Public Infrastructure and Economic Growth A Dynamic General Equilibrium Analysis with Heterogeneous Agents #

Public Infrastructure and Economic Growth A Dynamic General Equilibrium Analysis with Heterogeneous Agents # Yazid Dissou * Selma Didic January Very Preliminary and Incomplete Comments are Welcome Department of Economics University of Ottawa # This study is part of the Research Project on the Distributive Impacts of Growth Strategies funded by the Australian Agency for International Development (AusAID). We would like to thank Benoit Carmichael, John Cockburn, Bernard Decaluwe, Jean-Yves Duclos, and seminar participants at Laval University for their very useful and constructive comments and remarks. Usual caveats apply. * Corresponding author: ydissou@uottawa.ca.

Title: Public Infrastructure and Economic Growth A Dynamic General Equilibrium Analysis with Heterogeneous Agents Abstract The relationship between public investment and growth is now a ubiquitous topic in the economic literature in a context where the low level of investment in public infrastructure is considered as partly responsible for poor growth performance in developing countries. This paper develops a multisector, dynamic general equilibrium model with public capital and heterogeneous (forward-looking and myopic) consumers and firms to assess the growth and sectoral implications of increased government spending on infrastructure in a developing country. It uses a stock approach to model public capital in firm s technology and considers two financing methods of increased public investment: domestic financing through distortionary taxes and foreign financing through increased aid. It finds that in the presence of heterogeneous agents, the financing methods of increased public investment have dierent impacts on the investment response of the private sector in the short run. While increasing public investment has positive impacts on private investment of all agents in the long-run irrespective of the financing method, the investment level of myopic agents is adversely aected in the short run by the tax-financing method. The paper also finds that the typical crowding-out eects of private investment by public investment often emphasized in the literature are highly sensitive to the financing method and to the time horizon. Moreover, the simulation results suggest that access to the credit market is important for reaping the full benefits of increased capital stock. Forward-looking agents benefit more from the increase in public infrastructure than myopic agents do. Finally, the study finds that even though the increase in public investment leads to a Dutch disease in the short run, the increased production capacity of firms can reduce the severity of that phenomenon in the long run.

. Introduction This paper assesses the growth, sectoral and welfare implications of increased spending on infrastructure using a multisector intertemporal general equilibrium with public capital and heterogeneous agents. The last two decades have witnessed a revival of interest in growth theory and in a better understanding of the linkages between economic policy and economic growth. The relationship between investment in public infrastructure and growth has become a pervasive theme in the theoretical and empirical literatures on economic growth in both developed and developing countries alike. Much of the recent debate on the means to reduce persistent poverty in developing countries and to spur growth in all countries has revolved around the idea of significantly boosting investment in public infrastructure. The rationale behind that idea is the belief that infrastructure services have a strong impact on growth via their positive eects on the productivity of private firms. The seminal works of Aschauer (989) and Barro (99) have paved the way to a substantial volume of studies that aim to provide a better grasp of the contribution of public infrastructure to economic growth. The theoretical literature has mostly focused on modeling public infrastructure as an input in firm technology so as to account for its externality in production. In doing so this literature mainly adopts two approaches, whereby public investment is introduced as either a flow or a stock variable in endogenous growth models and neoclassical Ramsey growth models. While both approaches generate identical qualitative insights, there seems to be an agreement over the idea that the stock approach is more realistic, while the flow approach is more tractable. Several studies in the empirical literature on infrastructure and growth have employed a variety of econometric techniques to find support for a positive impact of public infrastructure on growth. Aschauer (989), Calderon and Serven (4), and Sahoo and Dash (9) are few examples among several others. Some of these studies have been heavily criticized for obtaining overly high output elasticities of public investment because of methodological weaknesses. Several authors like Gramlich (994) and Estache and Fay, (9), among others, have cast doubt on the reliability of those estimates on the ground of methodological weaknesses, such as the non-stationarity of variables, reverse causation, and the level of data aggregation. Yet, a good understanding of the multiple linkages through which investment in public infrastructure exerts an impact on economic growth is required. In that respect, econometric regressions do not provide an adequate framework for tracing the transmission mechanisms that we See Rivas (3), Yakita (4), and Ohdoi (7) for examples of studies that use the flow approach to model infrastructure in growth models. On the other hand, see Fischer and Turnovsky (998), Turnovsky (4), Tamai (7), Kalaitzidakis & Kalyvitis (4), and Tsoukis and Miller (3) as examples of studies that model infrastructure as a stock variable. Aaron (99) is an some example of studies pointing out that this literature most likely mis-specifies the dynamic eect exercised by infrastructure, arguing that much of the public capital stock does not have the implied short-term impact on the supply of aggregate output. 3

need to understand. In particular, they do not allow for an analysis of important general equilibrium feedback eects of spending on public infrastructures as well as their fiscal implications. The latter aspect is all the more important since any increase in public investment needs to be financed somehow by either increasing taxes or foreign aid. The increase in taxation may discourage private investment, and thereby aect economic growth negatively. The overall eects of increasing public investment in infrastructure depend thus on the trade-o between the positive productivity eect of public investment and the distortionary eects of taxes. It follows that the failure of the econometric studies to capture the disincentive eects linked to financing of public investment, which might retard growth, makes them less attractive. The abovementioned deficiency has led some authors to develop computable general equilibrium (CGE) models to assess the relationship between infrastructure and growth with extension to poverty reduction in developing countries. CGE models provide an excellent framework for incorporating the linkages that both economic theory and empirical analysis consider important. Several CGE studies, such as those of Lofgren and Robinson (4), Adam and Bevan (6), Perrault et al. (), have been developed to tackle the issue of modeling the eects of higher public investment in infrastructure on either growth or poverty reduction using dierent financing mechanisms. Nevertheless, these CGE studies are of a recursive-dynamic nature in the sense that they are simply stacked static models that are linked by a simple adjustment of the stocks of primary factors from one period to another. Identical to the approach of static models, saving and investment decisions are determined in an ad hoc manner where households and firms are assumed to behave myopically. Yet, saving and investment decisions, which are crucial to the growth process, are purely intertemporal decisions that take into consideration expectations on variables in the future. Thus, pure sequential CGE models provide an unsatisfactory policy tool for assessing the impacts of government policies, such as infrastructure development on factor accumulation that, in turn, has important implications for factor remunerations and hence for household welfare. Intertemporal CGE models, in which firms and households are no longer myopic, are better suited to adequately capture the adjustment, the transmission mechanisms, and the growth and distributive implications of the proposed policy change. These models solve the deficiencies of recursive-dynamic CGE models as they make it possible to model these crucial saving and investment behaviors in a consistent manner. This paper develops a multisector, intertemporal general equilibrium model with public capital and heterogeneous agents to assess the growth and sectoral implications of increased government spending on infrastructure in a developing country. We use a stock approach to model public capital in firm s technology. The introduction of heterogeneity among agents stems from the desire to take into account a peculiar characteristic of developing countries where a significant proportion of households and firms do not or cannot display forward-looking behavior as they lack access to the credit market. The model considers two categories of households and two categories of firms. It 4

distinguishes on the one hand, between forward-looking and myopic households, and on the other hand, between forward-looking and myopic firms. Previous papers such as Campbell and Mankiw (989), Carmichael and Samson (995), McKibbin and Vines () and Berg et al. () have also introduced heterogeneity among households in intertemporal models. Nevertheless, in contrast to those models, which assume that myopic households consume all their one-source income (wages), we assume that myopic households have an additional source of income to their wages, (capital income), as they are the owners of the myopic firms. They do not consume all of their disposable income; they only consume a constant fraction of it (less than one, as in a Solow growth model). It follows that in our model, myopic households do save; their savings are used to fund investment in physical capital made available to myopic firms. In contrast, the savings of forward-looking households are used to fund investment in forward looking firms that they own. Thus, the model establishes an isomorphism between the set of household categories and the set of firm categories as far as the return to capital is concerned. In contrast to forward-looking firms in which managers maximize the discounted sum of dividends, managers of myopic firms maximize their current profits. We are not aware of any dynamic model with public capital and heterogeneous agents, or any other intertemporal model with heterogeneous agents in which myopic households have savings. The model makes it possible to assess the impact of increased spending on public infrastructure on private formation of capital, while taking into consideration the peculiar features of developing countries. We consider two financing methods of increased public investment, namely (i) domestic financing through distortionary taxes and (ii) foreign financing through increased aid. We elect to use the model to study the growth implications of increased public capital in an African country, Benin, which is a small-open economy of West-Africa where international organizations have started to place a strategic emphasis on public infrastructure as an important means for achieving stronger economic growth and poverty reduction. A recent World Bank assessment of this country (World Bank, 9) clearly emphasizes the need to raise the level of public infrastructure that is partly responsible for the low levels of private investment and entrepreneurship. The paper is organized as follows. Section presents the models and Section 3 discusses the data, the calibration and numerical strategies. We discuss the simulation results in the fourth section and conclude in the last one.. The Model. Overview Consider an infinite-horizon small open economy that produces tradable and non-tradable goods and has access to the world capital market. The economy consists of households, firms, and the government. We introduce agent heterogeneity in the model by considering two types of households and two types of firms. The rationale for agent heterogeneity stems from the desire to incorporate a 5

ubiquitous characteristic of developing countries where some households and some firms are liquidity-constrained; they lack access to the oicial credit market to smooth their consumption or to finance investment. Households are distinguished by their ability to participate in the formal capital market. The first category is represented by forward-looking consumers who have access to the world credit market and who can smooth their consumption; they are labeled type f households. The second category of households is represented by liquidity-constrained consumers who do not have access to the credit market and are compelled to consume based on their current income only. It ensues that they hold myopic expectations; and are labeled type m households. However, in contrast to existing papers with liquidity-constrained households, we do not assume that the saving of myopic households is equal to zero. We rather assume that myopic households have Keynesian-type saving behavior, whereby they save a constant and strictly positive fraction of their disposable income. Akin to household disaggregation, we distinguish firms by their capacity to have access to the formal credit market. The first category of firms is represented by myopic firms that do not have access to the formal credit market; they are owned by myopic households whose savings are used to provide them private physical capital for production activity. The second category of firms is represented by forward-looking firms that are owned by households of type f. They have access to the formal capital market. Besides, we assume both types of households do not value leisure and have an inelastic labor supply that is mobile across industries. From this description, it is straightforward to assume that type m agents will have static behavior, while type f agents will have forward-looking behavior. The production sector is decomposed into twelve industries and the disaggregation is such that only one category of firms exists in each industry 3. Public capital generates an externality in production; we assume that it enhances the output of firms albeit at varying degrees. Rather than disaggregating infrastructure into various sectors, such as roads, telecommunications, electricity, and irrigation as in Perrault, et al. (), we assume that only one type of public capital exists; its productivity eects dier by industry. Public capital is an input in the production function. We model it as a pure public good because we assume that the services derived from public capital are not subject to congestion. In all industries, firms combine labor, private and public physical capital, and intermediate inputs to produce a composite output that can be sold in the domestic and world markets 4. Production exhibits constant returns to scale in all factors (private and public). It follows that the presence of public capital in the production function generates endogenous rents (pure profit) that are returned to the owners. Finally, it is important to note that all variables are expressed in per eiciency unit of labor. 3 See table for the list of industries. 4 The stock of public capital is not a decision variable for the firm. 6

