# Chow Test

# Chow Test

The term *Chow test* refers to a family of statistical tests used mainly, but not exclusively, in econometrics. The aim of all the tests in the family is to test for parameter constancy across all the observations of the sample of data under analysis. In econometric modeling, parameters usually have some economic interpretation, such as the responsiveness, or elasticity, of some variable to changes in another. If a model is to have any predictive power, it is important to check the assumption of parameter constancy. A Chow test is a way to perform such a check.

Economic data frequently take the form of time series. A time series constitutes a record of the history of an economic variable, such as the unemployment rate. Each individual observation of a time series is associated with a given period of time, which may be a year, a quarter, or even, in the case of financial data, a few minutes. In time series modeling, one looks for patterns in the dynamic evolution of a set of series. Such patterns can take various general forms, but all of them depend on parameters, the values of which are usually unknown.

From time to time the economic environment undergoes structural changes. A classic example is the Great Depression of the 1930s, a later one the abandonment in the 1990s of many European national currencies in favor of a single currency, the euro. Changes of this importance can be expected to lead to changes in the values of at least some of the parameters of economic models, and these changes often can be detected by a Chow test.

The term *cross-section data* is used to designate data sets that record aspects of economic units, such as firms, households, or governments, at a particular point in time. Failure of parameter constancy can arise in cross-section models if the observed units display too much heterogeneity so that, for instance, men may be described by parameters different from those suitable for women, rich countries may differ from poor ones, and small firms from large ones.

In 1960 Gregory Chow, then an associate professor at Cornell University (and from 1970 to 2001 a professor of economics at Princeton University, where the Econometric Research Program is now named in his honor), published a paper in *Econometrica* in which he laid out various versions of the Chow test. Chow’s main research interest at that time was the demand for automobiles in the United States. In earlier work he had proposed an econometric model based on data for the years 1921 to 1953, and as data had become available for the period 1954 to 1957, Chow wanted to see whether his old model could explain the new data. He used the tests he had developed in his earlier paper for this purpose, and concluded that the old model was still good.

Students of econometrics in the 1960s found Chow’s paper hard to understand. Consequently, in 1970 Franklin Fisher, a professor of economics at the Massachusetts Institute of Technology, published an article in *Econometrica* in which he set Chow’s tests in the context of the statistical literature, and showed how they all could be viewed as F tests, that is, standard tests used to check whether a parameter or parameters are significantly different from zero. As a result of Fisher’s exposition, the Chow test became a very widely used tool of applied econometrics, implemented in all standard software.

**SEE ALSO** *Test Statistics*

## BIBLIOGRAPHY

Chow, Gregory C. 1960. Tests of Equality Between Sets of Coefficients in Two Linear Regressions. *Econometrica* 28: 591-605.

Fisher, Franklin M. 1970. Tests of Equality Between Sets of Coefficients in Two Linear Regressions: An Expository Note. *Econometrica* 38: 361-366.

*Russell Davidson*

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