DIVERSE ORGANIZATIONS AND THE COMPETITION FOR TALENT

We propose a theory of firm production that requires diverse inputs. We show that in a competitive labor market, firms differ in their skill composition. Organizations with higher total factor productivity (TFP) are larger and hire from a broader range of skills. Technological progress leads to an increase of all wages and results in downsizing. Quantifying productivity using our model shows that a constant elasticity of substitution (CES) production function generates unbiased estimates of TFP but biased estimates of marginal product and elasticity of substitution across skills. Our model also generates estimates of the TFP distribution based on CEO compensation alone.     

A Fiscal Stimulus and Jobless Recovery

We analyze the effects of a government‐spending expansion in a dynamic stochastic general equilibrium model with Mortensen–Pissarides labor‐market frictions, deep habits in private and public consumption, investment adjustment costs, a constant elasticity of substitution (CES) production function, and adjustments in employment at both intensive and extensive margins. The combination of deep habits and CES technology is crucial. The presence of deep habits magnifies the responses of macroeconomic variables to a fiscal stimulus, while an elasticity of substitution between capital and labor in the range of available estimates allows the model to produce a scenario compatible with the observed jobless recovery.     

Two‐level CES Production Technology in the Solow and Diamond Growth Models*

The two‐level CES aggregate production function—that nests a CES into another CES function—has recently been used extensively in theoretical and empirical applications of macroeconomics. We examine the theoretical properties of this production technology and establish existence and stability conditions of steady states under the Solow and Diamond growth models. It is shown that in the Solow model the sufficient condition for a steady state is fulfilled for a wide range of substitution parameter values. This is in sharp contrast with the two‐factor Solow model, where only an elasticity of substitution equal to one is sufficient to guarantee the existence of a steady state. In the Diamond model, multiple equilibria can occur when the aggregate elasticity of substitution is lower than the capital share. Moreover, it is shown that for high initial levels of capital and factor substitutability, the effect of a further increase in a substitution parameter on the steady state depends on capital–skill complementarity.     

Non‐Homothetic Multisector Growth Models

Multisector growth (MSG) models are dynamic versions of computable general equilibrium (CGE) models. Non‐homothetic preference (utility) functions are required for the evolution of factor allocations and industrial structures in accordance with consumption expenditure patterns implied by the non‐unitary income elasticities observed in all budget data since Engel in the 1850s. But comparative static general equilibrium solutions and particularly solving the dynamics of MSG models require explicit specifications of all demand and cost (price) functions. On the demand side, the constant differences of elasticity of substitution (CDES) non‐homothetic indirect utility functions and Roy's identity provide the explicit Marshallian demand functions and budget shares. Sectorial constant elasticity of substitution (CES) cost functions and Shephard's lemma provide the explicit relative commodity price functions and the sectorial cost shares and capital–labor ratios. Walrasian equilibria are given by one equation and the multisector dynamics by three differential equations. Benchmark solutions are given for three cost regimes of a 10‐sector MSG model. History patterns of industrial/allocational evolutions are recognized.     

CES Production Functions and Economic Growth

We examine inconsistencies and controversies related to the use of CES production functions in growth models. First, we show that not all variants of CES functions commonly used are consistently specified. Second, using a simple growth model, we find that a higher elasticity of substitution leads to a higher steady state and makes the emergence of permanent growth more probable. It is also pointed out that the effect of a higher elasticity of substitution on the speed of convergence depends on the relative scarcity of the factors of production. Finally, we discuss possible explanations of variations in the elasticity of substitution.
JEL classification: O 41; O 11     

Micro-foundation for a constant elasticity of substitution production function through mechanization

We consider an increase in the range of capital use as a form of mechanization. A constant elasticity of substitution (CES) production function is dynamically derived from Leontief production functions through the endogenous complementary relationship between capital accumulation and mechanization. This implies that a CES production function can be resolved into technological change that does not involve changes in total factor productivity. Furthermore, using the normalizing procedure of the CES production function developed by de La Grandville [de La Grandville, O., 1989. In quest of the Slutsky diamond. American Economic Review 79, 468–481], we investigate how mechanization is related to the elasticity of substitution in our endogenous growth model.     

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.     