.. Households Consider an economy with a continuum of households of unit mass indexed by h [, ]. Households of type f belong to the segment [, φ), while myopic households belong to the segment [φ, ]. The forward-looking households have access to the capital market where they can borrow and lend at the world fixed interest rate r* to smooth their consumption over time. The myopic households do not have access to world markets. Both types of households derive utility from the consumption of commodities; they do not value leisure. Total labor supply is inelastic with a proportion φ coming from households of type f and the remaining (- φ) coming from households of type m. Their other sources of income consist of capital income, transfers from the government and net foreign transfers from the rest of the world. They pay taxes to the government on factor incomes. It is interesting to note that capital income includes the returns to both private capital and public capital. Recall that the return to public capital is the rent generated by the externality of public capital on firm s technology. The two types of households dier in the characteristics and the composition of the return to private capital. Households of type f receive dividends from firms of type f and returns from foreign assets they hold in their portfolio. The return to capital of myopic households consists of the return to capital made available to myopic firms. Within each period, both types of households have CES (constant elasticity of substitution) preferences over the consumption goods and they maximize utility subject to the constraint that total expenditures must equal the available resources for spending on consumption goods. As discussed earlier, in each period, myopic households spend a fixed fraction of their disposable income and the remainder goes for saving, which is used for investing in the capital stock made available to myopic firms. In contrast, total current spending of household of type f is not proportional to their current income. They can increase or decrease their saving to smooth their consumption over time. It follows that households of type f determine optimally the stream of their total spending on consumption. h Let us denote by HHHHHH tt (h = f, m) the total expenditures on consumption in period t by each type of household. The optimal consumption demand for each commodity by each household type is determined by solving the following problem: h MMMMMM CC tt = AAAA h h CCCC ii cc iiii h ρρ CC h ss. tt. PPPP iiii cc iiii h ii = HHHHHH tt h h =, mm where CC tt h is the index of consumption goods for each type of household, PPPP iiii is the consumption h price of commodity i, CCCC denotes the share parameter for each type of household, and ρρ CC h is defined by the elasticity of substitution, σσ cc h, as ρρ CC h = σσ cc h σσ cc h. ρρ h CC 7

The solution to the problem is: cc h iiii = AAAA h σσ cc h h CCtt αα h h σσcc h CCCC PPPPtt PPPP iiii (+ττ CC ii ) PPPP h tt = αα h σσ cc h AAAA h CCCC [PPPP iiii ( + ττ CC ii )] σσ cc h ii σσh cc h =, mm h =, mm PPPP tt h CC tt h = HHHHHH tt h h =, mm h with PPPP tt being the index price of consumption goods of each type of household, PPPP iiii, is the individual price of the consumption good, and ττ CC ii is the consumption tax rate. While this optimization problem is suicient for myopic households, forward-looking households need to solve an intertemporal problem to determine HHHHHH h tt. Hence, given the index price, PPPP tt, the forward-looking households determine the optimal time path of aggregate consumption CC tt by maximizing an intertemporal utility function subject to a sequence of budget constraints, while respecting the No-Ponzi-game constraint: MMMMMM UU = tt= +nn + ρρ tt lncc tt ss. tt. FF tt+ ( + nn) = rr FF tt + HHHHHHHH tt wwheeeeee HHHHHHHH tt = ( ττ yy )φww tt LLLL tt + KKKK tt jj ξξ + TTTTTT jjjj tt + EEEE tt TTTTTTTT tt ττkk jj DDDDDD jjjj tt PPPP tt CC tt tt where FF tt represents the forward-looking household s total financial wealth, HHHHHHHH tt, its saving, ττ yy the labor income tax rate for forward-looking consumers, WW tt is the wage rate, LLLL tt is total household labor supply, TTTTTT tt the government s exogenous transfers to forward-looking households, TTTTTTTT tt the exogenous net transfers of the rest of the world 5. EEEE tt is the nominal exchange rate (conversion factor between currencies), ττ kk tax on forward-looking firm s dividends, KKKK tt the stock of public capital, ξξ jjjj, the implicit return rate to public capital in forward-looking firm. The parameter n is the exogenous population growth rate, rr is the world interest rate, and ρ the rate of time preference. τ k is the tax rate on the dividend income, jj DDDDDD jjjj, received by forward-looking households. The first order conditions specified below in (.) and (.) are the traditional Euler equation and the budget constraint determining the optimal inter-temporal allocation of spending. The Euler 5 For the sake of simplicity, we assume that the total transfers from the rest of the world accrue to the forward-looking households. 8

equation (.) expresses the relationship between consumption levels in two consecutive periods, suggesting that the consumer of type f will equalize the marginal rate of substitution between aggregate consumption in two consecutive periods to the marginal rate of transformation. Given the imposed No-Ponzi-game constraint that implies that the present value of consumption expenditure must be equal to the present value of net income, the first order conditions of the problem are suicient for determining the optimal values of the path of aggregate consumption, CC tt. CC tt+ CC tt PPPP tt + ρρ PPPP tt+ + rr = (.) FF tt+ ( + nn) = rr FF tt + ττ yy φww tt LLLL tt + TTTTTT tt + EEEE tt TTTTTTTT tt + KKKK tt jj ξξ jjjj PPPP tt CC tt ττ kk jj DDDDDD jjjj tt.3 Firms Following the general idea that private inputs represented by private capital and labor are not a close substitute for public inputs, we make public capital, KG t as a separate argument of the private production function in order to take account of the external eect of infrastructure on production. As in Kalaitzidakis & Kalyvitis (4), Tamai (7), and Turnovsky (4) we introduce public infrastructure as a stock variable in the production function of firms. The superiority of the stock approach over the flow approach stems from the idea that the accumulated flows of investment in infrastructures are the ones that generate externality on firm technology. The representative firms in all industries share the same technology that can be represented by a series of nested production functions. Gross output, XXXXXX jjjj in industry j is a CES aggregate of the index of intermediate inputs, IIIIII jjjj, and of the index of value added and public capital, VVVVVV jjjj. The latter is a Cobb-Douglas production function of value added, VVVV jjjj and public capital, KKKK tt. Value added is specified as a CES composite of labor, LLLL jjjj and private capital KK jjjj. Finally the index of intermediate input, IIIIII jjjj, is a Leontief function of intermediate inputs, VV iiiiii. As discussed above, the stock of public capital, KKKK tt, is not a decision variable for the firms. The latter consider its level as given and determine residually the accrued rents that are returned to the households in each period. They pay production taxes on gross output at the rate ττ pp jj. While firms of type f have to decide on investment in private physical capital in the presence of capital installation costs, myopic firms have only to decide on the optimal level of their desired level of capital, given the total level of total capital stock made available to them by myopic households. Capital is mobile across industries with myopic firms and its rental rate adjusts to clear its market. In contrast, because of the presence of installation costs, capital is immobile in the short run among industries with forward-looking firms. (.) 9

In what follows, we discuss the optimization problem of the forward-looking firms followed by that of the myopic firms. The optimal decisions of the forward-looking firms involve both static and inter-temporal decisions..3. The optimization problem of forward-looking firms In each industry, the representative firm chooses the optimal levels of variable inputs and of investment in physical capital so as to maximize it values, VVVV jjjj, which is the discounted sum of net cash flows, subject to a capital accumulation constraint in the presence of adjustment costs. These cash-flows (dividends) include expenditures on capital goods, i.e. we implicitly assume that the representative firm can finance its investment expenditures through retained earnings. At the beginning of each period, the capital stock is predetermined by the previous period s investment decision. Its reallocation among sectors is achieved only in the long run through accumulation. Following Hayashi (98), Lucas (967) and Treadway (969), we consider a quadratic adjustment cost function, which is linear homogeneous in both of its arguments, i.e., investment and capital stock. The firm s intertemporal problem is as follows: MMMMMM VVVV jj = +nn tt + rr tt DDDDDD jjjj s.t. KK jjjj + ( + nn) = IIIIII jjjj + δδ jj KK jjjj, with KK jj gggggggggg DDDDDD jjjj = ττ jj pp PPPPPPPP jjjj XXXXXX jjjj WW tt LLLL jjjj PPPP tt IIIIII jjjj + AAAA jjjj PPPPPPPP jjjj IIIIII jjjj ξξ jjjj KKKK tt and AAAA jjjj = ββ KKKKKK IIIIII jjjj KK jjjj Where XXXXXX jjjj, PPPPPPPP jjjj and ττ jj pp represent, respectively, the volume, the price and the production tax on the composite output. LLLL jjjj, DDDDDD jjjj, IIIIII jjjj and KK jjjj are labor demand, dividends, investment by destination sector, and the stock of private capital respectively. IIIIII jjjj and PPPPPPPP jjjj stand for the volume of the aggregate intermediate inputs and its price respectively. PPPP tt is the purchase price of capital good, and δδ jj is the capital depreciation rate. AAAA jjjj represents the capital adjustment costs that are assumed to be quadratic in investment and linear homogenous in investment and capital stock, and ββ jj is the adjustment cost parameter. Note that the dividend expressions accounts for the payment to households of the implicit return to public capital. Through this optimization problem, the firm determines the optimum paths for investment, labor, and other intermediate inputs. Given the nested structure of the technology and its constantreturns-to-scale property, a sequential approach can be used to find the optimal levels of factor uses. Apart from the investment decision, no other decisions have an intertemporal dimension. They are

purely intra-temporal or static decisions. Firms use these input factors up to the point where their marginal products equal their prices. The latter is either the price of the input as available in the market or the dual price when the input is an index. It is worth mentioning that with regard to the stock of public capital, the firm still equalizes its marginal product to its price. In contrast to private inputs for which the firm considers their prices as given and determines their optimal quantities, the firm considers the level of public capital as fixed and determines endogenously its price, i.e. its rate of return. Hence, the rate of return to public capital needs not be equal in all industries. The first-order conditions are as specified in Equations.3-.6. PPPPPPPP jjjj ττ jjjj pp = AAAA jj (αα PPPP ) σσ XXXX PPPPPPPP jjjj σσ XXXX + ( αα PPPP ) σσ XXXX PPPPPPPP jjjj σσ XXXX σσ XXXX (.3) (σσ VVVVVV jjjj = AAAA XXXX ) jj XXXXXX jjjj αα pp σσ XXXX PPPP PPPPPPPP jjjj ττ jjjj PPPPPPPP jjjj (.4) (σσ IIIIII jjjj = AAAA XXXX ) jj XXXXXX jjjj ( αα pp σσ XXXX PPPP )PPPPPPPP jjjj ττ jjjj PPPPPPPP jjjj (.5) PPPPPPPP jjjj = AAAA jj (αα GGGG ) σσ GGGG ξξ jjjj σσ GGGG + αα GGGG σσ GGGG PPPPPP jjjj σσ GGGG σσ GGGG (.6) (σσ VVVV jjjj = AAAA GGGG ) jj VVVVVV jjjj ( αα σσ GGGG )PPPPPPPP GGGG jjjj PPPPPP jjjj (.7) (σσ KKKK tt = AAAA GGGG ) jj VVVVVV jjjj αα σσ GGGG PPPPPPPP GGGG jjjj ξξ jjjj (.8) ρρ WW tt = PPPPPP jjjj αα VVVV AAAA VVVVVV VVVV jj jjjj σσ VVVVVV LLLL jjjj (.9) PPPPPPPP jjjj = ii PPPP iiii aa iiii (.) VV iiiiii = aa iiii IIIIII jjjj (.) Equations.3,.4,.5 represent, respectively, the expressions for the dual price of gross output, the conditional demands for the index value-added-public-capital, VVVVVV jjjj and for the index of intermediate input, IIIIII jjjj. Equations.6 -.8, are the expressions required for computing the dual price of the index of VVVVVV jjjj, the demand for value added, and the implicit return to public capital. Equation (.9) represents the demand for labor. Equation. is the dual price of the index of intermediate inputs and Equation. represents the demand for individual intermediate input. At the intertemporal level, the firm determines the optimal level of investment to equalize its marginal cost to the shadow price of capital. This gives the expression of investment demand by sector of destination (.). The shadow price of capital is the marginal benefit (evaluated in terms of the change in the value of the firm) of a change in the capital stock by one unit. The firm s

