Trade and Environment revisited: Assessing the Effects of International Technology Spillovers

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1 Trade and Environment revisited: Assessing the Effects of International Technology Spillovers Enrica De Cian January, 2008 Abstract This papers extends the GTAP-E model to include endogenous technical change. Input augmenting technical change, which in the current GTAP-E version is exogenous, is modified so as to reflect the empirical evidence on international technology spillovers. The empirical evidence support the existence of a positive relationship between capital and energy technical change and imports in capital goods. Using a modified version of the GTAP-E model with technical change, this paper revisits the relationship between trade and the environment when trade is also related to growth through technical change. The first part of the paper develops a simple toy model, with 2 countries producing 2 goods to illustrate how international technology spillovers affect production structure. The second part extends this analysis to a fully-fledged computable general equilibrium models, calibrated on real world data. The major finding are that international technology spillovers play an important role in determining the effects trade liberalization can have on the environment. When spillovers have a positive effect on energy productivity, they tend to reduce the rate of carbon leakage. This result emerges from both the toy model and the GTAP-E model. Results are robust to sensitivity analysis on parameter values. Key words: International technology spillovers, trade, environment, computable general equilibrium model; JEL codes: F18; O47; Q55; Q56; School of Advanced Studies in Venice and Fondazione ENI Enrico Mattei. This paper is part of the PhD dissertation I am writing under the supervision of Carlo Carraro and Reyer Gerlagh, whose comments and help is greatfully acknowledged. I am also grateful to Ramiro Parrado for his help. 1

2 1 Introduction The relationship between trade and the environment has receved increasing attention since the seminal work of Grossman and Kruger (1993). In assessing the environmental effect of the North Free Trade Agreement (NAFTA), they found that the liberalization in trade between Canada, USA and Mexico could increase environmental quality in Mexico. Copeland and Taylor (2003) developed a neat theoretical framework to study both aspects of the trade environment relationship. Not only trade affects environmental quality through a reallocation of production activites, but environmental policy can also influence the choice of plant location, affecting trade flows. Another branch of literature has considered the relationship between trade, technical change and growth. International trade increases the number and the varieties of inputs and technologies that can be used for domestic production. Moreover, it provides a further channel for the exchange of idea and thus it increases the opportunities of imitation. As a consequence, iternational trade can generate international technology spillovers that increases domestic productivity. This is the idea behind the model of endogenous growth with international trade developed by Grossman and Helpman (1991). The existence of international spillovers was empirically supported by the seminal empirical work of Coe and Helpman (1995). These two strands of literature remain quite separated and a systematic attempt aimed at merging them into a unified framework is still missing. This paper tries to fill this gap by considering simoultaneously the effects that trade can have on both the environment and growth, through technical change. Trade liberalization has a direct effect on the environment, but it also has an indirect effect which goes through technical change. For example, if the effect of trade is to induce energy saving technical change, then trade can have a positive effect also on the environment. The key difference with respect to the works of Copeland and Taylor (1994; 2003; 2004) is the relationship between trade and technical change, which was always excluded in their works. Copeland and Taylor (1994) analyzed the trade environment relationship assuming that the technology of production is not affected by trade flows. In their approach, only environmental policy can have a technique effect, which is defined as a reduction in pollution intensity per unit of output. This paper relaxes the assumption of constant technology and it develops a model in which the production technology is affected by trade flows. Such model will be used to assess the effect of trade liberalization on the environment when the technology responds to trade policy. A similar analysis was carried out by Kuik and Gerlagh (2007) who assessed the effect of energy saving international technology spillovers on carbon leakage using both an analytical and an applied general equilibrium model. This paper differs from that work mainly in the empirical foundation of the specification of international spillovers. The empirical support for the relationship used in this paper is De Cian (2008). One result emerging from that paper is that embodied technology spillovers augment not only the productivity of energy, but also that of capital. First a stylized toy model with embodied international spillovers is developed. The formulation used in this model differs from the existing ones as international technology spillovers affect the productivity specific to each input. Such a simple model provides an analytical framework that helps to identify the channels of interactions between trade the environment. In the second part, an fully-fledged general equilibirum model, calibrated on real world data, is modified so as to accomodate for these types of embodied technology spillovers. Using this model the effect of spillovers on trade and climate policies is assessed. The rest of the paper is organized as follow. The first three sections review the literature on trade and the environment, on the treatment of technical change in applied general equilibium models and on international technology spillovers. Section 5 describes the technical features of the simple toy model and how technical change has been implemented. The empirical results used to define the functional form for technical change are briefly recalled. The model is solved numerically and it is used to assess the effects of policy scenarios that can affect the spillovers of technology between the countries. In particular, it will be analyzed how a reduction in import 2

