A. Households

In our model, households live for three periods, each of which lasts twenty years. The three periods correspond to one period of childhood and two periods of adulthood. Households make saving, fertility, and schooling decisions. They value their consumption over the two periods of adulthood $\left(c_t^y,c_{t+1}^o\right)$ and the adult earnings (w_t+1h_t+1) of all their children (n_t+1). Earnings are the product of the after-tax market rental rate for skills (w_t+1) and the embodied skills, or human capital (h_t+1), of the worker. Preferences are given by

where 0 < β < 1 and ψ > 0 are preference parameters. This preference specification is a simple way of capturing the idea that parents value both the quantity and the quality of their children. It has been use extensively in the literature on fertility and growth (e.g., Galor and Weil, 2000; Greenwood and Seshadri, 2002; Hazan and Berdugo, 2002; Lord and Rangazas, 2005; and Moav, 2005).

Adults inelastically supply one unit of labor when young and zero units when old. Children have an endowment of T < 1 units of time that they can use to attend school (s_t) or work (T − s_t). Children have less than one unit of time to spend productively because early in childhood they are too young to either attend school or to work, and in the middle years they do not have the mental or physical endurance to school or work as long as an adult.

While children may work as they become older, they are also expensive to care for and feed. To raise each child requires a loss of adult consumption equal to a fixed fraction τ of the adult’s first period wages.

The government decrees that younger children receive some education during their early years. So each child invests at least $\overline{s}$ units of time into learning during the first portion of their childhood.⁴ This gives older children $\gamma {\overline{h}}_t=\gamma {\overline{s}}^{\theta }$ units of human capital that can be used in production during the later years of childhood, where 0 < θ <1 is a parameter that gauges the effect of schooling on human capital accumulation and 0 < γ < 1 reflects the fact that children lack relative physical strength or experience in applying knowledge to production compared to an adult. Adult human capital of the same person in the next period is $h_{t+1}=s_t^{\theta }$. Thus, a person is more productive in adulthood than in childhood because of greater strength and experience (1 > γ) and additional schooling $\left(s_t\ge \overline{s}\right)$.

The household maximizes utility subject to the lifetime budget constraint,

In addition to the standard first order conditions for life-cycle consumption, the choices of n_t+1 and s_t yield

where λ_t is the Lagrange multiplier.

Equation (1a) says the marginal utility of additional child quality must be equated to the marginal value of consumption lost from allowing children of working age to attend school. The strict inequality holds when the marginal cost of educating children beyond the schooling received in their early years, $\overline{s}$, exceeds the marginal benefit. In this case, parents are content to set $s_t=\overline{s}$.

Equation (1b) says the marginal utility of additional children must be equated to the marginal value of lost consumption. Consumption is lost from having additional children because we assume the cost of children exceeds the earnings that older children bring to the household.

Solving the model gives us the following demand functions for children, schooling, and financial assets for retirement (a_t+1)

Assuming that s_t−1 is sufficiently high, a dynamic results that causes economic growth and a demographic transition. Greater schooling raises adult earnings relative to older children’s earnings. This raises the net cost of having children, so fertility declines. Lower fertility and greater consumption lower both the quantity and the value of forgone earnings from schooling children, and so schooling rises further. Thus, the sole factor driving fertility down is the rise in schooling. It is also important to note that the dynamics is independent of the country’s conventional fiscal policy. The after-tax factor prices or rental rate on physical and human capital are the only variables that are affected by conventional fiscal policy.

Since the effect of schooling has a diminishing effect on human capital formation and wages, the transition equation given by (2b) would exhibit the standard properties of neoclassical growth if not for one additional feature. Children receive a minimum level of schooling or learning ($\overline{s}$) while they are young and unable to work. This creates a non-convexity in the transition equation, where the schooling during childhood must be greater than or equal to $\overline{s}$.

