# In Praise of Partial Equilibrium

I have had it verified by those in a position to know that among many economists in the city of Minneapolis, there is a 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:

To illustrate my definition I highlight four distinctive characteristics of price theory that follow from this basic philosophy. First, diagrams in price theory are usually used to illustrate simple solutions to rich models, such as the supply and demand diagram, rather than primitives such as indifference curves or statistical relationships. Second, problem sets in price theory tend to ask students to address some allocative or policy question in a loosely-defined model (does the minimum wage always raise employment under monopsony?), rather than solving out completely a simple model or investigating data. Third, measurement in price theory focuses on simple statistics sufficient to answer allocative questions of interest rather than estimating a complete structural model or building inductively from data. Raj Chetty has described these metrics, often prices or elasticities of some sort, as “sufficient statistics”. Finally, price theory tends to have close connections to thermodynamics and sociology, fields that seek simple summaries of complex systems, rather than more deductive (mathematics), individual-focused (psychology) or inductive (clinical epidemiology and history) fields.

I view most of the economics I do on this blog as price theory in Glen Weyl's sense: "analysis that reduces rich and often incompletely specified models into 'prices' sufficient to characterize approximate solutions to simple allocative problems." My analysis of negative interest rate policies—and in particular what I wrote in "Even Central Bankers Need Lessons on the Transmission Mechanism for Negative Interest Rates" and "Negative Rates and the Fiscal Theory of the Price Level"—is a good example.

**Conclusion**

The moral is *don't put unnecessary constraints on the tools you use. Use the tool that best fits the purpose. *Sometimes that will be general equilibrium; sometimes it will be partial equilibrium.

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