Remittances in a Business Cycle Framework

This chapter examines the properties of remittances and the relation of those properties to optimal policies and allocations in a stochastic monetary economy composed of a representative household, a representative firm, a government, and remitters. The household in this economy receives utility from leisure and two consumption goods, a cash good and a credit good, and earns income through domestic production by supplying labor to firms. Output is produced according to a production function that combines capital, labor, and technology in which the process governing technology is assumed to be exogenous and stochastic. The household values money, since it must be accumulated to facilitate consumption of the cash good.¹ Under this specification, anticipated inflation acts as a distorting tax on activities involving the use of cash.

Given the preponderance of evidence supporting the altruistic motive for remitting, including the evidence presented in Chapter 4, and the treatment of these flows in balance of payments accounting as discussed in Chapter 2, the representative household receives remittances, which are exogenously specified as countercyclical real income transfers that augment the income the household receives from production.² The countercyclical remittance function used in the model results in increased real transfers to the household when domestic output falls below the equilibrium level of output and in reduced real transfers during economic expansions. Remittance flows to the household, however, are assumed to be less than fully compensatory in nature, only partly offsetting changes in domestic output.³ The level of remittances and their sensitivity to the business cycle are varied in the calibration process.

The government is considered benign in that policymakers maximize the welfare of the average household in the economy subject to raising revenues sufficient to cover the exogenously determined level of government expenditures. The government raises revenue through taxation, printing money, or debt issuance via one-period real bonds and uses this revenue to finance its spending and service existing debt. The model includes an exogenous shock to government spending, and this shock and the shock to technology are the two main sources of uncertainty in the model. According to evidence from various studies (e.g., World Bank, 2005, p. 93) that indicates that governments do not typically tax remittances directly, the government in the model is not permitted to levy a direct tax on remittance transfers. Instead, following the evidence from Gordon and Li (2006), the model includes two different tax structures: one in which the government imposes a tax on labor income and a second in which the government raises revenue through a consumption tax.⁴ Government policies that change the growth rate of the money supply or the tax rates on labor income and consumption impose an excess burden on households and distort economic decisions, causing households to alter their decision making in response to changes in government policy.⁵ Consequently, the government must search for a revenue policy mix that satisfies its budget constraint while simultaneously minimizing the welfare costs of this policy mix for households.

The model is calibrated to match the features of the Chilean and U.S. economies. These countries serve as reasonable case studies, since remittance activity relative to GDP is negligible in both countries, the required data to calibrate the model properly are available, and the two countries differ with respect to economic structure. Though the United States is the largest source country of remittance flows, with $39 billion in outward remittances in 2004 (World Bank, 2005), this total amounts to only 0.3 percent of the country’s GDP. Remittance flows into Chile amounted to $13 million in 2004, or 0.1 percent of GDP. Chile and the United States differ with respect to the level of government debt and business cycle volatility, with Chile having relatively lower debt-to-GDP ratios and more pronounced business cycles. The process governing technology in Chile is more volatile and persistent than in the United States, but only slightly so. The process for government spending, however, differs greatly in the two countries, as Chile experiences much larger spending shocks and significantly less persistence relative to those found in the United States. Finally, Chile is a cash-based economy—that is, more of its transactions are accomplished with the use of cash—whereas credit-based transactions dominate in the United States. Calibration of the model to these two economies provides a rich set of characteristics through which to examine remittance flows and their effect on activity and policy. The initial calibration procedure captures the economic relationships in a non-remittance-dependent setting, in which the ratio of the level of remittances to GDP is zero. To these baselines, the model adds remittances-to-GDP ratios ranging from 5 percent to 25 percent.

The calibration procedure for Chile uses quarterly data from 1986–2000 and follows the procedures outlined by Bergoeing and Soto (2002).⁶ The calibration process results in a ratio of government spending to GDP in Chile of 12 percent and of total government debt to GDP of 13 percent. The fraction of time spent working is 0.43, which is markedly higher than that found in developed countries. Bergoeing and Soto attribute the difference to established practices in the formal labor market that discourage part-time work. The U.S. model is calibrated to match the general features of the post–Korean War economy. Using quarterly data from 1990–2002, the ratio of government spending to GDP in the United States is 14 percent and the ratio of federal government debt held by the public to GDP is 39 percent.⁷ The fraction of time spent working is set at 0.31, in accordance with Juster and Stafford (1991). Finally, the real interest rate is higher in Chile than in the United States, with annual real rates in Chile averaging 9.3 percent versus 3.6 percent in the United States, reflecting the historical country risk premium for investing in Chile.

The remaining parameters for both countries, including the marginal utility of leisure and the depreciation of the capital stock, are derived from first-order conditions and the nonstochastic steady-state government budget constraint. Once properly specified, each model economy is solved and simulated under the effects of technology and government spending shocks. The following sections discuss the results from this process, with the results under labor taxation presented first, followed by a discussion of the main differences under a system of consumption taxes.

Results with Labor Income Taxation

Table 6.1 reports the steady-state values for both Chile and the United States under labor income taxation for the baseline case without remittances and for various remittances-to-GDP ratios. The presence of remittances provides the household with additional disposable income, and the household spreads these resources over each of the consumption goods as well as leisure. Consequently, as remittances are added to the model economies, steady-state consumption of the cash and credit goods increases, whereas steady-state labor supply decreases. For example, Table 6.1 reports that as the remittances-to-income ratio rises to 25 percent in Chile, the steady-state labor supply declines by 23 percent and output falls by slightly more than 16 percent relative to the baseline. A similar pattern is found for the United States. Despite the decline in domestic output as the household chooses more leisure, the household is still able to increase overall consumption, since disposable income has risen. In other words, the reduction in output resulting from a decline in household labor supply is not sufficient to offset fully the increase in remittances. The increase in household disposable income—income from production plus remittances—leads to an increase in steady-state consumption of both the cash and credit goods.