Figure 1 sketches the schooling transition equation. The vertical intercept of the graph is at –θT/(1 – θ), rather than its usual position at the origin. This implies that the graph intersects the 45-degree line twice, at A and B. For schooling to increase over time, the schooling level for parents, when they were children, must be to the right of A. Starting to the right of A will cause schooling to rise, but in relatively small increments. As the level of schooling rises, the increments in schooling across generations become larger, until the economy nears the stable steady-state at B when the increments converge to zero. So, provided that schooling is sufficiently high initially, the model predicts relatively small increments in schooling initially, an acceleration of schooling in the middle of the transition, and then a slowdown as the steady-state is approached. Lord and Rangazas (2005) show that this model fits the qualitative pattern observed over the last two centuries of United States history.

Dynamics of Schooling

Citation: IMF Working Papers 2006, 014; 10.5089/9781451862744.001.A001

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Dynamics of Schooling

Citation: IMF Working Papers 2006, 014; 10.5089/9781451862744.001.A001

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Dynamics of Schooling

Citation: IMF Working Papers 2006, 014; 10.5089/9781451862744.001.A001

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B. Firms

Production takes place within standard neoclassical firms that combine physical capital (K_t) and human capital (H_t) to produce output from a Cobb-Douglas technology

where D_t is a productivity variable associated with production in firms.

The productivity variable, D, is a function of disembodied technology, A, and government capital per adult worker, G, and is given by

where 0 < µ < 1 is a constant parameter. We assume that A progresses at the exogenous rate q. This specification of the impact of government capital is similar to Aschauer (1989) and Clarida (1993).

Firms operate in perfectly competitive factor and output markets. This implies the profit-maximizing factor mix must satisfy

where δ is the rate of depreciation on physical capital, σ is the income tax rate (net of transfers back to the private sector), g ≡ G/A, and k ≡ K/AH.

C. Capital Market Equilibrium

The firm’s demand for private physical-capital intensity is given by (5). The supplies of private capital comes from the household’s asset demand for retirement assets and the human capital they rent to the market,

where $h_t^A\equiv h_t+\gamma {\overline{h}}_t\left(T-s_t\right)n_{t+1}$. Substituting (2c), (5b), and (6b) into (6a), gives the equilibrium difference equation for physical-capital intensity,

D. Government

We assume that the government officials who determine fiscal policy are some fraction, ε, of the population of private households, N_t. Government officials value their own consumption $\left(c_t^g\right)$ as well as the welfare of the representative citizen according to the period utility function, ${ln}{c}_{t+i}^g+\varphi U_{t+i}$, where ϕ is a positive preference parameter that gauges the relative weight the government places on the welfare of private households. We assume that the current government also cares about the government as an ongoing institution (i.e., they care about the future operations of the government and the welfare of future government officials) and the welfare of the country’s future citizens. The preferences of the government are given by

The government budget constraint, per young household, is

The left-hand side gives the government’s consumption expenditures. The right-hand side is the difference between government tax revenue, net of transfers, and government expenditures on public capital. Public capital evolves according to the equation

where $I_t^g$ is government investment and δ^g is the rate of depreciation of government capital.

The government chooses sequences of tax rates and government capital to maximize the discounted utility of government officials and private households, given by (8), subject to the budget constraint and capital accumulation equation given above.⁵ In addition, the government takes into account how their policy choices affect all private sector decisions. This includes only (7), since (2a) and (2b) are independent of fiscal policy.⁶ Finally, to obtain analytical solutions, we assume δ = δ^g = 1, so that over our twenty-year periods, the capital stocks fully depreciate.

The solution to the government’s problem is (see the Appendix):

where Γ ≡ 1 + β + 1 + (ψ/β) + (βα(1 + β)) + β (α − 1) + ψα)/(1 − αβ).

One can show that the constant tax rate σ is decreasing in ϕ. From (11b), the public saving rate out of national income is a constant, βµ(1−α). Thus, a more selfish government, with a lower ϕ, will collect more in taxes but invest a smaller fraction of tax revenue in public capital—so as to maintain the same investment rate out of national income.

