An integration of equilibrium theory and turnpike theory

A turnpike theorem is proved for a general equilibrium model with finitely many immortal consumers.     

Indirect inference and calibration of dynamic stochastic general equilibrium models

We advocate in this paper the use of a sequential partial indirect inference (SPII) approach, in order to account for calibration practice where dynamic stochastic general equilibrium models (DGSE) are studied only through their ability to reproduce some well-chosen moments. We stress that, despite a lack of statistical formalization, the controversial calibration methodology addresses a genuine issue on the consequences of misspecification in highly nonlinear and dynamic structural macro-models. We argue that a well-driven SPII strategy might be seen as a rigorous calibrationnist approach, that captures both the advantages of this approach (accounting for structural “a-statistical” ideas) and of the inferential approach (precise appraisal of loss functions and conditions of validity). This methodology should be useful for the empirical assessment of structural models such as those stemming from the real business cycle theory or the asset pricing literature.     

On the smoothness of optimal paths II: some local turnpike results

We study the local turnpike property for two classes of infinite-horizon discrete-time deterministic maximization problems which have common applications, e.g., optimal growth theory. We follow a functional-analytic approach and rely on an implicit function theorem for the space of the sequences which converge to zero. We shall assume the existence of an optimal path which is not necessarily a steady-state. Relying on material developped in Blot and Crettez (Decis Econo Finance 27:1–34, 2004), “On the smoothness of optimal paths” Decis Econ Finance, 21:1–34, 2004), we provide conditions under which a variation in the initial conditions (i.e., capital stock and discount rate) yields an optimal solution which converges toward a reference solution when time becomes infinite. We also provide new results on bounded solutions of difference equations. We gratefully thank the editor, Silvano Holzer, and two anonymous referees for remarks and advices on a previous version of this paper.     

Econometric analysis of linearized singular dynamic stochastic general equilibrium models

In this paper I propose an alternative to calibration of linearized singular dynamic stochastic general equilibrium models. Given an a-theoretical econometric model as a representative of the data generating process, I will construct an information measure which compares the conditional distribution of the econometric model variables with the corresponding singular conditional distribution of the theoretical model variables. The singularity problem will be solved by using convolutions of both distributions with a non-singular distribution. This information measure will then be maximized to the deep parameters of the theoretical model, which links these parameters to the parameters of the econometric model and provides an alternative to calibration. This approach will be illustrated by an application to a linearized version of the stochastic growth model of King, Plosser and Rebelo.     

The primal route to the turnpike and asymptotic stability

Asymptotic turnpike theorems in the case where the future is discounted are traditionally derived under the assumptions that a utility function is twice differentiable and that is Hessian is negative definite. Replacing these assumptions by a weaker one. I give a proof of the theorem simpler than existing ones.     

The general equilibrium effects of congestion externalities

This is the second in a series of three articles on the topic of congestion externalities. We use an urban general-equilibrium model to compute two types of cities: the market-equilibrium city, in which congestion externalities occur, and the optimum city. The optimum city has a more dispersed distribution of employment, and a more concentrated distribution of residence. If the population of the city is fixed, the optimum pricing of transportation generates a per capita welfare gain of $3.78 per week. If the population of the city is endogenous, the internalization of congestion externalities causes the city to grow.     

The current non-status of general equilibrium theory

This paper argues that the abandonment of general equilibrium theory by microeconomists was a mistake. It provides counter arguments to two of the reasons for that abandonment—lack of both generality and consistency with methodological individualism in uniqueness and stability analysis of equilibria—and urges microeconomists to refocus some of their attention on it.     

