بودجه متعادل کننده در مقابل هموارسازی مالیات در یک اقتصاد باز کوچک : مقایسه رفاه

The objective of this paper is to investigate the effect of lending and borrowing constraints on the dynamics of public debt and optimal taxation policy in the context of a general equilibrium model with tax smoothing. The results from the numerical simulation of the model show significant welfare gains, provided that the policymaker is allowed to borrow and lend in order to smooth taxes across time instead of maintaining a balanced budget at all times. Moreover, for a specific process for asset prices, it is also shown that if the government can issue state-contingent debt then overall welfare can be further improved substantially.

Is a series of continuous budget deficits necessarily bad? Besides being a clear sign of fiscal prudence, does a balanced budget rule also improve social welfare? How should tax rates and, consequently, public debt respond to innovations in government expenditures? Theoretical advancements on solving stochastic intertemporal optimization problems with implementability constraints,1 have reinvigorated research on optimal debt issue and the implied structure of taxation policy.2 The present paper applies this new technique in the context of a small open economy, in which the social planner (the government) is faced with stochastic expenditures. The objective is to study the welfare implications if the policymaker adopts a fiscal policy plan that deviates from a strict balanced budget rule. It is shown that there are significant welfare gains to be made if the government equates revenues with expenditures in a present value sense, instead of every period, such that its intertemporal infinite horizon budget constraint is satisfied. Stockman (2001) has performed a comprehensive analysis of the welfare effects of balanced budget restrictions in the context of a closed economy with exogenous growth. Using a similar framework to the one used in Chari et al., 1994 and Chari et al., 1995, he considered the Ramsey problem for a model calibrated to the US economy, placing restrictions on the amount of debt that the government can issue. In his setting, he found substantial welfare losses associated with the balanced-budget restriction: depending on preference parameterization, consumption would have to increase from 0.61% up to 1.45% at each date and for each state in order to make the representative household indifferent between fiscal policy regimes. Stockman’s study builds on the work by Lucas and Stokey (1983) who considered a general equilibrium model with complete markets, exogenous Markov government expenditures and state-contingent taxes. The Lucas and Stokey framework emphasizes the role of state-contingent debt as an “insurance” against bad times, that allows the government to smooth tax distortions across both time and states of nature. As a result, in times of temporary increases in government expenditures, the level of public debt falls. In addition, Lucas and Stokey show that the serial correlations of optimal tax rates are closely related to those for government expenditures. In their model, tax rates are smooth only to the extent that they exhibit a smaller variance than a balanced budget would imply. Aiyagari et al. (2002) reconsider the Lucas and Stokey economy under the restriction that the government cannot issue state contingent debt; but rather it can borrow and lend at an endogenous risk-free rate. In their attempt to replicate Barro (1979) classic “tax smoothing” result in a general equilibrium environment, they show that this restriction (i.e., market incompleteness) imposes additional implementability constraints with respect to the equilibrium allocation, beyond the single implementability constraint imposed under complete markets. In particular, these constraints require the allocation to be such that at each date the present value of the budget surplus evaluated at current period Arrow prices be known one period ahead. Under the condition that an ad hoc limit is imposed on the government’s asset holdings, the authors show that the Ramsey equilibrium exhibits features shared by both Barro’s and Lucas and Stokey’s economies, but the dynamics of debt and taxes actually resemble more closely Barro’s “tax-smoothing” result.3 Recently, several authors have reported tax smoothing behavior for various small open economies. Among others, Strazicich (1997) using annual time-series data over the period 1929–1990, fails to reject the tax-smoothing hypothesis for the Canadian federal government. Cashin et al. (1998) find that the behavior of the central government of India is consistent with the tax-smoothing hypothesis for the period 1951–1952 to 1996–1997. A similar result is obtained by Cashin et al. (1999) for Pakistan during the period 1956–1995, but the hypothesis is rejected for Sri Lanka during 1964–1997. Strazicich (2002) considers a panel of 19 industrial countries over the period 1955–1988 and finds evidence in support of tax smoothing as a theory of public debt. Adler (2006) finds that Barro’s model can explain about 60 percent of the variability in the Swedish central government budget surplus for the period 1952–1999. These empirical studies point to the need to analyze the tax smoothing motive in the context of a small open economy facing exogenous asset prices. This provides one motivation for the present paper. We consider an asymmetric small open economy with respect to accessibility to financial markets: households are allowed to perform transactions involving state-contingent financial claims, while the government is restricted to borrow and lend only at a constant risk-free interest rate.4 A possible justification for this assumed financial asymmetry might be the inherent “moral hazard” that is present if the government is allowed to issue state-contingent debt or bonds. The return on these bonds would have been linked to the level of macroeconomic variables, such as the inflation rate or the Debt/GDP ratio. However, these variables are under the strong influence of the government’s actions, thus damaging the marketability of these bonds among private agents. Another justification for such an asymmetry follows from the work of Sleet, 2004 and Sleet and Yeltekin, 2006, who demonstrate that if the government has access to a complete set of contingent claims markets but is unable to either commit to future debt repayments or truthfully reveal private information regarding its spending needs, then the market for public debt becomes endogenously incomplete. Studying the implications of the coexistence of complete and incomplete markets in a small open economy is new in the literature on optimal taxation. 5 Furthermore, if one wishes to maintain the representative agent framework, the simplest environment to discuss the implications of this asymmetry is that of a small open economy.6 In our setting, the government is required to determine the optimal fiscal policy plan as of time zero that maximizes the welfare of the representative household, given a stream of stochastic government expenditures. These expenditures are financed by taxing labor income and issuing debt. In contrast to Aiyagari et al. analysis, here the price of government bonds is assumed to be exogenously determined. Another contribution of the present paper is to provide an extensive numerical analysis of the tax smoothing motive and welfare gains with alternative assumptions regarding the stochastic process for government expenditures. For the incomplete markets case, we consider three stochastic processes: (i) serially uncorrelated, (ii) serially correlated, and (iii) serially correlated expenditures whose volatility is adjusted to be equal to that of uncorrelated expenditures. We study the implications of each process for the optimal fiscal policy as the government’s lending and borrowing constraints are relaxed. The comparison of the various cases is based on the persistence and other descriptive statistics of the equilibrium tax rates, as well as the distribution of the government’s asset and debt holdings. It is shown that providing more flexibility to the government in terms of the amounts it can borrow and lend, leads to smoother tax rates across time and higher social welfare compared to a balanced budget policy regime. In other words, as the government’s lending and borrowing range becomes wider, the persistence of the equilibrium tax rates increases and their volatility declines for all types of government expenditures considered. As a consequence, welfare increases. These findings are consistent with the arguments against balanced-budget rules in closed economies, as in Schmitt-Grohé and Uribe, 1997 and Stockman, 2001. Our results demonstrate also that one does not have to restrict access to complete markets for both sectors of the economy (private and public) in order to retain the random walk property of tax rates. An additional implication is that minimizing tax distortions is the most significant factor influencing the decision of the fiscal authority. In Aiyagari et al. the government has to consider the effect of debt issue on interest rates. By abstracting completely from interest rate effects, we still obtain the tax smoothing result, which implies that the quantitative results of Aiyagari et al. are relevant even for small open economies. Further, using a particular stochastic process for the prices of the state-contingent bonds and complete financial markets for the government, we show that overall welfare significantly improves relative to the balanced budget and incomplete markets cases. In addition, compared to the incomplete markets case, the resulting welfare gains increase as the persistence of the government expenditures shocks rises. These results can be interpreted as the “cost” of the moral hazard problem that was used to justify the assumed asymmetry between the public and private sectors of the economy. 7 Finally, it should be noted that the improvement in welfare when the government shifts from maintaining a balanced budget to issuing state-contingent debt is slightly higher than the one reported by Stockman (2001) in the context of a closed economy, although admittedly the differences in model specification do not permit a completely satisfactory comparison of the two models.8 The rest of the paper is organized as follows. Section 2 describes the theoretical model for the small open economy and defines the Ramsey problem that maximizes the representative household’s utility. Section 3 provides details regarding the parameterization of the model for the numerical analysis. Section 4 reports the quantitative results and compares the welfare results for different types of government expenditures and borrowing and lending constraints for the government. Section 5 performs welfare analysis under the assumptions of complete financial markets for the government and a specific process for asset prices, and compares the results to the case of incomplete financial markets and balanced government budget. Section 6 concludes the paper.