It is important to note that the model is recursive. The private sector schooling and fertility dynamics can be solved independently of fiscal variables and physical capital intensity. The fertility-schooling dynamic then plays a role in determining the dynamics of government and private capital intensity, for a given optimal tax rate.

E. Steady-State Equilibria

A country with sufficiently high initial schooling will experience growth and converge to a steady-state as determined by (2) and (11). However, if $s_{t-1}=\overline{s}$, it may be the case that $\frac{\theta \left(\tau -\gamma T\right)}{\gamma \left(1-\theta \right)}<\overline{s}$. If this is true, then $s_t=\overline{s}$ and the economy is in a poverty trap where neither schooling nor fertility changes over time. For an economy with this initial condition, the only possible dynamics stem from the government and private physical capital accumulation in (11). Thus, initial conditions may cause economies with identical structures to come to rest at very different steady-state equilibria; with one steady-state having higher values of h, g and k, and lower levels of n, than the other.

It is also possible that economies differ in terms of the weight, ϕ, that their governments place on household welfare in setting fiscal policy. Economies with higher ϕ will have higher private capital-labor ratios and higher levels of public capital. This will cause higher worker productivity, even if the steady values of s and n are the same.

Thus worker productivity may differ either because of a poverty trap or because of policy differences. The next question is whether these sources of income differences are quantitatively important.

A. Calibration

To quantify the model’s predictions about income differences across these two equilibria, we calibrate the parameters to the rich country steady-state. The physical capital income share, α, is set to the standard value of 1/3. The output elasticity for public capital, μ, is set to 0.30 somewhat less than the values estimated by Aschauer (1989) and Clarida (1993). However, the values of α and μ place µ(1 − α) at 0.2, an intermediate value of the estimates surveyed by Glomm and Ravikumar (1997). Based on Lord and Rangazas (2005), we set γ = 0.28 and T = 0.50. This implies potential earnings of a child that are about 14 percent of an adult’s earnings. The annualized after-tax return to capital is set to 4 percent, the after-tax real rate of return to capital in the United States at the end of the 20^th century (Poterba, 1997, Table 1). The annualized rate of growth of exogenous technological change, q, is set to 1.0 percent (Rangazas, 2002, 2005). This is intended to reflect a worldwide, transferable, component of exogenous technological change.

Table 1.

Selected Low-Income Countries with Large Governments (1985)

Source: Alan Heston, Robert Summers, and Bettina Aten, Penn World Table Version 6.1, Center for International Comparisons at the University of Pennsylvania, October 2002.

Table 1.

Selected Low-Income Countries with Large Governments (1985)

Country	G/Y	yUS / yCountry
Angola	0.36	11
Burkina Faso	0.29	33
Central African Republic	0.44	17
Comoros	0.49	10
Ethiopia	0.28	40
Gambia	0.37	17
Mozambique	0.31	33
Uganda	0.28	33
Average	0.32	24

Source: Alan Heston, Robert Summers, and Bettina Aten, Penn World Table Version 6.1, Center for International Comparisons at the University of Pennsylvania, October 2002.

View Table

Table 1.

Selected Low-Income Countries with Large Governments (1985)

Country	G/Y	yUS / yCountry
Angola	0.36	11
Burkina Faso	0.29	33
Central African Republic	0.44	17
Comoros	0.49	10
Ethiopia	0.28	40
Gambia	0.37	17
Mozambique	0.31	33
Uganda	0.28	33
Average	0.32	24

Source: Alan Heston, Robert Summers, and Bettina Aten, Penn World Table Version 6.1, Center for International Comparisons at the University of Pennsylvania, October 2002.

The remaining parameters are set to match certain targets. We set ϕ^rich to match σ = 0.15, about the ratio of government purchases to GDP in the United States.⁷ In the rich equilibrium steady-state, we targeted n = 1, s = 0.5 (children spend all their available time in school, similar to the current value in the United States), and a value of k consistent with an annualized after-tax return of 4 percent.