3 tariffs affects the technology of production in the liberalizing country. As the model contains also the input energy, it allows evaluate also the effect of trade liberalization on the use of energy and thus on the environment. Section 6 performs the same analysis, but using a larger CGE model calibrated on real world data. This model explictly contains a climate module that links the use of energy to carbon emissions. Using this second model, a mix of climate and trade policies is also analyzed. Finally, a conclusion summarizes the major results of the paper. 2 Trade and environment revised Technical change can have an impact of the environment because it can modify the input mix used in production. The literature has focused manly on the relationship between growth and the environment on the one hand and trade and the environment on the other hand. The empirical evidence of a relationship between growth, as higher income, and pollution dates back to the work of Grossman and Helpman (1993) who found an inverse u relationship between per capita income and some pollutants. Economic development is associated with a structural transformation of the economy toward less pollution intensive industries. Moreover, growth seems to be associated with the use of more efficient and less dirty technologies. James Andreoni and Arik Levinson (2000) found that as the scale of output increases, the switch to cleaner techniques of production occurs independently of policy implemenation. Antweiler, Copeland and Taylor (2001) develops a theoretical model that allows to quantify the different effects that can explain the relationship between growth and the environment, also referred to as scale, composition and technique effect. They found that an 1 percent increase in the scale of economic activity raises pollution 1 by 0.25 to 0.5 percent. The technique effect associated with the expansion in economic activity reduces pollution by 1.25 to 1.5 percent, with a net positive effect for the environment. Trade can affect the relationship between growth and the environment as it introduces competitivness concerns that affect production allocation. Trade allows to chose which goods to produce and which goods to import. The pollution haven hypothesis says that with free trade firms tend to reallocate dirty production in the countries where environmental regulation is less stringent. This effect is also called environmental dumping. In the case of climate change, the reallocation of dirty industries from the constrained to the non constrained countries leads to an increase in carbon emissions in the latter countries. This effect is known as carbon leakage. If trade were not allowed, the possibility of international reallocation would be reduced as the consumption possibilities of a closed economy coincide with the production possibilites. On the other hand, countries may have an incentive to set tighter environmental policy to induce innovation, ensuring a competitive advantage ahead of other countries. Formulated by Porter (1991), this hypothesis is known as Porter Hypothesis. The economic assessment of the effects of trade liberalization on environment has developed around the decomposition pioneered by Grossman and Kruger (1993) and extensively applied by Copeland and Taylor (1994; 2003; 2004). The analysis of Copeland and Taylor relies on a static general equilibrium model. In this context, trade can have an effect on the environment only through substitution and a change in output composition, but dynamic effects on growth and the possibilities of technology transfers across countries are ruled out. This framework puts some constraints on the size of the technique effect, which together with the composition effect could make trade liberalization good for the environment. In the Copeland and Taylor s model, trade affects the environment only through the scale and the composition effect. The scale effect, which is the expansion of economic activity without changing the input and output mix, is negative for the environment if economic activities are polluting. The composition effect, which is a change in the output mix for example from dirty to clean sectors, can be positive or negative for the environment, depending on comparative advantage. If a country has a comparative advantage in a clean sector and this sector expands with trade liberalization, then trade is likely to be good 1 In their paper, pollution was represented by sulfure dioxide concentration. 3

4 for the environment. Only environmental policy can have a technique effect and they abstract from the effect that trade can have on production technologies. Copeland and Taylor s analysis does not take into account the relationship between trade and growth, as analyzed by Grossman and Helpman (1991). In turn, the analysis of Grossman and Helpman (1991) does not consider the environment. If international trade affects the process of technical change, economic processes may have a positive effect not only on growth, but also on the environment and there could be scope for win win outcomes. In the framework of Grossman and Helpman international trade can have a positive effect on growth via increased number and quality of goods. Quality improvements can go in the direction of lowering the pressure on the environment. This paper improves on the approach of Copeland and Taylor by introducing international technology spillovers between countries. Whether trade liberalization is good or bad for the environment is reassessed using a framework in which trade, growth and the environment are connected with each other. 