What inventories tell us about aggregate fluctuations—A tractable approach to (S,s) policies

We estimate a DSGE model with (S,s) inventory policies. We find that (i) taking inventories into account can significantly improve the empirical fit of DSGE models in matching the standard business-cycle moments (in addition to explaining inventory fluctuations); (ii) (S,s) inventory policies can significantly amplify aggregate output fluctuations, in contrast to the findings of the recent general-equilibrium inventory literature; and (iii) aggregate demand shocks become more important than technology shocks in explaining the business cycle once inventories are incorporated into the model. An independent contribution of our paper is that we develop a solution method for analytically solving (S,s) inventory policies in general equilibrium models with heterogeneous firms and a large aggregate state space, and we illustrate how standard log-linearization methods can be used to solve various versions of our inventory model, generate impulse response functions, and estimate the model׳s deep structural parameters.     

Business cycle fluctuations and learning-by-doing externalities in a one-sector model

We consider a one-sector Ramsey-type growth model with inelastic labor and learning-by-doing externalities based on cumulative gross investment (cumulative production of capital goods), which is assumed, in accordance with Arrow (1962), to be a better index of experience than the average capital stock. We prove that a slight memory effect characterizing the learning-by-doing process is enough to generate business cycle fluctuations through a Hopf bifurcation leading to stable periodic orbits. This is obtained for reasonable parameter values, notably for both the amount of externalities and the elasticity of intertemporal substitution. Hence, contrary to all the results available in the literature on aggregate models, we show that endogenous fluctuations are compatible with a low (in actual fact, zero) wage elasticity of the labor supply.     

Indeterminacy in discrete-time infinite-horizon models with non-linear utility and endogenous labor

We consider a discrete-time two-sector model with sector specific externalities in which the technologies are given by CES functions with asymmetric elasticities of capital–labor substitution, and the preferences of the representative agent are given by a CES additively separable utility function defined over consumption and leisure. We first show that when the labor supply is infinitely elastic, the steady state is always saddle-point stable, no matter what the elasticity of intertemporal substitution in consumption and the size of externalities are. We then prove that when the elasticity of intertemporal substitution in consumption is sufficiently large, local indeterminacy requires a low enough elasticity of the labor supply.     

Endogenous business cycle propagation and the persistence problem: The role of labor-market frictions

Contrasting sharply with a recent trend in DSGE modeling, we propose a business cycle model where frictions and shocks are chosen with parsimony. The model emphasizes a few labor-market frictions and shocks to monetary policy and technology. The model, estimated from U.S. quarterly postwar data, accounts well for important differences in the serial correlation of the growth rates of aggregate quantities, the size of aggregate fluctuations and key comovements, including the correlation between hours and labor productivity. Despite its simplicity, the model offers an answer to the persistence problem (Chari et al., 2000) that does not rely on multiple frictions and adjustment lags or ad hoc backward-looking components. We conclude modern DSGE models need not embed large batteries of frictions and shocks to account for the salient features of postwar business cycles.     

An estimation of US industry-level capital–labor substitution elasticities: support for Cobb–Douglas

A key parameter that determines the distributional impacts of a policy shift in general equilibrium models is the elasticity of substitution between capital and labor. Despite the importance of this parameter in applied modeling, its identification continues to pose a challenge. Given the structure of most growth models, we posit that the true relationship between capital and labor is likely to be close to Cobb–Douglas. Using a rich new data set from the Bureau of Economic Analysis (BEA), we estimate substitution elasticities for 28 industries that cover the entire economy, and provide an indication of the long- and short-run ranges of those estimates. We fail to reject the Cobb–Douglas specification in 20 of the 28 industries. These findings lend support to the Cobb–Douglas specification as a transparent starting point in simulation analysis.     

Capital–labor substitution and equilibrium indeterminacy

This paper examines the quantitative relationship between the elasticity of capital–labor substitution in production and the conditions needed for equilibrium indeterminacy (and belief-driven fluctuations) in a one-sector growth model. With variable capital utilization, the substitution elasticity has little quantitative impact on the minimum degree of increasing returns needed for indeterminacy. However, when capital utilization is constant, a below-unity substitution elasticity sharply raises the minimum degree of increasing returns because it imposes a higher effective adjustment cost on labor hours. Overall, our results show that empirically-plausible departures from the Cobb–Douglas production specification can make indeterminacy more difficult to achieve.     