In the poor country equilibrium, we targeted n = 3.5, which implies 7 children per couple. Despite the fertility decline in Africa over the last two decades, many of its poorest countries have total fertility rates of 7 children per female (Bongaarts, 2002). In addition, the parameter settings must to be consistent with an optimal schooling level below $\overline{s}$. The minimal schooling level for young children is set to 0.08. This value implies that children in the rich country spend 6.25 times as much time in school over their childhoods than children from poor countries. If poor children spend 2 years in school, then rich children spend 12.5 years in school (assuming school years of equal length). Finally, we set ϕ^poor in the poor country so that σ = 0.35.

Table 1 gives examples of poor countries (1/10 of U.S. worker productivity, denoted by y^US, or less) with levels of σ = G/Y that are at least double those of the United States.⁸ Table 2 summarizes the parameter settings.

Table 2.

Calibrated Parameter Values

Table 2.

Calibrated Parameter Values

Parameter		Target
γ	0.2800	relative child’s earning
T	0.5000	relative child’s earnings
τ	0.1646	steady state fertility (poor)
θ	0.4049	steady state schooling (rich)
α	0.3333	standard value for capital share
µ	0.3000	intermediate empirical estimate
ψ	0.2956	steady state fertility (rich)
β	0.4999	steady state return to capital (rich)

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Table 2.

Calibrated Parameter Values

Parameter		Target
γ	0.2800	relative child’s earning
T	0.5000	relative child’s earnings
τ	0.1646	steady state fertility (poor)
θ	0.4049	steady state schooling (rich)
α	0.3333	standard value for capital share
µ	0.3000	intermediate empirical estimate
ψ	0.2956	steady state fertility (rich)
β	0.4999	steady state return to capital (rich)

B. Worker Productivity Differences

Table 3 presents the steady-state worker productivity ratio, across rich and poor countries, generated by the model. The features included in the model cause the rich country to be over 28 times richer than the poor country. The decomposition of the worker productivity ratio in Table 3 is based on the following expression for worker productivity,

Table 3.

Steady-State Worker Productivity Differential: Rich vs. Poor Countries

Table 3.

Steady-State Worker Productivity Differential: Rich vs. Poor Countries

Rich to Poor Ratios	Model Prediction
kα	3.68
gµ(1−α)	2.09
hA /[1+n(T−s)]	3.68
y	28.25

View Table

Table 3.

Steady-State Worker Productivity Differential: Rich vs. Poor Countries

Rich to Poor Ratios	Model Prediction
kα	3.68
gµ(1−α)	2.09
hA /[1+n(T−s)]	3.68
y	28.25

The poverty trap causes the term $h_t^A/(1+n_{t+1}\left(T-s_t\right))$, average human capital per worker, to be 3.7 times higher in the rich country for two reasons. First, since s_t = 0.5 in the rich equilibrium and $s_t=\overline{s}=0.08$ in the poor-equilibrium, adult human capital differs across countries. This causes output per worker in the rich country relative to that in the poor country to be 2.10, a value similar to that estimated by Hall and Jones (1999) using a much different approach. Second, the high fertility in the poor country implies that their workforce contains a sizable fraction of young workers, who are less productive than adult workers due to less strength and experience (captured by γ = 0.28). This causes worker productivity to be 1.75 times higher in the rich country. This determinant of low worker productivity has been overlooked in previous studies.

The poverty trap also causes low values of k and g. High population growth increases the size of next period’s workforce relative to the current period’s savers.⁹ This spreads saving and capital accumulation more thinly across workers in the future, lowering k. Lower values of k and h^A also lower the tax base and reduce public investment for any given tax rate. Differences in ϕ raise tax rates and further reduce private saving and private capital formation. Indirectly, this also lowers public capital formation by reducing the level of national income and the tax base. These various effects that serve to lower public and private physical-capital intensities cause worker productivity to be 7.7 times higher in the rich country. This is over four times as high as the productivity ratio that Hall and Jones (1999) attribute to differences in capital intensity. There are several reasons why the estimate in Table 3 is higher.

