A Toolbox for the Numerical Study of Linear Dynamic Rational Expectations Models

By simplifying the computational tasks and by providing step-by-step explanations of the procedures required to study a linear dynamic rational expectations (LDRE) model, this paper and the accompanying ``LDRE Toolbox' of Matalb functions guide a researcher with almost no experience in computational work to resolve and study his own model. After coding the model following specific guidelines, a single function call is all that is needed to log-linearize the model; simulate it under exogenous sequences of shocks; compute sample and population moment conditions; and obtain impulse-response functions. Three classical models in the Real-Business-Cycles literature are solved and studied throughout to give detailed examples of the steps involved in solving and studying LDRE models using the LDRE Toolbox. Namely, the economies in Brock and Mirman (Optimal Growth and Uncertainty: the Discounted Case, Journal of Economic Theory, 4(3): 479-513; 1972); King, Plosser, and Rebelo (Production, Growth and Business Cycles I: The Basic Neoclassical Model, Journal of Monetary Economics 21: 195-232; 1988); and Mendoza (Real Business Cycles in a Small Open Economy, American Economic Review 81(4): 797-818; 1991).RBC models; Solution method; Toolbox of Matlab functions; Log- linear approximation techniques

Sustainable Fiscal Policy with Rising Public Debt-To-Gdp Ratios

In financial and economic policy circles concerned with public debt in developing countries, a rising debt-GDP ratio is interpreted as a signal of overborrowing, warning of debt defaults if strong fiscal corrections are not adopted in time. This paper shows why this interpretation is incorrect by building a simple model of fiscal policy in which upward-sloping debt paths are observed even though the probability of default is ``almost surely" equal to zero.public debt; fiscal policy; debt sustainability; debt limits

World Interest Rate, Business Cycles, and Financial Intermediation in Small Open Economies

The consensus about the ability of the standard open-economy neoclassical growth model to account for interest-rate driven business cycles has changed over time: whereas early research concluded that business cycles are neutral to interest-rate shocks, more recent investigations suggest that these shocks can explain a large extent of the business cycles of a small open economy when firms borrow to pay for their labor cost before cashing their sales. The first goal of this paper is to show that the recently found effectiveness of interest-rate shocks to cause business cycles rests more on the statistical properties of the shocks than on the working-capital constraint; in particular, recent results are only valid when the level and volatility of the interest rate are high and when the interest rate is negatively correlated with total factor productivity. The paper also shows that interest-rate shocks cannot be the sole driving force of business cycles even when the canonical model is augmented to include a working-capital constraint. The second goal of the paper is to quantitatively explore the dynamic properties of the neoclassical growth model extended to include financial intermediation. It is shown that the extended model with external effects in financial intermediation can match the negative correlation between GDP and a domestic borrowing-lending spread in emerging countries if the economy is subject to productivity shocks but not when the model is subject to both productivity and interest-rate shocks.financial intermediation; open-economy business cycles; interest rates; capital inflows

A Toolbox for the Numerical Study of Linear Dynamic Rational Expectations Models

By simplifying the computational tasks and by providing step-by-step explanations of the procedures required to study a linear dynamic rational expectations (LDRE) model, this paper and the accompanying ``LDRE Toolbox" of Matalb functions guide a researcher with almost no experience in computational work to resolve and study his own model. After coding the model following specific guidelines, a single function call is all that is needed to log-linearize the model; simulate it under exogenous sequences of shocks; compute sample and population moment conditions; and obtain impulse-response functions. Three classical models in the Real-Business-Cycles literature are solved and studied throughout to give detailed examples of the steps involved in solving and studying LDRE models using the LDRE Toolbox. Namely, the economies in Brock and Mirman (Optimal Growth and Uncertainty: the Discounted Case, Journal of Economic Theory, 4(3): 479-513; 1972); King, Plosser, and Rebelo (Production, Growth and Business Cycles I: The Basic Neoclassical Model, Journal of Monetary Economics 21: 195-232; 1988); and Mendoza (Real Business Cycles in a Small Open Economy, American Economic Review 81(4): 797-818; 1991).

