Stochastic Neoclassical Growth Model Research Articles

Convergence stories of post‐socialist Central‐Eastern European countries

AbstractThis paper views the growth and convergence process of five Central‐Eastern European economies between 1996 and 2019—the Czech Republic, Hungary, Poland, Slovenia and Slovakia—through the lens of an open economy, stochastic neoclassical growth model with simple financial frictions. Our main question is whether shocks to the growth rate of productivity (‘trend’) or shocks to the external interest premium are more important to understand the volatility of GDP growth and its components. We find that while GDP growth fluctuations can be traced back to productivity shocks, the composition of GDP—and consumption in particular—was driven particularly by premium shocks. Investment‐specific and labor market shocks are also important. Our panel estimation allows us to separate global and local components for the productivity‐trend and interest premium shocks. Results indicate that the global trend component is well approximated by the growth rate of the advanced European Union economies, and we also find tentative evidence that recent investment behavior is driven to a large extent by European Union funds.

The welfare and distributional effects of fiscal volatility: A quantitative evaluation

This study explores the welfare and distributional effects of fiscal volatility using a neoclassical stochastic growth model with incomplete markets. In our model, households face uninsurable idiosyncratic risks in their labor income and discount factor processes, and we allow aggregate uncertainty to arise from both productivity and government purchases shocks. We calibrate our model to key features of the U.S. economy, before eliminating government purchases shocks. We then evaluate the distributional consequences of the elimination of fiscal volatility and find that, in our baseline case, welfare gains increase with private wealth holdings.

Recursive Equilibria in Dynamic Economies With Stochastic Production

In this paper we prove the existence of recursive equilibria in stochastic production economies with infinitely lived agents and incomplete financial markets. We consider a general dynamic model with several commodities, which encompasses heterogeneous agent versions of both the Lucas asset pricing model and the stochastic neo-classical growth model as special cases. Our main assumption is that there are atomless shocks to fundamentals that have a purely transitory component and a component that does not depend on last period's shocks directly.

A comparison of programming languages in macroeconomics

We solve the stochastic neoclassical growth model, the workhorse of modern macroeconomics, using C++14, Fortran 2008, Java, Julia, Python, Matlab, Mathematica, and R. We implement the same algorithm, value function iteration, in each of the languages. We report the execution times of the codes in a Mac and in a Windows computer and briefly comment on the strengths and weaknesses of each language.

International Credit Flows and Pecuniary Externalities

This paper develops a dynamic two-country neoclassical stochastic growth model with incomplete markets. Short-term credit flows can be excessive and reverse suddenly. The equilibrium outcome is constrained inefficient due to pecuniary externalities. First, an undercapitalized country borrows too much since each firm does not internalize that an increase in production capacity undermines their output price, worsening their terms of trade. From an ex ante perspective each firm undermines the natural “terms of trade hedge.” Second, sudden stops and fire sales lead to sharp price drops of illiquid capital. Capital controls or domestic macro-prudential measures that limit short-term borrowing can improve welfare. (JEL F32, F43, G15, O41)

International Credit Flows and Pecuniary Externalities

This paper develops a dynamic two-country neoclassical stochastic growth model with incomplete markets. Short-term credit flows can be excessive and reverse suddenly. The equilibrium outcome is constrained inefficient due to pecuniary externalities. First, an undercapitalized country borrows too much since each firm does not internalize that an increase in production capacity undermines their output price, worsening their terms of trade. From an ex-ante perspective each firm undermines the natural “terms of trade hedge.” Second, sudden stops and fire sales lead to sharp price drops of illiquid capital. Capital controls or domestic macro-prudential measures that limit short-term borrowing can improve welfare.

Corporate Cash Hoarding in a Model with Liquidity Constraints

This paper studies the role of uncertainty in the corporate cash hoarding puzzle. The baseline model is a stochastic neoclassical growth model featuring idiosyncratic and uninsurable productivity shocks and a cash-in-advance constraint on new in- vestments on the individual firm level. Individual agents' choices regarding cash holdings are analyzed. After a wealth threshold is reached, the cash-in-advance con- straint ceases to have an effect on the agent's behavior. The resulting aggregate cash holdings of households increases with uncertainty. Aggregate consumption is also higher, but the added volatility of consumption decreases lifetime utility. Al- lowing firms to borrow and lend available unused cash increases average variables. An exogenous increase in the interest rate at which they intermediate funds leads to increased intermediation activity, corresponding to the lending channel of monetary policy transmission.