In Table 3 we are assuming that the poor country is a perfectly closed economy. In the next section, we open the economy to international capital flows. This reduces the differences in capital intensity across rich and poor countries, although not completely. Since the typical poor country is neither perfectly open nor perfectly closed, our estimates would bound the Hall and Jones (1999) estimates, if not for other considerations that suggest their estimates may be too low. Pritchett (2000) estimates that the actual capital stock in poor countries is only between 57 percent and 75 percent of the officially measured stock. Thus, in poor countries government consumption is underestimated and investment is overestimated. This causes estimates of productivity differences that are based on direct estimates of the capital stock differences to be too small.

The Hall and Jones (1999) approach also treats private and public investment as perfect substitutes in production. The estimates of the output-elasticity of public capital suggest that this is not the case; the elasticity for public capital is less than two-thirds the elasticity for private capital (Glomm and Ravikumar, 1997). Since poor countries have relatively more public capital, the perfect-substitutes assumption overstates the productivity of the capital stock in poor countries. This, in turn, lowers the estimated role of capital differences in explaining worker productivity differences.

A. Opening the Economy

Section III assumes that the poor country’s economy is perfectly closed. What happens if the economy is opened to trade and international capital flows? What will be the effect on different generations of households in the poor country? Will opening the economy make the poor country’s government better off, or will the government oppose the policy?

To answer these questions, the model must first be re-solved under the assumption that the economy is open and that private capital flows will equate the poor country’s interest rate to the exogenous world interest rate (which we take to be the steady-state interest rate in the rich country). Next, the dynamic path under the open economy assumption is computed as the economy goes through the transition from the initial closed economy steady-state to the open economy steady-state. Unlike most neoclassical growth models, the “small” poor economy will not adjust to the new steady-state in a single period when interest rates are equalized in an open world capital market. This is because the government’s public capital accumulation will adjust gradually to the opening of the economy. Equation (5a) shows that interest rates can be equalized due to private capital adjustments alone. Finally, welfare comparisons are made to see who benefits and who loses from opening the economy, an analysis that includes computing the welfare effect on the poor country’s government itself.

After the economy is opened, the poor country’s r will converge to the world interest rate, r^w, which we take to be the steady-state interest rate of the rich country. The equilibrating force is assumed to be private capital mobility. The poor country’s private capital intensity will then be determined by substituting r^w in (5a) and then solving for the new value of k. Note that this does not mean that k is equated across rich and poor countries because g may differ across countries. Smaller values of g lower the marginal product of k and imply that smaller values of k are needed to drive the return to physical capital down to the world interest rate.

With k determined internationally, the government’s optimal policy will change. The government now maximizes (8) not subject to (7), as in the closed economy, but subject to the k determined by international capital markets as described above. The optimal policy in an open economy becomes (see the Appendix for the derivation)

where $B=\frac{\mu \beta +\varphi \mu \left(\beta \left(1+\beta \right)+\psi \right)}{1+\varphi \mu \left(\beta \left(1+\beta \right)+\psi \right)}$. The coefficient B represents the share of the government budget that is invested in public capital. The product Bσ is the share of national output that is invested in public capital.

Fiscal Policy in an Open Economy

One can compare the effect of opening the economy on the fiscal policy of the poor country. Consider the extreme case where ϕ = 0. We then have $B^{\mathit{open}}\equiv \beta \mu >\beta \mu \frac{1-\alpha }{1-\alpha \beta }\equiv B^{\mathit{closed}}$, σ^open≡ 1 − α < 1 − αβ ≡ σ^closed, and (Bσ)^open =βµ(1 − α) = (Bσ)^closed, where all inequalities hold when future utility is discounted, i.e., when β < 1. Thus, opening the economy raises the portion of the budget that is invested and lowers the tax rate, but leaves the fraction of national output invested the same.