marginal cost of investment includes the purchase price of the capital good, as well as the additional capital installation costs. We assume that the capital or the investment good is homogenous, in the sense that it is identical for all users who pay the same price (PPPP tt ) to acquire it. The marginal benefit of the investment takes into account the marginal impact of investment on current and future periods profits. Its expression can be recovered by integrating the dierence equation (.3) which represents the motion equation of the shadow price of capital. It is straightforward to show that, by imposing the appropriate transversality condition, the shadow price of capital is equal to the present value of the marginal product of private capital plus the benefits accrued from the reduction in the adjustment costs brought about by the higher level of the capital stock 6. qq jjjj = ββ KKKKKK qq jjjj + IIIIII jjjj KK jjjj + PPPP tt (.) δδ jj = qq jjjj ( + rr ) PPPPPP jjjj + RRRR jjjj + KK jjjj + ( + nn) = KK jjjj δδ jj + IIIIII jjjj VVVV jjjj = AAAA jj αα VVVV KK jjjj σσ VVVVVV + αα VVVV LLLL jjjj PPPP tt+ ββ KKKKKK σσ VVVVVV σσ VVVVVV σσ VVVVVV IIIIII jjjj + KK jjjj + (.3) (.4) (.5) RRRR jjjj = VVVV VVVV jjjj = qq jjjj KK jjjj + AAAA ρρ VVVVVV jj VVVV jjjj KK jjjj σσ VVVVVV (.6) (.7) In each industry with forward-looking firms, equations (.)-(.6) represent, respectively, investment demand (by destination) of the firm, the motion equation of the shadow price of capital, the motion equation of the stock of capital, the expression of value added, the definition of the physical marginal productivity of capital, RRRR jjjj. Finally, because of the constant return-to-scale property of the technology, the value of the firm is simply the product of the shadow price of capital (Equation.7) 7..3. The optimization problem of the myopic firms As mentioned earlier, the optimization problem of the myopic firms is static. Their optimal decisions are similar to the intra-temporal decisions of the forward-looking firms for all inputs, 6 These cost savings come from the fact that the adjustment cost function is decreasing in the level of private capital stock. 7 Assuming the linear homogeneity of the production function the dividend may also be written as : DDDDDD jjjj = PPPPPP jjjj RRRR jjjj PPPP tt IIIIII jjjj + AAAA jjjj

except the level of capital stock. For the sake of space, we will not repeat those optimal decisions. It will suice to mention that myopic firms will demand for capital up to the point where its marginal product is equal to its rental rate. In total, from the above-discussed behavioral equations of both firms, we can see how public capital aects their optimal decisions regarding the use of private inputs. Fundamentally, everything equal, an increase in the stock of public capital increases the marginal products of all private inputs. In particular, it increases the incentives of forward-looking firms to invest in physical capital through the increase in the shadow price of capital. The latter is the discounted sum of current and future marginal products of private physical capital. It follows that increased investment in public capital will have some growth impacts that will only occur in the transitional period because of the presence of diminishing marginal returns to capital in the technology..4 Government The government collects indirect taxes levied on production activities, on domestic and international transactions, and on direct taxes from the remuneration of primary factors. The latter consists of proportional taxes on labor incomes of both types of households and of a proportional tax on the capital income (dividends) of forward-looking households. The government derives other incomes from transfers from the rest of the world that are fixed. Its outlays consist of spending on commodities, GG iiii, on infrastructure, IIIIIIII tt, and on transfers to both types of households, TTTTTTTT tt and TTTTTTTT mm tt. We assume that GG iiii is exogenous, i.e., the government real spending on commodities grows at the same rate as the population growth rate augmented by the rate of technological progress. We further assume that the ratio of the value of spending on infrastructure to current GDP is exogenous. The latter ratio is a policy variable that is used to increase the level of public infrastructure in the economy. Transfers to households in per-eiciency unit of labor are constant; they grow at the same rate as their spending on commodities, GG iiii. The government is not allowed to increase its indebtedness; its balance, i.e., the dierence between its revenue and its outlays, GGGGGGGG tt, is kept constant in each period. The adjustment variable to respect this constraint is either, a uniform proportional increase in the sectoral tax rates on production or, an increase in foreign transfers to the government through increased foreign aid. pp YYYY tt = jj ττ jjjj PPPPPPPP jjjj XXXXXX jjjj + iiττ CC ii PPPP iiii cc iiii + ττ IIIIII ii PPPPPPPPPP iiii DDDDDDDD iiii + ττ MM ii PPPPPP iiii MM iiii + ττ EEEE ii PPPPPP iiii EEEE iiii ] + ττ yy YYLL tt + ττ mm yy YYLL mm tt + ττ kk jj DDDDDD jjjj (.8) GGGGGGGG tt = YYYY tt + TTTTTTTTTT tt ii PPPP iiii GGGG iiii PPPP tt IIIIIIII tt TTTTTTTT TTTTTTTT mm (.9) PPPP tt IIIIIIII tt = γγ GGGG GGGGGGGG tt (.) GGGGGGGG tt = ii PPPP iiii cc h iiii + PPPPPPPPPP iiii DDDDDDDD iiii + PPPP iiii DDDDDDDD iiii + PPPP iiii GGGG iiii + PPPPPPPP iiii EEEE iiii PPPPPP iiii MM iiii (.) 3

Government investment in public infrastructure adds to the residual existing stock to increase its level in the next period. The motion equation of public capital is as follows: KKKK tt+ ( + nn) = IIIIIIII tt + δδ gg KKKK tt (.) Where KKKK tt+ is the raw stock of public infrastructure, and δδ gg its depreciation rate. Note the stock of capital presented in Equation (.) is not identical to the one in the production function, which is the eective capital stock. Following Rioja (), we assume that the government provides to firms an eective stock of public infrastructure, KKKK tt that is linearly related to the raw stock of public infrastructure KKKK tt, by an eectiveness parameter, θ: KKKK tt = θθkkkk tt where θ (, ] (.3).5 Investment demand by sector of origin As alluded to before, the saving, SSSSSS tt mm, of myopic households serves to buy the investment mm mm good, IIIIII tt that increases the stock of capital KK tt available to myopic firms. Equations (.4)- (.6) represent the expressions for investment demand by myopic households and the motion law of the capital stock available for the myopic firms. IIIIII tt mm = SSSSSS tt mm PPPP tt (.4) SSSSSS tt mm = ss mm YYYY tt mm (.5) KK mm tt+ ( + nn) = IIIIII mm tt + ( δδ mm mm )KK tt (.6) where ss mm, YYYY mm tt, and δδ mm are, respectively, the saving rate, the disposable income of the myopic household, and the depreciation rate of the capital of myopic firms. From the description of the model, we can see that we have three types of investors: myopic households, forward-looking firms, and the government. As mentioned before, we assume that the investment good is homogeneous across users and is sold at a unique price PPPP tt. Still, we assume that total investment, TTTT tt, used to increase the capital stock by various agents is a Leontief composite of investment demand by sector of origin, DDDDDDDD iiii that appears in the expression of GDP at market prices. Equation (.7) gives the expression for total investment by sector of destination. Given the specified functional form, the price of the capital good and the demand for investment by sector of origin have the following expressions: TTTT tt = ii JJ iiii + IIIIII mm tt + IIIIIIII tt (.7) PPPP tt TTTT tt = ii PPPP iiii ( + ττ iiiiii ii )DDDDDDDD iiii (.8) 4

DDDDDDDD iiii = ββ KKKK TTTT tt (.9) where ββ KKKK is a Leontief parameter..6 Other demand component Total demand for each commodity, XXXX iiii, consists of the demand for consumption by households and government, for intermediate inputs by firms and for investment by firms, households and government. Equation (.3) shows the expression for the demand of total commodity. XXXX iiii = cc mm iiii + cc iiii + GGGG iiii + DDDDDDDD iiii + DDDDDDDD iiii + jj VV iiiiii (.3).7 Foreign trade We model trade with the rest of the world using the traditional assumption of commodity dierentiation, both on the demand and on the supply sides. On the supply side, gross output in each industry is a CET (Constant Elasticity of Transformation) composite of domestic sales and aggregate exports. A revenue-maximizing rule allows the determination of the optimal composition of supply in each market. PPPPPPPP jjjj = AAAA ii δδ XXXX σσ XXXX PPPPPP jjjj + σσ XXXX + δδ XXXX σσxxxx PPPP jjjj + σσ XXXX + σσ XXXX (.3) EEEE jjjj = + σσ XXXX XXXXXXjjjj AAAA ii XXXXXX jjjj = + σσ XXXX AAAA jj XXXXXX jjjj PPPPPP jjjj δδ XXXX PPPPPPPP jjjj PPPP jjjj ( δδ XXXX )PPPPPPPP jjjj σσ XXXX (.3) σσ XXXX (.33) Equation (.3) is the dual price of this maximization problem; it is the composite of the export price, PPPPPP jjjj, and the domestic good price, PPPP jjjj. Equations (.3) and (.33) are the supply functions of, respectively, exports, EEEE jjjj and domestic sales, XXXXXX jjjj. On the demand side, total domestic demand for each commodity, XXXX jjjj, is a CES composite of the locally produced good, XXXXXX jjjj, and imports, MM jjjj. An expenditure minimization rule allows the determination of the optimal composition of the composites. PPPP jjjj = AAAA jj δδ MMMM σσ MMMM PPPP jjjj σσ MMMM + δδ MMMM σσmmmm PPPP jjjj σσ MMMM σσ MMMM (.34) MM jjjj = AAAA jj σσ MMMM XXXXjjjj δδ σσ MMMM PPPP MMMM jjjj (.35) PPPP jjjj 5

XXXXXX jjjj = AAAA jj σσ MMMM XXXXjjjj δδ σσ MMMM PPPP MMMM jjjj (.36) PPPP jjjj The dual price of the minimization problem, which is the composite of the import price, PPPP jjjj and the domestic good price, PPPP jjjj is displayed in Equation (.34). Equations (.35) and (.36) are the demand functions of, respectively, imports and the domestic good. In each period, the current account deficit, FFFFFFFF tt, reduces to the stock of foreign assets holdings by households of type f, or equivalently adds to the stock of foreign debt of the country, BBBB tt. The current account deficit is the sum of the trade deficit, net government and household transfers abroad. FFFFFFFF tt = PPPPPP jjjj MM jjjj PPPPPPPP jjjj EEEE jjjj TTTTTTTT + TTTTTTTT mm jj jj tt TTTTTTTTTT tt (.37) BBBB tt+ ( + nn) = ( + rr )BBBB tt + EEEE tt FFFFFFFF tt (.38).8 Equilibrium conditions, dynamics and steady states conditions A dynamic general equilibrium of this economy consists of sequences of prices, quantities, and stock variables, such that all markets clear in each period and all agents respect their budget constraints while maximizing their respective objective functions. In particular, the wage adjusts to clear the labor market, and the price of domestic good is the adjusting variable that clears the goods market. By Walras law, total savings must be equal to financing needs. As discussed before, myopic households use their saving to fund investment in the capital of myopic firms. The dividends paid to forward-looking firms are net of investment expenditures. Foreign savings are already taken into account in the net stock of foreign assets that are part of the total financial wealth of forward looking households. It follows that the sum of the savings of the forward-looking households and of the government minus the value of inventory changes must be equal to zero as all investment needs have already been paid for. HHHHHHHH tt + GGGGGGGG tt ii PPPP iiii DDDDDDDD iiii = (.39a) Defining the net financial wealth of forward-looking households, FF tt, as the dierence between the sum of the values of the firms and foreign debt, the household budget constraint can be transformed into an economy-wide budget constraint as follows: 6

