This paper presents two extensions to Hall and Sen’s [Hall, A.R. and Sen, A. 1999. Structural stability testing in models estimated via generalized method of moments. J. Bus. Econ. Stat., 17, 335–348.] analysis of their structural stability tests. First, we approximate the p-values for the non-standard asymptotic null distribution for the structural stability test statistics proposed by Hall and Sen (1999). The p-value response surfaces are approximated by a parametric function using the methodology proposed by Hansen [Hansen, B.E., 1997. Approximate asymptotic P-values for structural change tests. J. Bus. Econ. Stat, 15, 60–67.] Second, we show how Hall and Sen’s (1999) testing methodology can be used to diagnose the source of instability in Euler equation models. To illustrate this issue, we examine the stability of the dividend capital asset pricing model proposed by Hagiwara and Herce [Hagiwara, M. and Herce M.A., 1997. Risk aversion and stock price sensitivity to dividends. Am. Econ. Rev. 87, 738–745]. Hagiwara and Herce (1997) estimate the model using annual data from 1889–1994 and find the model is not rejected using the over-identifying restrictions test. Using the same data, we find some evidence of structural instability in the model. Interestingly, the tests reveal that the model appears to be correctly specified for the period up until 1942 but incorrectly specified in the post 1942 part of the sample.