Table 6.1.

Steady-State Values Under Labor Taxation

Source: Authors’ calculations. Note: “Output” is output from production (excluding remittances). The inflation rate, real interest rate, and money growth rate are expressed as quarterly growth rates in net terms. The tax rate is expressed as a percentage of labor income.

Table 6.1.

Steady-State Values Under Labor Taxation

	Remittances-to-Income Ratio
	Chile (Cash-Based Economy)				United States (Credit-Based Economy)
Variable	0%	5%	15%	25%	0%	5%	15%	25%
	(In percent)
Output	1.61	1.55	1.44	1.35	1.73	1.67	1.55	1.45
Remittances	0.08	0.22	0.34	0.08	0.23	0.36
Cash good	0.85	0.86	0.88	0.90	0.49	0.50	0.50	0.51
Credit good	0.28	0.29	0.31	0.32	0.63	0.64	0.67	0.69
Labor	0.44	0.41	0.37	0.34	0.31	0.29	0.26	0.23
Shadow price of debt	0.11	0.10	0.08	0.05	0.14	0.13	0.12	0.11
	(In percent)
Inflation rate	−2.2	1.0	4.5	4.6	−0.9	1.1	4.2	5.9
Real interest rate	2.2	2.2	2.2	2.2	0.9	0.9	0.9	0.9
Money growth rate	−2.2	0.9	4.4	4.5	−0.9	1.1	4.1	5.7
Tax rate	25.0	22.8	20.4	21.9	31.4	31.7	32.5	34.1

Source: Authors’ calculations. Note: “Output” is output from production (excluding remittances). The inflation rate, real interest rate, and money growth rate are expressed as quarterly growth rates in net terms. The tax rate is expressed as a percentage of labor income.

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Table 6.1.

Steady-State Values Under Labor Taxation

	Remittances-to-Income Ratio
	Chile (Cash-Based Economy)				United States (Credit-Based Economy)
Variable	0%	5%	15%	25%	0%	5%	15%	25%
	(In percent)
Output	1.61	1.55	1.44	1.35	1.73	1.67	1.55	1.45
Remittances	0.08	0.22	0.34	0.08	0.23	0.36
Cash good	0.85	0.86	0.88	0.90	0.49	0.50	0.50	0.51
Credit good	0.28	0.29	0.31	0.32	0.63	0.64	0.67	0.69
Labor	0.44	0.41	0.37	0.34	0.31	0.29	0.26	0.23
Shadow price of debt	0.11	0.10	0.08	0.05	0.14	0.13	0.12	0.11
	(In percent)
Inflation rate	−2.2	1.0	4.5	4.6	−0.9	1.1	4.2	5.9
Real interest rate	2.2	2.2	2.2	2.2	0.9	0.9	0.9	0.9
Money growth rate	−2.2	0.9	4.4	4.5	−0.9	1.1	4.1	5.7
Tax rate	25.0	22.8	20.4	21.9	31.4	31.7	32.5	34.1

Source: Authors’ calculations. Note: “Output” is output from production (excluding remittances). The inflation rate, real interest rate, and money growth rate are expressed as quarterly growth rates in net terms. The tax rate is expressed as a percentage of labor income.

Results with Consumption Taxation

The use of a tax on labor income has the undesirable effect of making the government rely more on inflation to appropriate resources as the level of remittances increases. This is especially problematic given the current trend among countries to establish inflation targets as the focus of monetary policy. If an inflation target were imposed on the optimal government policy problem, then the government in our model would not be allowed to use inflation to tax remittances indirectly and would instead have to resort to further labor income taxation, which harms output. An alternative would be to allow the government to use a consumption tax rather than a labor tax.¹¹ Table 6.2 presents the steady-state equilibrium under optimal government policy in both levels and growth rates under consumption taxes for the case of Chile. (The results for the calibrated U.S. economy are similar.)

Table 6.2.

Steady-State Values Under Consumption Taxation

Source: Authors’ calculations. Note: “Output” is output from production (excluding remittances). The inflation rate, real interest rate, and money growth rate are expressed as quarterly growth rates in net terms. The tax rate is expressed as a percentage of household consumption.

Table 6.2.

Steady-State Values Under Consumption Taxation

	Chile (Cash-Based Economy) Remittances-to-Income Ratio
Variable	0%	5%	15%	25%
	(In levels)
Output	1.56	1.51	1.42	1.34
Remittances		0.08	0.21	0.34
Cash good	0.84	0.86	0.90	0.93
Credit good	0.28	0.28	0.29	0.31
Labor	0.42	0.40	0.36	0.33
Shadow price of debt	0.09	0.08	0.04	0.01
	(In percent)
Inflation rate	−2.2	−2.2	−2.2	−2.2
Real interest rate	2.2	2.2	2.2	2.2
Money growth rate	−2.3	−2.3	−2.2	−2.2
Tax rate	18.8	18.4	17.7	17.1

Source: Authors’ calculations. Note: “Output” is output from production (excluding remittances). The inflation rate, real interest rate, and money growth rate are expressed as quarterly growth rates in net terms. The tax rate is expressed as a percentage of household consumption.

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Table 6.2.