FF tt+ ( + nn) = FF tt ( + rr ) + ττ yy φwwtt LLLL tt + TTTTTT tt + EEEE tt TTTTTTTT tt + KKKK tt jj ξξ jjjj ττ kk DDDDDD jjjj jj (.39b) PPPP tt CC tt ii PPPP iiii DDDDDDDD iiii + GGGGGGGG tt where FF tt = VVVV jj jjjj BBBB tt (.39c) The model s dynamics are characterized by the presence of state and jumping (co-state) variables. mm Past conditions determine the current values of state variables (KK iiii, KKKK tt, KK tt and BBBB tt ), while those of the jumping variables (CC tt, qq iiii ) depend on future conditions. The latter are sensitive to changes in future values of exogenous variables. However, functional forms selected for dierent behavioral functions and the imposed transversality conditions keep the model from exploding. In the steady state, all variables, expressed per eiciency unit, are constant. Finally, the conversion factor between currencies (the nominal exchange rate), EEEE tt, is chosen as numéraire. The equations for market equilibrium and steady states can be found in the full listing of equations in the Appendix. 3. Data, calibration and numerical solution strategy Given the high nonlinearity of the model, we do not attempt to find analytical solutions. We rather have recourse to numerical solution methods. We calibrate the dynamic CGE model to the benchmark equilibrium dataset as reflected in the SAM (Social Accounting Matrix) of the economy of Benin for 6, which is the latest year for which detailed required information on national accounts and sectoral data were available. The 6 SAM is built on 6 national accounts data and on the structure of the Input-Output (I-O) table of 999 using the biproportionate adjustment technique called RAS 8. Table presents some key characteristics of the economy in the base run. We standardize observed total labor supply adjusted for technological progress to unity. It follows that the wage rate is equal to total wages paid, and sectoral employment is the share of total labor used in each industry. We assume that the economy is in a long-run equilibrium with a conservative growth rate of %; all quantity variables expressed per eiciency unit of labor and prices are constant in the steady state. Calibrating the model requires the techniques used in both static and dynamic models. Since most readers are familiar with the issues related to static models, 8 The philosophy behind the RAS techniques and their mathematical properties techniques can be found in Bacharach (97) and Schneider and Zenios (99). 7

for the sake of space, we narrow down our discussions on the calibration of the dynamic aspect of the model. Basically, the calibration of a dynamic general equilibrium model involves recovering the values of the unobserved data and of some behavioral parameters so as to reproduce the observed steady state with the model. This is usually done by using the observed data, some extraneous parameters, first-order conditions, and steady state conditions. Table () presents some of the extraneous parameters we draw from our literature search on the economy of Benin. Those values are taken directly from studies on Benin or from studies on some economies that are close to that country. According to our review of this literature, the estimated public capital output elasticity averages at around.3. This is not substantially dierent from the Benin-specific value of.9 obtained by Calderon, Moral-Benito & Serven (9) 9. Following Adam and Bevan (6), we assume the output elasticity of public capital to be the same across all sectors. This made it possible to split capital remuneration as it appears in the standard I-O table between the remuneration of public capital and that of private capital. The world risk-free real interest rate is set to 6% and the rate of depreciation of all types of capital stock is set to.5. The adjustment cost parameter in the installation cost function is set to as in most studies. The volumes of investment by sector of destination in forward-looking firms are calibrated using the data on capital stock derived from the SAM, and Equation (.). In this calculation, we dierentiate gross investment by sector of destination (with adjustment cost) from the net investment that eectively increases the stock of capital in these firms. We then calibrate the index price of the capital good, using the equality between the total value of investment by sector of origin and the total value of investment by sector of destination, and the calibrated values of gross investment by sector of destination in forward-looking firms. It is interesting to note that we make use of the fact that the value of investment in myopic firms is equal to the saving of myopic households. From equation (.) using the calibrated values of investment and capital stock in forwardlooking firms and of the price of the capital good, we get the shadow price of capital in forwardlooking firms. The value of each forward-looking firm can hence be computed. Using the steady state conditions, the value of foreign assets and total financial wealth of forward-looking households can be calculated. 9 We would like to thank these authors for some discussions and for sharing their results on Benin with us. 8

Several strategies exist in the literature for solving forward-looking dynamic models. The challenge in finding numerical solutions for this class of models has bearing with the presence of dynamic jumping or co-state variables. In contrast to predetermined dynamic variables whose levels in each period are completely known based on past information, the values of jumping variables depend on expectations of future variables. We use the extended deterministic path method suggested by Gagnon (99) that solves the model as system of nonlinear equations containing dierence equations. We make use of the static and dynamic first-order conditions discussed earlier, and impose initial values for the state variables such as the capital stock, and steady state conditions for the jumping variables. In a recent comparison of numerical methods for solving standard business cycle models, Heer and Maußner (8) find that the extended path approach is an accurate method. Finally, for the numerical solution, we truncate the infinite-horizon model to a sixty-period model within which a steady state has been attained in all our simulations. 4. Simulations Using the model described above, we conduct two simulations to analyze the growth and sectoral implications of increasing investment in public capital in Benin under dierent financing rules. In both simulations, we consider a permanent, % increase in the ratio of public infrastructure investment to GDP. In the first simulation, we assume that the increase in public infrastructure investment is financed by a uniform percentage increase in the production tax imposed on the output of myopic and forward-looking firms. In the second simulation, we assume that the increase in public infrastructure investment is financed by an increase in foreign aid inflows. We quantify the dynamic aggregate and sectoral eects of variables as percentage changes from their base run values, unless otherwise stated. We report these eects for three dierent points in time. Namely, we present the response for the first year following the shock (immediate eect), the response for the fifth year (short-run), and the response for the 6th year (long-run).the results of the dynamic simulation analysis are presented in various tables and graphs for both of the financing scenarios. In order to avoid the black-box syndrome related to the results of numerical models, we strive to discuss in detail the transmission channels at play. For each of the two All capital stock variables, however, are reported for the second year since these are assumed fixed in the first period. 9

simulations, we first analyze the aggregate impact of the policy change followed by a discussion of sectoral eects. 4. Simulation : Increase in public infrastructure investment under production tax financing In this policy experiment, a % increase in the ratio of public investment in infrastructure to GDP is simulated assuming that this increase in government spending is financed by a uniform percentage increase in the production tax imposed proportionally on all myopic and forward-looking firms. The rationale for this simulation is to account for the trade-o as well as the distortionary impact that an increase in public investment might have. Table 3 reports the aggregate impacts and Tables 4-5 present the sectoral impacts on selected volume and price variables. The sets of Figures -3 depict the transitional dynamics of selected variables. 4.. The aggregate impacts From the presentation of the model in Section, an increase in public investment has direct impacts on both the supply and the demand side of the economy. As investment made in the current period will only be wholly eective in the next period, the immediate productivity impact of increased public capital stock cannot be manifested in the first period. We can only capture the direct eect on the demand side of the economy. Nevertheless, we do observe indirect adjustment eects on the supply side in the first period. The increase in the ratio of public investment to GDP amounts to an increase of that variable by 9.8% in the first period in comparison to the base run. The additional spending requires a uniform increase of the production tax rate by almost 3% in the same period to balance the budget. This increase in the production tax rate exerts a negative supply shock on the economy that reduces the return to labor by.3%. The rental rate of capital of myopic firms has barely changed (.%). It follows that the myopic households disposable income falls by.4%. They react to this shortfall in disposable income by reducing their demand for consumption goods in the first period. In contrast, the forward-looking households do not act as abruptly as myopic households in terms of their short-run consumption decision. They have the possibility to smooth their consumption that increases in real terms by.77%. Nevertheless, total consumption falls slightly in the same period. As the income of myopic households falls, their demand for investment declines by.9%, owing not only to the fall in their saving but also to the rise in the price of the capital good (.79%) induced by increased public investment.

The mechanisms at play are dierent for forward-looking firms that decrease their investment in the first period by a lower magnitude (.63%). The reason for the decline in the investment of these firms in the first period has to do with the large increase in the production tax rate needed to finance additional public expenditure that reduces their incentives to invest in the first period. In total, it appears that public investment crowds out private investment in the first period. This is a typical result obtained in most analyses of the eects of public investment in static models. As we discuss below, additional insights are provided by this dynamic framework. Nevertheless, the crowding out is not total as total investment rises by.87%. As the demand for capital goods increases, demand for imports increases as well. The appreciation of the real exchange rate brought about by the increase in the prices of domestic goods, is not favorable to exports. They fall in the first period by.9%. Nevertheless, real GDP increases by.49% in the first period despite the fall in net exports. The changes in GDP in the subsequent periods are more significant when the supply side eect of increased public capital starts to take eect from the second period onward. As expected, the positive output eects are strengthened over time, and yield sizeable benefits to the Beninese economy. The results in Table 3 demonstrate that the expansion in Benin s stock of public capital adds more to growth in the short and the long-run (.8% and.39%, respectively) than during the first year. The larger stock of public capital exerts positive eects on the marginal productivity of private capital and labor. Over the first few years following the boost to public investment in infrastructure, the increase in these marginal products is quite steep as demonstrated by the top two panels of Figure. In this context, both the forward-looking and myopic firms face strong incentives to increase their investment spending. For example, the myopic households now receive a higher capital income reflecting the rising productivity of capital due to new infrastructure. In addition, labor income of these households rises in line with the increase in the wage rate brought about by the greater demand for labor. Everything equal, their total disposable income and thereby their saving increase. Consequently, myopic firms investment rises in the short-run, and starts to exceed its benchmark value after year 8, before stabilizing at.4% in the long-run. In contrast, the forward-looking firms investment rises to a positive value already by the second year reaching.77% by the end of the 6th period. This higher long-run level of forwardlooking firms investment compared to that of the myopic firms is reflective of their ability to anticipate enhanced future capital productivity. It appears then that public infrastructure investment

starts to crowd in private investment in the short and the long-run through an indirect complementarity eect. As mentioned before, this supply-side eect of public investment in infrastructure on the marginal products of private capital and labor comes into operation only gradually as additional public capital is accumulated. The rising output has a positive impact on the price of the investment good that gradually falls, thus adding a further impetus to firms to increase private investment demand. Moreover, the higher stock of public capital allows for a gradual decrease in the production tax rate needed to finance the public infrastructure investment thereby contributing to greater output expansion over time. It follows that government revenue starts to fall in comparison to the previous periods, but is still higher than in the base run. The importance of the productivity enhancing eect of public infrastructure is further highlighted when we analyze Benin s external economic performance. Public investment in infrastructure produces a short-run appreciation of the real exchange rate, whereby imports increase by.4% and exports decrease by.9%. However, as public capital and begins to generate positive productivity eects on private inputs, the appreciation eect on the real exchange rate weakens in the short-run, but nonetheless remains present. It is precisely due to this gradual rise in marginal productivity that exports are able to increase over the short-run despite the presence of an appreciated real exchange rate, although not as much as imports. Consequently, the economy experiences a somewhat weak Dutch Disease eect in the first period. Accordingly, the trade balance deteriorates leading to current account deficits that aggravate the foreign debt. However, in the long run, public capital accumulation has a positive impact on the real exchange rate that depreciates and boosts more exports. It ensues that the economy overcomes the initial Dutch Disease eects as the positive supply-side eects on the productivity of the private economy strengthen over time, eventually expanding aggregate supply to match the increase in aggregate demand created by higher government spending. 4.. Sectoral impacts The aggregate results discussed so far have some implications at the sectoral level that will be briefly delineated below. At a disaggregated level, all sectors benefit equally from increased public investment in all periods owing to the Leontief function form of the index of capital good. The increasing demand for investment goods acts as a main driver in raising the total domestic demand for all sectoral commodities, particularly in the long-run. However, in the first period, productiontax financed infrastructure investment produces a modest negative eect on total domestic demand

for the non-tradable sectors of the economy, namely Utilities, Transportation-Communications, and Bank Services. This is largely explained by the fact that these sectors do not benefit from increased investment demand in conjunction with decreased consumption demand and decreased demand for intermediate use. Nonetheless, increased total domestic demand in the first period, particularly in the Cotton and Other Industrial Handicraft sectors drives up first period consumption prices in every sector, but Food Agriculture, where it falls by.8%. As import prices are fixed, the rise in consumption prices is the consequence of the rise in the domestic prices. The net impact of the rise in domestic price in all sectors, except Food Agriculture is first to reduce exports in the first period because of the appreciation of the sectoral real exchange rate. In contrast, the most formalized sectors of the economy, such as Utilities, Transportation-Communication and Bank Services are most negatively aected in terms of output, which falls in the first period by.8%,.66% and.47% respectively. These contractionary eects, which are somewhat attenuated in the short-run, but nonetheless persist, are mainly attributable to the distorting fiscal mechanism used to finance government infrastructure investment that in turn lowers domestic production in these sectors, but also to the non-tradable nature of these sectors implying that all negative shocks on industries are translated onto them. Output in the manufacturing sector does not expand in the first period. This is due largely to decreased export supply as well as domestic production, whereby the increases in the total domestic demand of these industries, such as Agro-Industry, Other Modern Industries and Industrial Textiles are mainly met by increased imports. Consequently, resources flow from the contracting manufacturing and service sectors of the economy towards the expanding agricultural sectors of the economy. The shadow price of capital increases in all sectors during the early phase of transition but gradually decreases over time; it eventually falls below its initial steady state value. However, the ratio of shadow price to purchase price of capital increases in only three sectors in the first period, namely Cash Crop, Cotton and Other Modern Industries. Accordingly, investment in these sectors rises, particularly in the Cotton sector where it increases by.4%, while there is a crowding-out of investment in the other sectors in the first period. Lower private investment in the other sectors, however, reduces the marginal product of labor thereby driving down employment in those sectors. As the supply-side eects of public capital expansion strengthen over time, output expansion takes place over the short and the long-run in every sector. The higher productivity of private inputs drives down the prices of domestic goods in all sectors over time and raises the ratio 3

