Trade Policy, Poverty, and Development in a Dynamic General Equilibrium Model for Zambia

Trade Policy, Poverty, and Development in a Dynamic General Equilibrium Model for Zambia Edward F. Buffie and Manoj Atolia January 2008

1. Introduction Many LDCs suffer from low levels of private investment, from acute shortages of social and physical infrastructure, and from widespread poverty and underemployment. How can trade policy help combat these problems? Neoclassical trade theory objects that the premise of the question is incorrect. According to the Principle of Targeting, it is better to use other policy instruments to counteract market imperfections and to target social objectives. Instead of interfering with free trade, the government should increase domestic taxes to pay for employment subsidies, investment subsidies, transfers to the poor, and additional public investment in infrastructure. Policy makers reject this advice as impractical. Large-scale direct transfers to the poor and extensive employment and investment subsidies can be implemented with the stroke of a pen in a textbook. The real world is not so accommodating. Good information and skilled administrators are needed to prevent transfer/subsidy schemes from being undermined by fraud. Both are in scarce supply in low-income LDCs. Presumably fraud is less of a problem for public spending on infrastructure. It is naïve, however, to think that domestic taxes alone can pay for all the socially desirable infrastructure projects: tax handles are too few, tax bases are too small, and infrastructure needs are too great. Until development is far along, easy-to-collect trade taxes have a place in the government’s optimal tax program. The upshot of these considerations is that passive trade policy is a luxury LDCs cannot afford. Unfortunately, recognition of this reality has been slow to take hold in the research community. The perception that free trade is first-best has acted as a formidable barrier to the construction of analytical frameworks that shed light on the channels through which different structures of protection and export promotion affect economic development. Serious, meaningful debate about

1 Electronic copy available at: http://ssrn.com/abstract=1285133

the merits of activist trade policy ended a while back; exhortations to liberalize as much and as fast as possible have taken its place. Our objective in this paper is to restart the policy dialogue. In what follows, we build a dynamic general equilibrium trade model that is rich in structural detail and policy instruments but not a black box. The model features a full array of imports (intermediates, consumer goods, and capital goods), heterogeneous agents, sector-specific capital, two types of infrastructure, learning externalities, and a dualistic labor market. It is also firmly grounded in optimizing behavior. Private agents possess perfect foresight and solve distinct optimal control problems. The general equilibrium dynamics for the economy emerge from the intersection of marketclearing conditions with the government budget constraint and the solutions to private agents’ optimization problems. We use the model to investigate how trade policy affects poverty, underemployment, aggregate capital accumulation, and real output in Zambia. Throughout the analysis focuses on basic issues, e.g.: Does poverty reduction conflict with broader development objectives? Is the ranking of policies sensitive to the impact on government revenue and investment in infrastructure? Are there important intertemporal tradeoffs on the transition path to the new long-run equilibrium? Previewing the bottom line, the results consistently recommend policy packages that combine an escalated structure of protection with an escalated structure of export promotion.

There is no support for the view that free trade or a low uniform tariff is

approximately optimal. The rest of the paper is organized into seven sections. In Sections 2-4 we discuss the model and how it was calibrated to the data for Zambia. Section 5 prepares the ground for the numerical simulations, explaining how trade policy interacts with the imperfections in factor markets that distort the free trade equilibrium. Following this, Section 6 examines the effects of different combinations of trade taxes in the standard trade theoretic scenario where lump-sum taxes/transfers adjust to balance the fiscal budget. Section 7 changes the scenario by letting tariff revenue underwrite more public investment in either roads or power.

The final section

summarizes the main findings and argues that future research should concentrate on developing a typology for trade policy.

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2. The Model Table 1 collects the equations of the model and defines notation. Since our objective is to develop a tool for policy analysis, a certain amount of detail and complexity is unavoidable. Below we discuss the components of the model seriatim. 2.1 Sectoral Structure and Technology There are five sectors: primary agriculture, food processing, other manufacturing, services, and mining. Services are nontraded and mining is treated as an exogenous source of dollars. Power and roads are infrastructural inputs supplied by the state. Private inputs consist of capital, skilled labor, unskilled labor, land and imported intermediates. Skilled labor is used in services, food processing, and manufacturing (short for other manufacturing), but not in primary agriculture (where its cost share is extremely small). The input-output coefficient for raw materials in the food-processing sector is fixed at c. Elsewhere in the production functions, each grouping of inputs is modeled as a CES function. In equation (1c), for example, the labor input L is a CES function of skilled and unskilled labor; at the next level up, labor, capital, and imported intermediates combine in another CES function, etc. Roads and learning externalities affect production like Hicks-neutral technical progress. Learning depends on capital accumulation (Arrow, 1962), which serves as a vehicle for the introduction of new technology. Spillovers from learning are confined to firms in the industry. The road network, however, is a pure public good that enhances productivity in all sectors. 2.2 Prices and Trade Taxes The economy exports lots of mineral products and some cash crops. Imports comprise machinery and equipment, intermediate inputs, and a mix of agricultural and manufactured consumer goods (processed food and other manufactures). World prices are fixed at unity, so domestic import and export prices depend only on trade taxes. The mineral export is the numeraire. Private capital, roads, and power plants are assembled by combining structures with imported machinery in fixed proportions. Structures are built by construction firms using labor and imported intermediates. We choose units so that one imported machine is required to produce

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one capital good. When the model is calibrated, the higher cost share of construction in building roads vs. power plants is reflected in higher input-output coefficients for labor and intermediates. 2.3 Sectoral Factor Demands Equations (4a)-(7e) employ cost functions to specify factor demands in primary agriculture and the food processing, services, and manufacturing sectors. We assume that firms view input prices as parametric, that technology exhibits constant returns to scale,1 and that private capital stocks are sector-specific. Since firm owners choose the path of the capital stock, equations (4a), (5a), (6a), and (7a) are not genuine factor demand equations. Rather they help to pin down the capital rental at each point in time. (This information is needed to solve the firm's intertemporal optimization problem. See the next section). It should also be noted that rjs is the shadow rental of power in sector s, not the rental firms pay for power; in Zambia and many other LDCs, user fees are far below the scarcity rent. Factor demands in the construction sector take a different form because input-output coefficients are fixed and the scale variable is investment instead of output. The terms v(Ig/Kg – δ)2Kg/2, g = a,x,i,n, capture adjustment costs incurred in changing the capital stock. 2.4 Wages and the Dualistic Labor Market Labor is mobile across sectors. In the case of skilled labor, this ensures that all firms pay the same wage ws. The unskilled labor market, by contrast, is dualistic. In construction, services, and primary agriculture, the wage w is determined by market forces. Food processing and manufacturing belong to the formal sector, where unions and/or minimum wage laws compel firms to pay the higher wage w(1+b), b > 0. 2.5 Capital Accumulation and Intertemporal Optimization The canonical representative agent model assumes that wide, deep financial markets pool savings of different agents. This is scarcely credible for LDCs. Accordingly, we treat capitalists in the four sectors as separate agents who solve distinct optimization problems. In each optimization problem, the capitalist (capitalist-landowner in the case of primary agriculture) chooses consumption and investment to maximize a time-separable utility function. Purchases of individual consumer goods are subsumed in the indirect utility function V(•) and the restricted

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profit function π(•). The budget constraints say that total spending on consumption and investment cannot exceed profits net of taxes and user fees paid for power. Capital accumulation is subject to increasing, strictly convex adjustment costs. Equation (12) simply relates growth of the capital stock to net investment. 2.6 Preferences and Demand Functions Preferences for all agents are described by the same two-tiered CES utility function. At the lower tier, aggregate food consumption is a CES aggregate of processed and unprocessed food. At the upper tier, food, manufactures, and services combine in another CES function. The demand functions in equations (13a)-(13d) are retrieved via Roy's Identity [Dg = (∂V/∂Pg)/∂V/∂E]. Workers do not save. Hence total expenditure equals expenditure of capitalists plus total wage income plus transfers to workers (Tw). 2.7 Public Sector Investment and the Government Budget Constraint The government collects revenue from tariffs, from user fees charged for electricity, from aid donors, and from the sale of mineral products. It invests in roads and power plants. Lump-sum taxes/transfers balance the budget at the initial equilibrium. Nine policy instruments appear in equation (14). Eight of these can be chosen independently. The remaining instrument adjusts endogenously to satisfy the budget constraint. The instrument that adjusts depends on the policy experiment under investigation. In the pure trade policy scenarios, infrastructure stocks are constant and the lump-sum tax absorbs changes in tariff revenue and export subsidies. When trade policy is used both to alter relative prices and to combat infrastructure bottlenecks, the lump-sum tax is held constant and increases in net tariff revenue finance higher investment in roads or power. 2.8 Zero-Profit and Market-Clearing Conditions Finally, the model is closed with the zero-profit conditions in the four sectors and the conditions that demand equal supply in the markets for services, skilled labor, and unskilled labor.