Distribution Costs and International Business Cycles

Backus, Kehoe, and Kydland (International Real Business Cycles, JPE, 100(4),1992) documented several discrepancies between the observed post-war business cycles of developed countries and the predictions of a two-country, complete-market model. The main discrepancy termed as the “quantity anomaly†that cross-country consumption correlations are higher than that of output in the model as opposed to data, has remained a central puzzle in international economics. In order to resolve this puzzle mainly two strategies: restrictions on asset trade, and introducing non-traded goods in the model, have been employed by researchers. While these extensions have been successful in closing the gap to some extent, the ordering of correlations has stayed unchanged: consumption correlations still exceed that of output. This paper attempts to resolve the quantity puzzle by introducing non-traded distribution costs in the retailing of traded goods. In a standard two-good model traded output and traded consumption, by definition, are identical goods. With distribution costs, traded output and consumption are two distinct entities as each unit of final traded consumption good incorporates a unit of traded good and a fixed amount of non-traded goods. Thus, effectively, the model with distribution costs can be viewed as a model without distribution costs but with a modified utility function that has a substantially stronger complementarity between traded and non-traded goods. In a simple two-good extension of the Backus, Kehoe, and Kydland model, it is shown that the cross-country consumption and output correlations are 0.55 and 0.30, respectively, whereas with distribution costs consumption correlation reduces to 0.09, output correlation to 0.23. Incorporating distribution costs, in addition, improves the model’s performance in matching the volatility of real exchange rates and the correlation of net exports with output. These improvements are achieved without sacrificing the model's performance in any other dimension.open economy business cycles; quantity puzzle; distribution costs

Optimal Banking Sector Recapitalization

Government-financed bank restructuring programs, occasionally costing up to 50% of GDP, are commonly used to resolve banking crises. We analyze the Ramsey-optimal paths of bank recapitalization programs that weigh recapitalization benefits and costs under different financing options. In our model bank credit is essential, due to a working capital constraint on firms, and banks are financial intermediaries that borrow from households and lend to firms. A banking crisis produces a disruption of credit and a fall in output equivalent to those in developing countries affected by banking crises. Full recapitalization of the banking system immediately after the crisis is optimal only if international credit is available. One-shot recapitalization is not optimal with domestically-financed programs, even if the government has access to non-distortionary taxes. The welfare cost of a crisis is substantial: the equivalent permanent decline in the no-crisis steady state consumption ranges between 0.51% and 0.65%, depending on the source of financing the recapitalization program.financial intermediation; bank recapitalization; banking crises; banking capital

International Business Cycles with Mutliple Input Investment Technologies

Backus, Kehoe, and Kydland (International Real Business Cycles, JPE, 100 (4), 1992) documented several discrepancies between the observed post-war business cycles of developed countries and the predictions of a two-country, complete-market model. The main discrepancy dubbed as the quantity anomaly, that cross-country consumption correlations are higher than that of output in the model as opposed to the data, has remained a central puzzle in international economics. The main thesis of this paper is that when the standard two-country model with traded and non-traded goods and complete ¯nancial markets, as in Stockman and Tesar (Tastes and Technology in a Two Country Model of the Business Cycles: Explaining International Comovements, 85 (1), AER, 1995) is extended to include capital goods sectors that utilize both traded and non-traded goods as intermediates, and when the non-traded aggregate is reclassi¯ed to include distribution and transportation services, the model produces the correct ordering of the cross-country correlations of consumption and output.International business cycles; Quantity anomaly; Distribution costs; Cross-country correlations.