Optimal portfolios with wealth-varying risk aversion in the neoclassical growth model

This paper provides a rationale for fixed portfolios that exhibit fund separation as an optimal general equilibrium strategy when heterogeneous investors have wealth-varying relative risk aversion in the context of the standard stochastic neoclassical growth model. Agents’ wealth heterogeneity varies endogenously through time. Preferences exhibit linear risk tolerance with respect to consumption, consumption and labor are separable and the momentary utility function for leisure is isoelastic. Production possibilities are represented by J neoclassical technologies which are subject to shocks. I show that any competitive equilibrium allocation that is Pareto optimal can be supported by means of constant portfolios with only a few assets: a mutual fund of stocks, a consol and two other securities perfectly linearly correlated with aggregate labor income and the wage rate. Remarkably, this result holds in spite of the changing degree of agents’ heterogeneity and wealth-varying relative risk aversion, both stemming from movements in the stock of capital.

Size, trend, and policy implications of the underground economy

We study the underground economy within a dynamic and stochastic general equilibrium framework. Our model combines limited tax enforcement with an otherwise standard two-sector neoclassical stochastic growth model. The Bayesian estimation of the model based on Italian data provides evidence in favor of an important underground sector in Italy, with a size that has increased steadily over the whole sample period. We show that this pattern is due to a steady increase in taxation. Fiscal policy experiments suggest that a moderate tax cut, along with a stronger effort in the monitoring process, causes a sizeable reduction in the size of the underground economy and provides a positive stimulus for the regular economy. Both of these effects jointly increase total fiscal revenues.

Heterogeneous technology and the technological catching-up hypothesis: Theory and assessment in the case of MENA countries

Long run convergence implies that the convergence hypothesis will be rejected if the income differential is not stationary. However, this definition is valid only if the catching-up process between the two countries is already over. If we take into account catching-up dynamics, then poorest countries should obtain a faster growth than developed countries. Thus, income gaps should integrate decreasing time trends. We formalise this hypothesis theoretically using a stochastic neoclassical growth model with heterogeneous technology. We then apply this model to the issue of per-capita GDP catching-up of eight MENA countries towards the level of income in Europe. We approximate the nonlinear deterministic trend by a linear function with breaks and apply panel unit root tests with breaks. The analysis reveals firstly that the periods of divergence outnumber the periods of convergence. Secondly, since the year 2000 all countries but Syria have been converging toward the European per-capita income level.

Methods versus substance: Measuring the effects of technology shocks

Calibration and modern (Bayesian) estimation methods for a neoclassical stochastic growth model are applied to make the case that the identification of key parameters, rather than quantitative methodologies per se, is responsible for empirical findings. For concreteness, the model is used to measure the contributions of technology shocks to the business cycle fluctuations of hours worked and output. Along the way, new insights are provided in the parameter identification associated with likelihood-based estimation, the sensitivity of likelihood-based estimation to the choice of structural shocks is assessed, and Bayesian model averaging is used to aggregate findings obtained from different DSGE model specifications.

Estimating the Size of the Underground Economy: A DSGE Approach

We study the underground economy in a dynamic and stochastic general equilibrium framework. Our model combines limited tax enforcement with an otherwise standard two-sector neoclassical stochastic growth model. The Bayesian estimation of the model based on Italian data provides evidence in favor of an important underground sector in Italy, with a size that has steadily increased over the whole sample period. We show that this pattern is due to a persistent increase in taxation. Fiscal policy experiments suggest that a moderate tax cut, along with a stronger eff ort in the monitoring process, causes a sensitive reduction in the size of the underground economy and positive stimulus to the regular sector that jointly increase the total fiscal revenues.

Computing DSGE Models with Recursive Preferences and Stochastic Volatility

This paper compares different solution methods for computing the equilibrium of dynamic stochastic general equilibrium (DSGE) models with recursive preferences such as those in Epstein and Zin (1989 and 1991) and stochastic volatility. Models with these two features have recently become popular, but we know little about the best ways to implement them numerically. To fill this gap, we solve the stochastic neoclassical growth model with recursive preferences and stochastic volatility using four different approaches: second- and third-order perturbation, Chebyshev polynomials, and value function iteration. We document the performance of the methods in terms of computing time, implementation complexity, and accuracy. Our main finding is that perturbations are competitive in terms of accuracy with Chebyshev polynomials and value function iteration while being several orders of magnitude faster to run. Therefore, we conclude that perturbation methods are an attractive approach for computing this class of problems.

Computing DSGE Models with Recursive Preferences and Stochastic Volatility

This paper compares different solution methods for computing the equilibrium of dynamic stochastic general equilibrium (DSGE) models with recursive preferences such as those in Epstein and Zin (1989 and 1991) and stochastic volatility. Models with these two features have recently become popular, but we know little about the best ways to implement them numerically. To fill this gap, we solve the stochastic neoclassical growth model with recursive preferences and stochastic volatility using four different approaches: second- and third-order perturbation, Chebyshev polynomials, and value function iteration. We document the performance of the methods in terms of computing time, implementation complexity, and accuracy. Our main finding is that perturbations are competitive in terms of accuracy with Chebyshev polynomials and value function iteration while being several orders of magnitude faster to run. Therefore, we conclude that perturbation methods are an attractive approach for computing this class of problems.