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Equation (21) is the national income accounting identity that the current account inclusive of aid equals zero. This is not an independent equation in the model. It is derived by aggregating the budget constraints of the private agents and the government.

3. Remarks on the Specification of the Model The current formulation of the model imposes many restrictions: tariffs on intermediate inputs, tariffs on capital goods, the supply price of capital, and elasticities of substitution in production are the same in all sectors; private agents have identical preferences qua consumers; roads are a pure public good used by all producers, etc. It is easy to relax these and other restrictions by adding subscripts to variables already in the model. We have not done so because we do not want to get lost in too much detail and taxonomy. Our goal at this point is to acquire a general sense of the tradeoffs associated with different trade strategies, not to cross all the t’s and dot all the i’s. It is also fairly easy to extend or modify the structure of the model to meet the demands of other scenarios. This is particularly relevant to policies aimed at agriculture. Since technology is modeled flexibly with cost functions, we could highlight the importance of fertilizer by pulling it out of the input list and creating a separate CES nest for non-fertilizer inputs and a composite input produced by fertilizer and a public delivery system. To give another example, it would not be difficult to develop a plug-in module for countries where conditions are conducive to adoption of the Green Revolution technology. The power stock in the current model could readily be converted into a Green Revolution input that nests a fertilizer-seeds-pesticides input with power and irrigation; learning externalities in agriculture would then be a function of availability/utilization of the composite Green Revolution input and, perhaps, extension services. Several other extensions of the model are desirable. The most important, we believe, is the addition of a second agricultural sector.

In Zambia, smallholders cultivate staples while

medium-sized and large commercial farms produce 35% of the country’s maize and all of its nontraditional exports (cotton, sugar, coffee, horticulture and floriculture). The present model mixes

the

import-competing/smallholder/staples

sector

with

the

commercial/large

farm/nontraditional exports sector. Consequently, we cannot distinguish between protectionist and export-promoting policies in agriculture: a positive ta is a tariff on imported foodstuffs plus an equal rate subsidy for nontraditional exports. More generally, because of the aggregation 6

built into the one-sector setup, we cannot trace distributional effects very far within agriculture or analyze policies that specifically target smallholders. We will return to these points in Section 8 when we discuss the need for models of different prototype economies.

4. Calibration of the Model Calibration of the model requires data on cost shares, elasticities of substitution, consumption shares, wage differentials, depreciation rates, sector shares in GDP, and marginal rates of return on infrastructure at the benchmark equilibrium. Once values are set for these parameters, all other variables that enter the model can be tied down by budget constraints, the first-order conditions associated with the solution to the private agents' optimization problems, and various adding-up constraints. The values in Table 2 are based on a mixture of data and guesstimates. We discuss below the rationale for the value assigned to each parameter and the problems that arose in calibrating certain parts of the model: •

Sector shares in GDP. The sector shares in GDP are taken from IFPRI's 2001 Social Accounting Matrix (SAM). In a model that ignores public services and the financial sector, the 2001 numbers translate into output shares of 29.2% for agriculture, 7% for food processing, 7% for other manufacturing, 42.2% for services, 11.5% for mining, and 3.1% for construction. (The numbers for 2006 are similar.)

•

Aid. Aid and concessional loans financed current account deficits of 15-20% of GDP in the period 2000-2004. What is needed for the model is the real resource transfer financed by aid. We approximate this by the trade balance deficit. The figure for 2001 works out to 11.5% of GDP.

•

Consumption shares. The weights for food, manufactures, and services in the current CPI are .571, .193, and .236. Retail prices, however, incorporate substantial trade and transport costs. Since the model ignores inter-industry transactions, the joint-product nature of consumption has to be taken into account by lowering the weights for food and manufactures and increasing the weight for services. The adjusted weights are consistent with the share of marketed food production, the guesstimate of marketing margins in Thurlow et al. (2004), and the data on net imports of primary agricultural goods and processed food.

•

Factor (value added) shares in agriculture. It is no secret that there are problems with the data for labor, land and capital costs in the agricultural sector. Given the limitations of the data, our preference is to consult a variety of sources and hope that a rough consensus emerges about the likely values for factor shares. This hope is partly satisfied in Table 3. 7

The shares reported in Lofgren et al. (2004) are dubious because a substantial fraction of income from land and part of capital income are counted as labor income.2 Nevertheless, it is clear that Zambian agriculture is extremely labor intensive. We decided therefore to set the share for labor slightly higher and the shares for land and capital slightly lower than the values recommended for Sub-Saharan Africa by GTAP. The share for power is a guess. We do not have data on electricity sales to agriculture. •

Factor (value added) shares in manufacturing, food processing, and services. The data source for factor shares in these sectors is IFPRI's 2001 SAM.3 Workers who did not complete primary school are classified as unskilled. Again, the shares for power are educated guesses. Their high values reflect the fact that the shares in the model are computed at a high shadow rental. Since power subsidies inflate the measured income share of capital, the shares for capital in Table 2 are lower than in the 2001 SAM.4

•

Elasticities of substitution between non-power inputs. Estimates of the elasticity of substitution between capital and labor generally lie between .5 and 1. For LDCs, not much is known about substitution elasticities involving other inputs or about the degree of substitutability between skilled and unskilled labor. Absent such information, we set all substitution elasticities in the lower tiers of the production functions at .75.

•

Elasticity of substitution between power and other inputs. There are no estimates of this parameter in the existing literature, but it is hard to believe it could be larger than the elasticity of substitution between non-power inputs. In keeping with this view, we experiment with values of .50 and .25 for the elasticity of substitution between power and non-power inputs.

•

Time preference rate and the depreciation rate. Across steady states, the return on private capital equals ρ + δ in all sectors. We set δ at .05 and assume private capital earns a net return of 10%. (The social return is higher when the learning externality operates.)

•

Elasticities of substitution in consumption. We fix β1 at .50 as estimates of compensated elasticities of demand tend to be small at high levels of aggregation,5 especially when food claims a large share of total consumption. A higher value of .75 is assigned to β2 on the assumption that it is easier to substitute between processed and unprocessed food than between food and other goods.

•

Intertemporal elasticity of substitution. The assigned value of .40 equals the point estimate for Zambia in Ogaki, Ostry and Reinhart (1996). It is also close to the estimate for Africa (.45) in Ostry and Reinhart (1992).

•

Cost shares of labor and imported intermediate inputs in the production of capital goods. The values for αk1-αk3 [which map into the input-output coefficients ak1-ak3 in equation (3a) in the model] are computed from data in IFPRI's SAM on cost shares in construction and domestic capital goods industries and from national income accounts data on the ratio of imported machinery to gross fixed capital formation. The values for αz1-αz3 and

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αj1-αj3 assume that roads are built entirely by the construction sector and that power plants are highly import-intensive. •

q-elasticity of investment spending. Evaluated at a steady state, the elasticity of investment with respect to Tobin's q (the ratio of the demand or shadow price of capital to the supply price of capital) is Ω =1/δv, where δ is the depreciation rate and v is the parameter that determines adjustment costs to changing the capital stock.6 There are no reliable estimates of this elasticity for LDCs. The assigned value of ten yields plausible dynamics.7

•

Initial rates of return on power and roads. The initial returns on power and roads are 30%. These are high numbers, but power is very scarce in all sectors and the road network has yet to recover from neglect suffered during the macro-stabilization programs of the nineties. More generally, there is plenty of evidence that the return on infrastructure is high in LDCs. Estimated rates of return on power projects in India are well above 30% (e.g., World Bank, 1997). Studies of agricultural productivity also find that the return on investment in road infrastructure is extremely high and less prone to diminishing returns than other types of public investment (Fann, Thorat and Rao, 2003).

