What is this Chow test thing?

In a wide variety of economic applications a critical question arises as to whether the same model is appropriate for two potentially different subsamples. Has trade liberalization altered the historical relationship between monetary policy and inflation? In what year did information technologies shift the production parameters associated with scale economies in financial services? Do consumers in different markets around the globe exhibit the same price elasticity of demand for breakfast cereal? These are all questions to which the Chow test and related statistical procedures could provide valuable insight.

In your empirical analysis exercise the question is whether labor market returns to observable characteristics (education, experience, etc.) are the same across your two groups (union/nonunion, female/male, etc.). If not, the burden is on the analyst (that would be you) to indicate potential sources of unequal returns.

related references

G. C. Chow, "Tests of Equality Between Sets of Coefficients in Two Linear Regressions," Econometrica, 1960.

test procedure

Note the residual sum of squares for the restricted model (RSSr). This refers to the full sample regression in which slope coefficients are viewed as equal across groups. Note the residual sum of squares from each of the subsample regression results (RSS1 and RSS2). Add these two values to form the residual sum of squares for the unrestricted model (RSSur). Other required values are N1 and N2 (number of observations in each subsample), and k (the number of restrictions to be tested, in this case the number of estimated parameters in the subsample regressions). Now calculate the test statistic:

F k , N1 + N2 - 2k = [ ( RSSr - RSSur ) / ( k ) ] / [ ( RSSur ) / (N1 + N2 - 2k) ]

and perform an F test for equality of the coefficients across subsamples. If your calculated F value exceeds the critical value in the table then reject pooling. That is, treatment of the data as two different subsamples is more appropriate than assuming that the same model parameters apply equally to both groups.