3 Technical change in general equilibrium models Improving the description of technical change has been the focus of the recent applied literature on climate-economy models. Whereas in the short and medium run the key factor of adjustment to environmental policies is susbtitution between inputs, in the long run technical change offers a further channel of adjustment. Two are the major approaches that have been used to describe technical change. A first generation of computable general equilibirum modesl (CGE) 2 have represented technical change as an exogenous process that improves energy efficiency. This type of technical change is conventionally parametized by the so called autonomous energy efficiency improvement (AEEI) paramter. Typically it is consistent with a yearly improvement in energy efficiency between 1% and 2%. Another way of modeling technical change is to introduce a backstop technology in the production of energy. Such technology enters into force when energy prices reach a threshold level, exogenously decided my the modelers, and it is available at a constant marginal cost. These are typically clean technologies that allow to produce energy without emissions. The key parameter of this approach is the price at which this technology is activated. The limit of both approaches is that technical change is not related to any economic variable of the model, excluding the possibility of endogenous and induced technical change. The second generation of climate-economy models tackled this issue and it endogenized the process of technical change. R&D and learning by doing have become the two major sources of technical change. Seminal works are the models of Goulder and Schneider (1999) and Goulder and Matahi (2000) where technical change responds to economic incentives. Another important dimension of the process of technical change is technology diffusion across countries. International trade is an important source of international technology spillovers, as emphasized by the theoretical work of Grossman and Helpman (2001). Next section reviews more in detail the empirical literature on international technology spillovers. 4 International technology spillovers The nature of knowledge and technology as partial public goods naturally brings up the issue of externalities and spillovers. A commonly used definition of technology spillovers is that of Griliches (1979) who defines technology spillovers as the technological progress that is available at a lower than the original cost paid by the inventor. According to Weyant and Olavson (1999), spillovers are any positive externality that results from purposeful investments in technological 2 CGE models are not the only type used in climate-economy literature. Other models include optmal growth models or energy system models. For a broader review see for example Loschel,

5 innovation or development. Diffusion and adoption is another important phase of the process of technical change during which an innovation becomes widely available to other firms, sectors or countries. Considering the fact that R&D is highly concentrated in three countries (Japan, Germany and US), the diffusion of new technologies can have important implications for non innovating countries. International technology spillovers can be of two types, disembodied and embodied. Disembodied international technology spillovers are the flow of ideas that take place without the exchange of commodities. Example of situations in which disembodied spillovers may occur is with workers mobility, students exchange programs, international conferences and journals. Embodied international technology spillovers instead are linked to the exchange of goods. Being technological change the application of new knowledge to production processes and products, the cumulative production of goods can approximate the technology level of an economy (Arrow, 1962). In particular capital goods and the use of new equipment and machineries in the manufacturing and in the industrial sector are considered important sources of technological progress and thus of economic growth (Jaffe, Newell and Stavins, 2005). Trade of such goods is expected to generate spillovers of the technology embodied in them. In fact, the use of capital goods requires the acquisition of the knowledge that actually enables the use of these goods. Trade in capital goods can be taken as a proxy of international technology spillovers. The literature on trade and growth has emphasized the role of equipment and machinery imports. DeLong and Summers (1991) found that equipment investments have a higher impact on growth than non equipment investments. Mazumdar (2001) differentiated between domestic and imported equipment, finding a stronger impact for imported capital goods. The intuition is that more spillovers are likely to stem from goods that are relatively intensive in R&D. A shown in table 1, OECD countries concentrate most of their R&D expenditure on machinery and equipment: T able 1 The major suppliers of capital goods are also the bigger innovators. These figures are consistent with the study of Eaton and Kortum (2001) who found a positive correlation between R&D intensity, specialization in machinery and equipments and their production and export. Trade in machinery and equipments can be expected to be a major channel of embodied spillovers from developed countries, where capital goods are improved, to all importing countries. The degree of technological spillovers is related to the level of capital imports, which in turns depends on country specific trade policies. Trade in different classes of goods leads to different degree of knowledge spillovers because technology intensity varies across sectors, leading to different degrees of embodied technology. Technology spillovers are neither automatic nor costless but they require adoption capabilities, e.g. human capital and indigenous research capacity. The absorptive capacity of a country is related to its economic, human and technological development. However, not all types of transfers require the same effort. Most empirical studies tried to capture disemboided technology spillovers. Coe and Helpman (1995) found that not only domestic R&D is an important explanatory variable of TFP, but also foreign R&D plays a significant role. Other empirical studies on disemboidied spillovers are those of Bernstein and Mohnen (1998), Eaton and Kortum (1996), Keller (1998) and Nadhiri (1993). The first piece of evidence on embodied international technology spillovers goes back to the study of Coe et al. (1997) who found that an increase in aggregate imports has a positive effect on total factor productivity growth. Their approach has been applied also to industry data (Cameron et al. 2005), with similar results. The approach of Coe et al. (1997) has two major drawbacks. First, it applies to very generic aggregate measures of productivity. Productivity is measured as total factor productivity, tf p, computed as the residual of output growth that cannot be explained by factor accumulation. Therefore it is not completely clear how much of this growth is due to technical progress and how much is due to other things. Second, the aggregate imports are a too generic aggregate. 5