•

Wages. The ratio of the skilled wage to the unskilled wage is computed from data in Thurlow et al. (2004) on the percentage of the labor force with different amounts of education and their shares in total household. We do not have any hard data on how much the blue-collar wage in the food-processing and manufacturing sectors exceeds the wage for identical labor in primary agriculture and service industries. The value of b (.75) is around the middle of estimates of the formal sector wage premium in LDCs.

•

Initial trade taxes. There is abundant, detailed information on trade taxes in the WTO's 2002 Trade Policy Review for Zambia. In 2001, tariffs ranged from 18% to 25% on food, beverages and tobacco; from 15% to 25% on textiles, clothing, and other manufactured consumer goods; and from 7-18% on capital goods (although agricultural machinery enters duty-free). Duties clustered at 5% for raw materials and at 15% for intermediate inputs. In primary agriculture, the simple average of tariff lines was 18.7%, but the duty on cereals --- including maize --- was only 5%. Aiming for an approximation of this tariff structure, we set the initial tariffs at 10% for agriculture, intermediate inputs, and capital goods, and at 20% for food processing and manufacturing. The current tariff structure is similar (Mwanawina, 2006).

•

Learning externalities. There are no learning externalities in the base run. In the runs that allow for learning effects, the parameter ξ is set so that the social return to capital is twice the private return at the initial equilibrium.

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5. How Things Work in the Model Before presenting the numerical results, we take some time to explain in broad intuitive terms how things work in the model. Section 5.1 expands on the underlying sources of market failure in the economy, while Section 5.2 develops the logical of attacking the distortions with escalated structures of protection and export promotion. 5.1 Factor Market Distortions at the Free Trade Equilibrium The private capital stock, employment of skilled labor in manufacturing, and the stock of infrastructure are all below their socially optimal levels at the free trade equilibrium. This is shown in Figures 1-3. For illustrative purposes, we combine food processing and other manufacturing into a single manufacturing sector (indexed by i), ignore the services and construction sectors, and limit infrastructure to roads (Z). Efficient allocation of labor requires that workers’ marginal value product, measured at world prices, be the same in all activities. This occurs at point B in Figure 1, with employment La1 = Oa-N in agriculture and Li1 = Oi-N in manufacturing. Because manufacturing pays a much higher wage than agriculture, employment levels at free trade are Oa-V and Oi-V. The loss in real output from underemployment in manufacturing equals area JRB. Consider next the relationship between the private and the socially optimal capital stock. In both agriculture and manufacturing, firm owners accumulate capital up to the point where its marginal product (MPK) equals the time preference rate multiplied by the real supply price of capital ( Pk = Pk / Ps , s = i, a ). Since all world prices equal unity, MPK s = ρ ,

s = i, a

and the aggregate capital stock is Ko = Kao + Kio under free trade. Multiple distortions affect private investment. First, the social marginal product of capital (SMPK) is greater than the private marginal product of capital when capital accumulation is a source of learning externalities in the industry. Second, if a general concern for the welfare of future generations or a desire to promote national economic development would motivate individuals to save more in a social contract than they would acting on their own, then the social time preference rate ρ* is less than the private time preference rate ρ (Feldstein, 1964; Sen, 10

1967). In the case depicted in Figure 2, both distortions operate: SMPKa > MPKa, SMPKi > MPKi, and ρ* < ρ. A third factor comes into play when trade taxes are employed as a revenue-raising device. In Figure 3 public investment in infrastructure is sub-optimal as the marginal product of roads (MPZ) exceeds the social time preference rate.

Standard trade theoretic analysis treats

government revenue and Z as exogenous. The constrained optimum is thus (K1, Zo). (K = Ka + Ki refers to the aggregate capital stock.) Underinvestment in infrastructure does not interact with underinvestment in private capital. Reaching the full unconstrained optimum requires the government to invest in roads until MPZ = ρ*.

At first glance, this calls for Z to increase to Z1.

But more investment in

infrastructure raises the return on private investment and vice versa: roads and private capital are gross complements (∂MPK/∂Z, ∂MPZ/∂K > 0), so increases in Z shift out the MPK and SMPK schedules in the first quadrant while increases in K shift out the MPZ schedule in the second quadrant. The positive feedback effects increase the socially optimal values of K and Z from K1 and Z1 to K2 and Z2. 5.2 How Trade Policy Affects Factor Market Distortions and Economic Welfare Trade policy is successful when it moves the economy closer to the social optimum. In the standard trade theoretic analysis where Z is fixed, the constrained optimum is (K1, Zo, Li1). (See Figures 1 and 3.) When investment in infrastructure is allowed, the target is the unconstrained optimum (K2, Z2, Li1).8 The objective of increasing aggregate capital accumulation is best served by an escalated structure of protection and export promotion. Consider Figure 4. When tariffs and export subsidies increase only the firm’s output price, the real prices of imported intermediate inputs and imported machinery decline. The decrease in the real price of imported machinery directly reduces the real supply price of capital. Furthermore, in the normal case where factors are gross complements, the productivity of the capital stock rises as purchases of intermediates increase from Ho to H1. The joint effect of the reduction in Pk and the outward shift of the MPK schedule is to increase the equilibrium capital stock from Ko to K1. When trade policy lowers the real cost of imported intermediates and imported capital goods to all sectors, all labor demand schedules shift out. This makes it difficult to predict how the

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sectoral allocation of labor and high-wage employment will change. But though underemployment might worsen, there is a very strong presumption real wages will increase. Again this reflects the principle of gross complementarity at work. When firms accumulate more capital and buy more intermediates, the marginal product of labor rises. Since MPL = w/Ps in sector s, the economy-wide increase in labor productivity raises the wage relative to firms’ output prices and the overall price level. The preceding remarks pertain to balanced escalated structures of protection and export promotion.

In unbalanced structures the impact on real wages and aggregate capital

accumulation depends on the set of trade taxes that change and factor intensities in more- vs. less-protected sectors. This will be discussed in detail in the next section. Two more points should be mentioned in connection with the welfare arithmetic. First, trade taxes create a variety of byproduct distortions. Thus, when the analysis ignores distributional objectives, the welfare outcome turns on how the gains from reducing underemployment and underinvestment compare with the losses from the byproduct distortions. This ambiguity means that too much intervention can be harmful. It does not preclude clean results, however. A net welfare gain is assured as long as protection + export promotion is not too extreme, for, at the free trade equilibrium, the gains from mitigating the factor market distortions are first-order large while the losses from interfering with free trade are second-order small. The other point concerns the real wage for skilled labor. Strictly speaking, changes in the real skilled wage do not affect the welfare calculations. Informally, we view increases as a positive development. The skilled labor group includes many poor semi-skilled workers. (Recall than anyone with 6+ years of schooling is counted as skilled.) Also, an increase in the real skilled wage promotes economic development by encouraging more investment in human capital. This benefit does not show up in the current model because the supply of skilled labor is exogenous. In a more general model, the supply of skilled labor would be endogenous and the gap between the social and private rates of time preference would imply underinvestment in both physical and human capital.

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6. Pure Trade Policy Experiments In this section we assume that free trade prevails at the initial equilibrium and that lump-sum taxes adjust to satisfy the government budget constraint. These assumptions are common in traditional trade theory. They provide a neutral benchmark for the evaluation of commercial policy. The free trade equilibrium is not observable. To approximate it, we computed the steadystate equilibrium with all trade taxes set equal to zero.9 This affects mainly the pattern of production and the sectoral trade balances. Going from the tariff-ridden equilibrium to free trade, exports of agricultural goods rise from 3.7% to 10.6% of GDP while imports of processed food and other manufactured consumer goods increase from 1.8% to 6% of GDP and from 4.9% to 5.7% of GDP. Table 4 shows what happens in the long run. In the upper panel, trade taxes change one-byone. Four results stand out: 1. Protection of agriculture is highly effective in reducing poverty. Protecting primary agriculture with a 20% export subsidy increases the real wage for unskilled labor by 15%.10 This runs counter to the mainstream view that the impact on poverty is uncertain in sign and probably small in magnitude. Most of the analysis in the literature is of the “on the one hand . . . on the other hand” variety. In fact, the typical discussion (e.g., World Bank, 2005; McCalla and Nash, 2007) requires several hands to enumerate everything on the point-counterpoint list: on the first hand, poverty is overwhelmingly concentrated in agriculture; on the second hand, higher food prices hurt landless laborers and the urban poor and do little to help small farmers, who produce mainly for own consumption; on the third hand, unskilled labor in agriculture might benefit from higher wages; on the fourth hand, labor demand is likely to contract in other sectors, so it is not clear in general equilibrium whether protection of agriculture raises overall demand for unskilled labor in the economy, or, if it does, that wages increase more than the CPI for the poor; etc. The anything-could-happen answer might be correct for some countries, but not for Zambia. Zambian agriculture is extremely intensive in its use of unskilled labor. The value added share for unskilled labor is 40% greater than in food processing and 3-4 times larger than in services and other manufacturing. Consequently, growth of labor demand in agriculture dominates everything else: despite layoffs in manufacturing and services, the wage for unskilled labor increases 22% ─ three times as much as the increase in the exact consumer price index. Although protection of agriculture helps in the battle against poverty, it is bad for economic development. Real GDP, aggregate consumption, and the aggregate capital stock do not change much, but the share of unskilled workers with high-wage jobs falls from 4.8% to 2.4% and the decrease in the real wage for skilled labor weakens the