On estimation of the CES production function—Revisited

Estimation of the non-linear Constant Elasticity of Scale (CES) function is generally considered problematic due to convergence problems and unstable and/or meaningless results. These problems often arise from a non-smooth objective function with large flat areas, the discontinuity of the CES function where the elasticity of substitution is one, and possibly significant rounding errors where the elasticity of substitution is close to one. We suggest three (combinable) solutions that alleviate these problems and improve the reliability and stability of the results.     

Productivity versus elasticity: a normalized constant elasticity of substitution production function applied to historical Soviet data

This study tests the extensive growth hypothesis, which would attribute the Soviet economic slowdown to low elasticity of substitution and over-investment rather than deteriorating productivity growth. To circumvent the low availability of data, widely applicable new methods for estimating productivity and elasticity of substitution were developed based on the normalized constant elasticity of substitution (CES) production function. One is an extended version of the Solow residual calculation, and the other is a direct estimation of the time-varying parameter normalized CES production function. The application of the methods to the Soviet data showed a decreasing trend in productivity growth and a low elasticity of substitution of approximately 0.25. The results neither reject nor support the extensive growth hypothesis because of uncertainty in the interpretation of the low elasticity of substitution. The results suggest that it is reasonable to assert that both deteriorating productivity growth and low elasticity of substitution caused the Soviet economic slowdown. Further empirical studies on productivity and elasticity of substitution in the Soviet and other economies are necessary to fully understand relations between productivity growth, elasticity of substitution and economic development.     

Looking back, looking ahead: Biased technological change, substitution and the wage gap

The implications of ICT on wage inequality are studied by applying a CES production function with skilled and unskilled labour. Skill-biased technological change increases wage inequality. The result is reinforced in a two-sector general equilibrium model if the income elasticity of the demand for high-tech goods and the elasticity of substitution between final goods are larger than one.     

ESTIMATING TEMPTATION AND COMMITMENT OVER THE LIFE CYCLE

This article estimates the importance of temptation for consumption smoothing and asset accumulation in a life‐cycle model. We use two complementary estimation strategies: first, we estimate the model‐implied Euler equation; second, we match liquid and illiquid wealth accumulation using the method of simulated moments. In both cases, we find that the utility cost of temptation is one‐quarter of the utility benefit of consumption. Further, temptation is crucial for correctly estimating the elasticity of intertemporal substitution (EIS): EIS estimates are biased downward when ignoring temptation. Finally, the model only matches the share of illiquid wealth if temptation is in the preference specification.     

Who provides the capital for Chinese growth: the public or the private sector?

We focus on the role of the government in the provision of investment in China, through the medium of a Dynamic Stochastic General Equilibrium model of the economy in which the form of the production function reflects this governmental role. Using indirect inference, we estimate and test for the elasticity of substitution between government and nongovernment capital in both Constant Elasticity of Substitution (CES) and Cobb–Douglas technologies. The results underscore the strong substitution relationship between government and nongovernment capital from 1949, supporting CES rather than the Cobb–Douglas technology. They also show that the orientation of public investment changed after the start of the ‘Socialist Market Economy’ in 1992: government capital became more complementary to nongovernment capital as it focused more on infrastructure and withdrew from industrial production, intervening only in times of crisis, for stabilization purposes, indirectly via the state banks.     

Transmission of Nominal Exchange Rate Changes to Export Prices and Trade Flows and Implications for Exchange Rate Policy*

We discuss how the welfare ranking of fixed and flexible exchange rate regimes in a New Open Economy Macroeconomics model depends on the interplay between the degree of exchange rate pass‐through and the elasticity of substitution between home and foreign goods. We identify combinations of these two parameters for which flexible and fixed exchange rates are superior with respect to welfare as measured by a representative household's utility level. We estimate the two parameters for six non‐EMU European countries (Czech Republic, Hungary, Poland, Slovakia, Sweden, and the UK) using a heterogeneous dynamic panel approach.     

Productivity,the Terms of Trade,and the Real Exchange Rate: Balassa–Samuelson Hypothesis Revisited

The paper examines how the Balassa–Samuelson hypothesis is affected by a modern variation of the standard model that allows product differentiation (within the traded and nontraded goods sectors) with the number of firms determined exogenously or endogenously. The hypothesis is found to be fragile in the modified framework. Small variations in the elasticity of substitution between home and foreign traded goods (within the range of estimates suggested in the literature), for example, can make the effect of a traded‐goods productivity improvement on the real exchange rate negative or positive, as well as small or large. This result provides a potential explanation of the mixed empirical results that have been obtained on the relationship between productivity and the real exchange rate.     

