Avoiding Mis-estimation of the CES Function: Unit Matters

ABSTRACT

We demonstrate that unit errors of measurement will lead to significant biases in estimating the constant elasticity of substitution (CES) function. Monte-Carlo simulations show that estimation results tend to reach Cobb–Douglas (CD) functions or extreme values if units of input variables are incorrectly used. To avoid this problem, we suggest adding an overall efficiency parameter and a unit correction parameter which is similar to biased technological change parameter when estimating CES functions. Any unit error of measurement can be captured by these two parameters while allowing researchers to get unbiased estimation results of other parameters.     

Renewable energy and unemployment: A general equilibrium analysis

Using a three-sector general equilibrium model, the impact of renewable electricity support policies on the rate of equilibrium unemployment is analyzed. In a simple two-factor version of the model, the paper shows analytically that renewable electricity support policies lead to an increase in the rate of unemployment. A numerical analysis is conducted with an expanded three-factor model. In this version, most scenarios analyzed also lead to an increase in equilibrium unemployment. However, the paper identifies conditions in which renewable energy support policies can decrease the rate of equilibrium unemployment. In particular, when the elasticity of substitution between capital and labor is low, when capital is not mobile internationally, and when the labor intensity of renewable generation is high relative to conventional generation, renewable electricity support policies may reduce the rate of equilibrium unemployment. The model is parameterized to represent the US economy, such that the magnitudes of quantities can be observed. Although there is some variation in the results depending on parameters, the findings suggest in general that reducing electricity sector emissions by 10% through renewable electricity support policies is likely to increase the equilibrium unemployment rate by about 0.1–0.3 percentage points.     

Renewable energy and unemployment: A general equilibrium analysis

Using a three-sector general equilibrium model, the impact of renewable electricity support policies on the rate of equilibrium unemployment is analyzed. In a simple two-factor version of the model, the paper shows analytically that renewable electricity support policies lead to an increase in the rate of unemployment. A numerical analysis is conducted with an expanded three-factor model. In this version, most scenarios analyzed also lead to an increase in equilibrium unemployment. However, the paper identifies conditions in which renewable energy support policies can decrease the rate of equilibrium unemployment. In particular, when the elasticity of substitution between capital and labor is low, when capital is not mobile internationally, and when the labor intensity of renewable generation is high relative to conventional generation, renewable electricity support policies may reduce the rate of equilibrium unemployment. The model is parameterized to represent the US economy, such that the magnitudes of quantities can be observed. Although there is some variation in the results depending on parameters, the findings suggest in general that reducing electricity sector emissions by 10% through renewable electricity support policies is likely to increase the equilibrium unemployment rate by about 0.1–0.3 percentage points.     

Comment on “Unwrapping some euro area growth puzzles: Factor substitution, productivity and unemployment”

This paper estimates the factor elasticity of substitution of the aggregate production function and then uses these estimates to resolve two puzzles relating to the Euro Area. The paper is novel in three ways: First it uses the CES production technology in the empirical strategy to understand real world economic phenomena; second it uses a frontier empirical methodology; and third it uses a new dataset.     

Exchange rate devaluation,monetary policy and wages: A general equilibrium analysis for Chile

A range of devaluation, monetary and wage policy mixes are analysed for the Chilean economy using a 10 sector comparative static model built along neoclassical lines. The model, while focusing on the real side of the economy, also contains a simple monetary sector. Quantifying the short-run implications of each policy mix for key macroeconomic and sectoral variables enables judgements to be made about the effectiveness of each mix in reaching specified targets and their feasibility. Money wage flexibility downwards is crucial if balance of trade and employment targets are to be achieved with lower domestic inflation and a smaller nominal devaluation.     

The role of miniatures in computable general equilibrium modelling : Experience from ORANI

ORANI is a large general equilibrium model of the Australian economy used by policy analysts and university research workers. This paper describes the role of miniature models in the development and application of ORANI. Miniature versions of ORANI have been useful in (a) explaining results; (b) detecting errors; (c) conducting sensitivity analyses; (d) experimenting with new specifications; and (e) teaching. The present paper concentrates mainly on (a) and (b). A miniature model is developed to explain ORANI results for the effects of increases in protection, reductions in the real costs of labour, increases in oil prices and increases in real aggregate demand.     

