One-sector Real Business Cycle Model Research Articles

Income Taxation Rules and Stability of a Small Open Economy

This paper examines the stability of a small open economy under alternative income taxation rules. Using a one-sector real business cycle model with external increasing returns, we show that if the income tax schedule is linear, the small open economy will not generate equilibrium indeterminacy, but it exhibits a diverging behavior under certain conditions. In this case, an appropriate choice of nonlinear tax on the factor income may recover the saddle-point stability. We also reveal that if the taxation on the interest income on financial assets is regressive, then the small open economy may exhibit equilibrium indeterminacy. In this situation, a progressive tax rule on the interest income can contribute to eliminating sunspot-driven fluctuations.

Progressive taxation as an automatic destabilizer under endogenous growth

It has been shown that in an otherwise standard one-sector real business cycle model with an indeterminate steady state under laissez faire, sufficiently progressive income taxation may stabilize the economy against aggregate fluctuations caused by agents’ animal spirits. We show that this previous finding can be overturned within an identical model which allows for sustained endogenous growth. Specifically, progressive taxation may operate like an automatic destabilizer that leads to equilibrium indeterminacy and sunspot-driven cyclical fluctuations in an endogenously growing macroeconomy. This instability result is obtained under two tractable progressive tax policy formulations that have been considered in the existing literature.

A NOTE ON NOMINAL GDP TARGETING AND MACROECONOMIC (IN)STABILITY

Benhabib and Farmer show that in a laissez-faire one-sector real business cycle model under aggregate increasing returns, under sufficiently high degrees of productive externality, the demand-side effect in the labor market triggered by agents' expectations about the economy's future outweighs the supply-side effect, making agents' expectations become self-fulfilling. This paper analytically demonstrates that the conduct of monetary policy under nominal gross domestic product (GDP) targeting reinforces the supply-side effect in the labor market, thereby making belief-driven aggregate fluctuations more difficult to occur. This reinforcement effect on labor supply is absent under nominal consumption targeting and inflation targeting. Hence, under these two monetary regimes, the necessary and sufficient conditions for the economy to display equilibrium indeterminacy and sunspot fluctuations are identical to those in Benhabib and Farmer's laissez-faire economy. The results are robust to an endogenous growth extension of the model, implying that targeting the nominal GDP growth rate is more desirable than targeting the nominal consumption growth rate or the inflation rate in terms of macroeconomic stability.

NEWS ABOUT TAXES AND EXPECTATIONS-DRIVEN BUSINESS CYCLES

This paper analyzes the possibility of expectations-driven business cycles to emerge in a one-sector real business cycle model if the unique driving force is news about future income tax rates. We find that good news about labor income tax rates cannot generate expectations-driven business cycles, whereas good news about capital income tax rates can. We show that a one-sector real business cycle model enriched with (i) variable capital utilization and (ii) investment adjustment costs and driven solely by news shocks about capital income tax rates is able to generate qualitatively and quantitatively realistic business cycle fluctuations. In contrast to numerous studies in the news-driven business cycle literature, our model maintains separable preferences.

Balanced-Budget Rules, Elasticity of Substitution, and Macroeconomic (In)Stability

This paper examines the relation between factor substitution and (local) stability of equilibria in a one-sector real business cycle model under balanced-budget rules. We show that under non-unitary elasticity of factor substitution, the Schmitt-Grohé-Uribe indeterminacy result can be altered. Using the two-step normalization procedure, we highlight two opposing effects of factor substitution, namely, the efficiency effect and the distribution effect, on aggregate stability. With endogenous distortionary taxes and gross substitutability between capital and labor, the existing literature overlooks the distribution effect and finds that balanced-budget rules are likely to deliver indeterminacy. However, if capital stock is relatively more abundant, a higher elasticity of substitution generates a source of stability due to the distribution effect. Our calibration shows that the distribution effect is always the dominating force.

News about aggregate demand and the business cycle

The plausibility of expectations-driven cyclical fluctuations in an otherwise standard one-sector real business cycle model with variable capital utilization and mild increasing returns-to-scale in production is examined. Due to a dominating wealth effect, our model is able to generate qualitatively as well as quantitatively realistic aggregate fluctuations driven by news impulses to future consumption demand or government spending on goods and services. When the economy is subject to anticipated total factor productivity or investment-specific technology shocks, the relative strength of the intertemporal substitution effect needs to be enhanced for our model to exhibit positive macroeconomic co-movement and business cycle statistics that are consistent with the data.