Steady-State Values Under Consumption Taxation

	Chile (Cash-Based Economy) Remittances-to-Income Ratio
Variable	0%	5%	15%	25%
	(In levels)
Output	1.56	1.51	1.42	1.34
Remittances		0.08	0.21	0.34
Cash good	0.84	0.86	0.90	0.93
Credit good	0.28	0.28	0.29	0.31
Labor	0.42	0.40	0.36	0.33
Shadow price of debt	0.09	0.08	0.04	0.01
	(In percent)
Inflation rate	−2.2	−2.2	−2.2	−2.2
Real interest rate	2.2	2.2	2.2	2.2
Money growth rate	−2.3	−2.3	−2.2	−2.2
Tax rate	18.8	18.4	17.7	17.1

Source: Authors’ calculations. Note: “Output” is output from production (excluding remittances). The inflation rate, real interest rate, and money growth rate are expressed as quarterly growth rates in net terms. The tax rate is expressed as a percentage of household consumption.

As in the case of labor taxation in Table 6.1, optimal government policy with consumption taxes in the baseline case without remittances follows the Friedman rule by setting money growth equal to the rate of time preference. The presence of remittances under consumption taxation still leads to a reduction in steady-state labor supply as the household spreads the additional resources across consumption and leisure. As in the labor tax case, the overall level of household disposable income still increases, since the drop in domestic output is not enough to fully offset the increase in remittance income. Therefore, the use of a consumption tax leads to an increase in the tax base, as the government now taxes total consumption, derived from domestic production and exogenous remittances, instead of taxing income from declining domestic production under labor taxation. As the level of remittances increases, the government finds that it can reduce the tax rate on consumption while still having enough resources to cover exogenous government expenditures, pay debt service costs, and maintain the Friedman rule. In the case of Chile, the tax on consumption, expressed as a percentage of total consumption of cash and credit goods, falls from 18.8 percent in the baseline economy without remittances to 17.1 percent at the 25 percent level of the remittances-to-income ratio. In contrast to what takes place in the economies with labor taxation, therefore, optimal government policy does not deviate from the Friedman rule in the presence of remittances so long as the government has the ability to enact a consumption tax. At each level of the remittances-to-income ratio, the optimal policy of equating the ex ante real returns on money and government bonds remains in place.

With declining steady-state tax rates on consumption and constant money growth rates, government policy becomes less distortionary. Government policy is relatively more distortionary under labor taxation after remittances are introduced, since the government finds it optimal to increase money supply and labor taxation. With the labor tax base falling, the government switches to a separate instrument—the inflation tax—that imposes additional welfare costs through the cash-in-advance constraint by distorting the choice between the cash and credit goods. Policy is relatively less distortionary under consumption taxation, since the tax base on consumption is increasing and the government has the proper instrument to act upon this base. With the proper instrument already in place, the government can refrain from imposing additional costs through the cash-in-advance constraint.

Under consumption taxes, the presence of remittances also leads to a larger reduction in the shadow price of debt and greater improvement in debt sustainability than is found under labor taxes. Under labor taxes, for example, the shadow price of debt in Table 6.1 declines almost 55 percent, from 0.11 to 0.05, when the economy moves from the baseline to a remittances-to-income ratio of 25 percent. Under consumption taxation, the shadow price of debt in Table 6.2 declines 88 percent in value. The relatively larger decline in the shadow price of debt under consumption taxation as the remittances-to-income ratio increases suggests that debt sustainability should improve more in the country or, equivalently, country risk should be reduced more through the implementation of a consumption tax system. Remittances as countercyclical income transfers create a countercyclical revenue base for the government, and the consumption tax provides direct access to this base without driving a wedge between cash and credit consumption. The relatively larger decline in the shadow price of debt under consumption taxation indicates that the consumption tax system is more efficient at extracting resources to service existing or new debt than a combination of the labor tax and the inflation tax.

Remittances and Macroeconomic Risks

Table 6.3 reports summary statistics on the moments of the business cycle for the calibrated Chile economies. As is commonly found in most real business cycle models, the baseline economy without remittances generates about half of the standard deviation of output as is found in the actual Chilean economy. However, the model economies without remittances generate volatilities for consumption, prices, and inflation that more closely match the features of actual data as reported by Bergoeing and Soto (2002).¹² Although money supply has very little volatility in either of the baseline economies without remittances, the volatilities for the price level and rate of inflation in each period are also determined by the volatility of the cash good, as a result of the cash-in-advance specification. The volatility of the interest rate is lower than that found in other studies, since the values reported here are based on the filtered value of the gross interest rate series as opposed to a series of net interest rates.

Table 6.3.

Standard Deviation of Calibrated Chile Economies

(In percent)

Source: Authors’ calculations. Note: “Output” is standard deviation of output from production (excluding remittances). The standard deviation of the interest rate is based on the gross real interest rate, whereas the standard deviation of the tax rate is based on the tax on labor income or consumption.

Table 6.3.