The fiscal policy differences are due to the timing of the impact of fiscal policy on private capital formation in open versus closed economies. In a closed economy, government policy affects private capital formation by affecting the after-tax wage of savers that fund the next period’s private capital intensity. In an open economy, government policy affects private capital intensity by affecting the marginal product of private investments in the poor country—reducing it with higher tax rates and raising it with higher public capital intensity. International capital flows will anticipate and respond to these changes in private returns to investment, until the after-tax return to investment are equalized across countries. Thus, in an open economy, government policy has a more immediate effect on private capital formation—this period’s policy affects this period’s capital intensity rather than this period’s saving flow and next period’s capital intensity (as in a closed economy). With discounting of the future (β < 1), the cost of high taxes and low public investment, in lowering private capital intensity, is smaller in the closed economy due to the one-period delay in effect. In this sense, opening the economy makes private capital formation more responsive to policy changes. The government reacts to the new environment by choosing a more “pro-growth” fiscal policy stance.

Table 4 gives the fiscal policies in open and closed economies for the calibration in Table 2 where ϕ = 0.7461.

Table 4.

Fiscal Policy in the Closed and Open Economy

Table 4.

Fiscal Policy in the Closed and Open Economy

Fiscal Parameter	Closed Economy	Open Economy
σ	0.35	0.26
B	0.29	0.31
σ B	0.10	0.08

View Table

Table 4.

Fiscal Policy in the Closed and Open Economy

Fiscal Parameter	Closed Economy	Open Economy
σ	0.35	0.26
B	0.29	0.31
σ B	0.10	0.08

The result with ϕ = 0.0 extends to a higher values of ϕ; taxes are lower and the fraction of the government budget invested is higher in an open economy. However, the share of national output that is invested in public capital is lower in the open economy when ϕ > 0, as B rises less than σ falls when the economy is opened. Thus, opening the economy lowers the economy’s rate of investment in public capital.

Growth Effects of Opening the Economy

Table 5 gives the effects on economic growth in worker productivity of opening the economy. Rapid growth occurs in the first period as capital inflows narrow the gap in private capital intensity between rich and poor countries. The gain in the tax base offsets the fact that the rate of investment in public capital is lower. This causes the public capital intensity to rise over time to a new, lower steady-state value. The rise in the public capital intensity raises the marginal product of private capital and causes the private capital intensity to increase further. The modest additional increases in public and private capital intensities keeps the growth rate in worker productivity above the exogenous rate of technological change until period 4, when the economy has approximately converged to its new physical capital intensities.

Table 5.

Growth in Worker Productivity: The Effect of Openness¹

¹The values are the average annualized percentages over 20 years.

Table 5.

Growth in Worker Productivity: The Effect of Openness¹

Period	1	2	3	4	5
Growth Rate	6.5	1.3	1.1	1.0	1.0

¹The values are the average annualized percentages over 20 years.

View Table

Table 5.

Growth in Worker Productivity: The Effect of Openness¹

Period	1	2	3	4	5
Growth Rate	6.5	1.3	1.1	1.0	1.0

¹The values are the average annualized percentages over 20 years.

The extent to which inflows of private capital narrow productivity differences is given in Table 6; the counterpart to Table 4 in a perfectly open, rather than perfectly closed, economy. Comparing Table 6 to Table 3, one sees that worker productivity gaps are narrowed by opening the economy. The rich country’s advantage in worker productivity is now less than one-third of what it was in a closed economy setting, although a ninefold difference still remains.

Table 6.

Steady-State Worker Productivity Differential: The Effect of Openness

Table 6.

Steady-State Worker Productivity Differential: The Effect of Openness

Rich to Poor Ratios	Model Prediction
kα	1.41
gμ(1 – α)	1.73
hA /[1 + n(T − s)]	3.68
y	8.98

View Table

Table 6.

Steady-State Worker Productivity Differential: The Effect of Openness

Rich to Poor Ratios	Model Prediction
kα	1.41
gμ(1 – α)	1.73
hA /[1 + n(T − s)]	3.68
y	8.98

B. Eliminating the Poverty Trap

Schooling is low in the poor country because the value of forgone earnings associated with sending older children to school is high. The value of forgone earnings is high because households have many children and because parental earnings are low. The poverty trap can be removed if parental earnings are increased relative to the earnings of older children. This would make it more costly to have many children (because of the forgone wages and consumption of parents associated with child rearing) and it would lower the relative value of children’s work in total family income.