Evaluation of dynamic stochastic general equilibrium models based on distributional comparison of simulated and historical data

We take as a starting point the existence of a joint distribution implied by different dynamic stochastic general equilibrium (DSGE) models, all of which are potentially misspecified. Our objective is to compare “true” joint distributions with ones generated by given DSGEs. This is accomplished via comparison of the empirical joint distributions (or confidence intervals) of historical and simulated time series. The tool draws on recent advances in the theory of the bootstrap, Kolmogorov type testing, and other work on the evaluation of DSGEs, aimed at comparing the second order properties of historical and simulated time series. We begin by fixing a given model as the “benchmark” model, against which all “alternative” models are to be compared. We then test whether at least one of the alternative models provides a more “accurate” approximation to the true cumulative distribution than does the benchmark model, where accuracy is measured in terms of distributional square error. Bootstrap critical values are discussed, and an illustrative example is given, in which it is shown that alternative versions of a standard DSGE model in which calibrated parameters are allowed to vary slightly perform equally well. On the other hand, there are stark differences between models when the shocks driving the models are assigned non-plausible variances and/or distributional assumptions.     

Efficient estimation of general dynamic models with a continuum of moment conditions

There are two difficulties with the implementation of the characteristic function-based estimators. First, the optimal instrument yielding the ML efficiency depends on the unknown probability density function. Second, the need to use a large set of moment conditions leads to the singularity of the covariance matrix. We resolve the two problems in the framework of GMM with a continuum of moment conditions. A new optimal instrument relies on the double indexing and, as a result, has a simple exponential form. The singularity problem is addressed via a penalization term. We introduce HAC-type estimators for non-Markov models. A simulated method of moments is proposed for non-analytical cases.     

Myopia and pensions in general equilibrium

The US social security tax rate has doubled in the last half century. Does the degree of myopic behavior that we observe in the US justify the size of the social security program? To study this question we build a computable general equilibrium model that is composed of life-cycle permanent-income consumers who save optimally and “hand-to-mouth” consumers who just consume their disposable income. Our model is a continuous-time, general equilibrium extension of the model by Cremer et al. (Int Tax Public Financ 15(5):547–562, 2008), though we abstract from the redistributive function of social security to focus on myopia. Retirement is a choice variable in our model and the social security program is designed to mimic the US program in which the annuity value of benefits increases with the retirement age. Also, we allow for delayed claiming beyond the date of retirement. The model matches a variety of important data targets relating to saving and retirement. We find that small reductions in the social security tax rate provide significant welfare gains to both groups of consumers.     

Perturbed utility and general equilibrium analysis

We study general equilibrium theory of complete markets in an otherwise standard economy with each household having an additive perturbed utility function. Since this function represents a type of stochastic choice theory, the equilibrium of the corresponding economy is defined to be a price vector that makes its mean expected demand equal its mean endowment. We begin with a study of the economic meaning of this notion, by showing that at any given price vector, there always exists an economy with deterministic utilities whose mean demand is just the mean expected demand of our economy with additive perturbed utilities. We then show the existence of equilibrium, its Pareto inefficiency, and the upper hemi-continuity of the equilibrium set correspondence. Specializing to the case of regular economies, we finally demonstrate that almost every economy is regular and the equilibrium set correspondence in this regular case is continuous and locally constant.     

Simple solutions to the initial conditions problem in dynamic,nonlinear panel data models with unobserved heterogeneity

I study a simple, widely applicable approach to handling the initial conditions problem in dynamic, nonlinear unobserved effects models. Rather than attempting to obtain the joint distribution of all outcomes of the endogenous variables, I propose finding the distribution conditional on the initial value (and the observed history of strictly exogenous explanatory variables). The approach is flexible, and results in simple estimation strategies for at least three leading dynamic, nonlinear models: probit, Tobit and Poisson regression. I treat the general problem of estimating average partial effects, and show that simple estimators exist for important special cases. Copyright © 2005 John Wiley & Sons, Ltd.     

Migration and the wage and unemployment gaps between urban and non-urban sectors: A dynamic general equilibrium reinterpretation of the Harris–Todaro equilibrium

This paper offers a dynamic general equilibrium reinterpretation of the static partial migration equilibrium by Harris and Todaro [Harris, J., Todaro, M., 1970. Migration, unemployment and development; a two-sector analysis. American Economic Review 60, 126–142], under (i) flexible urban and rural wages and (ii) free mobility of workers and free entry of firms. The proposed model accounts for the set of stylized facts in developing countries: rural to urban migration and higher urban wages and unemployment.The model allows us to view the wage gap as a compensating differential for the negative amenities associated with job destruction and subsequent costly search on the consumption side, which can also be seen as a match-specific premium based on a sectoral productivity differential on the production side. Our model predicts the comovements among urban and non-urban wages and migration flows to the urban sector, an empirical regularity observed over the urbanization process of developing economies. Finally, we also conduct a welfare analysis.     