Standard Deviation of Calibrated Chile Economies

(In percent)

	Remittances-to-Income Ratio
	Labor Taxation					Consumption Taxation
Variable	0%	5%	15%	25%		0%	5%	15%	25%
Output	1.17	1.25	1.39	1.56		1.18	1.24	1.37	1.49
Remittances		0.62	0.70	0.78		0.62	0.68	0.75
Cash good	1.67	1.68	1.65	1.59		1.66	1.61	1.52	1.43
Credit good	1.66	1.54	1.39	1.36		1.66	1.61	1.52	1.43
Labor	0.26	0.13	0.10	0.37		0.23	0.13	0.07	0.26
Shadow price of debt	3.78	3.90	3.86	3.87		3.41	3.26	2.87	8.83
Price level	1.67	1.70	1.82	1.76		1.41	1.38	1.30	1.23
Inflation	1.21	1.18	1.13	1.10		1.03	1.00	0.94	0.89
Real interest rate	0.05	0.05	0.03	0.03		0.03	0.03	0.02	0.02
Debt	0.20	0.23	0.24	0.29		0.26	0.24	0.21	0.17
Money growth rate	0.02	0.15	0.29	0.29		0.00	0.00	0.00	0.00
Tax rate	1.56	1.33	0.90	1.13		1.90	1.87	1.80	1.73

Source: Authors’ calculations. Note: “Output” is standard deviation of output from production (excluding remittances). The standard deviation of the interest rate is based on the gross real interest rate, whereas the standard deviation of the tax rate is based on the tax on labor income or consumption.

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Table 6.3.

Standard Deviation of Calibrated Chile Economies

(In percent)

	Remittances-to-Income Ratio
	Labor Taxation					Consumption Taxation
Variable	0%	5%	15%	25%		0%	5%	15%	25%
Output	1.17	1.25	1.39	1.56		1.18	1.24	1.37	1.49
Remittances		0.62	0.70	0.78		0.62	0.68	0.75
Cash good	1.67	1.68	1.65	1.59		1.66	1.61	1.52	1.43
Credit good	1.66	1.54	1.39	1.36		1.66	1.61	1.52	1.43
Labor	0.26	0.13	0.10	0.37		0.23	0.13	0.07	0.26
Shadow price of debt	3.78	3.90	3.86	3.87		3.41	3.26	2.87	8.83
Price level	1.67	1.70	1.82	1.76		1.41	1.38	1.30	1.23
Inflation	1.21	1.18	1.13	1.10		1.03	1.00	0.94	0.89
Real interest rate	0.05	0.05	0.03	0.03		0.03	0.03	0.02	0.02
Debt	0.20	0.23	0.24	0.29		0.26	0.24	0.21	0.17
Money growth rate	0.02	0.15	0.29	0.29		0.00	0.00	0.00	0.00
Tax rate	1.56	1.33	0.90	1.13		1.90	1.87	1.80	1.73

Source: Authors’ calculations. Note: “Output” is standard deviation of output from production (excluding remittances). The standard deviation of the interest rate is based on the gross real interest rate, whereas the standard deviation of the tax rate is based on the tax on labor income or consumption.

Although the results of the simulation procedure presented in the previous sections confirm some of the preconceived ideas about the benefits derived from remittances—increased consumption, potential poverty reduction, and more robust debt sustainability—they indicate that these benefits come at a cost. As remittances are added to the baseline economies in Table 6.3, the reported standard deviation of output rises, indicating that the presence of remittances leads to increased business cycle volatility. This result holds regardless of the tax system in place. Business cycle volatility rises by one-third under the labor tax case and by one-fourth under the consumption tax case. The increase in business cycle volatility arises because the presence of remittances increases the correlation between labor supply and output. In each of the model economies for Chile, household labor supply is reacting to information from two channels, the domestic production process channel and the remittance channel. As the ratio of remittances to income increases, the household begins to respond more forcefully to the remittance channel, and it is through this channel that labor supply becomes more procyclical.

The increased correlation between labor and output in response to remittances and the resulting amplification in business cycle volatility behavior can best be understood by examining the demand and supply for labor in general equilibrium. Figure 6.1 illustrates the market for labor. The quantity demanded for labor, D, is decreasing in the real wage rate, whereas the quantity of labor supply, S, is increasing in the real wage rate. The figure illustrates the response of labor supply and demand to a positive technology shock in the baseline economy without remittances and in the economies with remittances. In the baseline economy without remittances, the labor market is initially in equilibrium at point A, with H₁ hours of labor supplied at a real wage of W/P₁. The realization of the positive shock to technology leads to an increase in the demand for labor among firms, since workers are more productive, causing the demand for labor curve to shift outward for every level of real wages. On the other hand, increases in technology that lead to higher levels of income through the production function lead to more consumption, so that workers require a higher real wage rate to provide the same amount of hours worked. The magnitude of the decline in labor supply depends on the marginal disutility of supplying additional labor. In the U.S. and Chile cases, the calibrated values for the marginal disutility of labor are sufficiently high that the resulting decline in labor supply is large enough to offset fully the increased demand for labor, leading to a decline in the equilibrium level of hours worked and a higher real wage.¹³ This is the situation illustrated in Figure 6.1 as the economy moves from initial equilibrium at point A to the new equilibrium at point B. Income to the household still rises despite the decline in labor (e.g., the decline in labor supply does not offset the impact of technology on production), and the household spreads these resources across consumption and leisure in equilibrium. Household labor therefore acts as a device to smooth shocks to consumption and leisure, resulting in an initial negative correlation between labor and technology.

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Labor Market Dynamics in Response to a Positive Technology Shock

Note: In the nonremittance economy, positive technology shocks cause the demand for labor to increase. However, increases in technology that lead to higher levels of income result in workers’ requiring a higher real wage rate to provide the same amount of hours worked. The resulting decline in labor supply is large enough to offset fully the increased demand for labor, creating a new equilibrium at point B. When remittances are included, the shift in demand for labor from D₁(θ₁, K) to D₂(θ₂,K) is larger than in the baseline case, since the marginal product of labor is larger. The supply for labor still shifts inward from S₁(θ₁) to S₂(θ₂), but the shift is smaller, since the household now has to balance countercyclical remittance flows in addition to income from production. Positive technology shocks that increase income from production lead to declines in remittance transfers, dampening the household’s desire to reduce labor supply in favor of leisure. In the economies with remittances, smoothing consumption and leisure against shocks requires the household labor supply to become more procyclical.