Using aid to encourage poor countries to increase the schooling of younger children (i.e., to increase $\overline{s}$) will increase earnings but will not remove the poverty trap.¹⁰ This policy would not raise the earnings of parents relative to those of older children (since they both receive the higher levels of education when they are young children). What is needed is more schooling of older children, so that when they become parents their earnings (based on $s_t>\overline{s}$) sufficiently exceed the earnings of their older children (based only on $\overline{s}$)—thereby making children more costly and relatively less important in generating family income.¹¹

One policy that can remove the poverty trap is similar to Mexico’s Progresa program.¹² Governments would subsidize the forgone earnings of older children who attend school. A sufficiently high subsidy would raise s_t sufficiently higher than $\overline{s}$, so that a transitional dynamic would result, sending the poor country to point B in Figure 1. The potential advantage of identifying and eliminating poverty traps is that aid need not be ongoing. Once sufficient aid has been provided to eliminate the poverty trap, no further aid is necessary.

To begin the analysis of the subsidy policy, introduce the policy parameter η that indicates the fraction of forgone earnings of older children that the government returns to the household. This introduces the expression $\eta w_t\gamma {\overline{h}}_t\left(s_t-\overline{s}\right)n_{t+1}$ on the right-hand side of the household lifetime budget constraint from section I. In face of the subsidy, household behavior becomes

The subsidy increases the optimal schooling level and, if it is sufficiently high, the optimal schooling level is pushed above $\overline{s}$. For a given level of s_t, fertility is also encouraged by the subsidy. However, if the subsidy raises s_t enough, then fertility will fall.

Of course, the subsidy must be financed out of tax revenues. In addition, as older children work less in order to attend school, the tax base shrinks. Government revenue is reduced by two factors in the first period—the subsidy payment and the decline in the tax base. This implies that government consumption and investment will fall initially, which may offset, or at least mediate, the early growth effects of the policy. As the stock of human capital rises and increases the tax base, government consumption and investment eventually rise.

Growth Effects of the Progresa Program

Table 7 gives the growth effects of the Progresa program with a subsidy, for a single period, that is similar in size to that offered in the Mexican Progresa program, η = 0.67. The relatively large one-period subsidy is more than enough to boost the economy out of the poverty trap and in fact creates something close to a “growth miracle.” The large rise in schooling and fall in fertility creates strong direct (via human capital per worker) and indirect (via physical and public capital intensities) growth effects for a number of periods.

Table 7.

The Progresa Program: Schooling, Fertility, and Growth Effects¹

¹Growth rates are the annualized value over twenty years.

Table 7.

The Progresa Program: Schooling, Fertility, and Growth Effects¹

Period	1	2	3	4	5	6	7	8	9	10
s	0.29	0.34	0.37	0.41	0.43	0.45	0.47	0.48	0.49	0.49
n	2.5	1.2	1.1	1.0	1.0	1.0	1.0	1.0	1.0	1.0
%Δy	2.4	8.6	3.0	2.0	1.6	1.4	1.3	1.2	1.1	1.1

¹Growth rates are the annualized value over twenty years.

View Table

Table 7.

The Progresa Program: Schooling, Fertility, and Growth Effects¹

Period	1	2	3	4	5	6	7	8	9	10
s	0.29	0.34	0.37	0.41	0.43	0.45	0.47	0.48	0.49	0.49
n	2.5	1.2	1.1	1.0	1.0	1.0	1.0	1.0	1.0	1.0
%Δy	2.4	8.6	3.0	2.0	1.6	1.4	1.3	1.2	1.1	1.1

¹Growth rates are the annualized value over twenty years.

C. Eliminating Anti-Growth Fiscal Policy

Attempting to reform conventional fiscal policy is a very common target for aid policy. We now consider the effects of imposing a fiscal policy in the poor country that would bring it in line with the fiscal policy of the rich country. In particular, we compute the effects of imposing the σ and B of the rich country, where the optimal values are 0.15 and 0.67, on the poor country, where the optimal values in the open economy are 0.26 and 0.31.

