In Praise of Partial Equilibrium – The Property Chronicle
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In Praise of Partial Equilibrium

The Economist

I have had it verified by those in a position to know that among many economists in the city of Minneapolis, there is an view that can be summarized as;

General equilibrium good, partial equilibrium bad.

I would like to contest the second half of this view, and qualify the first half. Here, when I speak of general equilibrium, I am thinking of a typical dynamic, stochastic general equilibrium model. When I speak of partial equilibrium, I am including models of a single agent’s decision problem, such as the model of household decision-making that leads to the empirical consumption Euler equation. In both cases, I am thinking of models being taken to the data as opposed to models that are pure theory.

Why Partial Equilibrium Has an Advantage over General Equilibrium Models for Empirical Analysis

The basic problem with a general equilibrium model is that if any part of the model is misspecified, then inference (formal or informal) about the relationship between any other part of the model and the data is likely to be messed up. If that is not true, then the general equilibrium model is equivalent, or nearly equivalent to a partial equilibrium model, putting that partial equilibrium model and the general equilibrium model on an equal footing. (If a general equilibrium model is equivalent to a partial equilibrium model, then the general equilibrium aspect of the general equilibrium model is just window dressing.)

By contrast, a partial equilibrium model—say one that makes predictions conditional on observed prices—can be robust to ignorance about big chunks of the economy. For example, given key assumptions about the household (rational expectations, maximization of a utility function of a given functional form, absence of preference shocks, no liquidity constraints, etc.) the consumption Euler equation should hold regardless of how the production side of the economy is organized.

That statement about the robustness of the consumption Euler equation to ignorance about big chunks of the economy holds true for a variety of different functional form assumptions. For example, if labor hours (or equivalently, leisure hours) are nonseparable from consumption, there is still a well-specified consumption Euler equation in which one only needs to know labor hours to condition on them. Here, for the purposes of understanding the determination of consumption, one need not know the structure of the labor market for the equation to hold, only the actual magnitudes of labor hours ground out by the labor market. (Susanto Basu and I talk about this in our still-in-the-works paper “Long-Run Labor Supply and the Elasticity of Intertemporal Substitution for Consumption.”)

As another example, I have begun supervising a potential dissertation chapter looking at a model that combines many sides of the economy, but derives results that are robust to ignorance about the stochastic processes of the shocks to the economy.

One way to think about partial equilibrium is that a partial equilibrium model represents a class of general equilibrium models. Showing that something is true for an entire class of general equilibrium models can be quite useful. Therefore, partial equilibrium can be quite useful.

Where General Equilibrium Models Come In

Because of their robustness to ignorance in other parts of the economy, partial equilibrium models have a real advantage over general equilibrium models for breaking the task of figuring out how the world works into manageable pieces. This is empirical analysis, in the literal sense of analysis as breaking things down.

Once one understands (to some reasonable extent) how the world works, general equilibrium models are the way to understand what the effects of different policies would be. The motto that “Everything affects everything else” is a useful reminder that studying the effects of policies often requires a general equilibrium approach. But that comes after one understands what the right model is. Partial equilibrium is often a better way to figure out, piece by piece, what the right model and the right parameter values are.

Price Theory

Even in policy analysis, sometimes a more partial equilibrium approach can be helpful. In policy analysis, a partial equilibrium approach can be called “price theory,” in line with Glen Weyl’s definition in his Marginal Revolution guest post “What Is ‘Price Theory’?”:

… my own definition of price theory as analysis that reduces rich (e.g. high-dimensional heterogeneity, many individuals) and often incompletely specified models into ‘prices’ sufficient to characterize approximate solutions to simple (e.g. one-dimensional policy) allocative problems.

Glen gives some examples:

The Economist

About Miles Kimball

Miles Kimball

Miles Kimball holds the Eaton Chair in Economics at the University of Colorado Boulder, and is Emeritus Professor of Economics and Survey Research of the University of Michigan. (Born in 1960, he is now 57.) Politically, Miles is an independent who grew up in an apolitical family. He holds many strong opinions—open to revision in response to cogent arguments—that do not line up neatly with either the Republican or Democratic Party.

Articles by Miles Kimball

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