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When remittances are included in the calibrated economy, the behavior in the labor market changes. In Figure 6.1 the initial equilibrium hours worked with remittances included in the economy, H₃, is lower than that in the baseline case, H₁, but with remittances, the equilibriums have higher output per worker and real wage rates. These results can be discerned from Tables 6.1 and 6.2. The outward shift in demand for labor by firms from D₁(θ₁,K) to D₂(θ₂,K) is larger when technology shocks occur in the presence of remittances, since the marginal product of labor is higher. The supply for labor still shifts inward from S₁(θ₁) to S₂(θ₂) in response to the technology shock, but the inward shift is smaller than in the baseline case. This dampened labor supply response is a consequence of the influence of the remittance channel on household labor supply decisions. Positive technology shocks lead to a net increase in income from production, despite the household’s desires to choose more leisure. The net increase in production income causes output to rise above steady-state output, leading to a reduction in remittances owing to the countercyclical nature of these flows. Since the household is now concerned with smoothing consumption and leisure using resources from a pool that includes income from both production and remittances, the household does not reduce its labor supply in the economies with remittances as much as it does in the economies without remittances. The inward shift in the labor supply curve is therefore reduced when remittances are present. The net impact of the technology shock in the presence of remittances is an increase in labor supply from H₃ to H₄ as the economy moves from point C to point D in Figure 6.1. The results of the simulations indicate that the correlation between labor hours and income, which starts out negative with no remittances, is positive at a remittances-to-income ratio of about 8 percent and reaches unity at a remittances-to-income ratio of 25 percent. In each case the household is interested in smoothing consumption and leisure in the face of shocks. Doing so in an economy with remittances requires household labor supply to become more procyclical. This increased procyclicality of labor, despite being derived from optimal behavior on the part of households, has the unsavory effect of producing additional business cycle volatility.

The simulation results also indicate that remittances’ ability to provide an insurance effect for shocks to consumption should be viewed as conditional. An insurance effect is present for consumption of the credit good, since remittances can be converted into consumption of this good in the same period the household receives the countercyclical income transfer. In contrast, the cash-in-advance constraint means the household has to transfer remittance resources across time to consume the cash good, and the more volatile inflation and output processes lead to increased volatility of cash good consumption, though mainly under labor taxation. In the U.S. case under labor taxation, for example, volatility of credit good consumption declines, whereas volatility of cash good consumption increases as the level of remittances rises. The credit-intensive nature of the calibrated U.S. economy is instrumental in this regard. Though the economy’s credit-based nature provides for an insurance effect on shocks to income, the need to use the inflation tax to access a small cash good tax base for revenues increases inflation and cash good consumption volatility.¹⁴ In contrast, volatilities for both the cash and credit good decline under consumption taxation. The ability of remittances to provide consumption insurance against shocks to household income depends on two factors: the relative importance of the cash and credit good in household consumption and the type of tax system in place.

Finally, the countercyclical nature of remittances and their procyclical effect on output has varying consequences for the volatility of government policy. In the economies without remittances in Table 6.3, nearly all the volatility in government policy appears in taxes, as the labor and consumption tax rates fluctuate to preserve the Friedman rule. As remittances are added to the economies, their effect on government policy risk is instrument dependent. Under labor taxation, the presence of remittances increases the mean equilibrium growth rate of money and also increases its volatility. Under consumption taxation, these effects are removed as the government finds itself with a countercyclical tax base, allowing for an improved set of optimal government policies. In both tax structures the volatility of the shadow price of debt increases, reflecting the optimality of using debt as a shock absorber, since the marginal cost of servicing debt falls in equilibrium when remittances are present.

A preliminary examination of the data from remittance-dependent economies generally confirms the model results that economies with higher reliance on remittance flows experience higher rates of output volatility and inflation. Figure 6.2 plots the standard deviation of output volatility and the average inflation rate in economies with remittances-to-GDP ratios of 5 percent or more during the period from 1990 to 2003. The data indicate that economies that received higher levels of remittances also experienced higher rates of output volatility and higher average inflation rates, with the relationship between remittances and business cycle volatility appearing particularly strong.¹⁵

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Remittance-Dependent Economies: Output Volatility and Inflation

Sources: World Bank (2006) and authors’ calculations.Note: Countries included registered average ratio of workers’ remittances to GDP of 5 percent or greater from 1990 to 2003. Volatility of output is calculated as the standard deviation of filtered logged real GDP per capita using the Hodrick-Prescott (1997) filter. Reported inflation figure is average annual CPI inflation from 1990–2003.

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Welfare Implications of Remittances

Any increase in household utility resulting from remittances depends on the extent to which the marginal gain from remittances outweighs the marginal cost from additional volatility, and to what degree the household prefers one tax structure over another. A certainty equivalence framework is used to measure the gain to households from remittances and to discern household utility under the different tax systems. To measure the gain from remittances, utility equivalence is measured as the per period increase in utility that makes the household indifferent between the economy without remittances and the economy with remittances under the selected tax structure. Utility equivalence measures are constructed for both the United States and Chile under labor income and consumption taxation. Computing the difference in utility gains under each tax system reveals the optimal tax system.