6 In the applied economic lieterature, some modelers tried to include technology spillovers in CGE models. 3 Goulder and Schneider (1999) have analyzed the effect of intra-sectoral spillovers. Each firm invests in R&D, contributing to built up the industry knowledge stock that has a positive externality on all firms belonging to that sector. Kemfert (2005) developed a multi-country and multi-sector CGE model in which countries not investing in R&D can benefit from other countries R&D proportionally to capital flow. Gerlagh and Kuik (2007) found that energy saving international technology spillovers reduce the rate of carbon leakage. van Meijl and van Tongeren (1999) studied the effect of international technology spillovers on production and welfare. Their work is based on the empirical evidence of Coe and Helpman (1995) and it analyzed also in detail the role of absorptive capacity. More recently, De Cian (2008) has estimated the relationship between imports in capital goods from OECD countries and factor augmenting technical change in the importing country. The knowledge content of good is higher the higher the stock of knowledge in the producing countries. For this reason, imports from those countries that perform most R&D can be expected to generate higher spillovers. One result found in this paper is that imports in machinery appear to be a more important explanatory variable than aggregate imports. Moreover, their effect is particularly strong on energy technical change. An increase in machinery imports from OECD of 1% boosts energy productivity by 0.09% and capital productivity by 0.023%. Such relationship was estimated only for OECD countries, using aggregate data for the all economy. The model for technical change that was estimated assumed that all technical change improve input efficiency and that neutral technical change was not changing over time. Next section develops an ad hoc model in which the general equilibrium effects of technical change, as estimated in this paper, can be studied. Only capital and energy technical change are modified to be endogenous. As regarding labor technical change, there were no empirical evidence of a relationship between imports and labor technical change. Labor and neutral technical change are therefore left exogenous. 5 A toy model for international technology spillovers 5.1 Description of the model The model consists of a world economy where there are two countries, country 1 and country 2 denoted by the subscript i = 1, 2, which have identical preferences and the same endowments. The production possibilities of each countries are described by a production technology frontier. The technology frontier has the same functional form in the two countries but it differs in the relative productivity of the two possible outputs. In both countries final output can be allocated between a consumption good, y i, and machinery, z i. Machinery are used as input in the intermediate sector, which delivers the intermediate input to be used in the production of the final good. The allocation possibilities of final production between the consumption good and machinery is described by a concave production possibility frontier (PPF), Gi(y i, z i ): G i (y i, z i ) = [ ( yi A i ) 1+σ ( ) ] 1 1+σ 1+σ zi + B i (1) This is a constant elasticity of transformation production function frontier, meaning that the rate at which consumption good can be transformed into machinery is constant. The elasticity of transformation measures the responsiveness of the ratio between the two possible outputs, y i 3 There are also other types of models with spillovers. Two examples of optimal growth models are those developed by Buonanno et al. (2002) and Bosetti et al. (2007). Here the attention is limited to CGE models. 6

7 and z i, to a change in the price of y i relative to the price of z i. In other words, it describes the degree of transformability between the two possible outputs. This degree is maximum in the linear case, obtained when σ =. If σ = 0 the two types of output cannot be transformed with each other at all. The relative productivity parameters, A i and B i, pin down the two extremes of the PPF. When machinery production is zero, z i = 0, and all resources are used to produce the consumption good, y i, its maximum production level is proportional to A i : y max i = G i (y i, z i )A i Similarly, when consumption good production is zero, y i = 0, and all resources are used to produce machinery, z i, its maximum production level is proportional to B i : z max i = G i (y i, z i )B i The productivity parameters A i and B i are chosen such that country 1 is relatively more productive in producing machinery and therefore has a comparative advantage in the sector z i. Such productivity distribution gives country 1 a comparative advantage in the machinery sector that translates into a lower domestic price of machinery relative to the consumption good, q i p i : A 2 > A 1 B 2 B 1 q 2 > q 1 p 2 p 1 The efficient allocation of production between consumption good and machinery requires each economy to maximize the total value of output under the technology constraint described by the technology possibilities frontier, which in turns depend on the amount of intermediate inputs available for production, x i : Max yi,z i p i y i + q i z i s.t. G i (y i, z i ) = x i First order conditions in the final sector require the equality between good price and the value of its marginal product evaluated with the shadow price λ, which is the Lagrangean multiplier associated with the constraint : q i = λg iz p i = λg iy (G i (y i, z i ) x i ) = 0 In equilibrium, the marginal rate of transformation between the two types of output is equal to the ratio between output prices, which can be re-written as follow: p i G iy = q i G iz (2) The quantity of intermediate input, x i constraints the production possibilities of final output and λ can be interpreted as the shadow price of such constraint. The intermediate good is produced using labor, energy, and the machinery produced by the final sector, which is denoted by m i to distinguish the demand from the supply, z i. Machinery is one possible output of the final sector and it is used as input in the production of the intermediate sector, denoted by good x i = F (l i, e i, k i ). The third first order condition requires the value of final output to be equal to the value of intermediates: 7

