“Generalized Method of Moments”: A Brief History

By Douglas Clement, Editor, The Region

In March 1979, Lars Peter Hansen, a young Ph.D. fresh out of the University of Minnesota, submitted a paper to the prestigious Econometrica. It described a statistical methodology that, in its final form, would allow economists to draw strong conclusions from models that weren’t completely specified (that is, not all variables, relationships or assumptions were included or precisely defined).

This “generalized method of moments” or GMM would give econometricians the ability to appraise alternative theories and investigate important economic phenomena without fully developing each of their elements. Researchers could rely on the most powerful explanatory variables and dispense with unnecessary assumptions. “GMM allows you to ‘do something without having to do everything simultaneously,’” Hansen explains.

But the GMM—abstract and mathematically challenging—was not immediately embraced by the field. (Indeed, Hansen’s initial draft was rejected by Econometrica, spurring him to refine and generalize his argument.) Hansen and his colleagues persevered, demonstrating the methodology’s power and range by applying it to exchange rates, asset pricing models and rational expectations theory. These and other examples gradually convinced economists of its utility and, with time, GMM became the gold standard. In 2013, Hansen received the Nobel Prize in economic sciences for his methodology, specifically in reference to its ability to evaluate asset pricing models.

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Hansen continues to study asset prices, focusing on linkages between financial markets and the broader macroeconomy. Recent work looks at uncertainty and risk tolerance in asset pricing behavior; he’s also developed methods to analyze and account for the uncertainty of the households and businesses that populate economic models, and also for the uncertainty that econometricians have about the adequacy of their models. Related research examines policymaking under uncertainty.

Q&A With Lars Peter Hansen

Region: When you were honored with the Nobel award in 2013 for your work on the GMM, the committee said that the GMM is “particularly well suited to testing rational theories of asset prices.” Could you give a brief description of the method and its importance to later work?

Hansen: I like to think about this as the following: Economists can build a full-scale model of a macroeconomy with many different equations, where they map out a really rich structure of financial markets and the macroeconomy. The question is: Is there a way that you can study the connections between asset prices and macroeconomic outcomes without necessarily getting all the other details exactly correct? For instance, an econometrician may wish to avoid specifying the precise information used by investors or detailing all of the ingredients that govern the evolution of the macroeconomy. My aim was to develop methods that allow for initial investigation of linkages without requiring a fully fleshed-out model.

Region: Which, of course, is always a challenge at the initial stages of model development.

Hansen: Right. The point is not even to make a pretense of believing that everything is fully specified. The econometrician’s jargon of a “partially specified model” applies where one tries to study linkages without having to spell out all the various different details. As you build models to use for policy purposes, you do have to specify many of those details. But as an initial step, it’s nice to be able to make assessments without all that detail. I like to say that the GMM allows you to “do something without having to do everything simultaneously.”

There’s a long history in formal econometrics behind this approach. Some of my research had an important antecedent, namely, the work of Denis Sargan back in the late 1950s. I was also very heavily influenced by lectures Chris Sims was giving back when I was a graduate student. While developing a formal justification for an econometric method, what excited me and helped my research gain some traction were the empirical applications I and others came up with.

Is there a way that you can study the connections between asset prices and macroeconomic outcomes without necessarily getting all the other details exactly correct? My aim was to develop methods that allow for initial investigation of linkages without requiring a fully fleshed-out model.

Region: What do you think was achieved by applying these methods, in your own work and in work by others?

Hansen: My initial applications included analyses of forward exchange markets with Bob Hodrick and investigation of pricing a cross section of asset returns with Ken Singleton. The Hodrick paper documented empirical challenges that have altered how researchers model exchange rate determination. The Singleton research exposed gaps in the existing macroeconomic models in terms of their implications for asset pricing. This work in turn encouraged Ravi Jagannathan, John Cochrane and me to characterize asset-pricing puzzles in more general terms. Scott Richard and I began to explore more abstract economic formulations of so-called stochastic discount factor models, where such factors simultaneously discount the future and adjust for risk. The empirical challenge to model builders is to understand why the implied risk prices are large and fluctuate over time in interesting ways. It’s been rewarding to observe the subsequent model extensions and refinements motivated by empirical challenges.

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