of shadow price to purchase price of capital over the short-run, eventually stabilizing at around zero in the long-run. On the one hand, falling domestic prices contain the initial onset of the Dutch Disease by promoting greater exports through their depreciating eect on the real exchange rate and by boosting total domestic demand in all sectors. On the other hand, the increasing ratio of shadow price to purchase price of capital stimulates increasing sectoral investment. The major sectoral investment increase takes place in the Cotton sector where it increases by 6.6% in the long-run. The Cotton sector also sees the largest boost in its exports, which in the long-run rise by 8.63% relative to the base line. Combining these two factors (increased investment and exports) with enhanced domestic production, Cotton records the greatest increase in its long-run output, which rises by 6.33% compared to the initial steady-state. In contrast, the most formalized sectors of the economy, including Utilities, Transportation- Communications and Bank Services see the lowest long-run output gains of all sectors. This is mainly due to their sole dependence on domestic production, particularly that of Utilities and Bank Services, while Transportation-Communication does not raise its exports in the long-run above its initial steady-state value. 4. Simulation : Increase in public infrastructure investment under foreign aid financing The objective of this simulation is to see how the foreign aid funding option for public infrastructure investment would change the performance of Benin s economy relative to the previous simulation. In this simulation therefore, we increase the ratio of public investment in infrastructure to GDP by % assuming that this increase in government spending is financed by foreign aid. Table 5 presents the dynamic aggregate eects of the simulation, while Tables 6 and 7 present the sectoral simulation results for selected volume and price variables, respectively. The sets of Figures 4 to 6 show the path of the dynamic adjustment. At first glance, the simulation results both at the aggregate and the sectoral level are qualitatively, although not quantitatively similar, particularly in the long-run, with few important qualitative dierences emerging in the short-run. At the aggregate level, these short-run qualitative dierences primarily pertain to households consumption choices and firms investment decisions. At the sectoral level, these dierences are largely due to sector-specific factors. In terms of quantitative dierences, we observe that aid-financed public infrastructure investment generates greater beneficial eects on Benin s economy, particularly in terms of key variables, such as public and private capital stocks and output. 4

4.. The aggregate impacts In contrast to the production tax financing scenario, myopic households increase their consumption spending in the first period by.56%. The increase in consumption reflects the rise in the myopic household s disposable income brought about by the aid transfer and by the increased capital and wage income realized in the absence of a distortionary tax. However, following the initial impact, myopic households slowly decrease their consumption spending to its long-run level of.5% owing largely to the gradual reduction in the aid inflows needed to finance new infrastructure. Nonetheless, the myopic households are able to attain higher consumption throughout the entire adjustment process to the long-run, such that the long-run increase in the myopic household s consumption is twice as large in comparison to the case in which the production tax financed the public investment in infrastructure. The income eect of the increase in wages leads the forward-looking households to also increase their consumption spending in the first and the short-run period, although by a lesser magnitude than the myopic households (. 65% and.%, respectively). Having the ability to smooth consumption, the forward-looking households allocate the increase in labor income between consumption and saving. Myopic households, however, view the productivity shock as unexpected and save a fixed fraction of their increased disposable income in each period, leaving the remainder for higher consumption. However, the foreign aid financing option allows forward-looking households to attain higher short-run and long-run consumption (an increase of.% and.8%, respectively) than under the production tax funding option. An important qualitative dierence from the previous simulation is that public investment in infrastructure has an immediate crowding-in eect on private investment. Both myopic and forward-looking firms increase their first-period investment spending by.9% and.47%. This greater private capital accumulation, although somewhat attenuated by a steeper rise in the price of the investment good, is largely made possible by the fact that the foreign aid financing mechanism does not play against the productivity enhancing role of public capital in the initial period. For example, the first-period rental rate of capital of myopic household rises by.76% as opposed to.% in the production tax financing scenario. Cognizant of future enhanced private capital productivity, the increase in the investment made by forward-looking firms in the initial stages of the transitional period is even steeper than that of the myopic firms as illustrated by Figure 5. Ultimately, aid-financed infrastructure investment produces a more favorable eect on long-run private sector investment that, in turn, results in a larger expansion of the long-run private 5

capital stock, relative to the first simulation. At the same time, the public capital stock reaches a larger long-run increase of.34% compared to the production tax scenario. Thus, in the absence of a distortionary financing mechanism the economy enjoys stronger marginal productivity eects during the whole adjustment process towards the long-run steady state. It follows that the enhanced private and public capital accumulation under the foreign-aid financing option consistently generates greater output gains, which, as in the production tax case, grow larger over time. With regard to trade variables, the qualitative results of the previous simulations still hold true. However, foreign-aid financed infrastructure investment translates into a stronger appreciation eect on the real exchange rate, particularly in the first period. The steep instantaneous increase in imports of.87% and a simultaneous fall in exports of.64% deteriorate the trade balance and create initial and short-run current account deficits that contribute to the worsening of the foreign debt, which over the same period increases more than in the production tax financing scenario. However, this is followed by a restoration of export performance consistent with real exchange rate depreciation. Our result is in line with those of Adam and Bevan (6). Dutch Disease eects are not a necessary outcome of aid inflows and may be overturned in the longer-run as public capital gradually accumulates and marginal products of private factors rise, particularly that of private capital. The additional impact that we get from this study is the dierentiated impact of the policy on myopic and forward-looking firms. The declining strength of Dutch Disease eects is crucially dependent upon how the aid inflow is spent. When aid is used to promote productive spending, as in this study and in Adam and Bevan s (6) model, then, as succinctly put by Moreira (), the longer-run positive supply side eects eventually outweigh the short-run, adverse demand-side eects on the real exchange rate. 4.. The sectoral impacts As in the production tax financing scenario, aid-financed infrastructure investment produces a dierentiated impact on sectoral output in the first-period. In contrast, however, the first-period collapse of some sectors is mainly driven by a deeper export contraction as opposed to a considerable decline in domestic production and investment. This greater contraction in exports is due to the fact that total domestic demand increases across the board leading to a steeper rise in first-period domestic prices, and thus a larger appreciation of the real exchange rate. The higher total domestic demand, in turn, is accommodated by greater sectoral imports at all periods. 6

In the absence of a distorting fiscal mechanism, aid-financed infrastructure investment works in favor of domestic production in the first-period for most of the sectors. The exception to this are certain manufacturing industries, such as the Agro-Industry, Other Modern Industries and Industrial Textiles where domestic sales decline, although generally less than in the production-tax financing case. In conjunction with the negative export supply response, these sectors experience the greatest output losses in the first period ranging from -.7% to -.4%. While the exportoriented sectors of Benin s economy, particularly Other Business Services and Cotton benefit from increased domestic production, they too record a decrease in their first-period output owing to a sizeable fall in their exports. In the longer-run, however, the productivity eects stemming from productive public investment and increased accumulation of both types of capital contribute to further increasing domestic supply and reversing the Dutch Disease eects present over the first to short-run period. In the long-run, exports increase across the board, although by slightly less than in the previous simulation. This has a bearing on Benin s most important export sector, Cotton where long-run output increases by 6.8% - which is some.5 percentage points lower than in the production tax financing scenario. Cash Crops sector is also slightly aected, with its long-run output being.% percentage points lower than in the earlier simulation. For other sectors, however, the lower increase in exports is mainly oset by greater long-run domestic production as well as greater long-run investment levels. Ultimately, all sectors, apart from Cotton and Cash Crops are able to realize greater long-run output gains that in the production tax financing scenario. 5. Conclusions Incorporating heterogeneous agents into a multisector, intertemporal CGE model with public capital, we have analyzed the aggregate and sectoral eects of externally and domestically-financed public investment in infrastructure on the economy of Benin from both the demand and supply sides. The simulation results suggest that the two fiscal instruments - production tax and foreign aid financing of public infrastructure investment - produce very dierent impacts on the investment response of the private economy, particularly in the very short run period. The absence of a distorting financing method allows public investment to increase without instantaneously crowdingout private sector investment, suggesting that the crowding-out eects typically emphasized in the literature are highly sensitive to the mode of financing chosen by the government. 7

However, more importantly, our experiments show that when agent heterogeneity is taken into account, public investment carries dierent implications for the economic behavior of myopic and forward-looking households and firms. When production taxes are raised to fund government investment, the crowding-out eects on private investment persist in the short-run, but only for myopic firms since increased taxation reduces the myopic household s disposable income, and thereby the level of the myopic firm s investment. The heavy burden of the distortionary production tax is further reflected in the twice as low increase in the myopic household s long-run consumption in comparison to the foreign-aid financing case where the instantaneous and the short-run consumption responses of the myopic households dominated those of the forwardlooking households. In addition, we show that the productivity eects of public capital are a critical element of the transmission mechanism that enables a supply-side response to the increased public investment coming from the demand-side. Although both financing mechanisms lead to considerable expansionary eects on the long-run levels of key variables, such as output, these are more pronounced in the case of foreign-aid financing of public investment. As public capital gradually accumulates, public investment amplifies the marginal productivity eects of private inputs that ultimately overturn the initial presence of Dutch Disease eects in the Beninese economy, particularly in the foreign-aid financing scenario. These findings further suggest that public investment in infrastructure, through the gradual onset of positive supply-side eects of public capital formation, can play a pivotal role in supporting private sector investment, and thereby sustaining a domestic process of capital accumulation. 8

References Adam, C. & Bevan, D. (6). Aid and the supply side: Public investment, export performance, and Dutch disease in low-income countries. The World Bank Economic Review,,, 6-9. Aaron, H.J. (99), Discussion, in: A.H. Munnell (ed.), Is There a Shortfall in Public Capital Investment? Federal Reserve Bank of Boston, Boston, USA. Aschauer. D. (989). Is public expenditure productive? Journal of Monetary Economics, 3, 77-. Bacharach, M., 97, Biproportional Matrices and Input-Output Change, Cambridge University Press. Barro R. J. (99). Government spending in a simple model of endogenous growth. Journal of Political Economy, 98, 5-, 3-5. Berg, A. Gottschalk, J., Portillo, R. & Zanna, L-F. (). The macroeconomics of medium-term aid scaling-up scenarios. IMF Working Paper /6. Washington, D.C.: International Monetary Fund. Calderón, C. & Chong, A. (4). Volume and quality of infrastructure and the distribution of income: An empirical investigation. Review of Income and Wealth, 5, 87-5. Calderón, C., Moral-Benito, E., & Servén, L (9). Is infrastructure capital productive? A dynamic heterogeneous approach, Mimeo, The World Bank and CEMFI, December. Calderon C., & Serven, L. (4). The eects of infrastructure development on growth and income distribution. World Bank Policy Research Working Paper No. 34. Washington, D.C.: World Bank. Campbell, J. Y. & Mankiw, N. G. (989). Consumption, income, and interest rates: Reinterpreting the time series evidence. In NBER Macroeconomics Annual, Eds. Blanchard and S. Fischer. Cambridge, MA: MIT Press, 85-6. Carmichael, B. and L. Samson (995) Taxation in small developing economy: The case of Senegal, mimeo, Department of Economics, Université Laval, Canada Estache, A. & Fay, M. (9). Current debates on infrastructure policies. Commission on Growth and Development, Working Paper No.49. Fisher, W. H. and S. J. Turnovsky (998), Public Investment, Congestion, and Private Capital Accumulation. The Economic Journal, 8, pp.399-43. Gagnon, J. E.(99)."Solving the stochastic growth model by deterministic extended path, Journal of Business & Economic Statistics, 8(), 35-36. Gramlich, E. M. (994). Infrastructure investment: A review essay. Journal of Economic Literature, 3, 3, 76 96. Hayashi, F. (98). Tobin s marginal q and average q: A neoclassical interpretation, Econometrica 5,(), 3-4. Heer, B. and a. Maußner (8), Computation of business cycle models: a comparison of numerical methods, Macroeconomic Dynamics,, 8, pp. 64-663. 9

