, but we emphasized that higher manufacturing productivity can also trigger industrialization through the adoption of a modern agricultural technology. Further, after the onset of industrialization we showed that the law of comparative advantage does seem to dominate other forces of structural transformation, as demonstrated by the negative relationship between agricultural productivity and changes in manufacturing labor share. Quantitative analysis showed that the model can plausibly explain the UK and the US s labor share as well as output share in agricultural sector. In our numerical experiments for a small open economy, a small, initial comparative advantage in manufacturing could lead to a major di erence in a country s industrialization process over time, which seems to explain particularly well the rapid structural transformation in some East Asian countries. In contrast, a small, initial comparative disadvantage can plausibly explain the slowdown of structural transformation in some Latin American countries. Learning-by-doing reinforces this pattern under open economy conditions; however, it is shown to be ine ective in a closed 3 The model, however, cannot explain the large cross-sectional di erence in nonagricultural productivity relative to agricultural productivity between developing and developed countries (see, e.g., Gollin et al. 2004). 26

27 economy. References [] Balassa, B., 965. Trade liberalisation and revealed comparative advantage. Manchester School 33(2): [2] Bils, M., Klenow, P.J., 998. Using consumer theory to test competing business cycle models. Journal of Political Economy 06(2): [3] Boldrin, M., Scheinkman, J.A., 988. Learning by doing, international trade and growth: a note. In: Anderson P., et al. (Eds.), The Economy as an Evolving Complex System. Addison Wesley, New York. [4] Buera, F.J., Kaboski, J.P., Can traditional theories of structural change t the data? Journal of the European Economic Association 7: [5] Chenery, H., Syrquin, M., 975. Patterns of Development: Oxford University Press, London. [6] Corrado, C., Hulten, C., Sichel, D., Intangible capital and U.S. economic growth. Review of Income and Wealth 55: [7] Echevarria, C., 995. Agricultural development vs. industrialization: E ects of trade. Canadian Journal of Economics 28(3): [8], 997. Changes in sectoral composition associated with economic growth. International Economic Review 38(2):

28 [9], International trade and the sectoral composition of production. Review of Economic Dynamics (): [0] Fei, J.C.H., Ranis, G., 964. Development of the Labour Surplus Economy: Theory and Policy. Richard D. Irwin for the Economic Growth Center, Yale University. [] Field, A.J., 978. Sectoral shift in Antebellum Massachusetts: A reconsideration. Explorations in Economic History 5(2): [2] Gollin, D., Parente, S.L., Rogerson, R., Farmwork, homework and international productivity di erences. Review of Economic Dynamics 7(4): [3],,, The food problem and the evolution of international income levels. Journal of Monetary Economics 54: [4] Hayami, Y., Ruttan, V.W., 985. Agricultural Development: An International Perspective. Johns Hopkins University Press, Baltimore. [5] Johnston, B.F., Mellor, J.W., 96. The role of agriculture in economic development. American Economic Review 5(4): [6] Johnston, B.F., Kilby, P., 975. Agriculture and Structural Transformation: Economic Strategies in Late-Developing Countries. Oxford University Press, London. [7] Kongsamut, P., Rebelo, S., Xie, D., 200. Beyond balanced growth. Review of Economic Studies 68(4):

29 [8] Krugman, P., 987. The narrow moving band, the Dutch disease, and the competitive consequences of Mrs. Thatcher: Notes on trade in the presence of dynamic scale economies. Journal of Development Economics 27( 2): [9] Kuznets, S., 966. Modern Economic Growth. Yale University Press, New Haven. [20] Laitner, J., Structural change and economic growth. Review of Economic Studies 67(3): [2] Lucas, R.E., 988. On the mechanics of economic development. Journal of Monetary Economics 22(): [22] Mitchell, B.R., 992. International Historical Statistics: Europe Stockton Press, New York. [23] Mitchell, B.R., 993. International Historical Statistics: The Americas Stockton Press, New York. [24] Mokyr, J., 976. Industrialization in the Low Countries, Yale University Press, New Haven. [25] Matsuyama, K., 992. Agricultural productivity, comparative advantage, and economic growth. Journal of Economic Theory 58(2): [26] Ngai, L.R., Pissarides, C.A., Structural change in a multisector model of growth. American Economic Review 97: [27] Restuccia, D., Yang, D.T., Zhu, X., Agriculture and aggregate productivity: A quantitative cross-country analysis. Journal of Monetary Economics 55:

30 [28] Schultz, T.W., 953. The Economic Organization of Agriculture. McGraw-Hill, New York. [29] Stokey, N.L., 200. A quantitative model of the British industrial revolution, Carnegie-Rochester Conference Series on Public Policy 55(): [30] Teignier, M., 202. The role of trade in structural transformation. Mimeo. [3] Timmer, C.P., 988. The agricultural transformation. In: Chenery, H., Srinivasan, T.N. (Eds.), Handbook of Development Economics, vol.. Elsevier, Amsterdam, pp [32] U.S. Department of Commerce, 975. Historical Statistics of the United States: Colonial Times to 970. Bureau of the Census, Washington D.C. [33] Wong, K., Yip, C.K., 999. Industrialization, economic growth, and international trade. Review of International Economics 7(3): [34] Wright, G., 979. Cheap labor and Southern textiles before 880. Journal of Economic History 39(3): [35] Yi, K.-M., Zhang, J., 20. Structural change in an open economy. Mimeo. 30

31 6 Appendix Condition (5), which is su cient to start industrialization, is derived from comparing the lifetime utility from consuming agricultural goods using only the traditional technology with that from consuming agricultural goods using the modern technology where all manufactured goods are used as intermediate inputs. In the former case, since all labor is allocated to agricultural sector (i.e., N t = 0 for all t), agricultural output is Y a t = A( N t ) = A. The lifetime utility is thus U = P t=0 t c a t = P t=0 t A = A=( ). In the latter case, agricultural output is Y a t = AX t ( N t ) = A(M t N t ) ( N t ). The rst welfare theorem, that competitive equilibrium is e cient, implies that the consumer s lifetime utility is maximized with respect to labor allocation. Hence, the maximization problem, max P t=0 t A(M t N t ) ( N t ), yields optimal labor allocation in the manufacturing sector, N t = ( ) ( ) +. Notice that _M t =M t = (M t+ M t )=M t = N t. Rearranging yields M t+ = M t! ( ) +. ( ) + 3

32 Therefore, the lifetime utility is ( ( ) U = A ( ) + ( ( ) = A ( ) + ) ) ( ) + X t=0 M0 ( ) + t M t " X t t=0! t # ( ) + ( ) +. If + ( ( )+, then the lifetime utility explodes to in nity. If + ( ( )+ <, then the lifetime utility is U = A ( ) ( )+ ( + ) ( )+ ( ) ( )+ M 0. Therefore, the lifetime utility using the modern technology is greater than not using it if and only if ( ( ) ( )+ + ) ( )+ ( ) ( )+ M 0 >. Since + ( ( )+ >, a su cient condition for the above inequality to hold is ( ) ( ( ) + ) ( ) + M 0. Rearranging yields condition (5). 32

33 Figure : Figure 2: 33

34 Figure 3: 34

35 Figure 4: 35

36 Figure 5: Figure 6: 36

37 Figure 7: Figure 8: 37

38 Figure 9: Figure 0: 38

39 Figure : Figure 2: 39

40 Figure 3: Figure 4: 40

41 Figure 5: 4