On the modeling of size distributions when technologies are complex

The study considers a stochastic R&D process where the invented production technologies consist of a large number $n$ of complementary components. The degree of complementarity is captured by the elasticity of substitution of the CES aggregator function. Drawing from the Central Limit Theorem and the Extreme Value Theory we find, under very general assumptions, that the cross-sectional distributions of technological productivity are well-approximated either by the lognormal, Weibull, or a novel “CES/Normal” distribution, depending on the underlying elasticity of substitution between technology components. We find the tail of the “CES/Normal” distribution to be fatter than the Weibull tail but qualitatively thinner than the Pareto (power law) one. We also numerically assess the rate of convergence of the true technological productivity distribution to the theoretical limit with $n$ as fast in the body but slow in the tail.     

Advantageous redistribution with three smooth CES utility functions

We present a parametric example of three-country advantageous redistribution with two Cobb–Douglas utility functions and one CES utility function for which the elasticity of substitution is 1/2. This paper indicates that the possibility of advantageous redistribution strongly depends on the three countries’ taste patterns, endowment distributions, and the elasticity of substitution. In particular, we will show with specific examples that greater difference between the donor and recipient’s taste patterns and a lower elasticity of substitution can increase the chance of advantageous redistribution.     

The effect of labor supply changes on output: empirical evidence from US industries

In this paper we examine the relationship between labor supply and industry-level output in the context of the specific factors model. Jones (Trade, balance of payment and growth: essays in honor of Charles P. Kindleberger, Amsterdam, pp 3–21, 1971) shows that a rise in the amount of labor in the economy will increase the output in all industries. We empirically show which industry output is predicted to expand more when the size of labor force grows. Unlike the commonly used Rybczynski Theorem (Economica 22:336–341, 1955) of the Heckscher-Ohlin model, the specific factors model shows that a comparison both of labor intensities and labor demand elasticities plays an important role in determining which output expands relatively more when the size of labor force grows. For this purpose, we illustrate the importance of the parameters of the model in determining how changes in the labor supply affect the output change, with special reference to elasticities of substitution in production. We estimate the elasticity of substitution by using CES production function and show how these estimates describe the general equilibrium of production with one mobile factor (labor) and 25 industries of the US economy using data for 1979–2001. We show that the increase in the supply of labor raise output in all industries, but the magnitudes of the increases in some industries are more than others depending on the value of the elasticity of substitution along with factor intensities between industries. The largest output effect occurs for educational, health care and social service, where a 1 % supply of labor increase would raise output 10.5 %. However, the growth in the labor supply has a small impact on output growth in the range of 0.1–0.6 % in agriculture, petroleum, coal product and finance and insurance industries.     

THE ELASTICITY OF CAPITAL–LAND SUBSTITUTION IN THE HOUSING CONSTRUCTION SECTOR OF A RAPIDLY URBANIZED CITY: EVIDENCE FROM TURKEY

This paper estimates the elasticity of capital-land substitution for the housing market in Ankara, the capital city of Turkey. Using constant elasticity of substitution (CES) and variable elasticity of substitution (VES) production functions and cross-section data, the paper provides new information to compare the housing supply elasticity of Ankara with that of the USA and the UK cases. Our regression results reveal that housing supply in Ankara is highly inelastic due to the uniform construction regime of local authorities. Moreover, we find that there is a considerable spatial differentiation of urban land density measures within the capital city. Because of the incomplete urbanization process, the elasticity of capital-land substitution is significantly higher in the outer parts of the city.     