This paper considered a small open economy in which only households have access to complete financial markets. On the other hand, the government is constrained to borrow and lend at a constant and exogenously determined risk-free interest rate. Allowing the policymaker to borrow and lend large amounts yields a Ramsey equilibrium that replicates Barro’s “tax-smoothing” result regarding the conduct of optimal fiscal policy in the presence of uncertainty. Considering three different stochastic processes for government expenditures, it is shown that relaxing the policymaker’s borrowing and lending constraints allows more flexibility to smooth tax rates across time, thus reducing the distortionary effect of taxation and improving social welfare. This is in contrast to a fiscal policy regime, in which the policymaker is constrained to maintain a balanced budget at all times. Allowing the government to issue state-contingent debt and given a specific stochastic process for the prices of the state-contingent financial claims, it is shown that overall welfare improves relative to the incomplete markets and balanced budget cases. Furthermore, compared to the incomplete markets case, the resulting welfare gains appear to be higher as the persistence in the stochastic process for government expenditures increases. It would be interesting to work out several extensions of the current model. For instance, the welfare comparison between the complete markets case with the incomplete markets and balanced-budget cases was based on assumption (22) about asset prices. This assumption allowed us to derive an analytic solution for the equilibrium allocation in the complete markets case. Future work should appropriately modify this numerical scheme and solve the complete markets model under assumption (20). This will enable us to get a sense of how the welfare gains resulting from issuing state-contingent debt depend on the assumed asset pricing process. Furthermore, given the overall focus of the paper on welfare, sensitivity analysis is especially important regarding the exogenous process for the price of state-contingent claims (20). It would also be interesting to consider preferences such as the ones discussed in Barro and Sala-i-Martin (2004, p. 423), that are consistent with the empirical regularities observed in the growth literature, as well as technology shocks in addition to stochastic government expenditures as in Marcet and Scott (2003). The basic model of this paper can be extended by endogenizing the choice of government expenditures and adding a maturity structure in the issue of public debt. These modifications will not only add more realistic features to the present setup, but will also facilitate a quantitative exercise in which the model is calibrated to an actual economy. Finally, an interesting question that needs to be addressed is whether the welfare loss resulting from a balanced budget rule is higher or lower in a small open economy compared to a closed one.