Kalaitzidakis, P., & Kalyvitis, S. (4). On the macroeconomic implications of maintenance in public capital. Journal of Public Economics, 88, 3-4, 695-7. Lucas, R. E., Jr. (967). Adjustment costs and the theory of supply, Journal of Political Economy, 75, 3 334. Lofgren, H. & Robinson, S. (4). Public spending, growth, and poverty alleviation in Sub-Saharan Africa: A dynamic general equilibrium analysis. Paper prepared for presentation at the conference Growth, poverty reduction and human development in Africa, Centre for the Study of African Economies, University of Oxford, March -, 4. Mckibbin, W. J. and D. Vines () Modeling reality: The Need for Both Intertemporal Optimization and Stickiness in Models for Policy- Making, Oxford Review of Economic Policy, 6, 4, pp.6-36. Ohdoi, R. (7), Productive Government Spending, Patterns of Specialization and Economic Growth in a Small Open Economy, The Japanese Economic Review, 58, pp.7-46 Perrault, J-F., Savard, L. & Estache, A. (). The impact of infrastructure spending in Sub-Saharan Africa: A CGE modelling approach. Policy Research Working Paper 5386, World Bank, Washington: DC. Rioja, F. K. (). Growth, welfare, and public infrastructure: A general equilibrium analysis of Latin American economies. Journal of Economic Development, 6,, 9-3. Rivas, L.A. (3) "Income Taxes, spending composition and long-run growth", European Economic Review, 47, pp. 477-53. Sahoo, P. & Dash, R. K. (9). Infrastructure development and economic growth in India. Journal of the Asia Pacific Economy, 4, 4, 35-365. Schneider, M.H. and S.A. Zenios (99) A comparative study of algorithms for matrix balancing. Operations Research, 38, 439 55. Tamai, T. (7). Public intermediate goods, endogenous growth, and indeterminacy. Economic Modelling, 4, 683-689. Treadway, A. B. (969). On rational entrepreneurial behavior and the demand for investment, Review of Economic Studies 36, 7 39. Tsoukis, C., & Miller, N. J. (3). Public services and endogenous growth. Journal of Policy Modelling, 5, 3, 97-37. Turnovsky, S. J. (4). The transitional dynamics of fiscal policy: long-run capital accumulation and growth. Journal of Money, Credit, and Banking, 36, 5, pp. 883 9. World Bank. (9). Benin: Constraints to Growth and Potential for Diversification and Innovation Country Economic Memorandum. Report No. 4833-BJ. Washington, D.C: World Bank. Yakita, A.(4) Elasticity of Substitution in Public Capital Formation and Economic Growth, Journal of Macroeconomics, 6, 39-48 3

Table : Characteristics of the SAM of Benin in the base run Sectoral shares Value added Consumption Total invest. (sector of origin) Government consumption Exports Imports Food Agriculture * 9% 9.%.%.%.7% 8.% Cash Crops 6%.%.%.%.3%.% Agri-Industries % 8.%.%.%.% 4.% Cotton %.%.9%.% 7.3%.% Agri-Handicrafts * 4%.%.%.%.7%.% Other Modern Industries %.% 3.5%.%.% 55.3% Utilities %.9%.%.%.%.% Industrial Textiles % 8.3%.%.%.% 5.6% Other Industrial Handicrafts * 6% 6.5% 44.4%.%.%.% Transports-Comm. 8%.%.%.%.7%.6% Bank Services %.6%.%.%.%.% Other Services * 4% 7.% 9.8%.% 69.9% 4.% Total % % % % % % * Myopic firms Table : Extraneous parameters used for calibration Parameters Values Substitution elasticity of CES function of forward-looking households.8 Substitution elasticity of CES function of myopic households.8 Substitution elasticity of first-level CES production function.5 Substitution elasticity of second-level CES production function.4 Substitution elasticity of third-level CES production function.4 Substitution elasticity of Armington CES function Substitution elasticity of CET function Rate of depreciation of capital of forward-looking firms.5 Rate of depreciation of capital of myopic firms.5 Rate of depreciation of public capital.5 Adjustment cost parameter Output elasticity of public capital.3 Public capital eectiveness parameter Share of public investment in total investment.5 Population growth rate incl. technological progress. World real interest rate.6 Share of myopic households in total consumption expenditures.7 Share of myopic households in total labor income.58 Share of myopic households in total income taxes. Share of myopic households in total government transfers. 3

Table 3: Simulation - % increase in the ratio of public investment in infrastructure to GDP Production tax financing Aggregate results (Percentage deviation from base run, unless otherwise mentioned) First period Short run Long run Rental rate of capital of myopic household..7.73 Wage rate -.3.9 3.35 Price of investment good.79.43 -.4 Real GDP.49.8.39 Total household consumption -.6..4 Myopic -.4.5.6 Forward looking.77.9.35 Total investment.87 3.3 4.6 Public investment 9.68.43. Private investment -.74.83.3 Myopic -.9 -.38.4 Forward looking -.63.54.77 Total capital stock.35.39 4.7 Public capital stock.6 5.9.99 Private capital stock -...5 Myopic -.5 -.36.4 Forward looking -.9.5.75 Total exports -.9.6 3.6 Total imports.4.74.4 Real exchange rate -.53 -.9.37 Foreign saving -3.79-3.89-4.6 Total income of myopic households -.4.5.6 Labor income -.3.9 3.35 Capital income..7.78 Government revenue 3.35 3..86 Increase in production tax rate (%).96 8.5 6.8 3

Table 4: Simulation - % increase in the ratio of public investment in infrastructure to GDP Production tax financing Sectoral impact on volume for selected variables (Percentage deviation from base run) Food Agric. * Cash Crops Agri- Industries Cotton Agri- Handicrafts * Other Modern Industries Utilities Industrial Textiles Other Industrial Handicrafts * Transport- Comm. Bank Services Other Services * Gross output First period.. -.37.6.6 -.38 -.8 -.37.6 -.66 -.47 -.34 Short run.55.64.3..5.88 -.73.7.59 -.47 -.9. Long run. 4.8.4 6.33.5 3.9. 3.7 3.3.75.99.3 Employment First period.6.34 -..39.9 -.5 -.67 -.5.95 -.56 -.6 -.3 Short run.8.7 -..84.8.63 -.95.7.37 -.7 -.68 -.8 Long run -.3 3.3.55 4.56 -.6.9 -.3.73.56 -.55 -.46 -. Investment by sector of destination First period.5 -.3.4.9 -.78 -.47 -.9 -.6 Short run 3.5.67 4..9 -.3.66 -.5 -.6 Long run 4.6.8 6.6 3.84.9 3.7.94.4 Exports First period.38 -.56 -.99 -.56 -. -. -.99 -.48 -.6 Short run.7.67 -..9.3.74.7 -.7 -.6 Long run.68 7. 3.7 8.63 3.89 6. 7. -.6.49 Domestic sales First period.. -.36.84.7 -.38 -.8 -.37.6 -.65 -.47 -.8 Short run.54.64.3..5.88 -.73.7.59 -.46 -.9.37 Long run. 4.8.3 4.7.5 3.9. 3.69 3.3.76.99.9 Imports First period.3.8.6.46.6.5..48 Short run..6.38...5.84.39 Long run.56.63.57.87.95.8.58.9 Total domestic demand First period.9..5.84.7.9 -.54.9.6 -.6 -.47 -.3 Short run.5.64.3..5.99 -.37.37.59 -.43 -.9.4 Long run.7 4.79.9 4.7.5.8.8.7 3.3.77.99.8 Consumption demand First period.3 -..8.9.9 -.9. -.8 -.57 -.8 -.44 Short run.5.34.9.6.3 -.3.37 -.9 -.58 -.39 -.6 Long run..65..74.96.85.6.3.48.77.88 Investment demand by sector of origin First period.87.87.87.87.87.87.87.87 Short run 3.3 3.3 3.3 3.3 3.3 3.3 3.3 3.3 Long run 4.6 4.6 4.6 4.6 4.6 4.6 4.6 4.6 Demand for intermediate use First period.8.6 -.3 -.53.3 -.9 -.99 -.54. -.7 -.69 -.3 Short run.45.87.7.64.47.7 -.49.63.4 -.9 -.8.39 Long run.7 5.35.53 3.59.39.56.49 3.58.7.4.6.85 33

Table 5: Simulation - % increase in the ratio of public investment in infrastructure to GDP Production tax financing Sectoral impact on prices for selected variables (Percentage deviation from base run) Food Agric. * Cash Crops Agri- Industries Cotton Agri- Handicrafts * Other Modern Industries Utilities Industrial Textiles Other Industrial Handicrafts * Transport- Comm. Bank Services Other Services * Price of gross output First period -..3 -.39.33 -..4-7.59 -.6-4.77-9.4 -.48-5.54 Short run -.9 -.4 -.5 -.8 -.64.5-7.8 -.66-5.7-8.75-9.96-5.64 Long run -.3 -.6-3.4 -.9 -.4 -. -7.7 -.99-5.76-8.9 -.6-5.79 Price of domestic good First period -.9.34.3.7.9.4.7.3..93.56.78 Short run -.6 -.. -.8 -.35.7.97 -.3.77.5.9.49 Long run -.8 -.4 -.77 -.8 -.5 -.99 -.8 -.66 -.9.4.4 -. Price of composite consumption good First period -.8.34..7.9.8.57.8..9.56.75 Short run -.4 -..4 -.8 -.35..79 -.6.77.4.9.48 Long run -.6 -.4 -.6 -.8 -.5 -. -.6 -.44 -.9.4.4 -. Shadow price of capital First period.8.47.4.83.7.67.. Short run.89.63.5.8.54.76.54.55 Long run -.4 -.4 -.4 -.4 -.4 -.4 -.4 -.4 Ratio of shadow price to purchase price of capital First period.39 -.3.6.5 -.7 -. -.58 -.58 Short run.47..6.39..34.. Long run........ 34

Figure : Simulation % increase in the ratio of public investment in infrastructure to GDP Production tax financing Dynamic impact on selected aggregate variables Rental Rate of Capital of Myopic Household Wage rate Price of Investment Good 3.5.5.5 3 4 5 6 7 4 3-3 4 5 6 7 % deviation from abse run.5 -.5 3 4 5 6 7 Real GDP Household Consumption Firm Investment.5.5 3 4 5 6 7.5.5 -.5 4 6 8 TOT CONS FORW TOT CONS MYOPIC AGGREGATE CONS 6 4-4 6 8 TOT INVESTMENT INVESTMENT FORW INVESTMENT MYOPIC Exports and Imports Government Revenue % deviation from abse run 4-3 4 5 6 7 TOT EXP TOT IMP 3 4 6 8 GOVT REVENUE % INCREASE IN PROD TAX RATE 35

Figure : Simulation % increase in the ratio of public investment in infrastructure to GDP Production tax financing Dynamic impact on selected sectoral volume variables Gross Output Investment by Sector of Destination 7 6 5 4 3 - - 4 6 Food Agric. Cash Crops Agri-Ind. Cotton Agri-Handicrafts Oth. Mod. Inds. Utilites Ind. Textiles Oth. Ind. Handicr. Transp-Comm. Bank Serv. Oth. Bus. Serv. 8 6 4 - -4 4 6 Cash Crops Agro-Ind. Cotton Oth. Mod. Inds. Utilites Ind. Textiles Transp- Comm. Bank Serv. 5-5 4 6 8 Exports Food Agric. Cash Crops Agri-Ind. Cotton Agric. Handicrafts Oth. Mod. Ind. Ind. Textiles Transp-Comm. Oth. Bus. Services 6 4 - Domestic Sales 4 6 8 Food Agric. Cash Crops Agri-Ind. Cotton Agri- Handicrafts Oth. Mod. Inds. Utilites Ind. Textiles Imports Consumption Demand 3.5.5.5 -.5 4 6 Food Agric. Cash Crops Agri-Ind. Oth. Mod. Ind. Utilites Ind. Textiles Transp-Comm. Oth. Bus. Services.5.5 -.5-4 6 8 Food Agric. Cash Crops Agri-Ind. Agri-Handicrafts Oth. Mod. Inds. Utilites Ind. Textiles Oth. Ind. Handicr. Transp-Comm. Bank Serv. Oth. Bus. Serv. 36