The gain to the household from higher consumption and leisure as a result of remittances is found to greatly outweigh the increased business cycle volatility. For example, the per period gain in utility in moving from the economy without remittances to the economy with a 5 percent remittances-to-income ratio under labor taxation is 5.0 percent for Chile, and this gain increases to 21.2 percent at the 25 percent level of remittances. Countercyclical remittances provide enough insurance effects for consumption to minimize the costs of economic volatility and increased government policy distortions. The increased levels of consumption and leisure also represent first-order increases in utility versus a second-order loss from additional output volatility, and business cycle models are known to have difficulty in replicating the amount of volatility present in actual data. Though these gains appear extremely large on their face, most of the increase comes from additional leisure, which represents nearly 60 percent of the overall rise in per period utility.

The results displayed in Table 6.4 indicate that consumption-based taxation is preferable to labor-based taxation in remittance-dependent economies in terms of its effects on remittance-receiving households. The numbers in the table reveal the difference in utility gains between the two tax systems, measured as the utility gains from various levels of remittances under consumption taxation minus those under labor taxation. The gains in total utility under consumption taxation are slightly higher in all cases than those under labor taxation. Per period increases in utility for Chile range from 0.05 percent to 0.51 percent. The results in the U.S. case are similar, with net per period gains increasing to 0.66 at a 25 percent remittances-to-income ratio. When the contribution to overall utility gains is examined, the relative gains from cash good consumption from restoration of the Friedman rule are revealed to be sufficient to outweigh the relative decline in leisure and credit good consumption when the household switches from labor taxation to consumption taxation. Marginal analysis can explain why the elimination of the inflation tax boosts the utility gains from the cash good by more than the decline in utility of the credit good. The presence of a significant inflation tax under labor income taxation drives the household toward more credit good consumption, increasing its level of satisfaction, but eroding the marginal utility of further credit good consumption. By switching to a consumption tax and eliminating the need for the inflation tax, the household returns to a more optimal balance between cash and credit consumption. On the margin this results in higher utility.

Table 6.4.

Utility Gains from Consumption Taxation Versus Labor Taxation

(Difference in per period increase in utility, in percent)

Source: Authors’ calculations. Note: The statistics reflect the difference in utility gains between the economies with remittances under consumption taxation and those under labor taxation. A positive value indicates that utility gains are larger under consumption taxation.

Table 6.4.

Utility Gains from Consumption Taxation Versus Labor Taxation

(Difference in per period increase in utility, in percent)

			Remittances-to-Income Ratio
			Chile			United States
			5%	15%	25%	5%	15%	25%
Total utility			0.05	0.22	0.51	0.05	0.29	0.66
	Consumption		1.60	3.77	6.12	1.45	3.98	6.32
		Cash good	8.66	18.89	24.52	2.82	7.41	10.73
		Credit good	−1.30	−2.54	−1.73	−0.23	−0.24	0.84
		Labor	−0.83	−1.80	−2.70	−0.98	−2.44	−3.55

Source: Authors’ calculations. Note: The statistics reflect the difference in utility gains between the economies with remittances under consumption taxation and those under labor taxation. A positive value indicates that utility gains are larger under consumption taxation.

View Table

Table 6.4.

Utility Gains from Consumption Taxation Versus Labor Taxation

(Difference in per period increase in utility, in percent)

			Remittances-to-Income Ratio
			Chile			United States
			5%	15%	25%	5%	15%	25%
Total utility			0.05	0.22	0.51	0.05	0.29	0.66
	Consumption		1.60	3.77	6.12	1.45	3.98	6.32
		Cash good	8.66	18.89	24.52	2.82	7.41	10.73
		Credit good	−1.30	−2.54	−1.73	−0.23	−0.24	0.84
		Labor	−0.83	−1.80	−2.70	−0.98	−2.44	−3.55

Source: Authors’ calculations. Note: The statistics reflect the difference in utility gains between the economies with remittances under consumption taxation and those under labor taxation. A positive value indicates that utility gains are larger under consumption taxation.

Although it appears to be small, the value of choosing the correct tax system is not negligible. The gains involved in moving from a system based on labor income taxes to one based on consumption taxes are roughly equivalent in magnitude to the cost of the business cycle volatility as reported by Lucas (1987) and the gains from eliminating moderate inflation reported by Cooley and Hansen (1991) and Aiyagari, Braun, and Eckstein (1998). Using the Lucas (1987) framework and the calibrated values from the current study yields a gain in per period utility of 0.9 percent through elimination of the business cycle. Employing a stochastic monetary economy similar to the one used in the current analysis, Cooley and Hansen (1991) report that transitioning from 5 percent and 10 percent inflation to zero inflation results in gains in lifetime utility of 0.4 percent and 0.6 percent, respectively.

Conclusion

The purpose of this chapter has been to explain how remittances affect the economy and the conduct of optimal government policy. The results are derived in a dynamic general equilibrium model in which households receive countercyclical remittance flows and government policy is enacted with distortionary effects. They indicate that remittances increase household consumption and leisure, confirming the widespread belief that remittances can be useful in reducing poverty levels. As a second main benefit, remittances are found to improve the sustainability of government debt. The reduction in the marginal cost of servicing debt occasioned by the presence of remittances in an economy allows the government to expand its debt or service existing debt with less distortionary costs to the economy, thereby reducing country risk. The additional sustainable debt can be used to improve infrastructure or public education if the remittance-receiving country has a public project with high positive net present value. Alternatively, if the positive net present value projects reside in the private sector, the government can use its increased flexibility to reduce country risk and encourage private investment or development of human capital. Either way the increase in debt sustainability from remittances can lead to higher long-run economic growth as investment in physical and human capital increases.