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incentive to accumulate human capital. Strong learning externalities in agriculture improve the chances of pro-development effects. But even when the marginal social return to capital is twice the private return, the results are mixed. The gains in real GDP and aggregate consumption are respectable, but the decrease in the skilled wage is about the same and the loss of high-wage manufacturing jobs is greater. 2. Protection of the import-competing manufacturing sector promotes economic development but worsens the distribution of income and exacerbates poverty. 20% tariffs on processed food and manufactured consumer goods (ti = tx = .20 in row 6) drive up the price of nontraded services by 9.3%. Joint expansion of the services and manufacturing sectors then increases the aggregate capital stock by 10% and the real wage for skilled labor by 20%. The demand for unskilled labor also increases, but not enough to prevent a decline in the real wage. There is some recompense, however, in the form of more good jobs in manufacturing. The share of high-wage jobs for unskilled workers more than doubles, rising from 4.8% to 10.1%. Since the formal sector pays 75% more than the informal sector, total real wage income decreases only 2.7%. 3. Protection of the food processing sector creates far more high-wage jobs than protection of other manufacturing sectors. The manufacturing sector is split between food processing industries and other manufacturing. Protecting only the food processing subsector causes the rest of manufacturing to contract. Conversely, food processing contracts when protection is confined to other manufacturing. The two policies have similar qualitative and quantitative effects, with one notable exception: protection of the food processing sector creates 6-9 times as many high-wage jobs as protection of other manufacturing.11 The marked asymmetry stems from two factors. First, food processing is much more unskilled labor intensive than other branches of manufacturing. Second, food processing falls into the category of light manufacturing. In this part of the manufacturing sector the shortage of power does not constrain supply responses as much as in heavier industries. 4. Ceteris paribus, escalated structures of protection are preferable to flat or de-escalated structures of protection. It is not a good idea to increase the relative prices of imported intermediates and capital goods. The ugly procession of negative signs in the rows for th = .20 and tm = .20 indicate that factor market distortions worsen and all groups lose. Of course the government may need to tax non-consumer imports to pay for export subsidies or investment in infrastructure. This scenario will be analyzed in Section 7. It is already clear, however, that tariffs should be higher on intermediates than on capital goods.

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6.1 Policy Packages Protecting either agriculture or manufacturing forces policy makers to decide whether it is more important to fight poverty or to promote economic development. But why choose? It is obvious from the results in the upper panel of Table 4 that policy makers can get everything they want ─ less poverty and more economic development ─ by combining an escalated structure of export promotion for agriculture with an escalated structure of protection for manufacturing. The choice set includes policy packages. Inward- vs. outward-oriented trade policy is a false dichotomy. Policy packages offer a better, wider menu of choices, but they do not eliminate tradeoffs. If poverty reduction is the paramount objective, then there is a strong case for mixing export promotion in agriculture with protection of the food processing branch of manufacturing. This policy package reconciles large increases in the real wage for unskilled labor with modest increases in real GDP and aggregate consumption (see the run for tx = tg = ta = .30). On the other hand, if poverty reduction and economic development are equally important objectives, it is more attractive to protect all manufacturing. Compare the run ta = tx = tg = .30 with the run for ta = tx = tg = ti = .30. When the 30% tariff covers all manufacturing, the increases in the aggregate capital stock, real GDP, and aggregate consumption are twice as large and the 12% rise in the real skilled wage encourages investment in human capital. The price paid for these gains is that the real wage for unskilled labor increases 10% instead of 16%. The poor get roughly the same deal as everyone else.12

7. Linking Trade Taxes to Investment in Infrastructure Policy packages that combine export promotion in agriculture with protection of domestic manufacturing and duty-free access to imported intermediates and capital goods get relative prices right. They encourage investment in physical and human capital while strengthening the demand for unskilled labor. Their main limitation is that tariff revenues do not cover the cost of export subsidies. At the free trade equilibrium, agricultural exports are slightly less than imports of processed food and other manufactured consumer goods. But after the policy package is put in place and domestic supply expands, agricultural exports exceed consumer imports, leaving the government with a net revenue loss. The runs in the lower panel of Table 4 assume that the

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revenue loss is offset by cuts in lump-sum transfers. This is not particularly realistic. Abundant casual evidence suggests that most of the burden of adjustment will fall on investment in infrastructure. In the case where ta = tx = tg = ti = .30 and expenditure on road maintenance bears all of the burden, we end up with the depressing results in the first row of Table 5. The real wage gains for skilled and unskilled workers decrease from something impressive to pocket change; private capital accumulation holds up, but the road network deteriorates so much that both real GDP and aggregate consumption decline in the long run. There is a silver lining in these results. Because mineral exports and aid pay for almost all imports of intermediate inputs and capital goods, net exports of agriculture and the importcompeting manufacturing sector do not have to be very large. The fiscal cost of the export promotion + protection package is quite manageable therefore: in the run with ta = tx = tg = ti = .30, for example, the net revenue loss is only 1.2% of GDP. Furthermore, since imports of intermediates and capital goods total 23% of GDP in Zambia, small tariffs on these items can generate enough revenue to finance both the remaining cost of export subsidies and ambitious increases in infrastructure investment. This configuration, and the favorable fiscal arithmetic that goes with it, is special to Africa. Elsewhere in the Third World, the final goods sectors usually run a large trade surplus to counterbalance large net imports of intermediates and capital goods.

Implementation of the policy packages we tout here then requires substantial

supplementary fiscal adjustment merely to maintain the balance between export promotion and import substitution. And schemes that mix tariffs with export subsidies and investment in infrastructure are not feasible at all unless trade policy has a pronounced protectionist bias. 7.1 Roads In rows 2-7 of Table 5 protection is limited to food processing and other manufacturing. When tariffs apply only to consumer goods (ti = .20 and tx = ti = .20), capitalists and skilled workers reap large gains and unskilled labor loses. The outcome is qualitatively the same as in the pure trade policy experiments. This appears to change in the runs where tg and th increase. Adding 20% tariffs on agricultural raw materials purchased by the food processing sector and on intermediate inputs increases government revenue by a couple of percentage points of GDP. In the run tx = tg = ti = th = .20, the extra revenue purchases a 234% expansion of the road network. The increase in productivity that comes with more roads induces firms to raise the real wage 7%