Progressive taxation and macroeconomic (in)stability with utility-generating government spending

We examine the theoretical interrelations between progressive income taxation and macroeconomic (in)stability in an otherwise standard one-sector real business cycle model with utility-generating government purchases of goods and services. When private and public consumption expenditures are complements in the household utility and the tax schedule is progressive, we analytically show that the economy exhibits indeterminacy and sunspots if and only if the degree of government-spending preference externality is higher than a critical threshold. Unlike traditional Keynesian-type stabilization policies, raising the tax progressivity may destabilize this version of our model by generating endogenous cyclical fluctuations. Moreover, the economy always displays saddle-path stability and equilibrium uniqueness under utility substitutability between private and public consumptions and progressive taxation.

Countercyclical markups and news-driven business cycles

The standard one-sector real business cycle model is unable to generate expectations-driven fluctuations. The addition of countercyclical markups and modest investment adjustment costs offers an easy fix to this conundrum. The simulated model replicates the regular features of U.S. aggregate fluctuations.

Methods to estimate dynamic stochastic general equilibrium models

This paper employs the one-sector real business cycle model as a testing ground for four different procedures to estimate dynamic stochastic general equilibrium (DSGE) models. The procedures are: (1) maximum likelihood, with and without measurement errors and incorporating priors, (2) generalized method of moments, (3) simulated method of moments, and (4) indirect inference. Monte carlo analysis is used to study the small-sample properties of these estimators and to examine the implications of misspecification, stochastic singularity, and weak identification.

Maintenance Expenditures and Indeterminacy under Increasing Returns to Scale

This paper develops a one-sector real business cycle model in which competitive firms allocate resources for the production of goods, investment in new capital, and maintenance of existing capital. Firms also choose the utilization rate of existing capital. A higher utilization rate leads to faster capital depreciation, while an increase in maintenance activity has the opposite effect. We show that as the equilibrium ratio of maintenance expenditures to GDP rises, the required degree of increasing returns for local indeterminacy declines over a wide range of parameter combinations. When the model is calibrated to match empirical evidence on the relative size of maintenance and repair activity, we find that local indeterminacy (and belief-driven fluctuations) can occur with a mild and empirically-plausible degree of increasing returns–around 1.08.

Government size and macroeconomic stability: A comment

We show that in a standard, technology shock-driven one-sector real business cycle model, the stabilization effects of government fiscal policy depend crucially on how labor hours enter the household's period utility function and the associated labor-market behavior. In particular, as Galí [European Economic Review 38 (1994), 117–132] has shown, when the household utility is logarithmic in both consumption and leisure, income taxes are destabilizing and government purchases are stabilizing. However, the results are reversed when preferences are instead convex in hours worked. That is, income taxes are now stabilizing and public spending is destabilizing. Furthermore, under both preference specifications, the magnitude of cyclical fluctuations in output remains unchanged when the income tax rate and the share of government purchases in GDP are equal (including laissez-faire).

Balanced-budget rules and macroeconomic (in)stability

It has been shown that under perfect competition and constant returns-to-scale, a one-sector real business cycle model may exhibit indeterminacy and sunspots when income tax rates are determined by a balanced-budget rule with a pre-set level of government expenditures. This paper shows that indeterminacy disappears if the government finances endogenous public spending and transfers with fixed income tax rates. Under this type of balanced-budget formulation, the economy exhibits saddle-path stability and equilibrium uniqueness, regardless of the source of government revenue and/or the existence of lump-sum transfers.

Increasing returns, capital utilization, and the effects of government spending

We show that a one-sector real business cycle model with mild increasing returns-to-scale, variable capital utilization and saddle-path stability is able to produce qualitatively realistic business cycles driven solely by disturbances to government purchases. Due to an endogenous increase in labor productivity, a positive spending shock can lead to simultaneous increases in output, consumption, investment, employment and real wage. Our analysis illustrates a close relationship between this result and the recent literature that explores indeterminacy and sunspots in real business cycle models under laissez-faire. In particular, the condition which governs the required magnitude of increasing returns for government spending shocks to generate procyclical macroeconomic effects is identical to that necessary for a laissez-faire one-sector real business cycle model to exhibit local indeterminacy.

Multiple equilibria and progressive taxation of labor income

This paper shows that in a one-sector real business cycle model with strong increasing returns in production, progressive taxation of labor income can stabilize the economy against sunspot fluctuations, even when the capital tax schedule is flat. This result is consistent with the US tax code in which labor-income taxation is more progressive than capital-income taxation.

Asset pricing in production economies

This paper studies asset returns in different versions of the one-sector real business cycle model. We show that a model with habit formation preferences and capital adjustment costs can explain the historical equity premium and the average risk-free return while replicating the salient business cycle properties. The paper also applies a solution technique that combines loglinear methods with lognormal asset pricing formulae.