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Retesting the CCAPM Euler equations

Samih Azar (Business and Economics Department, Haigazian University, Beirut, Lebanon)

International Journal of Managerial Finance

ISSN: 1743-9132

Article publication date: 26 September 2011



This paper seeks to reconsider the Euler equation of the Consumption Capital Asset Pricing Model (CCAPM), to derive a regression‐based model to test it, and to present evidence that the model is consistent with reasonable values for the coefficient of relative risk aversion (CRRA). This runs contrary to the findings of the literature on the equity premium puzzle, but is in agreement with the literature that estimates the CRRA for the purpose of computing the social discount rate, and is in line with the research on labor supply. Tests based on General Method of Moments (GMM) for the same sample produce results that are extremely disparate and unstable. The paper aims to check and find support for the robustness of the regression‐based tests. Habit formation models are also to be evaluated with regression‐based and GMM tests. However, the validity of the regression‐based models depends critically on their functional forms.


The paper presents empirical evidence that the conventional use of GMM fails because of four pathological features of GMM that are referred to under the general caption of “weak identification”. In addition to GMM, the paper employs linear regression analysis to test the CCAPM, and it is found that the regression residuals follow well‐behaved distributional properties, making valid all statistical inferences, while GMM estimates are highly unstable.


Four unexpected findings are reported. The first is that the regression‐based models are consistent with reasonable values for the CRRA, i.e. estimates that are below 4. The second is that the regression‐based tests are robust, while the GMM‐based tests are not. The third is that regression‐based tests with habit formation depend crucially on the specification of the model. The fourth is that there is evidence that market stock returns are sensitive to both consumption and dividends. The author calls the latter “extra sensitivity of market stock returns”, and it is described as a new puzzle.


The regression‐based models of the CCAPM Euler equation are novel. The comparison between GMM and regression‐based models for the same sample is original. The regression‐based models with habit formation are new. The equity premium puzzle disappears because the estimates of the CRRA are reasonable. But another puzzle is documented, which is the “extra sensitivity of market stock returns” to consumption and dividends together.



Azar, S. (2011), "Retesting the CCAPM Euler equations", International Journal of Managerial Finance, Vol. 7 No. 4, pp. 324-346.



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