Inequalities and fluctuations in a dynamic general equilibrium model

   Summary. In the present paper a tractable two-sector neo-classical growth model with heterogeneous agents is considered. The local dynamic properties of the equilibrium path are analyzed in relation with the underlying characteristics of the economy. In particular, the existence of fluctuations is related to the degree of heterogeneity in labor and in capital endowments. When applied to international trade theory, the analysis shows that free trade may distabilize a world economy that is originally stable under the regime of autarky. Received: December 28, 1998; revised version: October 29, 1999     

Moral hazard and general equilibrium in large economies

Summary. The paper analyzes a two period general equilibrium model with individual risk, aggregate uncertainty and moral hazard. There is a large number of households, each facing two individual states of nature in the second period. These states differ solely in the household's vector of initial endowments, which is strictly larger in the first state (good state) than in the second state (bad state). In the first period each household chooses a non-observable action. Higher levels of action give higher probability of the good state of nature to occur, but lower levels of utility. Households' utilities are assumed to be separable in action and the aggregate uncertainty is independent of the individual risk. Insurance is supplied by a collection of firms who behave strategically and maximize expected profits taking into account that each household's optimal choice of action is a function of the offered contract. The paper provides sufficient conditions for the existence of equilibrium and shows that the appropriate versions of both welfare theorems hold. Received: December 7, 1998; revised version: October 25, 1999     

Transportation capital and its effects on the U.S. economy: A general equilibrium approach

We analyze the effect of the US transportation system on economic activity by building a quantitative dynamic general equilibrium model with a taxpayer-funded transportation capital stock. We highlight stark differences between the positive welfare effects of additional infrastructure spending in the long run, and its potentially negative effects when we account for the large transition (time and delay) costs to build. We also quantify large differences between the effects of additional infrastructure spending and efficient transportation policies, such as congestion pricing and eliminating laws that artificially inflate input prices, concluding that taxpayer-funded transportation improvements that increase GDP significantly may produce smaller welfare gains than efficient policies that increase GDP modestly.     

Elasticity of substitution and growth: normalized CES in the Diamond model

Summary. It is often asserted that the more substitutable capital and labor are in the aggregate production the more rapidly an economy grows. Recently this has been formally confirmed within the Solow model by Klump and de La Grandville (2000). This paper demonstrates that there exists no such monotonic relationship between factor substitutability and growth in the Diamond overlapping-generations model. In particular, we prove that, if capital and labor are relatively substitutable, a country with a greater elasticity of substitution exhibits lower per capita output growth in transit and in steady state. Received: October 27, 2001; revised version: February 25, 2002     

Comment on “σ: The long and short of it”

I comment on some of the issues discussed by Robert Chirinko (Chirinko, R.S., 2008. σ: The long and short of it. Journal of Macroeconomics 30 (2), 671-686). I also offer some additional evidence and discuss the theoretical implications of the empirical findings regarding σ.     

Capital–labor substitution and balanced growth

This paper explores how different values of the elasticity of substitution between capital and labor (σ) impact on the balanced growth paths and growth potential of a country in exogenous growth models. The behavior of the system depends on the value of σ and the passage of σ through two critical values causes a qualitative change in the nature of the singular points and of its trajectories. The balanced growth path defined by a singular point in the form of a saddle-path exists and is locally stable if σ lies between two critical values.     

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.     

Skilled–unskilled wage inequality: A general equilibrium analysis

The paper develops a static three sector competitive general equilibrium model of a small open economy in which skilled labour is mobile between a traded good sector and a non-traded good sector and unskilled labour is specific to another traded good sector. The capital is perfectly mobile among all these three sectors. We examine the effects of change in different factor endowments and of globalization on skilled–unskilled wage inequality. We find that the effect of a change of a factor endowment on wage inequality depends on the factor intensity ranking between two skilled labours using sectors and on the relative strength of the marginal effects on demand for and supply of non-tradable good. We also find that a decrease in the price of the product produced by skilled (unskilled) labour using traded good sector lowers (raises) the skilled–unskilled wage inequality.     

Information and the operation of markets: tests based on a general equilibrium model of land leasing in India

This paper develops an estimable general equilibrium model of land leasing to test the extent to which information is commonly held in a village and whether village markets are efficient. Information regarding the relative farming skill of households is found to be widespread, but the assumption of perfectly efficient markets within the village is rejected. These results have ramifications for the estimation of agricultural household models and for our understanding of rural institutions. The model is derived from the primitives of the production technology, the extent of information and the distributions of assets and several household unobservables. Simultaneity and selection issues are dealt with explicitly in a two-stage maximum likelihood estimation procedure using panel data from India.     