Computing DSGE models with recursive preferences and stochastic volatility

This paper compares different solution methods for computing the equilibrium of dynamic stochastic general equilibrium (DSGE) models with recursive preferences such as those in Epstein and Zin (1989, 1991) and stochastic volatility. Models with these two features have recently become popular, but we know little about the best ways to implement them numerically. To fill this gap, we solve the stochastic neoclassical growth model with recursive preferences and stochastic volatility using four different approaches: second- and third-order perturbation, Chebyshev polynomials, and value function iteration. We document the performance of the methods in terms of computing time, implementation complexity, and accuracy. Our main finding is that perturbations are competitive in terms of accuracy with Chebyshev polynomials and value function iteration while being several orders of magnitude faster to run. Therefore, we conclude that perturbation methods are an attractive approach for computing this class of problems.

Explaining output volatility: The case of taxation

This paper presents strong empirical evidence that the observed heterogeneity of output volatility across countries and over time is partly endogenous. In particular, based on a closed-form solution we obtain a (long-run) equilibrium relationship between taxes and output volatility in the stochastic neoclassical growth model by showing that asymptotically the variance of output growth rates is affected by the level of taxes, without affecting the mean. We estimate the tax semi-elasticities on output volatility and provide convincing empirical evidence that taxes are important to understand differences in output volatility among OECD countries.

What is the Best Environmental Policy? Taxes, Permits and Rules under Economic and Environmental Uncertainty

We welfare rank different types of second-best environmental policy. The focus is on the roles of uncertainty and public finance. The setup is the basic stochastic neoclassical growth model augmented with the assumptions that pollution occurs as a by-product of output produced and environmental quality is treated as a public good. To compare different policy regimes, we compute the welfaremaximizing value of the second-best policy instrument in each regime. In all cases studied, pollution permits are the worst recipe, even when their revenues are used to finance public abatement. When the main source of uncertainty is economic, the best recipe is to levy taxes (on pollution or output) and use the collected tax revenues to finance public abatement. However, when environmental uncertainty is the dominant source of extrinsic uncertainty, Kyoto-like rules for emissions, being combined with tax-financed public abatement, are better than taxes. Finally, comparing pollution and output taxes, the latter are better

What is the Best Environmental Policy? Taxes, Permits and Rules Under Economic and Environmental Uncertainty

We study the importance of uncertainty and public finance to the welfare ranking of three environmental policy instruments: pollution taxes, pollution permits and Kyoto-like numerical rules for emissions. The setup is the basic stochastic neoclassical growth model augmented with the assumptions that pollution occurs as a by-product of output produced and environmental quality is treated as a public good. To compare alternative policies, we compute welfare-maximizing values for the second-best policy instruments. We find that, in all cases studied, pollution permits are the worst policy choice, even when their revenues finance public abatement. When the main source of uncertainty is economic, the most efficient recipe is to levy pollution taxes and use the collected tax revenues to finance public abatement. However, when environmental uncertainty is the dominant source of extrinsic uncertainty, numerical rules, being combined with tax-financed public abatement, are better than pollution taxes.

Solving Portfolio Problems with the Smolyak-Parameterized Expectations Algorithm

We propose a new numerical method to solve stochastic models that combines the parameterized expectations (PEA) and the Smolyak algorithms. This method is especially convenient to address problems with occasionally binding constraints (a feature inherited from PEA) and/or a large number of state variables (a feature inherited from Smolyak), i.e. DSGE models that incorporate portfolio problems and incomplete markets. We describe the proposed Smolyak-PEA algorithm in the context of a one-country stochastic neoclassical growth model and compare its accuracy with that of a standard PEA collocation algorithm. Despite estimating fewer parameters, the former is able to reach the high accuracy levels of the latter. We further illustrate the working of this algorithm in a two-country neoclassical model with incomplete markets and portfolio choice. Again, the Smolyak-PEA algorithm approximates the solution of the problem with a high degree of accuracy. Finally, we show how this algorithm can efficiently incorporate both occasionally binding constraints and a partial information approach.

Computing DSGE Models with Recursive Preferences

This paper compares different solution methods for computing the equilibrium of dynamic stochastic general equilibrium (DSGE) models with recursive preferences such as those in Epstein and Zin (1989 and 1991). Models with these preferences have recently become popular, but we know little about the best ways to implement them numerically. To fill this gap, we solve the stochastic neoclassical growth model with recursive preferences using four different approaches: second- and third-order perturbation, Chebyshev polynomials, and value function iteration. We document the performance of the methods in terms of computing time, implementation complexity, and accuracy. Our main finding is that a third-order perturbation is competitive in terms of accuracy with Chebyshev polynomials and value function iteration, while being an order of magnitude faster to run. Therefore, we conclude that perturbation methods are an attractive approach for computing this class of problems.