However, the results also indicate that these gains come at the cost of greater macroeconomic risk. Remittances that cause the labor supply to become more pro-cyclical increase the magnitude of the domestic business cycle. The countercyclical nature of remittances does provide some insurance against the increase in volatility of output and income from domestic production, but the level of insurance is dependent on the cash or credit intensiveness of the economy, indicating that the economy’s level of financial development plays a role in maximizing the benefits of altruistic income transfers.

Finally, the presence of remittances highlights the need for policymakers to select the correct—or least distortionary—set of policy instruments when implementing fiscal and monetary policy. A reliance on labor income taxation may force the government to use the inflation tax to access the revenue base provided by remittances, thereby injecting additional distortions into the economy. The ability to enact a consumption tax removes this incentive and allows the government to finance its budgetary expenditures with the least distortionary impact on economic activity. Governments, and the official institutions that advise them, should be aware that the efficient conduct of policy may require a different policy apparatus when remittance flows become significant and should therefore avoid a one-size-fits-all solution to tax structure and policy implementation across countries.

Appendix 6.1. The Model

This appendix briefly explains the model used to generate the results presented in this chapter. The model, which is an extension of that used in Chami, Cosimano, and Gapen (2006), combines a cash-in-advance and stochastic growth model, similar to those used in Cooley and Hansen (1995), Chari, Christiano, and Kehoe (1991), and Lucas and Stokey (1983). The economy comprises a representative household, a representative firm, a government, and remitters.

Production

Output, Y_t, is produced from a constant-returns-to-scale production function,

$\begin{array}{cc}\begin{array}{cc}{Y}_t=\exp \left({\theta }_t\right)H_t^{\alpha }{K}_t^{1-\alpha },& 0<\alpha <1,\end{array}& \left(6.1\right)\end{array}$

View Expanded

where K_t and H_t are the aggregate capital stock and labor supply, respectively, α is the share of income attributable to labor, and θ_t represents technology. Changes in technology are assumed to be the realization of an exogenous autoregressive stochastic process,

$\begin{array}{cc}\begin{array}{cc}{\theta }_t={\rho }_{\theta }{\theta }_{t-1}+{\varepsilon }_t,& 0<{\rho }_{\theta }<1,\end{array}& \left(6.2\right)\end{array}$

View Expanded

where the random variable, ε_t, is normally distributed with mean zero and standard deviation σ_θt. The realization of the shock to technology is known to all agents at the beginning of period t.

Investment in physical capital in period t produces capital in period t + 1 according to

$\begin{array}{cc}\begin{array}{cc}{K}_{t+1}=(1-\delta )K_t+X_{t,}& 0<\delta <1,\end{array}& \left(6.3\right)\end{array}$

View Expanded

where X_t is the level of investment and δ is the rate of depreciation. The capital stock is assumed to be fixed so that X_t = X = δK. The representative firm seeks to maximize profit by choosing labor supply resulting in the standard first-order conditions for the wage rate and rental rate on capital, adjusted for constant capital.

Households

The representative household obtains utility from consumption and leisure. Preferences are summarized by the following utility function:

$\begin{array}{cc}{E}_t{\displaystyle \sum _{t=0}^{\infty }{\beta }^t[a\log \left(C_{1t}\right)+(1-a)\log \left(C_{2t}\right)-\gamma H_t],}& \left(6.4\right)\end{array}$

View Expanded

where β is a discount factor, C₁ is a cash good, C₂ is a credit good, a is the relative weight of cash to credit goods in utility, γ is a positive constant measuring the marginal disutility of supplying additional labor, and 0 < β, a < 1. The specification of linear disutility of labor is derived from the assumptions that labor is indivisible and allocation of labor is determined by employment lotteries (Hansen, 1985; Rogerson, 1988). The household enters the period with previously accumulated assets composed of money holdings, M_t, and gross returns from government bonds, B_tR_t−1, where B_t is the stock of bonds and R_t−1 is the gross real interest rate.

Based on the existing evidence in the literature, which shows remittances to be countercyclical, the household receives remittances, η, equal to

$\begin{array}{cc}{\eta }_t=r_0{\left(\frac{\overline{Y}}{Y_t}\right)}^{r_1},& \left(6.5\right)\end{array}$

View Expanded

where $\overline{Y}$ is the steady-state level of output and r₀ and r₁ are positive constants, with the former determining the responsiveness of remittances to the business cycle and the latter equaling the steady-state level of remittances.

Labor Taxation

The model used to generate the results in this chapter does not allow direct taxation of remittances, but instead allows the government to use either a tax on labor income or one on consumption. When a labor income tax is employed, the household, government, and economy-wide resource constraints are as follows.

Previously accumulated assets, after-tax income from production, and remittance income are all used to finance household expenditures. Households know the past and current realization of technology and government spending. After these shocks are revealed and expectations are formed, the household then decides on labor supply, receives remittances, and chooses consumption of the cash and credit goods and government bonds and the amount of money to be carried into the next period. Overall, household allocations must satisfy the following budget constraint:

$\begin{array}{cc}{C}_{1t}+C_{2t}+\frac{M_{t+1}}{P_t}+B_{t+1}\le (1-{\alpha \tau }_t^{\text{h}})(Y_t-X)+{\eta }_t+\frac{M_t}{P_t}+B_t{R}_{t-1},& \left(6.6\right)\end{array}$

View Expanded

where P_t is the price level and τ^h is the tax applied to labor income.¹⁶ M_t+1 is the demand for money balances that are used in the next period and aggregated across households in relation to the money supply in equilibrium.