Figure 3: Simulation % increase in the ratio of public investment in infrastructure to GDP Production tax financing Dynamic impact on selected sectoral price variables Price of Gross Output Price of Domestic Good Food Agric..5 Food Agric. Cash Crops Cash Crops - -4-6 -8-4 6 8 Agri-Ind. Cotton Agri-Handicrafts Oth. Mod. Inds. Utilites Ind. Textiles Oth. Ind. Handicr. Transp-Comm..5 -.5 - -.5-4 6 8 Agri-Ind. Cotton Agri-Handicrafts Oth. Mod. Inds. Utilites Ind. Textiles Oth. Ind. Handicr. Transp-Comm. - Bank Serv. Oth. Bus. Serv. -.5 Bank Serv. Oth. Bus. Serv. Price of Composite Consumption Good Shadow Price of Capital.5.5 -.5 - -.5-4 6 Food Agric. Cash Crops Agri-Ind. Cotton Agri-Handicrafts Oth. Mod. Inds. Utilites Ind. Textiles Oth. Ind. Handicr. Transp-Comm. Bank Serv..6.4..8.6.4. -. -.4 4 6 Cash Crops Agri-Ind. Cotton Oth. Mod. Ind. Utilities Ind. Textiles Transp-Comm. Bank Services -.5 Oth. Bus. Serv. -.6 37

Table 5: Simulation - % increase in the ratio of public investment in infrastructure to GDP Foreign aid financing Aggregate results (Percentage deviation from base run, unless otherwise mentioned) First period Short run Long run Rental rate of capital of myopic household.76.9.39 Wage rate.48.56 4.5 Price of investment good.7.68 -.8 Real GDP.5.6.84 Total household consumption.5.86.45 Myopic.56.38.5 Forward looking.65..8 Total investment.87 3.98 4.96 Public investment.6.3.34 Private investment.4.64.49 Myopic.9.69.53 Forward looking.47.9 3.6 Total capital stock.5.83 5.9 Public capital stock.7 5.5.34 Private capital stock.6.48.43 Myopic.5.4.53 Forward looking.7.65 3.5 Total exports -.64 -.56 3. Total imports.87.9.87 Real exchange rate -.5 -.86.8 Foreign saving -3.87-3.97-4.3 Total income of myopic households.56.38.5 Labour income.48.56 4.5 Capital income.76.43.9 Government revenue 4.43 3.88 3.3 Additional foreign aid as percentage of base GDP.57.43.6 38

Table 6: Simulation - % increase in the ratio of public investment in infrastructure to GDP Foreign aid financing Sectoral impact on volume for selected variables (Percentage deviation from base run) Food Agric.* Cash Crops Agri- Industries Cotton Agri- Handicrafts * Other Modern Industries Utilities Industrial Textiles Other Industrial Handicrafts * Transport- Comm. Bank Services Other Services * Gross output First period.3. -.7 -.5.5 -.34 -.4 -.4.53.7.3 -.6 Short run.55.49.5.8.86.8.44.76.4.47.53.5 Long run.3 4.8.4 6.8.79 4.8.73 3.85 3.45.3.4.47 Employment First period.4 -.3 -.44 -.38.9 -.5 -.8 -.54.5.4.7 -.7 Short run -..67 -.9...9 -.6 -.6.7 -.4 -.6 -.4 Long run -.33.75.58 4.5..5..64.7 -.3 -. -.4 Investment by sector of destination First period. -.6.3. -.7 -.4.6.3 Short run 3.8.3 4..54.4.98.99. Long run 4.6.39 6.3 3.99.8 3.47.49.6 Exports First period -.9 -.8 -.7 -.87 -.5 -.4 -.44 -.75 -.98 Short run -.7.45 -.5.94 -.3.. -.7 -. Long run.68 6.5 3.6 8.4 3.43 5.8 6.8.3.4 Domestic sales First period.4. -.5.44.6 -.34 -.4 -.4.53.8.3.39 Short run.55.49.5.63.86.8.44.76.4.48.53.86 Long run.3 4.79.4 4.44.79 4.8.73 3.83 3.45.3.4.53 Imports First period 3.7.87.7.6.4.66.99 3.88 Short run.4.55.55.98.7.43.7.99 Long run.79 3.9.3.38.46.94.4.93 Total domestic demand First period.7.3.5.44.6..38..53..3.5 Short run.7.5..63.86.8.75.5.4.5.53.95 Long run.7 4.78.63 4.44.79.7.68.7 3.45.4.4.55 Consumption demand First period.9.66.3.6.4.65.8.4.6.3.6 Short run.68.95..96.9.84.9.7.49.5.56 Long run..7.56.6.54.49.7.59.5.9.5 Investment demand by sector of origin First period.87.87.87.87.87.87.87.87 Short run 3.98 3.98 3.98 3.98 3.98 3.98 3.98 3.98 Long run 4.96 4.96 4.96 4.96 4.96 4.96 4.96 4.96 Demand for intermediate use First period. -.7 -.4 -.48.36.43 -. -.49.95 -. -.9.6 Short run.69.6.6.8.88.3.58.79.8.54.55.8 39

Long run.38 5.8.8 3.76.66.88. 3.75 3.8.56.58.8 Table 7: Simulation - % increase in the ratio of public investment in infrastructure to GDP Foreign aid financing Sectoral impact on prices for selected variables (Percentage deviation from base run) Food Agr * Cash Crops Agri- Industries Cotto n Agri-Hand * Other Modern Industries Utilities Industrial Textiles Other Industrial Handi * Transpor t-comm. Bank Services Other Services * Price of gross output First period.47.89 -.47.84.4.95-6.35 -.3-3.8-7.66-8.45-4.6 Short run.88.49 -.9.4.3.4-6.65 -.99-4.53-7.97-8.9-4.7 Long run.4 -.84 -.98 -.89 -.6 -.84-7.5 -.7-5.5-8.56-9.74-5.37 Price of domestic good First period.5.9.98.67.4.97.4.4.57.44.58.7 Short run.9.5.5.83.5.44.8.33.8..6.4 Long run.7 -.8 -.58 -.68 -.8 -.8 -.3 -.4 -..45.5.9 Price of composite consumption good First period.39.9.33.67.4.9.9.7.57.4.58.67 Short run.85.5.7.83.5.9.65.9.8.9.6. Long run.5 -.8 -. -.68 -.8 -.7 -. -.37 -..44.5.9 Shadow price of capital First period.53..6.3..7.3.35 Short run.9.96.34.4.89.8.86.87 Long run -.8 -.8 -.8 -.8 -.8 -.8 -.8 -.8 Ratio of shadow price to purchase price of capital First period.6 -.5.34.5 -.7 -..4.8 Short run.5.7.66.45..39.7.8 Long run........ 4

Figure 4: Simulation % increase in the ratio of public investment in infrastructure to GDP Foreign aid financing Dynamic impact on selected on selected aggregate variables Rental Rate of Capital for Myopic Households Price of Investment Good Wage rate.5.5.5 4 6 8 % deviation from abse run.5 -.5 3 4 5 6 7 5 4 3 4 6 8 Real GDP Household Consumption Firm Investment.5.5 4 6 8.5.5 5 6 5 4 3 TOT CONS MYOPIC TOT CONS FORW AGGREG CONS 5 TOT INVESTMENT INVESTMENT FORW INVESTMENT MYOPIC 4

4 - -4 Exports and Imports 5 TOT EXP TOT IMP 5 5 5 Government Revenue 4 6 8 GOVT REVENUE % INCREASE IN PROD TAX RATE 4

Figure 5: Simulation % increase in the ratio of public investment in infrastructure to GDP Foreign aid financing Dynamic impact on selected on selected sectoral real variables 7 6 Gross Output Food Agric. Cash Crops 7 6 Investment by Sector of Destination 5 4 3-4 6 Agri-Ind. Cotton Agri-Handicrafts Oth. Mod. Inds. Utilites Ind. Textiles Oth. Ind. Handicr. Transp-Comm. Bank Serv. Oth. Bus. Serv. 5 4 3-4 6 Cash Crops Agro-Ind. Cotton Oth. Mod. Inds. Utilites Ind. Textiles Transp-Comm. Bank Serv. 8 6 4 - -4 4 6 8 Exports Food Agric. Cash Crops Agri-Ind. Cotton Agric. Handicrafts Oth. Mod. Ind. Ind. Textiles Transp- Comm. 6 5 4 3 - Domestic Sales 4 6 8 Food Agric. Cash Crops Agri-Ind. Cotton Agri- Handicrafts Oth. Mod. Inds. Utilites Ind. Textiles Oth. Ind. Handicr. Transp- Comm. Bank Serv. Imports Consumption Demand 4.5 4 3.5 3.5.5.5 4 6 Food Agric. Cash Crops Agri-Ind. Oth. Mod. Ind. Utilites Ind. Textiles Transp- Comm..5.5.5 4 6 8 Food Agric. Cash Crops Agri-Ind. Agri- Handicrafts Oth. Mod. Inds. Utilites Ind. Textiles Oth. Ind. Handicr. Transp- Comm. Bank Serv. 43

Figure 6: Simulation % increase in the ratio of public investment in infrastructure to GDP Foreign aid financing Dynamic impact on selected sectoral price variables Price of Gross Output Price of Domestic Good 4 - -4-6 -8-4 6 8 Food Agric. Cash Crops Agri-Ind. Cotton Agri-Handicr afts Oth. Mod. Inds. Utilites Ind. Textiles Oth. Ind. Handicr. Transp- Comm. Bank Serv..5.5 -.5 - -.5 5 Food Agric. Cash Crops Agri-Ind. Cotton Agri-Handi crafts Oth. Mod. Inds. Utilites - - Price of Composite Consumption Good Shadow Price of Capital Food Agric..5.5 -.5 - -.5-4 6 Cash Crops Agri-Ind. Cotton Agri- Handicrafts Oth. Mod. Inds. Utilites Ind. Textiles Oth. Ind. Handicr. Transp- Comm. Bank Serv. Oth. Bus. Serv..5.5 -.5 4 6 Cash Crops Agri-Ind. Cotton Oth. Mod. Ind. Utilities Ind. Textiles Transp-Comm. Bank Services 44

Model Equations List Households (a) CC tt+ CC tt + rr = + ρρ PPPP tt PPPP tt+ (b) FF tt+ ( + nn) = FF tt ( + rr ) + ττ yy YYLLtt + TTTTTTtt + EEEE tt TTTTTTTT tt + KKKK tt ξξ jjjj jj + GGGGGGGG tt ττ kk DDDDDD jjjj jj (c) YYLL tt = φww tt LLLL tt PPPP tt CC tt ii PPPP iiii DDDDDDDD iiii (d) DDDDDD jjjj = PPPPPP jjjj RRRR jjjj PPPP tt IIIIII jjjj + AAAA jjjj (e) cc iiii h = AAAA h σσ cc h h CCtt αα h h σσcc h CCCC PPPPtt PPPP iiii (+ττ CC ii ) (f) PPPP h tt = αα h σσ cc h AAAA h CCCC [PPPP iiii ( + ττ CC ii )] σσ cc h ii h h h (g) PPPP tt CC tt = HHHHHH tt mm (h) HHHHHH tt = ( ss mm mm ) YYYY tt (i)yyll mm tt = ( φ)ww tt LLLL tt σσh cc (j) YYYY tt mm = ττ yy mm YYLL tt mm + RReennnnkk tt mm KK tt mm + KKKK tt ξξ jjjj mm jj (k) SSSSSS tt mm = ss mm YYYY tt mm mm (l) KK TTTTTTTT + ( + nn) = KK mm TTTTTTTT ( δδ mm ) mm + IIIIII tt + TTTTTT tt mm + EEEE tt TTTTTTTT tt mm Firms (a) PPPPPPPP jjjj ττ jjjj pp = AAAA jj (αα PPPP ) σσ XXXX PPPPPPPP jjjj σσ XXXX + ( αα PPPP ) σσ XXXX PPPPNNNN jjjj σσ XXXX σσ XXXX (σσ (b) VVVVVV jjjj = AAAA XXXX ) jj XXXXXX jjjj αα pp σσ XXXX PPPP PPPPPPPP jjjj ττ jjjj PPVVVVVV jjjj (σσ (c) IIIIII jjjj = AAAA XXXX ) jj XXXXXX jjjj ( αα pp σσ XXXX PPPP )PPPPPPPP jjjj ττ jjjj PPPPPPPP jjjj (d) PPPPPPPP jjjj = AAAA jj (αα GGGG ) σσ GGGG ξξ jjjj σσ GGGG + αα GGGG σσ GGGG PPPPPP jjjj σσ GGGG σσ GGGG (σσ (e) VVVV jjjj = AAAA GGGG ) jj VVVVVV jjjj ( αα σσ GGGG )PPPPPPPP GGGG jjjj PPPPPP jjjj 45