16

and to increase the number of high-wage manufacturing jobs by 67%. These gains, however, take some time to materialize. Figure 5 shows the transition paths for real wages, the share of high-wage jobs, and total real wage income of unskilled workers. The real unskilled wage decreases 6.6% at t = 0 and then recovers slowly, taking eight years to climb back to its previous level and eighteen years to increase 3%. Inevitably most of the benefits on the transition path and across steady states accrue to the non-poor, especially skilled labor. The runs in the lower panel mix export promotion in agriculture with protection of manufacturing in an effort to secure more of the gains for the poor. Several schemes work well. The policy package ta = tx = tg = ti = .30, th = .20 and tm = .10 strikes a nice balance between poverty reduction and economic development. Across steady states, real GDP rises 14% and real wages for unskilled and skilled workers increase 17% and 21%, respectively. It is hard to improve on this. Moving the agricultural export subsidy away from 30% reduces the real unskilled wage either by decreasing growth in agriculture or by decreasing the stock of roads and labor productivity. A lower tariff on other manufacturing reduces the numbers for growth of GDP and the skilled wage without helping unskilled labor.13 There is something to be said, however, for raising the tariff on processed food. Bumping tx and tg up to 40% increases the real unskilled wage only .3% but adds another percentage point to the share of high-wage jobs and an extra six percentage points to the real skilled wage. To complete the case for balanced protection + export promotion as the best policy package, we need assurance that nothing goes awry on the transition path from the old to the new steady state. This is supplied by Figure 6. The early construction boom, persistent growth of the private capital stock, and rapid expansion of the road network generate continuous economywide increases in the demand for unskilled labor. As a result, the real unskilled wage is 9% higher at t = 10 and 12% higher at t = 20. Real GDP and the skilled wage also rise at a smooth, steady pace. 7.2 Power Table 6 shows the outcome when net tariff revenue is dedicated to additional investment in power.14 While protection + export promotion still delivers the best results, fewer of the gains go to the poor. A broad-based increase in the supply of power helps mainly manufacturing and services. Consequently, the aggregate capital stock, the share of high-wage employment, and the

17

skilled wage generally increase much more and the unskilled wage generally increases much less than in Table 5. Take the run ta = tx = tg = ti = .30, th = .20 and tm = .10. When the policy package targets power instead of roads, the increases in the skilled wage and the aggregate capital stock jump from 21% and 14% to 42% and 25%, but the increase in the unskilled wage drops from 17% to 12%.

8. Concluding Remarks In this paper we have argued that Zambia should jointly protect agriculture and manufacturing.

Our argument is firmly grounded in the principles of optimal tax theory.

Zambia wants the usual things: less poverty, more high-wage jobs, more private investment, and more infrastructure. Trade policy should therefore (i) supply the government with more revenue for infrastructure projects and (ii) encourage greater utilization of imported inputs complementary to labor and private capital. This can be achieved by balancing an escalated structure of protection in manufacturing with an escalated structure of export promotion for agriculture. Each component of this policy package serves a specific purpose. Protection of agriculture is essential to strengthen the demand for unskilled labor and reduce poverty. Protection of manufacturing is needed to increase revenue, to create more high-wage jobs, and to stimulate private capital accumulation. Escalated structures of protection and export promotion increase the demand for labor and raise the return on private investment by lowering the prices of imported intermediates and imported machinery relative to the prices of final goods. Although we did not solve the social planner’s problem, our results suggest that protection and export promotion should be moderate and that tariffs should be higher on intermediates than on capital goods. In the Zambian case, trade policy is both pro-poor and pro-development when a 30% export subsidy + tariff on agricultural products and manufactured consumer goods combines with a 20% tariff on intermediates and a 10% tariff on machinery and equipment. Across steady states, this policy package increases real wage for unskilled labor 17-%, aggregate consumption 10%, and the aggregate capital stock 14%. Unlike in static trade models, there is no need to apologize for small effects. Policy matters. Conventional wisdom holds that outward-oriented economies do better than inward-oriented economies and that LDCs should aim either for free trade or a low uniform tariff. Our results do not contradict the first claim.

Although our recommended policy package includes a 18

protectionist component, it is not generally inward-looking. Imports of consumer goods decline, but exports of agricultural products, imports of intermediates, and imports of machinery and equipment all increase. The economy does not trade less. It trades more and differently as part of a strategy to mitigate poverty, underemployment, and underinvestment by increasing imports of intermediates and capital goods. Clearly we disagree with the other part of the conventional wisdom.

The excesses of

protectionist policies in the pre-1980 period are well documented. But it does not follow from the fact that extreme protection was harmful in the past that free trade or a low uniform tariff is optimal today.

This line is pushed aggressively by the World Bank, the IMF, the U.S.

government, and the great majority of trade economists. It is not based, however, on any rigorous analysis of trade policy in dynamic models that resemble LDC economies. In truth, remarkably little is known about moderate protection and about policy packages that mix moderate protection with export promotion. Our paper and the papers of Conforti and Sarris (2007a, 2007b) fill a small part of this gap. Filling the rest requires a strategy for dealing with the immense structural diversity of LDC economies. The right strategy, in our view, is to build a typology in the space between one size fits all and one size for each. A blueprint for the typology does not yet exist, but it is easy to guess some of its requirements. At a minimum, we need more research on the welfare effects of trade policy in prototype economies differentiated along the following dimensions: •

Share of the import bill financed by aid and mineral exports. In Zambia the net trade position of agriculture + manufactured consumer goods is close to zero because aid and mineral exports pay for almost all imported intermediates and capital goods. This is why a balanced escalated structure of protection + export promotion (BESPEP) that spans agriculture and manufacturing supplies the government with revenue to attack infrastructural bottlenecks. In countries where the flow of dollars from aid and mineral exports is smaller ─ say 10% of GDP ─ BESPEP would be a drain on the fiscal budget and it would be more difficult to devise trade policy packages that are self-financing, pro-development, and pro-poor.

•

Wage-setting rules in the formal sector and intersectoral labor mobility. We abstracted from barriers to labor mobility and concentrated on the dualistic market for unskilled labor. These restrictions should be relaxed in future research. In some countries, dualistic labor markets encompass many types of skilled workers. Geography also matters. Jobs in agro-processing may be nearby and hence more accessible to rural workers than jobs in other branches of manufacturing. This can be captured either by introducing separate market-clearing conditions for labor groups in different regions or 19

by making adjustment costs to changing jobs a function of the sectors of origin and destination. Intuition suggests that the distributional effects of trade policy will be significantly different, and that the case for promotion of agro-processing as an antipoverty tool will be much stronger, than in models where labor is fully mobile across sectors. •

Commercial vs. smallholder agriculture. Our model has only one agricultural sector. Because of this limitation, an export subsidy has to be interpreted as a tariff on staples produced by smallholders paired with an equal rate export subsidy for nontraditional crops produced on large commercial farms. The two sectors should be separated. Besides the direction of trade, factor intensities are very different on large vs. small farms: smallholders practice labor-intensive, hand-hoe agriculture; commercial farms are mechanized, relatively capital-intensive operations. With two agricultural sectors, the model would be more flexible and the policy analysis better and more realistic. It becomes possible inter alia to distinguish between tariffs and export subsidies in agriculture. The analysis of distributional effects and poverty would also improve since the net gains in agriculture could be broken down between small farms, large farms, and landless laborers.

•

Tradable vs. nontradable agriculture. The spread between import and export parity prices for foodstuffs is often large in Sub-Saharan Africa. When the domestic price lands in-between, foodstuffs are nontradable. This changes the nature of sectoral interactions and the transmission mechanism for trade policy.15 We would not be surprised therefore if the ranking of policy packages proved sensitive to whether foodstuffs reside in the tradables or nontradables sector.

20

NOTES 1. There are increasing returns to scale when learning effects operate. 2. The shares in Lofgren et al. (2004) are based on the 1995 Agricultural Comparative Advantage Data Set. In that data set, payments to farm owners are counted as labor income and the “gross margins” portion of profits is allocated to labor and land using a 60/40 split. 3. The cost shares for other manufacturing are a weighted average of the cost shares for textiles + garments and wood + furniture + paper. The shares for food processing equal the shares in food + beverages + tobacco, while the shares for services are a weighted average of the shares for trade + transport and other private services. The cost shares for imported intermediates in all sectors were constructed from data in GTAP. 4. The combined shares of capital and power equal the cost share of private capital in the SAM. Since user fees are only a fraction of depreciation costs, almost all of the scarcity rents on power are counted as capital income in the data. 5. See Lluch et al. (1977, chapter 3), Deaton and Muellbauer (1980, p.71), Blundell (1988, p.35), and Blundell et al. (1993, Table 3b). 6. In each sector, the first-order condition for investment reads [1 + v(I/K – δ)]VEPk = ψ, where ψ is the multiplier associated with the constraint K& = I − δK . Since ψ/VE is the shadow price of K measured in dollars, ψ/VEPk is effectively Tobin’s q, the ratio of the demand price to the supply price of capital. Adopting this notation, we have that at a stationary equilibrium vδIˆ / qˆ = 1. Define Ω ≡ Iˆ / qˆ to be the q-elasticity of investment spending. Then v = 1/δΩ.