Anatomy of a balance-of-payments crisis : Application of a computable general equilibrium model to Turkey, 1978–1980

This paper analyses quantitatively the causes of the foreign exchange crisis in Turkey in the late 1970s through application of a multisector computable general equilibrium (CGE) model. The model incorporates some mechanisms that simulate the actual workings of the foreign exchange market during the turbulent foreign exchange disequilibrium period 1978–1980. It features the simultaneous operation of both quantitative controls and premium rationing schemes. Factors contributing to the foreign exchange crisis are analysed through counterfactual simulations which examine the implications for the Turkish economy of use of a flexible exchange rate, no oil price shock in the 1978–1980 period, and maintaining a constant price-level deflated affective exchange rate. Our results indicate that while exchange rate policy played an important role in bringing about the foreign exchange crisis, the influence of other factors was substancial.     

Adjusting the model to adjust the world: constructive mechanisms in postwar general equilibrium theory

Economic methodologists most often study the relations between models and reality while focusing on the issues of the model's epistemic relevance in terms of its relation to the ‘real world’ and representing the real world in a model. We complement the discussion by bringing the model's constructive mechanisms or self-implementing technologies in play. By this, we mean the elements of the economic model that are aimed at ‘implementing’ it by envisaging the ways to change the reality in order to bring it more in line with the model. We are thus concerned mainly not with the ways to change the model to ‘fit’ the reality, but rather with the model's own armature that is supposed to transform the world along theoretical lines. The case we study is Arrow–Debreu–McKenzie general equilibrium model. In particular, we show the following: gradient methods and stability could be regarded as constructive mechanisms of general equilibrium modeling in the context of market socialism debates; the obsession of general equilibrium theorists with these concepts can be partly explained by the fact that they hoped not to be faithful to reality, but rather to adjust it to fit the theoretical model; mechanism design theory initiated by the stability theorist Leonid Hurwicz could be seen as a successor of this position. We conclude by showing the relevance of this analysis for epistemic culture of much of contemporary economics and hence, claim that it is an important complement to the traditional philosophy of economic modeling.     

The role of factor substitution in the theory of economic growth and income distribution: Two examples

While much empirical evidence suggests that the Cobb–Douglas production function may be a reasonable benchmark for aggregate analysis, we argue that the practice, particularly prevalent in contemporary growth theory, of adopting the Cobb–Douglas technology, may lead to misleading implications. Using two examples, we show that key implications of the models are highly sensitive to small deviations of the elasticity of substitution from unity. The first employs the standard neoclassical model and emphasizes the sensitivity of the speed of convergence to small changes in the elasticity of substitution. This in turn has profound consequences for wealth and income distribution. The second deals with foreign aid and highlights how the relative merits of “tied” versus “untied” aid are also very sensitive to the elasticity of substitution.     

IS model: A general model of forecasting and its applications in science and the economy

Expanding the work of Marchetti and Modis on Lotka-Volterra competition systems, a general model of Interaction Systems (IS) is introduced to describe the dynamics of multiple member interactions among different populations concerning not only biological systems but other types of systems as well. The new IS model provides us with a general framework of analysis and forecasting, where all parameters, variables, and interactions have real meaning, by using basic knowledge of each system.The proposed model can be applied to many different fields covering economic, business, social, physical, and other phenomena giving us both numerical estimates and qualitative insights of the system's dynamics. This is illustrated in two case studies. In the first case, the IS model is applied to elementary chemical reactions in order to quantify the reactions' kinetics. The result is the well known rate law of chemical reactions kinetics thus providing evidence of the proposed model's validity. In the second case, the IS model is applied to the global economy. The resulting model is tested against real global GDP data. The new IS model gave reliable estimates and proved to be considerably more accurate as compared to a similar forecast of global GDP based on the logistic growth model. Furthermore, the new model presented a basic framework of understanding the nature of major economic shifts, including the recent global recession of 2009, by studying the dynamic relationship between demand and supply.     

Present bias and the inefficiency of the centralized economy: The role of the elasticity of intertemporal substitution

We analyze an endogenous growth model considering agents with an isoelastic utility. Preferences are characterized by a utility affected by a negative externality, and a level of impatience which decays with the time distance from the present. Agents who cannot commit the actions of their future selves, play a game against them. The stationary equilibrium of this game defines a balanced growth path with a slower growth when played by subsequent central planners than when played by decision makers in the market economy. First, we prove that the fast growing market economy implies higher welfare if the negative externality is small, while the centralized economy is welfare improving above a given threshold for the externality (obtained for a specific family of non-constant discount functions). Secondly, we observe that this threshold increases with the elasticity of intertemporal substitution in consumption. Therefore, the greater this elasticity the more likely it is that the externality lies below this threshold, where policy interventions would not be adequate. Finally, as one would expect, the range of values of the externality for which the market equilibrium provides higher welfare widens the more different from constant discounting time preferences are, due either to a wider range of variation for the instantaneous discount rates or because these decay more slowly.