RARE SHOCKS,GREAT RECESSIONS

We estimate a DSGE (dynamic stochastic general equilibrium) model where rare large shocks can occur, by replacing the commonly used Gaussian assumption with a Student's t‐distribution. Results from the Smets and Wouters (American Economic Review 2007; 97 : 586–606) model estimated on the usual set of macroeconomic time series over the 1964–2011 period indicate that (i) the Student's t specification is strongly favored by the data even when we allow for low‐frequency variation in the volatility of the shocks, and (ii)) the estimated degrees of freedom are quite low for several shocks that drive US business cycles, implying an important role for rare large shocks. This result holds even if we exclude the Great Recession period from the sample. We also show that inference about low‐frequency changes in volatility—and, in particular, inference about the magnitude of Great Moderation—is different once we allow for fat tails. Copyright © 2014 John Wiley & Sons, Ltd.     

Investment shocks and the comovement problem

Recent work based on sticky price-wage estimated dynamic stochastic general equilibrium (DSGE) models suggests investment shocks are the most important drivers of post-World War II US business cycles. Consumption, however, typically falls after an investment shock. This finding sits oddly with the observed business cycle comovement where consumption, along with hours-worked and investment, moves with economic activity. We show that this comovement problem is resolved in an estimated DSGE model when (i) the cost of capital utilization is specified in terms of increased depreciation of capital, as originally proposed by Greenwood et al. (1988) in a neoclassical setting, or (ii) there is no wealth effect on labor supply. The data, however, favors the first channel. Traditionally, the cost of utilization is specified in terms of forgone consumption following Christiano et al. (2005), who studied the effects of monetary policy shocks. The alternative specification we consider has two additional implications relative to the traditional one: (i) it has a substantially better fit with the data and (ii) the contribution of investment shocks to the variance of consumption is over three times larger. The contributions to output, investment, and hours, are also relatively higher, suggesting that these shocks may be quantitatively even more important than previous estimates based on the traditional specification.     

SUBSTITUTION ELASTICITIES IN A CONSTANT ELASTICITY OF SUBSTITUTION FRAMEWORK – EMPIRICAL ESTIMATES USING NONLINEAR LEAST SQUARES

Elasticities are key parameters for any economic analysis. Using the World-Input–Output Database, we estimate substitution elasticities for a three-level nested constant elasticity of substitution KLEM production structure using up to date nonlinear least squares estimation procedures. This allows us for the first time to use one coherent data set for the estimation process. Furthermore, it gives us the opportunity to derive elasticities from the same data which researchers can use to calibrate their models. On the basis of our estimations, we demonstrate that the practice of using Cobb–Douglas or Leontief production functions in economic models must be rejected for the majority of sectors. We provide a comprehensive set of estimated substitution elasticities covering a wide range of sectors. Our results suggest that no substantial change in input substitutability takes place during the time period we consider. Moreover, there is no substantial variation in substitution elasticities across regions.     

WHAT DETERMINES THE ELASTICITY OF SUBSTITUTION BETWEEN CAPITAL AND LABOR? A LITERATURE REVIEW

This paper provides the first comprehensive review of the empirical and theoretical literature on the determinants of the elasticity of substitution between capital and labor. Our focus is on the two-input constant elasticity of substitution (CES) production function. We start by presenting four concise observations that summarize the empirical literature on the estimation of . Motivated by these observations, the main part of this survey then focuses on potential determinants of capital–labor substitution. We first review several approaches to the microfoundation of production functions where the elasticity of substitution (EOS) is treated as a purely technological parameter. Second, we outline the construction of an aggregate elasticity of substitution (AES) in a multi-sectoral framework and investigate its dependence on underlying intra- and inter-sectoral substitution. Third, we discuss the influence of the institutional framework on the extent of factor substitution. Overall, this survey highlights that the effective elasticity of substitution (EES), which is typically estimated in empirical studies, is generally not an immutable deep parameter but depends on a multitude of technological, non-technological, and institutional determinants. Based on these insights, the final section identifies a number of potential empirical and theoretical avenues for future research.     

Variable elasticity of substitution in urban housing production

The notion that the elasticity of substitution in urban housing production should vary with changing intensities of land use seems to be realistic and theoretically viable. Hence the variable elasticity of substitution production function has been proposed by some authors. However, it suffers from a serious shortcoming that the elasticity of substitution should not exceed unity. To allow for flexibility in the range of the elasticity of substitution, we explore a general functional form for the housing production function, the weak disposability of inputs production function in particular. Our empirical findings, based on the Santa Clara County single-family housing data, provide evidence that this general function is a more accurate specification of urban housing production than the variable elasticity of substitution function.     