7. This is higher than most estimates for developed countries. There are good reasons to believe, however, that existing studies have substantially underestimated the q-elasticity of investment spending (Barnett and Sakellaris, 1998). 8. Changes in K and Z shift out the MPL schedules in Figure 1. It is not clear therefore whether the optimal level of employment in manufacturing is higher or lower than Li1 when K increases to K1 in the constrained optimum or when K and Z increase to K2 and Z2 in the unconstrained optimum. 9. We assume that the stocks of power and roads adjust so that their net returns still equal 30% at the initial equilibrium. 10. The real wage is computed precisely by deflating the wage by the exact consumer price index.

21

11. The cost share of the primary agricultural input is 40% in the food processing sector. Hence tx = .20 increases the effective rate of protection (ERP) in the food processing sector more than ti increases the ERP in other manufacturing. This effect is relatively small. In the run tx = tg = .20 vs. the run ti = .20, the ERP increases less in the food processing sector than in other manufacturing. Nevertheless, protection of food processing still creates six times more high-wage jobs than protection of manufacturing. 12. Real income of landowners increases 9.8%. The figure for capitalists is 16%, but to get all of this capitalists have to reduce consumption in the short and medium run. The figures cited here and for real wages in the text do not incorporate the reduction in real transfer payments to each group. The latter effect is large – real transfers fall 26% (a decrease exceeding 6% of net national product in the run for ti = tx = ta = tg = .30). 13. Raising the tariff on other manufacturing to 40% is also counterproductive. When ti = .40, other manufacturing starts exporting (ti then becomes an equal rate tariff plus export subsidy). Hence the policy package increases net revenue less. This leads to smaller increases in the stock of roads, real GDP, and the real unskilled wage. 14. To facilitate comparison with investment in roads, we set the user fee on sales of power equal to zero. 15. Protection of power is necessarily indirect, accomplished through tariffs and export subsidies that increase the right subset of tradables prices. Furthermore, since protection of agriculture is a byproduct of protection or export promotion of other sectors, the fiscal effects of trade taxes will be quite different.

22

Table 1: The Model Sectoral Structure and Technology Qa = φ a ( Z , K a ) F a [ B a ( K a , La , A), J a ]

(1a)

Q x = Min{G / c, φ x ( Z , K x ) F x {B x ( K x , L( Lsx , Lx ), H x ], J x }}

(1b)

Qi = φ i ( Z , K i ) F i {B i ( K i , L( Lsi , Li ), H i ], J i }

(1c)

Qn = φ n ( Z , K n ) F n {B n ( K n , L( Lsn , Ln ), H n ], J n }

(1d)

Prices and Trade Taxes Pa = 1 + t a

(2a)

Px = 1 + t x

(2b)

Pi = 1 + t i

(2c)

Ph = 1 + t h

(2d)

Pm = 1 + t m

(2e)

Pg = 1 + t g

(2f)

Pk = Pm + a k1 w + a k 2 ws + a k 3 Ph

(3a)

Pz = Pm + a z1 w + a z 2 ws + a z 3 Ph

(3b)

Pj = Pm + a j1 w + a j 2 ws + a j 3 Ph

(3c)

Sectoral Factor Demands K a = C ra (ra , r ja , w, f , Ph )Qa /φ a ( Z , K a )

(4a)

La = C wa (ra , r ja , w, f , Ph )Qa /φ a ( Z , K a )

(4b)

H a = C pa (ra , r ja , w, f , Ph )Qa /φ a ( Z , K a )

(4c)

J a = C rja (ra , r ja , w, f , Ph )Qa /φ a ( Z , K a )

(4d)

23

A = C af (ra , r ja , w, f , Ph )Qa /φ a ( Z , K a )

(4e)

K x = C rx (rx , r jx , wx , ws , Ph )Q x /φ x ( Z , K x )

(5a)

L x = C wx (rx , r jx , w x , ws , Ph )Q x /φ x ( Z , K x )

(5b)

x Lsx = C ws (rx , r jx , w x , ws , Ph )Q x /φ x (Z , K x )

(5c)

H x = C px (rx , r jx , wx , ws , Ph )Q x /φ x (Z , K x )

(5d)

J x = C rjx (rx , r jx , w x , ws , Ph )Q x /φ x (Z , K x )

(5e)

G = cQx

(5f)

K i = C ri (ri , r ji , wi , ws , Ph )Qi /φ i (Z , K i )

(6a)

Li = C wi (ri , r ji , wi , ws , Ph )Qi /φ i ( Z , K i )

(6b)

i Lsi = C ws (ri , r ji , wi , ws , Ph )Qi /φ i ( Z , K i )

(6c)

H i = C ip (ri , r ji , wi , ws , Ph )Qi /φ i (Z , K i )

(6d)

J i = C rji (ri , r ji , wi , ws , Ph )Qi /φ i ( Z , K i )

(6e)

K n = C rn (rn , r jn , w, ws , Ph )Qn /φ n ( Z , K n )

(7a)

Ln = C wn (rn , r jn , w, ws , Ph )Qn /φ n ( Z , K n )

(7b)

n Lsn = C ws (rn , r jn , w, ws , Ph )Qn /φ n ( Z , K n )

(7c)

H n = C np (rn , r jn , w, ws , Ph )Qn /φ n (Z , K n )

(7d)

J n = C rjn (rn , r jn , w, ws , Ph )Qn /φ n (Z , K n )

(7e)

Lc = a k1 I p + a z1 I z + a j1 I j

(8a)

Lcs = a k 2 I p + a z 2 I z + a j 2 I j

(8b)

where

(I a / K a − δ )2 K a (I x / K x − δ ) 2 K x (I i / K i − δ ) 2 K i (I n / K n − δ ) 2 K n I p = Ia + v + Ix + v + Ii + v + In + v . 2 2 2 2

24

Wages and the Dualistic Labor Market w x = wi = w(1 + b)

(9)

Capital Accumulation and Intertemporal Optimization In sector g, the representative capitalist solves the problem Max

∫

∞

{Eg ,I g } 0

V g ( E g , Pa , Pi , Px , Pn )e − ρt dt ,

(10)

subject to g

⎡ (I g / K g − δ ) 2 K g ⎤ E g = π [•] − Pk ⎢ I g + v ⎥ − uδPj J g − Tg , 2 ⎣⎢ ⎦⎥

(11)

K& g = I g − δK g .

(12)

The restricted profit functions associated with the four optimization problems are

π a [w, Ph , Paφ a (Z , K a ), K a , A, J a ], π x [ w x , ws , Ph , ( Px − vPg )φ x (Z , K x ), K x , J x ], π i [ wi , ws , Ph , Pi φ i ( Z , K i ), K i , J i ], π n [ w, ws , Ph , Pnφ n (Z , K n ), K n , J n ]. Preferences and Demand Functions Each agent’s indirect utility function is derived from a CES-CRRA utility function in which consumption of the primary agricultural goods and processed food form a CES sub-function, viz.:

V =

E 1−1 / τ β 2 1− β 2 c 2 Pi + c3β 2 Pf1− β 2 + (1 − c 2 − c3 ) β 2 Pn1− β 2 1 − 1/τ

[

25

]

(1−1 / τ ) /( β 2 −1)

,

where

[

Pf = c1β1 Px1− β1 + (1 − c1 ) β1 Px1− β1

]

1 /(1− β1 )

.

Demand functions for individual goods are

Dg = −

∂V / ∂Pg ∂V / ∂E

= D g ( E , Pa , Px , Pi , Pn ), g = a, x, i, n,

(13a)-(13d)

where E = E a + E x + Ei + E n + w( La + Ln + Lc ) + w(1 + b)( Lx + Li ) + ws ( Lsx + Lsn + Lsi + Lsc ) + Tw .

Public Sector Investment and the Government Budget Constraint T = Pj I j + Pz I z − t a ( Da − Qa ) − t g G − t x ( D x − Q x ) − t m − t i ( Di − Qi ) − t h H − uδPj J − X − Aid ,

(14)

Z& = I z − δZ ,

(15)

J& = I j − δJ ,

(16)

where X is output in the mining sector, uδPj is the user fee for electricity, and H = H a + H i + H x + H n + ak3 I p + a z3 I z + a j3 I j , J = Ja + Ji + J x + Jn , M = I p + Iz + I j.