Previously accumulated money balances are used to purchase the cash good in the current period and must satisfy the cash-in-advance constraint,

$\begin{array}{cc}{P}_t{C}_{1t}\le M_t.& \left(6.7\right)\end{array}$

View Expanded

Real government consumption, G_t, is assumed to follow an exogenous stochastic process. Government policy includes sequences of labor taxes and supplies of money and bonds, which must satisfy the following budget constraint:

$\begin{array}{cc}\frac{M_t}{P_t}+B_t{R}_{t-1}={\tau }_t^{\text{h}}\alpha \left(Y_t-X\right)-G_t+B_{t+1}+\frac{M_{t+1}}{P_t},& \left(6.8\right)\end{array}$

View Expanded

where the initial stocks of money, M₀, and bonds, B₀, are given. The money supply and government spending in period t are assumed to grow at the net rate of exp(g_t) − 1 and exp(μ_t+1) − 1, respectively. Thus, the level of government spending and money stock, respectively, are defined as

$\begin{array}{cc}{G}_t=\exp \left(g_t\right)G_{t-1}& \left(6.9\right)\end{array}$

View Expanded

and

$\begin{array}{cc}{M}_{t+1}=\exp \left({\mu }_{t+1}\right)M_{t\mathrm{.}}& \left(\begin{array}{c}6.10\end{array}\right)\end{array}$

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The random variable g_t is assumed to evolve according to

$\begin{array}{cc}\begin{array}{cc}{g}_t={\rho }_g{g}_{t-1}+{\xi }_t,& 0<{\rho }_g<1,\end{array}& \left(6.11\right)\end{array}$

View Expanded

where ξ_t is normally distributed with mean zero and standard deviation σ_gt. As with the shock to technology, the realization of the spending shock is known to all at the beginning of the period. Finally, the economy-wide resource constraint is

$\begin{array}{cc}{C}_{1t}+C_{2t}+X+G_t=Y_t+{\eta }_t,& \left(6.12\right)\end{array}$

View Expanded

which states that output from production plus remittances can be consumed by either the household or the government or used to replace depreciated capital.

Consumption Taxation

If the government chooses to implement a consumption tax instead of a labor income tax, equations (6.6)–(6.8) must be altered to account for the change in tax structure. Household allocations must satisfy the following budget constraint under consumption taxation:

$\begin{array}{cc}\left(C_{1t}+C_{2t}\right)\left(1+{\tau }_t^{\text{c}}\right)+\frac{M_{t+1}}{P_t}+B_{t+1}+X\le Y_t+{\eta }_t+\frac{M_t}{P_t}+B_t{R}_{t-1},& \left(6.13\right)\end{array}$

View Expanded

where τ^c is the tax on household consumption and is applied at the same rate to both the credit and cash good. The household pays the tax on credit good consumption with credit and that on cash good consumption with previously accumulated money balances according to¹⁷

$\begin{array}{cc}{P}_t{C}_{1t}(1+{\tau }_t^{\text{c}})\le M_t.& \left(6.14\right)\end{array}$

View Expanded

Government policy includes sequences of consumption taxes and supplies of money and bonds that must satisfy the following budget constraint:

$\begin{array}{cc}\frac{M_t}{P_t}+B_t{R}_{t-1}={\tau }_t^{\text{c}}(C_{1t}+C_{2t})-G_t+B_{t+1}+\frac{M_{t+1}}{P_t}.& \left(6.15\right)\end{array}$

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The equations for the remaining processes describing the growth of money, government spending, the shocks to technology and spending, and the economy-wide resource constraint are identical to those under labor-based taxation.

The Ramsey Equilibrium with Remittances

The government’s goal is to maximize the household’s welfare subject to raising revenues through distortionary means. After the shocks to the system are revealed, the government selects a policy profile and the household responds with a set of allocations that together satisfy budget and resource constraints and determine the equilibrium price system. The Ramsey problem is to choose a competitive equilibrium that maximizes household utility (Ramsey, 1927). The competitive equilibrium that solves the Ramsey problem is called the Ramsey plan or Ramsey equilibrium.

Like that of the household, the government’s maximization problem can be set up as a dynamic-programming problem. For example, under labor taxation the government seeks to maximize

$\begin{array}{cc}V\left(s_t\right)=\underset{{\Delta }_t}{\max }\{a\log \left(C_{1t}\right)+(1-a)\log \left(C_{2t}\right)-\gamma H_t+{\lambda }_t[{\tau }_t^{\text{h}}\alpha (Y_t-X)-G_t+B_{t+1}+\frac{M_{t+1}}{P_t}-\frac{M_t}{P_t}-B_t{R}_{t-1}]+\beta E_{t}V\left(s_{t+1}\right)\}& \left(6.16\right)\end{array}$

View Expanded

where Δ_t = (τ_t, μ_t+1, B_t+1) is the set of choice variables, s_t represents the set of state variables (B_t, M_t/P_t−1, θ_t−1, g_t−1, τ_t−1, R_t−1), and λ_t is the Lagrange multiplier on the government budget constraint or the value that the household places on the government’s ability to raise revenue from a source “outside” the economy. Such an ability would be equivalent to collection of a lump-sum tax, making the multiplier equal to the shadow value of reducing debt. Solving for the multiplier as an endogenous policy variable reveals how the shadow price of debt behaves relative to marginal taxation and money growth.

A similar set of equations can be developed for the case of consumption-based taxation. The Euler conditions from the Ramsey problem, the labor equation from the household’s problem, and the government budget constraint yield a set of operator equations that define the Ramsey equilibrium with remittances.