FACTOR SUBSTITUTION,MECHANIZATION, AND ECONOMIC GROWTH

This paper tries to explain the polarization of economic growth through mechanization. We derive a complementary relationship between capital accumulation and mechanization. While we assume an external effect that occurs as a result of mechanization, given the external effect, mechanization yields a constant‐elasticity‐of‐substitution production function in which the elasticity‐of‐substitution is greater than unity as the envelope of Cobb–Douglas production functions. When mechanization is difficult, which implies a low value for the elasticity‐of‐substitution, and the external effect is weak, there is potential for multiple steady states to exist.     

Factor Substitution, Income Distribution and Growth in a Generalized Neoclassical Model

Abstract. We analyze a generalized neoclassical growth model that combines a normalized CES production function and possible asymmetries of savings out of factor incomes. This generalized model helps to shed new light on a recent debate concerning the impact of factor substitution and income distribution on economic growth. We show that this impact relies on both an efficiency and a distribution effect, where the latter is caused by the distributional consequences of an increase in the elasticity of substitution. While the efficiency effect is always positive, the sign of the distribution effect depends on the particular savings hypothesis. If the savings rate out of capital income is substantial so that a certain threshold value is surpassed, the efficiency effect dominates and higher factor substitution accelerates the accumulation of capital and works as a major engine of growth.     

Oligopolistic Competition, Technology Innovation, and Multiproduct Firms

Firms' proliferation behavior in a differentiated product market is studied using an oligopolistic competition model with multiproduct firms. The model has the following characteristics: (1) the elasticity of substitution across firm's own products and the elasticity of substitution across different firms are allowed to differ; (2) the product managers of the same firm behave cooperatively rather than independently; (3) the number of firms is determined by a free-entry condition and so is endogenous. If the elasticity of substitution across the firm's own products increases, it is shown that the firm proliferates less and the number of firms in the market increases. If the elasticity of substitution across different firms increases, firms proliferate more and the number of firms in the market decreases.     

The macroeconomic effects of fiscal policy in a stochastically growing economy

This paper develops a stochastic model of endogenous growth with productive government expenditure. Herein, we specify the CES production function according to recent empirical evidence. The elasticity of substitution plays a key role in determining macroeconomic performance and the effectiveness of fiscal policy under uncertainty. Results demonstrate that a large elasticity of substitution provides a large expected growth rate and also large volatility of the growth rate. Regarding these effects, the growth-maximizing tax rate and welfare-maximizing tax rate under uncertainty are larger or smaller than those of deterministic economy according to the elasticity of substitution.     

Comparative advantage and strategic specialization

This paper shows that a strong comparative advantage is necessary for free trade and specialization in a 2 × 2 symmetric Ricardian model to be achieved in a Nash equilibrium. Governments strategically control labor distribution across industries, and representative agents maximize Cobb–Douglas utilities. A Nash equilibrium with complete specialization is achieved if and only if relative productivity exceeds a key value of 3, which is considered a very large number based on previous empirical studies. This paper also introduces a two‐stage game where each government chooses labor distribution first and then tariffs. In this two‐stage game, complete specialization is never achieved for any relative productivity level. Finally, by generalizing the Cobb–Douglas model into constant elasticity of substitution (CES) preferences, I show that if immiserizing growth effects exist, complete specialization could not be achieved for any level of relative productivity.     

Human Fallibility, Complementarity, and Fiscal Decentralization

This paper examines economic growth properties under alternative fiscal organizations when a bureau's decisions are fallible. A country consists of J jurisdictions, which need a public service. In a centralized government, one authority decides on services in every jurisdiction. In a decentralized government, J authorities are in charge of each public service. An authority can have high ability or low ability, and an authority with high ability draws a good project with higher probability. We first show that the decentralized government provides the same average quality of public services, with lower variance, than does the centralized government. We then apply this result to an economic growth model where the value of the Solow residual is a constant elasticity of substitution (CES) function of public services. We show that there is a critical value of the degree of complementarity below which fiscal decentralization is more desirable than fiscal centralization for an expected economic growth, and the decentralized government has a lower variance of GDP growth.