Zero-Profit and Market-Clearing Conditions Pa = C a (ra , r ja , w, f , Ph ) /φ a ( Z , K a ) Px − vPg = C x (rx , r jx , w x , ws , Ph ) /φ x ( Z , K x )

(17a) (17b)

Pi = C i (ri , r ji , wi , ws , Ph ) /φ i ( Z , K i )

(17c)

Pn = C n (rn , r jn , w, ws , Ph ) /φ n ( Z , K n )

(17d)

26

Dn ( Pa , Pn , Pi , Px , E ) = Qn

(18)

La + L x + Li + a k 1 I p + a z1 I z + a j1 I j = Lu

(19)

Lsx + Lsi + Lsn + a k 2 I p + a z 2 I z + a j 2 I j = Ls

(20)

Qa − Da − G + Qi − Di + Q x − D x − I p − I z − I j − H − Aid = 0

(21)

Notation English Subscripts: a = primary agriculture; x = food processing sector; i = other manufacturing; n = services; c = construction. A = stock of land ag1 = input-output coefficient for unskilled labor in the production of capital of type g (g = K, Z, J) ag2 = input-output coefficient for skilled labor in the production of capital of type g (g = K, Z, J) ag3 = input-output coefficient for imported intermediates in the production of capital of type g (g = K, Z, J) b = percentage difference between the wage paid to unskilled labor in the formal sector and the informal sector C g /φ g = unit cost function in sector g c = input-output coefficient for the agricultural good in the food processing sector Dg = consumption demand for good g Eg = consumption expenditure by the representative capitalist in sector g f = land rental G = purchases of the agricultural good by the food processing sector H = total purchases of intermediate inputs Hg = imported intermediate inputs in sector g Ig = gross investment in sector g Ip = total private investment, inclusive of adjustment costs J = total stock of power Jg = stock of power in sector g Kg = private capital stock in sector g Lg = employment of unskilled labor in sector g Lsg = employment of skilled labor in sector g Pa = domestic price of the primary agricultural good Pg = domestic price of agricultural input purchased by the food processing sector Ph = domestic price of imported intermediate inputs Pi = domestic price of the manufactured consumer good Pj = supply price of a power plant Pk = supply price for private capital 27

Pn = price of services Px = domestic price of processed food Pz = supply price of roads Qg = gross output in sector g rg = gross private capital rental in sector g rjg = gross shadow rental of power in sector g T = total lump-sum transfers Tg = lump-sum transfers to agent g (g = a, x, i, n, w) ta = trade tax on the primary agricultural good tg = trade tax on purchases of the agricultural input by the food processing sector th = trade tax on imported intermediate inputs ti = trade tax on manufactured consumer good tm = trade tax on imported machinery and equipment tx = trade tax on processed food Vg(•) = indirect utility function of the representative capitalist in sector g v = parameter that determines adjustment costs incurred in changing the capital stock u = user fee for power expressed as a percentage of depreciation costs w = wage for unskilled labor in agriculture and services wi = wage for unskilled labor in the manufacturing sector wx = wage for unskilled labor in the food processing sector ws = skilled wage Z = stock of roads Greek β1 = elasticity of substitution between processed and unprocessed food β2 = elasticity of substitution between food, manufactures, and services Φg(•) = shift factor in the production for good g πg(•) = restricted profit function in sector g η = elasticity of the shift factor in the production function with respect to the stock of roads ξ g = elasticity of the shift factor in the production function for good g with respect to the capital stock. τ = intertemporal elasticity of substitution

28

Table 2: Calibration of the Model Sector Shares in GDP primary agriculture = .292, food processing = .07, manufacturing = .07, services = .422, mining = .115, construction = .031 Aid Aid is fixed in absolute terms at 11.5% of initial GDP. Consumption Shares primary agricultural good = .23, processed food = .14, manufactures = .14, services = .49 Factor Shares in Agriculture capital = .19, unskilled labor = .65, power = .053, land = .107 Factor Shares in Food Processing capital = .28, unskilled labor = .46, skilled labor = .17, power = .09 Factor Shares in Manufacturing capital = .44, unskilled labor = .17, skilled labor = .19, power = .20 Factor Shares in Services capital = .50, unskilled labor = .22, skilled labor = .22, power = .06 Cost Shares of Intermediate Inputs Imported: agriculture = .06, food processing = .06, manufacturing = .23, services = .10 Domestic: food processing = .40 (purchased from primary agriculture)

29

Elasticities of Substitution in Production Elasticity of substitution between skilled and unskilled labor = .75 Elasticity of substitution between non-power inputs = .75 Elasticity of substitution between power and non-power inputs = .50 (base run) or .25 Time Preference Rate (ρ) and the Depreciation Rate (δ) ρ = .10, δ = .05 Elasticities of Substitution in Consumption Elasticity of substitution between food and other goods = .50 Elasticity of substitution between processed and unprocessed food = .75 Intertemporal Elasticity of Substitution(τ) τ = .50 for all agents q-Elasticity of Investment (Ω) Ω = 10 in all sectors Initial Rates of Return (net of depreciation) on Power and Roads .30 for power in all sectors .30 for roads Initial Wages unskilled wage in primary agriculture and services = 1 unskilled wage in food processing and manufacturing = 1.75 skilled wage = 6 in all sectors

30

Initial Trade Taxes ta = .10, tx = .20, ti = .20, th = .10, tg = .10, tm = .10 Notation: ta is the trade tax on the primary agricultural good; tx is the trade tax on processed food; ti is the trade tax on manufactured consumer goods; th is the tariff on imported intermediate inputs; tg is the trade tax on purchases of the agricultural good by the food processing sector; and tm is the tariff on imported machinery. Learning Externalities (ξg) No learning externalities in the base run (ξg = 0)

31

References Arrow, K., 1962, “The Economic Implications of Learning by Doing.” Review of Economic Studies 29, 153-173. Barnett, S. and P. Sakellaris, 1998, “Nonlinear Response of Firm Investment to Q: Testing a Model of Convex and Non-Convex Adjustment Costs.” Journal of Monetary Economics 42, 261-288. Blundell, R., 1988, “Consumer Behavior: Journal 98, 16-65.

Theory and Evidence – A Survey.”

Economic

Blundell, R., P. Pashardes, and G. Weber, 1993, “What Do We Learn About Consumer Demand Patterns From Micro Data?” American Economic Review 83, 570-597. Conforti, P. and A. Sarris, 2007a, “Staple Food Margins and Trade Policy in Africa: A Computable General Equilibrium Analysis for Tanzania.” Paper presented at workshop on Trade Policy for Food Products Conducive to Development in Eastern and Southern Africa (Food and Agriculture Organization, Rome). Conforti, P. and A. Sarris, 2007b, “Trade Policies under Different Structural Conditions for Exportable and Import Competing Sectors in the Context of a Commodity Boom: The Case of Tanzania.” Paper presented at workshop on Appropriate Trade Policies for Agricultural Development in a Globalizing World (Food and Agriculture Organization, Rome). Deaton, A. and D. Muellbauer, 1980, Economics and Consumer Behavior (Cambridge University Press, New York). Fann, S., S. Thorat, and N. Rao, 2003, “Investment, Subsidies, and Pro-Poor Growth in Rural India.” Preliminary report presented at workshop on Institutions and Economic Policies for ProPoor Agricultural Growth (Imperial College, London). Feldstein, M., 1964, “The Social Time Preference Rate in Cost Benefit Analysis.” Economic Journal 74, 360-379. Global Trade, Assistance and Production, GTAP3 Data Base (Department of Agricultural Economics, Purdue University). Lluch, C., A. Powell, and R. Williams, 1977, Patterns in Household Demand and Saving (Oxford University Press, London). Lofgren, H., J. Thurlow, and S. Robinson, 2004, “Prospects for Growth and Poverty Reduction in Zambia, 2001-2015.” DSGD Discussion Paper No.11 (International Food Policy Research Institute).