Convergence of Bayesian learning to general equilibrium in mis-specified models

A central unanswered question in economic theory is that of price formation in disequilibrium. This paper lays the groundwork for a model that has been suggested as an answer to this question in, particularly, Arrow [Toward a theory of price adjustment, in: M. Abramovitz, et al. (Ed.), The Allocation of Economic Resources, Stanford University Press, Stanford, 1959], Fisher [Disequilibrium Foundations of Equilibrium Economics, Cambridge University Press, Cambridge, 1983] and Hahn [Information dynamics and equilibrium, in: F. Hahn (Ed.), The Economics of Missing Markets, Information, and Games, Clarendon Press, Oxford, 1989]. We consider sellers that monopolistically compete in prices but have incomplete information about the structure of the market they face. They each entertain a simple demand conjecture in which sales are perceived to depend on the own price only, and set prices to maximize expected profits. Prior beliefs on the parameters of conjectured demand are updated into posterior beliefs upon each observation of sales at proposed prices, using Bayes’ rule. The rational learning process, thus, constructed drives the price dynamics of the model. Its properties are analysed. Moreover, a sufficient condition is provided, relating objectively possible events and subjective beliefs, under which the price process is globally stable on a conjectural equilibrium for almost all objectively possible developments of history.     

The timing of residential land development: A general equilibrium approach

A formal model of the development process is constructed in order to arrive at a better understanding of the land development process, the change in land prices over time, and the effects of public policy on these variables. The relationship between the rate of interest and the rate of price appreciation on land is shown to depend upon development costs, agricultural opportunity costs, market structure, and the level of Ricardian rents on land. The effects of a land tax and a capital gains tax on the rate of development are also analyzed.     

The effects of the property tax: A general equilibrium simulation

This paper uses a general equilibrium model of residential land use to study the effects of the property tax in a closed city. Two different specifications of the production technology for housing are used, and are found to yield similar results. The model is too complicated to be solved in closed form, but an efficient computational technique which utilizes a simplicial search algorithm was developed to solve it numerically. This type of model and computational technique can be applied to a wide variety of practical issues in urban economics.     

Spatial econometric analysis of spatial general equilibrium

A structural spatial econometric model for nine regions of Israel is estimated using non-stationary spatial panel data during 1987–2015. The model focuses on the relation between regional markets in labour, housing and capital when there is imperfect internal migration between regions, when capital is imperfectly mobile between regions, and when building contractors operate across regions. Since the regional panel data are non-stationary, the econometric methodology is based on spatial panel cointegration. The estimated model is used to simulate the temporal and spatial propagation of regional shocks induced, for example, by regional policy (land for housing, regional investment grants). Impulse responses are temporally and spatially state dependent. They are also highly persistent because of longevity in housing and capital.     

A general equilibrium analysis of strategic arbitrage

We analyze a general equilibrium framework with Cournot arbitrageurs and with price-taking investors who are subjected to restricted participation constraints. Restricted participation may leave some arbitrage opportunities unexploited by investors.We show existence of Cournot–Walras equilibria with an endogenous number of arbitrageurs. The number of arbitrageurs is endogenous since they have to sink entry costs in order to arbitrage across the relevant markets. We characterize equilibria and analyze the effects on equilibrium prices and quantities of increased competition among arbitrageurs due to lower entry costs.     

Urban general equilibrium models and simplicial search algorithms

This paper describes how simplicial search algorithms work, and discusses how they may be used to solve static theoretical urban models. If such algorithms are to be used, land must be treated as consisting of a number of discrete sections. It is argued that this is not a serious disadvantage, and that for many purposes such discrete models have significant advantages over models in which land is treated as continuous. In particular, it is possible to deal with several groups of people having different tastes and incomes. Several related models are described, and some interesting qualitative results are presented.