(σσ (f) KKKK tt = AAAA GGGG ) jj VVVVVV jjjj αα σσ GGGG PPPPPPPP GGGG jjjj ξξ jjjj ρρ (g) WW tt = PPPPPP jjjj αα VVVV AAAA VVVVVV VVVV jj jjjj σσ VVVVVV LLLL jjjj (h) PPPPPPPP jjjj = ii PPPP iiii aa iiii (i) VV iiiiii = aa iiii IIIIII jjjj (j) qq jjjj = ββ KKKKKK IIIIII jjjj KK jjjj + PPPP tt (k) qq jjjj + δδ jj = qq jjjj ( + rr ) PPPPPP jjjj + RRRR jjjj + (l) KK jjjj + ( + nn) = KK jjjj δδ jj + IIIIII jjjj PPPP tt+ ββ KKVVVV IIIIII jjjj + KK jjjj + (m) VVVV jjjj = AAAA jj αα VVVV KK jjjj σσ VVVVVV + αα VVVV LLLL jjjj σσ VVVVVV σσ VVVVVV σσ VVVVVV (n) RRRR jjjj = VVVV AAAA ρρ VVVVVV jj VVVV jjjj KK jjjj σσ VVVVVV (o) VVFF jjjj = qq jjjj KK jjjj + (p) PPPPPP jjjj mm = mm (αα mm AAAA VVVV ) σσ mm VVVVVV jj (q) RReeeeeeee mm tt = PPPPPP mm jjjj (αα mm VVVV )(AAAA mm jj ) ρρ mm VVVVVV mm (RRRRRRRRRRtt ) ( σσ mm VVVVVV ) + mm ααvvvv σσ mm VVVVVV mm VVVV jjjj σσ mm VVVVVV mm KK jjjj mm ( σσ WWtt VVVVVV ) σσ mm VVVVVV Relations with the Rest of the World (3a) PPXXXXXX jjjj = AAAA jj δδ XXXX σσ XXXX PPPPPP jjjj + σσ XXXX + δδ XXXX σσ XXXX PPPP jjjj + σσ XXXX + σσ XXXX (3b) EEEE jjjj = + σσ XXXX AAAA jj (3c) XXXXXX jjjj = + σσ XXXX AAAA jj XXXXXX jjjj XXXXXX jjjj σσ PPPPPP XXXX jjjj δδ XXXX PPPPPPPP jjjj σσ PPPP XXXX jjjj ( δδ XXXX )PPPPPPPP jjjj (3d) PPPP jjjj = AAAA jj δδ MMMM σσ MMMM PPPP jjjj σσ MMMM + δδ MMMM σσ MMMM PPPP jjjj σσ MMMM σσ MMMM 46

(3e) MM jjjj = σσ MMMM AAAA jj (3f) XXXXXX jjjj = σσ MMMM AAAA jj XXXX jjjj δδ σσ MMMM PPPP MMMM jjjj PPPP jjjj XXXX jjjj δδ σσ MMMM PPPP MM jj jjjj PPPP jjjj (3g) FFFFFFFF tt = PPPPPP jjjj MM jjjj PPPPPPPP jjjj EEEE jjjj TTTTTTTT tt TTTTTTTT mm jj jj tt TTTTTTTTTT tt (3h) BBBB tt+ ( + nn) = ( + rr )BBBB tt + EEEE tt FFFFFFFF tt Government (4a)YYYY tt = ττ jj pp jj PPPPPPPP jjjj XXXXXX jjjj + ττ ii CC PPPP iiii cc iiii + ττ ii IIIIII PPPPPPPPPP iiii DDiiiiii iiii + ττ ii MM PPPPPP iiii MM iiii + ii ττ ii EEEE PPPPPP iiii EEEE iiii ] + ττ yy YYLL tt + ττ yy mm YYLL tt mm + ττ kk DDDDDD jjjj jj (4b) GGGGGGGG tt = YYYY tt + TTTTTTTTTT tt ii PPPP iiii GGGG iiii PPPP tt IIIIIIII tt TTTTTT TTRRRR mm (4c) PPPP tt IIIIIIII tt = γγ GGGG GGGGGGGG tt (4d)GGGGGGGG tt = ii PPPP iiii cc h iiii + PPPPiiiiii iiii DDDDDDDD iiii + PPPP iiii DDDDDDDD iiii + PPPP iiii GGGG iiii + PPPPPPPP iiii EEEE iiii PPPPPP iiii MM iiii (4e) KKKK tt+ ( + nn) = IIIIIIII tt + δδ gg KKKK tt (4f) KKKK tt = θθkkkk tt Other Demand Components (5a) XXXX iiii = cc mm iiii + cc iiii + GGGG iiii + DDDDDDDD iiii + DDDDDDDD iiii + jj VV iiiiii (5b) TTTT tt = ii JJ iiii + IIIIII mm tt + IIIIIIII tt (5c) DDDDDDDD iiii = ββ KKKK TTTT tt mm (5d) IIIIII tt = SSSSSS tt mm PPPP tt (5e) JJ jjtt = IIIIII jjtt + ββ KKKKKK Prices IIIIII jjjj KK jjjj (6a) PPPP iiii = EEEE tt PPPPPP iiii ( + ττ ii MM ) (6b) PPPPPP iiii ( + ττ ii EEEE ) = EEEE tt PPPPPPPP iiii (6c) PPPPPPPPPP iiii = PPPP iiii ( + ττ ii iiiiii ) (6d) PPPP tt TTTT tt = ii PPPP iiii ( + ττ ii iiiiii )DDDDDDDD iiii 47

Market Clearing (7a) XXXXXX iiii = XXXXXX iiii (7b) jj LLLL jjjj = LLLL tt (7c) FF tt = VVFF jjtt jj BBBB tt mm (7e) KK mm mm jj jjjj = KK TTTTTTTT Steady State (8a) qq jjtt δδ jj + rr = PPPPPP jjjj RRRR jjjj + PPPP tt ββ KKKKKK (8b)FF tt (nn rr ) = IIIIII jjjj KK jjjj ττ yy YYLLtt + TTTTTT + EEEE tt TTTTTTTT tt + KKKK tt jj ξξ jjtt ii PPPP iiii DDDDDDDD iiii (8c) VV jjjj = jj qqjjjj KK jjjj (8d) BBBB tt (nn rr ) = FFFFFFFF tt + GGGGGGGG tt ττ kk DDDDDD jjjj jj PPPP tt CC tt 48

Definitions of variables XXXXXX jjjj : Gross output of industry j VVVV jjjj : Value added of industry j VVVVVV jjjj : Index of value added and public capital in industry j XXXXXX jjjj : Domestic supply KKKK tt : Eective stock of public capital KKKK tt : Raw stock of public capital KKGG tt : Eective stock of public capital KK mm jjjj : Private capital stock of myopic firms KK jjjj : Private stock of forward-looking firms LLLL jjjj : Labor demand cc iiii h : Household consumption demand of good i, (h = f, m) XXXX iiii : Total demand of commodity i LLLL tt : Total household labor supply MM iiii : Total imports EEEE iiii : Total exports VV iiiiii : Demand for individual intermediate input i by industry j DDiinnvv iiii : Demand for investment by sector of origin DDDDDDDD iiii : Inventory change (volume) for commodity i IIIIIIII tt : Government investment in public capital IIIIII jjjj : Investment by destination sector j IIIIII jjjj : Index of intermediate inputs XXXXXX iitt : Domestic demand of commodity i GGGGGGGG tt : Government savings GGGG iiii : Government consumption of commodity i TTTTTTTT tt : Government transfers to forward-looking households TTTTTTTT tt mm : Government transfers to myopic households TTTTTTTT tt : Rest of the world s transfers to forward-looking households TTTTTTTT tt mm : Rest of the world s transfers to myopic households TTTTTTTTTT: Rest of the world s transfers to government BBBB tt : Foreign debt FF tt : Total financial wealth of forward-looking households FFFFFFFF tt : Current account deficit VVFF jjjj : Value of the forward-looking firm DDDDDD jjjj : Forward-looking firms dividends RRRR jjjj : Physical marginal productivity of forward-looking firm s private capital stock RReennttkk tt mm : rental rate of capital for myopic firms WW tt : Wage rate qq jjjj : Shadow price of capital PPPPPPPP jjjj : Price of gross output PPPPPPPP jjjj : Price of the index value added and public capital 49

PPPP tt h : Index price of consumption goods of each type of household (h = f, m) PPPP iiii : Consumption price of individual commodity i PPPPPPPPPP iiii : Price of investment good by sector of origin PPPPPPPP jjjj : Index price of intermediate inputs PPPP iitt : Price of domestic good PPPP tt : Composite price of investment good ξξ jjjj : Implicit return rate to public capital in industry j PPPP iiii : Price of import good i PPPPPP iiii : Price of export good i PPPPPP iiii : World price of import good i PPPPPPPP iiii : World price of export good i EEEE tt : Nominal exchange rate (conversion factor between currencies) 5

Definitions of parameters AAAA jj : Shift parameter in the first level of nested CES production functions AAAA jj : Shift parameter in the second level of nested CES production functions AAAA jj : Shift parameter in the third level of nested CES production functions AAAA jj : Shift parameter in the first level of CET function AAAA jj : Shift parameter in the first level of Armington CES function σσ XXXX : Elasticity of substitution in the first level of nested CES production functions σσ GGGG : Elasticity of substitution in the second level of nested CES production functions σσ VVVVVV : Elasticity of substitution in the third level of nested CES production functions σσ MMMM : Elasticity of substitution in the first level of Armington CES function σσ XXXX : Elasticity of substitution in the first level of CET function σσ h cc : Elasticity of substitution in the CES demand function of each type of household, (h = f, m) αα PPPP : Share parameter in the first level of nested CES production functions αα GGGG : Share parameter in the second level of nested CES production functions αα VVVV : Share parameter in the third level of nested CES production functions αα h CCii: Share parameter in the CES utility function of each type of household, (h = f, m) δδ XXXX : Share parameter in the first level of nested CET functions δδ MMMM : Share parameter in the first level of Armington CES function ττ yy : Labor income tax rate on forward-looking households ττ yy mm : Labor income tax rate on myopic households ττ ii CC : Consumption tax rate ττ ii MM : Import tari rate ττ ii EEEE : Export tax rate ττ kk : Tax rate on dividends ττ jj pp : Production tax rate ττ ii IIIIII : Tax on investment goods ss mm : Myopic household s saving rate n: Population growth rate including technological progress rr : World interest rate ρρ : Rate of time preference δδ gg : Public capital stock depreciation rate δδ jj : Depreciation rate of private capital stock of forward-looking firms δδ mm : Depreciation rate of private capital stock of myopic firms ββ KKKK : Share parameter in the demand for investment by sector of origin : Parameter in the adjustment cost function ββ KKKKKK 5