Fiscal Policy and Macroeconomic Uncertainty in Emerging Markets: The Tale of the Tormented Insurer

Governments in emerging markets often behave like a "tormented insurer", trying to use non-state-contingent debt instruments to avoid sharp adjustments in their payments to private agents despite sharp fluctuations in public revenues. In the data, their ability to sustain debt is inversely related to the variability of their revenues, and their primary balances and current expenditures follow a procyclical pattern that contrasts sharply with the evidence from industrial countries. This paper proposes an equilibrium model of a small open economy with incomplete markets and aggregate uncertainty that can rationalize this behavior. In the model, a fiscal authority that chooses optimal expenditure and debt plans given stochastic revenues interacts with private agents that also make optimal consumption and asset accumulation plans. The competitive equilibrium of this economy is solved numerically as a Markov perfect equilibrium using parameter values calibrated to Mexican data. If perfect domestic risk pooling were possible, the ratio of public-to-private expenditures would be constant. With incomplete markets, however, this ratio fluctuates widely and results in welfare losses that dwarf previous estimates of the benefits of risk sharing and consumption smoothing. The model also yields a negative relationship between average public debt and revenue variability similar to the one observed in the data, and a correlation between output and government purchases that matches Mexican dataoptimal debt, fiscal solvency, procyclical fiscal policy, incomplete markets

Public Debt, Fiscal Solvency, and Macroeconomic Uncertainty in Latin America: The Cases of Brazil, Colombia, Costa Rica, and Mexico

The ratios of public debt as a share of GDP of Brazil, Colombia, and Mexico were 12 percentage points higher on average during the period 1996-2005 than in the period 1990-1995. Costa Rica's debt ratio remained stable but at a high level near 50 percent. Is there reason to be concerned for the solvency of the public sector in these economies? We provide an answer to this question based on the quantitative predictions of a variant of the framework proposed by Mendoza and Oviedo (2006). This methodology yields forward-looking estimates of debt ratios that are consistent with fiscal solvency for a government that faces revenue uncertainty and can issue only non-state-contingent debt. In this environment, aversion to a collapse in outlays leads the government to respect a ``natural debt limit" equal to the annuity value of the primary balance in a ``fiscal crisis." A fiscal crisis occurs after a long sequence of adverse revenue shocks and public outlays adjust to their tolerable minimum. The debt limit also represents a credible commitment to remain able to repay even in a fiscal crisis. The debt limit is not, in general, the same as the sustainable debt, which is driven by the probabilistic dynamics of the primary balance. The results of a baseline scenario question the sustainability of current debt ratios in Brazil and Colombia, while those in Costa Rica and Mexico are inside the limits consistent with fiscal solvency. In contrast, current debt ratios are found to be unsustainable in all four countries for plausible changes to lower average growth rates or higher real interest rates. Moreover, sustainable debt ratios fall sharply when default risk is taken into account.

Public Debt, Fiscal Solvency and Macroeconomic Uncertainty in Latin America: The Cases of Brazil, Colombia, Costa Rica, and Mexico

Ratios of public debt as a share of GDP in Brazil, Colombia, and Mexico were 10 percentage points higher on average during 1996-2002 than in the period 1990-1995. Costa Rica's debt ratio remained stable but at a high level near 50 percent. Is there reason to be concerned for the solvency of the public sector in these economies? We provide an answer to this question based on the quantitative predictions of a variant of the framework proposed by Mendoza and Oviedo (2004). This methodology yields forward-looking estimates of debt ratios consistent with fiscal solvency for a government that faces revenue uncertainty and can issue only non-state-contingent debt. In this environment, aversion to a collapse in outlays leads the government to respect a "natural debt limit" equal to the annuity value of the primary balance in a "fiscal crisis". A fiscl crisis occurs after a long sequence of adverse revenue shocks and public outlays adjust to a tolerable minimum. The debt limit also represents a credible commitment to be able to repay even in a fiscal crisis but is not, in general, the same as the sustainable debt, which is driven by the probabilistic dynamics of the primary balance. The results of a baseline scenario question the sustainability of current debt ratios in Brazil and Colombia, while those in Costa Rica and Mexico seem inside the limits consistent with fiscal solvency. In contrast, public debt ratios are found to be unsustainable in all four countries for plausible changes to lower average growth rates or higher real interest rates. Moreover, sustainable debt ratios fall sharply when default risk is taken into account.