Production Technology Estimates and Balanced Growth

Capital‐labour substitution and total factor productivity (TFP) estimates are essential features of many economic models. Such models typically embody a balanced growth path. This often leads researchers to estimate models imposing stringent prior choices on technical change. We demonstrate that estimation of the substitution elasticity and TFP growth can be substantially biased if technical progress is thereby mis‐specified. We obtain analytical and simulation results in the context of a model consistent with balanced and near‐balanced growth (i.e. departures from balanced growth but broadly stable factor shares). Given this evidence, a constant elasticity of substitution production function system is then estimated for the US economy. Results show that the estimated substitution elasticity tends to be significantly lower using a factor‐augmenting specification (well below one). We are also able to reject conventional neutrality forms in favour of general factor augmentation with a non‐negligible capital‐augmenting component. Our work thus provides insights into production and supply‐side estimation in balanced‐growth frameworks.     

Competitive equilibrium cycles with endogenous labor

In this paper, we study a two-sector optimal growth model with elastic labor supply. We show that the modified golden rule is saddle-point stable when the investment good is capital intensive. To characterize stability with a capital intensive consumption good, we focus on either additively separable or homothetic preferences. In the first specification, we show that optimal oscillations require the elasticity of intertemporal substitution in consumption to be high enough while the elasticity of labor needs to be low enough. At the same time, we prove that with a linear utility in leisure the modified golden rule is always saddle-point stable. In the second specification for preferences, we show that the local dynamic properties of the optimal path depend instead on the shares of consumption and leisure into total utility. We prove that endogenous fluctuations are even more likely with homothetic preferences.     

Consumer misperceptions,uncertain fundamentals,and the business cycle

This paper estimates the importance of shocks to consumer misperceptions “noise shocks” for U.S. business cycle fluctuations. I embed imperfect information as in Lorenzoni (2009) into a Smets and Wouters (2007)-type DSGE model. Agents only observe aggregate productivity and a signal about the permanent component contaminated with noise. Based on this information agents form beliefs about the temporary and the permanent component of productivity. Shocks to the signal (noise shocks) trigger aggregate fluctuations unrelated to changes in productivity. Bayesian estimation shows that noise shocks explain up to 14 percent of output and up to 25 percent of consumption fluctuations. Nominal rigidities and the specification of the monetary policy rule are crucial for the importance of noise shocks. These features help to resolve conflicting results in the previous literature.     

Testing Part of a DSGE Model by Indirect Inference

We propose a way of testing a subset of equations of a DSGE model. The test draws on statistical inference for limited information models and the use of indirect inference to test DSGE models. Using the numerical small sample distribution of our test for two subsets of equations of the Smets–Wouters model we show that the test has accurate size and good power in small samples, and better power than using asymptotic distribution theory. In a test of the Smets–Wouters model on US Great Moderation data, we reject the specification of the wage‐price but not the expenditure sector. This points to the wage‐price sector as the source of overall model rejection.     

The (un)importance of unemployment fluctuations for the welfare cost of business cycles

This paper studies the cost of business cycles within a real business cycle model with search and matching frictions in the labor market. We endogenously link both the cyclical fluctuations and the mean level of unemployment to the aggregate business cycle risk. The key result of the paper is that business cycles are costly: fluctuations over the cycle induce a higher average unemployment rate since employment is nonlinear in the job-finding rate and the past unemployment rate. We show this analytically for a special case of the model. We then calibrate the model to U.S. data. For the calibrated model, too, business cycles cause higher average unemployment; the welfare cost of business cycles can easily be an order of magnitude larger than Lucas's (1987) estimate. The cost of business cycles is the higher the lower the value of nonemployment is, or, equivalently, the lower is the disutility of work. The ensuing cost of business cycles rises further when workers' skills depreciate during unemployment.