8 G i = x i = F i (3) Moreover, the marginal product of an additional machinery in the final output is equal to the marginal value of an additional machinery in the intermediate sector: G iy = F m (4) The intermediate good x i = F (l i, e i, m i ) is produced with technology that allows to substitute inputs at a constant rate, γ. Production uses one primary factor, labor l i, energy e i and one output of the final sector machinery, m i. The functional form chosen for F (l i, e i, m i ) is thus more flexible than a Cobb Douglas, where the elasticity of substitution among inputs is constrained to be equal to one. The choice of a constant elasticity production (CES) function with a substitution value different from one is based on the econometric results that were discussed in the previous chapters. The Cobb Douglas production structure was always rejected and therefore a production function with a value different from one seems to reflect better the data. Intermediate production, x i, is described by the following CES: x i = F i = H i [(A Mi m i ) γ 1 γ + (A Ei e i ) γ 1 γ + (A Li l i ) γ 1 γ ] γ γ 1 Besides inputs and output, the production function also includes four coefficients, H i, A E, A L, A M, that describe the level of technology available in the economy and the productivity of each input. The parameters A j for j = (E, L, M)describe the productivity of the three inputs. In principle these three coefficients could be different. These coefficients are also referred to as input augmenting technical change because they describe the effective productivity of each input. For example, consider the case using one unit of input j with productivity A j = 2. The effective amount of input that can be used in production is 1XA j = 1X2. This is equivalent to use two units of the input with productivity one, 2XA j = 2X1. It can said that the effective or the actual amount of input available for production depends on the productivity level together with the input quantity. In addition to input specific technical change, there is a further coefficient, H i, that can represent the productivity of the overall sector. This parameters is also often referred to as neutral technical change as it describes a type of technical progress that improves the efficiency of all input equally (Barro and Sala-i-Martin, 1995) 4. Instead, the coefficients A i represent a technical progress that is input specific, as there are no reasons to assume that A E = A M = A L. Moreover, different countries can be expected to have different productivities level. Production in the intermediate sector is characterized by constant return to scale and the aggregate producer maximizes profits. Optimality conditions require the equality between the value of the marginal product of each factor and its price: p x F li = w i p x F ei = p ei p x F mi = q i Energy is assumed to be elastically supplied with elasticity of supply ɛ. Being energy production very much capital or machinery intensive, in this simple model it is assumed that the energy price,p e, follows exactly the price of machineries, q i : e i = ɛp e = ɛq i 4 It should be pointed out that H is a residual measures that captures what is not expalained by factor accumulation and productivity. It could therefore include also other factors, not directly related to technical change, such as the quality of institutions, the type of culture and so on. 8

9 This assumption is quite restrictive, but to the purpose of this model it is enough. It will be removed in the bigger model used in the second part of the paper. Under this structure for energy supply, the optimality conditions in the intermediate sector can be reduced to the equality between the marginal product of energy and machinery: F ei = F mi (5) The difference in domestic prices create an incentive to trade. Both countries can have an advantage from producing more of the good they are good at and importing the other good. International trade can be seen as an indirect way of producing as it allows specialization in the good where there is a comparative advantage without constraining consumption possibilities. A very simplified trade structure is assumed and trade goes only in one direction. Each country only exports the good whose production has a productivity advantage, though a more realistic model of international trade would have intra-industry trade, with both countries producing and consuming both goods. The productivity coefficients in the transformation frontier are such that country 1 exports machinery and imports consumption good, c 1, whereas country 2 has the opposite pattern of specialization: y 1 < c 1 ; z 1 > m 1 z 2 < m 2 ; y 2 > c 2 where c i denoted the demand of the consumption goods. Free trade leads to a convergence in relative prices. In country 1 the relative price of machinery increase, whereas in country 2 the relative price of consumption good would increase, with a terms of trade gain for both countries. Such gain will eventually increase consumption possibilities and therefore have a positive welfare effect. When trade is distorted by some imports tariffs or export subsidies, prices are no longer equalized. In this model trade is assumed to be distorted by some trade policies that drive a wedge between domestic prices and the international price. In particular each country is imposing a tariff on the imported good, country 2 on machinery, t z, and country 1 on consumption good, t y : q 1 p 1 = q W p W (1 + τ y ) (6) p 2 q 2 = p W q W (1 + τ z ) (7) In this simple model trade flows are assumed to balance and therefore the value of imports at the international prices must equalize the value of exports in each country: q W (z 1 m 1 ) = p W (c 1 y 1 ) (8) q W (m 2 z 2 ) = p W (y 2 c 2 ) (9) To close the model, all markets must clear and world demand needs to equalize world supply. World production of final good must all be consumed (equation 10). World production of machinery, z 1 + z 2, must equal the demand of machinery from the intermediate sector, m 1 + m 2, and from the energy sector, e 1 + e 2 (equation 11). It is in fact assumed that, in order to produce energy, some machinery are required as input: 9

