- 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.
-
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.
-
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.
|