Production and Uncertainty in Dynamic General Equilibrium

Ph.D. Dissertation, 1998

Pedro José Gutiérrez Diez

University of Valladolid 
Department of Economics 
School of Business and Administration 



Thesis Supervisor

  • Zenón Jiménez Ridruejo

Examining Board

  • José Luís García Lapresta
  • Carlos Hervés
  • Antonio Manresa
  • Jorge Nieto Vázquez
  • José Miguel Sánchez Molinero
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Summary

Uncertainty in Dynamic General Equilibrium

  • The extension to an uncertainty environment of the basic general equilibrium models, based on the work of Walras (1877), was done by Arrow (1964), while Debreu (1959) was the first to introduce intertemporal considerations. This first formulation of the general equilibrium with time and uncertainty is known as Arrow-Debreu Equilibrium, basically a Walrasian Equilibrium. Radner (1991) extended the analysis to a sequential markets environment, giving rise to a new definition of general equilibrium, the Radner Equilibrium. Together with these two formulations there is a third, based on the recursive theory of Bellman (1957), that provides a very powerful method for analyzing and computing dynamic general equilibrium models. The relationships among these three definitions of Dynamic General Equilibrium are studied in an uncertain environment, placing particular emphasis on the role played by assets and on the importance of asset structure. In this respect, the complete/incomplete asset structure is a crucial question, related to the equivalence between Arrow-Debreu Equilibrium and Radner Equilibrium, existence of equilibrium, Pareto Optimality, firm behavior, and asset formation. Specification of uncertainty sources is also important. Broadly speaking, this literature has traditionally identified two categories or sources of uncertainty. The first kind is called "technological uncertainty'', with an exogenous nature and concerning variables beyond agents control. On the contrary, the second type of uncertainty is the result of the behavior of agents in an asymmetric information environment, and for this reason is known as "market uncertainty''. Specifically, the thesis focus on the first kind of uncertainty, that is, the exogenous or technological uncertainty. In fact, this is strictly speaking the only uncertainty source in the economy, as the second one can be identified with informational asymmetries.

Dynamic General Equilibrium Models with Production and Uncertainty

  • The study of production activity in a dynamic environment with uncertainty requires the use of a general equilibrium framework, linking in a natural way the households decisions under uncertainty, the input demand decisions of firms, and the returns of producer issued assets. Indeed, general equilibrium theory has devoted since the 50's considerable attention to production, uncertainty and risk, reaching fruitful results, among other fields, in finance theory, welfare economics, and business cycle theory. Since the main results concerning uncertainty and risk in exchange economies have already been obtained, I focus on the relationships between production and uncertainty leaving aside those aspects of risk not linked to production. I analyzes three topics on production and uncertainty.

    First, I provide an extended discussion of welfare theorems, aggregation results, and recursive formulation when prodution is incorporated.

    Secondly, I analyze the role of production assets in hedging against risk. It is well known that the exogenous uncertainty situations arising from independent risks at the individual level can be totally removed from the economy thanks to the functioning of the insurance markets, as a result of consumers heterogeneity with respect to uncertainty and the law of large numbers. Indeed, the households heterogeneity condition has been in the economic literature the traditional perspective to deal with the risk hedging subject, leaving aside the role played by producer issued assets. In my thesis it is shown that insurance markets based on Arrow-Debreu securities, issued by uncertainty-heterogenous households and with no production behind, are not the only possible.

    Finally, through the formulation of a multiprocess general equilibrium model, I derive a Real Business Cycle model with several production processes where aggregate fluctuations are a consequence of sectoral shocks. Making use of the dynamic programming algorithm, I simulate this RBC model under five different stochastic specifications, concluding that, together with the stylized facts of growth, this multiprocess RBC model implies more general results impossible to obtain with the standard RBC models.

Asset Markets

  • When production and uncertainty is introduced, the dynamic general equilibrium models give rise to the consumption-based capital asset pricing models (CAPM). CAPM have been, since the works of Lucas and Prescott (1971), Lucas (1978), Brock (1982), and Donaldson and Mehra (1984), an alternative to the Portfolio Models pioneered by Markowitz (1952) and developed by Sharpe (1964), Lintner (1965) and Mossin (1966). Unlike the portfolio models, where returns are specified exogenously, the CAPM provide a framework in which equilibrium prices, returns and risk premia are endogenously determined and arise from the interactions of profit maximizing firms and utility maximizing individuals. Since the CAPM are general equilibrium models where the uncertainty sources are identified and linked with the underlying production technology, they allow a sound analysis of risky asset prices. However, these general equilibrium models have rarely introduced the possibility of coexistence of several production processes, just analyzing the asset prices in a one-sector general equilibrium model. In this respect, the thesis formulates a multisector CAPM with interesting properties. In particular, together with standard properties such as the absence of arbitrage opportunities and the existence of risk-premia, the model allows us to study the circumstances under which a complete asset structure appears, and makes possible a better fit to the data in explaining volatility, risk premia and equity premia.
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Contents

  • Introduction
    • Dynamic General Equilibrium Theory under Uncertainty
    • Basic and Extended Models. The Recursive Method.
    • Asset Markets
  • Dynamic General Equilibrium, Production and Uncertainty
    • Assumptions
    • Equilibrium
      • Economy Environments
      • Arrow-Debreu Equilibrium and Radner Equilibrium
    • Relationships
    • The Complete Markets Assumption
    • Financial Properties of Equilibrium
    • The Transversality Condition
    • Equilibrium Prices
    • Complete Markets and Production
  • Extended Models
    • Introduction
    • HARA Class of Preferences and the Representative Consumer
    • The Two-Periods Problem
      • The Recursive Method
    • Real Business Cycle Models
    • Excess Returns and Equity Markets
      • Equilibria and Relationships
      • Equilibrium Properties
      • The Social Planner's Problem
      • Complete Markets and Equities
    • The Role of Expectations
  • Dynamic Programming
    • A Computer Program
    • A Multiprocess RBC Model
    • Complete Markets and Real Interest Rates
  • Conclusions
  • Appendix A: The Basic Model
    • Equilibria Relationships
    • Equilibrium Properties
    • Complete Markets from the Point of View of Production
  • Appendix B: Extended Models
    • Aggregation
    • Recursive Formulation
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