10 y 1 + y 2 = c 1 + c 2 (10) m 1 + e 1 + m 2 + e 2 = z 1 + z 2 (11) Wage can also be determined although it does not play any role in determining the equilibrium because labor is used only in the intermediate sector and it is fix supplied: L i = w i F l (l i, e i, m i ) (12) The model has 13 variables to be determined, (y,z,m,c,e, q p ) x 2 = 12 plus the relative world price, q W pw, and 13 equations, ( ) x 2 = 8 + (6), (7), (8), (10), (11). So far the model does not include international technology spillovers and it is a standard general equilibrium model with international trade. International technology spillovers are considered to be an important element in the picture because they can modify the traditional effects of trade liberalization. Spillovers affect the technology of production and therefore can affect the technique, composition and scale effects trade liberalization brings about. Next section describes how technology spillovers have been introduced in the model. 5.2 Introducing international technology spillovers International technolgy spillovers are modelled according to the empirical evidence found in De Cian (2008). That paper has estimated the effect of international technology spillovers embodied in machinery on the productivity of different inputs. Imports in machinery and equipments were assumed to affect the productivity according to the following functional form: A j = e δ0 j t M&E(t) δ j for j = E, L, K This equation identifies the innovation possibility frontier that describes how the productivity of inputs used in this model to produce intermediate inputs evolves with a change in machinery and equipment imports, M&E. The parameters of the innovation possibility frontier for each input were estimated from an input demand system. The results obtained lead to the following innovation possibility frontier: A E = e 0.002t M&E(t) 0.09 A L = e 0.014t A K = e 0.005t M&E It can be seen how machinery and equipments have a higher impact on energy productivity. Also, from a statistically point of view, the effect of machinery and equipments on labor and capital was never statistically significant. In order to stick as much as possible to the empirical evidence, the model will include the effect of spillovers only on energy and capital productivity. The elasticity of technology with respect to imports, δ i, is positive but less than one. Therefore productivity is increasing with machinery imports, but at a decreasing rate. Despite these common tendencies, the magnitude of the effect of imports on input technical change is input specific. Energy is the most responsive input to imports in machinery, whereas the effect on labor is nearly null. The estimation of the input demand system allowed to estimate also the elasticity of substitution, whose estimated values ranges between 0.38 and

11 In the model described in this section, international technology spillovers are assumed to affect the technology parameters in the production of the intermediate good. The three parameters that describe input technology of intermediate production are now no longer constant but instead they are variables related to imports, which are endogenously determined by the model. Therefore, input productivity also becomes endogenous. Although the estimation results for technical change also include a time dimension, the model described here is static. The innovation possibility frontier can be adjusted to a static framework by specifying only the part related to the variable M&E that in this model is represented by machinery imports, M&E = m i z i : A j = (m i z i ) δ j j = E,M A variation of imports following the implementation of trade policies would also affect technology parameters. Recall that the model develops in this section is characterized by unilateral trade and only country 2 imports machinery. Consistently with the definition of technical change used in this section, only country 2 benefits from spillovers related to machinery imports. Therefore the production function for country 1 is left unchanged whereas country 2 is now characterized by a production structure that includes machinery produced in country 1: x 2 = H 2 [((m 2 z 2 ) δ E m 2 ) γ 1 γ 5.3 Calibration of the model + ((m 2 z 2 ) δ E e 2 ) γ 1 γ + (A L l 2 ) γ 1 γ ] γ γ 1 The model has been calibrated on fictitious data chosen so as to reflect the productivity advantage of country 1 in machinery. A Social Accounting Matrix (SAM) describes the flow of values for each country in the benchmark year. The SAM for both countries is described in table 2 and 3. Since in the benchmark all prices are assumed equal to 1 the entries in the table can be interpreted as quantities. Each cell in the table can be identified by a column and a row sector. A positive number represents the output of the column sector. A negative number is to be read as an expense of the column sector to buy the good of the row sector. It corresponds to an outflow of money from the column sector to the row sector. For example, the final sector Go produces 20 of yo and 40 of zo in country 1, using as input 60 units of xo. Labor is an endowment of the consumer who receives its marginal value as compensation that can be used to buy 30 units of final good, yo. Finally, trade can be considered as a production activity that allows to increase the production of some goods through imports. In order to buy these additional units of good a country needs also to sell something to this country, in order to earn some local currency to pay for the imports. Therefore each country exports the excess of the goods not consumed to the other country. Country 1 has an excess supply of zo, which is sold to country 2 to cover its excess demand. These data are used to calibrate the technology parameters in the production function frontier, A i and B i, and the coefficient describing neutral technical change in the intermediate sector, H i. The elasticity of transformation between the two possible outputs is the only parameter to be assumed. The remaining parameters are estimated. Table 4 summarizes the values used for each parameter, describing also the methodology with which these values were obtained. 5.4 Analyzing trade liberalization T able 2 T able 3 T able 4 This section describes how the presence of technology spillovers affect the analysis of trade liberalization. By analysing the effect of on energy demand, impliticitely something can be said 11