Growth Effects of Fiscal Policy Reform

The effect of fiscal policy reform on the growth rates of worker productivity are given in Table 8.

Table 8.

Fiscal Reforms and Growth in Worker Productivity: No Aid¹

¹The values are the average annualized percentages over 20 years

Table 8.

Fiscal Reforms and Growth in Worker Productivity: No Aid¹

Period	1	2	3	4	5
%Δy	1.78	1.13	1.01	1.00	1.00

¹The values are the average annualized percentages over 20 years

View Table

Table 8.

Fiscal Reforms and Growth in Worker Productivity: No Aid¹

Period	1	2	3	4	5
%Δy	1.78	1.13	1.01	1.00	1.00

¹The values are the average annualized percentages over 20 years

The growth effects are relatively modest and short-lived. In part, this is due to the fact that we begin the policy experiment from a perfectly open economy. Opening the economy brings the fiscal policy of the poor government closer to that of the rich government (see Table 4). This has the effect of making the differences in tax policy less dramatic and the returns to accumulating private and public capital smaller (since capital intensities are higher in the open economy than in the closed economy). Since the poor economy is relatively close to the rich country’s capital intensities to begin with (see Table 6) the transition to the new steady-state is short.

A. Ignorance about Growth Policies

Our results suggest that opening the economy to international capital flows and a Progresa-style subsidy have the potential to generate significant growth effects. The open economy computational experiment is consistent with econometric evidence which clearly identifies that countries with open economies grow faster than those with closed economies (e.g., Frankel and Romer, 1999). However, the profession is much more divided on the best policies for opening a previously distorted economy to international capital flows (e.g., Rodrik, 2004; and Rodriguez and Rodrik, 2001). Our experiment assumes that the poor country was initially closed by law (say, for political reasons) because it was unaware of the economic benefits on international investment. However, many poor economies are likely closed because of the indirect effects of chosen domestic or international policies. With the exception of anti-growth fiscal policy, our model contains no specific policy that prevents capital inflows and thus cannot provide guidance on the best policy reforms to open the economy. The best policy for opening the economy may be highly specific to the initial conditions of the economy that led it to be closed in the first place. The standard textbook advice of removing all possible trade barriers may not be convincing to the poor country’s government. The key is to encourage international investment and how best to do this is not yet known.

The computational Progresa-style experiments are consistent with direct empirical evidence on the ground showing that the real-world Progresa experiment has been a success in Mexico (Krueger, 2002). Why wasn’t this policy carried out earlier and in other countries? Probably because no one had previously thought of it. Before Progresa was implemented, there was no formal analysis of its possible effects in the academic literature and it certainly has never been a required condition for receiving aid.

In summary, some of the best policies for promoting growth are still out there to be discovered, and some of policies that we do recommend are misguided because they are too general and their effects have never been properly evaluated.

B. Aid Cost

Fiscal reforms are often part of the conditions for receiving aid. Our analysis suggests that reforms of domestic fiscal policy are likely to be the least successful of the three that we examined. First, the growth effects of fiscal reform are relatively modest and short-lived. Second, the aidcost of “buying” the reforms from the poor country’s government are enormous. Unless the aid keeps flowing to the poor country in sufficient quantity, the domestic government will do what it can to revert back to a high-tax, low-investment regime. In fact, the cost of maintaining effective reforms will increase over time as the government’s budget, and the potential to increase government consumption, grows. In practice, aid is likely to be far less than what is necessary to keep the government indifferent and thus fiscal reforms may be doomed from the beginning.

Even if the aid is carried out in sufficient amounts indefinitely, there will be little correlation between aid and economic growth in the data. The growth effects occur early on, while the aid continues into the future during periods where the growth effects have long since vanished. If aid is cut somewhat, rather than increased, then there will be a reversion in fiscal policy and growth. Thus, aid will be flowing to a country experiencing negative growth.