32

McCalla, A. and J. Nash, 2007, “Agricultural Trade Reform and Developing Countries: Issues, Challenges and Structure of the Volume.” In, A. McCalla and J. Nash, eds., Reforming Agricultural Trade for Developing Countries (World Bank; Washington, D.C.). Mwanawina, I., 2006, “SADC Trade Performance Review: Zambia.” (South African Development Community) Ogaki, M., Ostry, J., and C. Reinhart, 1996, “Saving Behavior in Low- and Middle-Income Developing Countries.” IMF Staff Papers 43, 38-71. Ostry, J. and C. Reinhart, 1992, “Private Saving and Terms of Trade Shocks.” IMF Staff Papers 39, 395-417. Sen, A., 1967, “Isolation, Assurance and the Social Rate of Discount.” Quarterly Journal of Economics 81, 112-124. Thurlow, J., D. Evans, and S. Robinson, 2004, “A 2001 Social Accounting Matrix for Zambia.” International Food Policy Research Institute (Washington, D.C.) World Bank, 1997, “Haryana Power Economic Appraisal.” Mimeo (Washington, D.C.). World Bank, 2005, Agricultural Growth for the Poor: (Washington, D.C.)

33

An Agenda for Development

Table 3: Value-Added Shares in Agriculture. Labor

Capital

Land

Lofgren et al. (2004)

80.4

14.5

5.1

IFPRI SAM1

50-86

4-34

8-18

GTAP values for SSA2

67.4

22.2

10.4

GTAP recommended values for SSA

60

25

15

GTAP values for India

58.2

16.8

25.1

GTAP values for South Asia, excluding India

40.4

34.6

25.0

1

The cited range of values excludes fishing and sugar, which are exceptionally capital intensive.

2

All GTAP numbers are from Global Trade, Assistance and Production project’s GTAP3 Data Base (https://www.gtap.agecon.purdue.edu/databases).

34

Table 4: Long-Run Effects of Pure Trade Policy Experiments.1 Policy2

ωu

ωs

K

HWE

GDP

C

ta = .20

14.7

-7.1

3.6

-.024

.1

-.4

ta = .20 + learning externalities3

19.9

-6.5

5.3

-.030

2.4

1.5

tx = .20

-2.9

12.6

5.0

.047

2.2

1.3

tx = tg = .20

-2.9

7.5

3.5

.029

1.7

1.0

ti = .20

-3.8

7.5

5.3

.005

1.7

.9

ti = tx = .20

-6.5

20.3

10.3

.053

4.0

2.5

ti = tx = tg = .20

-6.5

15.0

8.8

.034

3.5

2.1

th = .20

-2.7

-3.6

-3.0

-.004

-1.3

-.9

tm = .20

-4.5

-5.6

-9.9

-.003

-3.7

-2.4

Policy2

ωu

ωs

Policy Packages K HWE

GDP

C

ta = tx = tg = .30

16.1

.9

10.5

.002

3.0

1.5

ta = tx = tg = ti = .30

10.0

11.8

18.3

.008

5.8

3.4

1

ωu is the real wage for unskilled labor; ωs is the real wage for skilled labor; K is the aggregate capital stock; HWE is the share of unskilled labor employed in the high-wage formal sector ; GDP is real gross domestic product exclusive of mining, and C is aggregate real consumption. The entry for HWE is the change in the share of high-wage employment. All other entries show the percentage change in the variable relative to its initial steady state.

2

ta is the export subsidy for the primary agricultural good; tx is the tariff on processed food; ti is the tariff on other manufactured consumer goods; tg is the tariff on purchases of the primary agricultural good by the food processing sector; th is the tariff on intermediate inputs; and tm is the tariff on machinery and equipment

3

The learning parameter is set so that the social return to capital in primary agriculture is twice the private return at the initial equilibrium.

35

Table 5: Long-run effects of trade policy when increases in net tariff revenue are dedicated to investment in roads and free trade is the initial equilibrium.1 Policy

ωu

ωs

K

HWE

GDP

C

ta = tx = ti = tg = .30

1.0

1.7

14.5

.007

-2.2

-2.9

ti = .20

-1.8

10.0

6.1

.006

3.6

2.3

tx = ti = .202

-7.5

18.9

9.9

.052

3.0

1.7

tx = ti = tg = .20

1.7

27.0

11.9

.035

11.5

8.0

tx = ti = th = .20

2.1

34.2

11.5

.051

14.2

9.8

tx = tg = .20

2.8

14.8

5.6

.030

7.1

5.0

tx = ti = th = tg = .20

7.2

36.9

11.0

.032

18.2

12.1

Policy Packages K HWE

GDP

C

Policy

ωu

ωs

ta = ti = tx = tg = .30, th = .20, and tm = .10

17.1

20.9

14.1

.005

14.0

9.6

ta = .40, ti = tx = tg = .30, th = .20, and tm = .10

16.0

8.6

13.6

-.006

7.8

5.2

ta = .20, ti = tx = tg = .30, th = .20, and tm = .10

14.7

30.8

13.4

.017

17.4

11.8

ta = tx = tg = .30, ti = .20, th = .20, and tm = .10

17.4

15.0

11.3

.003

11.7

8.1

tx = tg = .40, ta = ti = .30, th = .20, and tm = .10

17.4

27.0

16.0

.016

16.3

11.1

1

See footnotes 1 and 2 in Table 4 for definitions of terms.

2

Results in a net revenue loss because the food processing becomes an export sector.

36

Table 6: Long-run effects of trade policy when increases in net tariff revenue are dedicated to investment in power and free trade is the initial equilibrium.1 Policy

ωu

ωs

K

HWE

GDP

C

ti = .20

-2.7

11.1

7.0

.007

2.9

1.8

tx = ti = tg = .20

-3.1

34.9

16.7

.055

9.2

6.1

tx = ti = th = .20

-4.9

45.5

18.1

.089

10.9

7.3

tx = tg = .20

.8

21.9

9.1

.047

6.3

4.4

tx = ti = th = tg = .20

-3.7

64.5

25.7

.088

16.6

10.6

Policy packages K HWE

GDP

C

Policy

ωu

ωs

ta = ti = tx = tg = .30, th = .20, and tm = .10

11.9

42.2

25.5

.027

14.7

9.4

ta = .40, ti = tx = tg = .30, th = .20, and tm = .10

16.1

17.3

18.4

≈0

8.8

5.6

ta = tx = tg = .40, ti = .30 th = .20, and tm = .10

16.4

33.9

24.9

.024

13.4

8.6

1

See footnotes 1 and 2 in Table 4 for definitions of terms.

37

MPL

MPL

E

R

w

E

B w

J

=

MPL 0

E

MPL

=

V L

E

N

E

0 L

=

Figure 1: The welfare loss from underemployment in manufacturing.

=

=

MPK, SMPK

H

H*

SMPK K

a

MPK

a

K

a1

SMPK

MPK

i

i

a

K

ao

0

K

io

Figure 2: The relationship between the private capital stock and the socially optimal capital stock.

K

i1

K

i

MPZ, MPK, SMPK

H

H*

MPZ2(K2) Z

o

Z2

SMPK2 (Z )

SMPKo(Zo) MPKo(Zo)

MPZo(K ) Z1

Zo

0

Ko

K1

2

K2

Figure 3: The interdependence of underinvestment in infrastructure and underinvestment in private capital.

K

MPK

H

P

H -k

MPK1(H1

MPKo(Ho) 0

Ko

K1

Figure 4: The impact of an escalated structure of protection + export promotion on the aggregate capital stock.

K

FAO2 Figures.nb

1

Real Skilled Wage 40

Real Unskilled Wage 10

35 30

7.5

25 20

2.5

5

15

Years 0

10 5

5

10

15

20

25

30

-2.5 -5 Years 0

5

10

15

20

25

30

High Wage Employment

Total Real Unskilled Wage Income 10

9 8

8

7

6 4

6

2 Years

5 -2

4 Years 0

5

10

15

20

25

30

0

5

10

15

20

25

30

-4 -6

Figure 5: Transition paths for real wages, high-wage employment, and total wage income of unskilled labor when tx = ti = th = tg = .20.

FAO2 Figures.nb

2

Real Skilled Wage

Real Unskilled Wage

20

20

15

15

10

10

5

5 Years 0

5

10

15

20

25

Years

30

0

5

Capital

10

15

20

25

30

20

25

30

Real GDP

14

14

12

12

10

10

8

8

6

6

4

4

2

2 Years 0

5

10

15

20

25

30

Years 0

5

10

15

Figure 6: Transition path when ta = tx = ti = tg = .30, th = .20, and tm = .10.