12 on the the effects of trade on the environment. In fact, energy use is related to the emissions of greenhouse gases, one important cause of climate change. To this end, the approach introduced by Grossman and Krueger (1993) is used. They decomposed the effect of trade liberalization on the environment into scale, technique and composition effects. The scale effect is the expansion of the economic activity following trade liberalization, without changing the mix of produced goods. This effect harms the environment because most economic activities require the use of energy. However, trade liberalization, by affecting relative prices can also affect output composition and the share of various industry over total output can change. Finally, trade may change the mix of inputs and the technology used for production. If the technology of production is not allowed to change, the only effect that can reduce energy demand for a given level of output is price induced substitution. If instead international trade can directly affect the production function, a technique effect can go in the direction of saving the energy per unit of output required. This is the new component with respect to the analysis carried out by Copeland and Taylor. The question is how this feature changes the analysis of trade liberalization and the environment. In the baseline scenario, both countries restrict their import with a tariff. Countries 2 imports machinery whereas country 1 imports consumption good. In the policy scenario the machinery importing country removes completely its tariffs. These two scenarios are compared with and without international technology spillovers. First, the effects without spillovers are described, with particular attention to the importing country. Then, spillovers are activated and their effects on the previous results is assessed. The first effect of trade liberalization is to reduce machinery price in country 2 and therefore to push machinery demand in this country and, at the same time, on the world market. This leads to an increase in the world price of machinery that causes a negative terms of trade effect in the liberalizing country. This negative effect explain why welfare, as it can be represented by consumption, remains basically unaffected in country 2 but increases significantly in country 1, where the terms of trade effect goes in the opposite direction. The scale effect is positive in country 2, where an expansion of trade leads also to an expansion of total production. The composition effect increases the output of consumption good and decreases the output of machineries, as they can be imported at a cheaper price. The technique effect in the absence of technology spillovers is totally driven by substitution toward the cheaper inputs. By construction, production shifts proportionally toward energy and machinery because the two prices have been assume to be equal. The effect on the labor market is totally absorbed by an increase in wage because labor is fix supplied. The variable that in this model can approximate the effect on the environment is the use of energy in the production process. In more sophisticated models carbon emissions are typically associated with energy use. If there are no international technology spillovers 5, both the scale and the technique effects are detrimental for the environment. In fact, the reduction in energy price drives up its demand. It should be also pointed out that the composition effect in this model does not play any role in terms of environmental damage because energy is used in the same proportions to produce both types of output. The left hand side panel in figure 1 summarizes the percentage change of the main variables in country 2. To be noted the reduction in machinery output and energy price. Consumption increases, but by little. When international technology spillovers are switched on, trade liberalization has an effect on technology that affects the magnitude of the technique effect. The first order effect of spillovers is to push up the productivity of capital and energy. Energy benefits relatively more from technology transferred. Therefore, as before intermediate production shifts toward energy and machinery, but now the increase in no longer proportional. Whereas in the case with no spillovers the change in the energy demand relative to machinery was one, when there are spillovers the 5 The other assumption is that there is no environmental policy in place aimed at reducing carbon emissions. The focus here is simply of the effects of trade liberalization. What happens in the presence of climate policy will be analyzed in the next section, using a fully-fledged model. 12

13 increase in energy is 47% lower than the increase in machinery demand. Therefore the energy demand, relative to machinery demand decreases. This result can be seen by comparing the two panel in figure 1. On the left hand side panel, machinery and energy demand increase by 11%. With spillovers energy demand goes up only by 0.09% and machinery demand by 13%. Since energy is elastically supplied, an increase in its productivity is to some extent similar to an increase in supply, which therefore drives down the energy price even further. Being energy price equal to machinery price, trade liberalization also reduces energy price. The increase in energy productivity generates a further reduction. Energy price goes down by 22% whereas in the previuos case with no spillovers it was going down by 20%. In this simple model, when spillovers are switched off trade liberalization cannot affect the technology of production, which remain unchanged before and after the removal of the tariff. Instead, when imports are allowed to affect the technology parameters of the intermediate sector, trade liberalization has a further technique effect. The production technology becomes more efficient and it requires less of each input to produce the same quantity of output. Since technical change affects each input differently, there is also a reallocation in the input mix. Energy demand still increases, driven by the scale effect, but by less when there are spillovers. In the presence of spillovers the technique effect reallocates production away from energy, which is the input whose efficiency improve the most, toward labor and machineries. Spillovers have also an effect on the scale of the economy, which now expands more. This effect partially explains the higher increase in consumption. A neat way to see the interactions between scale, technique and the substitution effect is by looking at input demand for energy, described by the following equation: e = }{{} x + γ(p p e ) (1 γ)a }{{}}{{} e scale effect substitution effect technical change effect If technology is not allowed to change, both the scale and the substitution effects increase energy demand because this input becomes cheaper: e = }{{} x + γ(p p e ) }{{} scale effect substitution effect }{{}}{{} >0 >0 If instead spillovers are included, there is a further term that goes in the opposite direction when the elasticity of substitution is less than one. The net final effect on energy demand depends on the relative size of substitution, induced by the price effect, and the technology effect. Since the elasticity of substitution is relatively small, the technology effect prevails. The technique effect, which is explicitly accounted for only in the spillover scenario, partially offsets the scale effect. The scale effect generates an output expansion in the liberalizing country. To face higher production, more inputs are to be used. If the production technology does not change both energy and machinery are increased by the same amount. If instead the changes in technologies are accounted for, the inputs composition shift toward machinery and away from energy. In this very simple model, energy demand is taken as a very rough approximation of environmental damage. In this context, it seems that international technology spillovers have a double benefit. On the one hand, they increase consumption. On the other hand, they change the input mix so that less energy is demanded to produce a higher level of final output. In fact, the increase in the scale of the economy is higher, but the relative demand of energy decreases. The positive effect on consumption is driven by a stronger term of trade effect and a higher scale effect. F igure 1 (13) 13

14 5.5 Sensitivity analysis The aim of sensitivity analysis is to assess the stability of the results to different parameter values. A critical parameter for the final effect on energy demand is the elasticity of substitution among labor, machinery and energy in the intermediate sector. The value of the elasticity of substitution is sensitive to the assumption made on neutral technical change. Here neutral technical change, which is represented by the parameter H in the intermediate production function, is assumed not to change. Under this assumption, the estimated elasticity of substitution is higher, because part of the price effect that would be captured by neutral technical change here is absorbed by the elasticity of substitution. The value of the elasticity of transformation was assumed equal to an arbitrary value and therefore it is necessary to evaluate the robustness of spillovers effect to different possibility of substitution in the output mix. Sensitivity analysis is to be performed with respect to the elasticity of substitution and transformation. The cases to be analyzed are summarized in the table 4. A higher value of transformation is experimented, with the initial level of substitution. The two other values for the elasticity of substitution have been obtained by adding and subtracting the standard error from the estimated mean values. T able 5 First, the effect of trade liberalization is analyzed under a different value for the elasticity of transformation between machinery and the consumption good. A higher elasticity, ρ = 2 is experimented. The percentage changes of the relevant variables are reported in figure 2. When the elasticity of transformation increases, it means that the economy can reallocate its production more easily. Table 5 reports the output levels in the benchmark for both countries. Output levels are higher when the economies are more flexible, that is to say when the transformation possibilities between two output are higher. Moreover, in this case there is more specialization. Since the ability to substitute one output with the other is higher, countries can specialize more in the good where they have a comparative advantage because the ability to adjust to price changes is higher. Trade flows are also higher when σ = 2. T able 6 Output reallocation between machinery and consumption good production is determined by the change in relative prices that occurs when trade is liberalized. As described before, one of the first effect of a reduction in import tariff is to increase world demand the imported good. In the liberalizing country the tariff reduction decreases domestic machinery output and therefore the relative domestic price of the consumption good increases. This occurs because the importing country (country 2) has a comparative advantage in the other good. When the elasticity of transformation is higher, the flow of trade is higher and therefore the terms of trade effect will be stronger. In this scenario the terms of trade effect is more negative for the importing country, country 2, and more positive for country 1. The composition effect does not have implications on the use of energy because the two final goods have the same input structure. Energy demand is affected only by the reduction in energy price, which is lower when ρ = 2. The expansion of consumption good output and the fall in its demand reduce domestic price of consumption good and thus increases the machinery domestic price. This effect partly compensates the reduction brought about by the tariff reduction. The composition effect has also an effect on the terms of trade. In country 2, the consumption good is the exporting sector and therefore the increase in world relative supply of consumption good will reduce its relative price, p W qw. Such change in terms of trade penalizes country 2 and advantages country 1, which is exporting machinery at the world price q W pw. Table 6 compares the percentage change of some variables in the presence of spillovers under the two scenarios, for country 2. The top part of table 6 reports the changes following trade liberalization when 14