Why GMM J-Tests Can Miss Poor Asset-Pricing Performance

Summary

The document raises a question about a consumption-based asset-pricing model with power utility, estimated using generalized method of moments. In the described unconditional estimation, the base assets are used as moment conditions. The resulting J-test does not reject the model, even though a comparison of expected and predicted returns suggests weak empirical performance.

When managed portfolios are added to the base assets for a conditional estimation, the J-test rejects the model, and the predicted returns also appear poor. The author asks why the test outcomes differ. The document supplies no explanation or resolution; it reports the contrast in an example associated with Cochrane’s work and frames a question about interpreting specification tests. Its useful lesson is that a failure to reject a J-test with one set of moments should not be taken as proof of strong predictive performance, while changing the moments can change what the test detects.

Key ideas

• A GMM J-test evaluates whether the chosen moment restrictions are jointly consistent with the model.
• An unconditional estimation based on base assets may fail to reject despite weak expected-return predictions.
• Adding managed portfolios changes the moment conditions and can lead the J-test to reject.
• J-test conclusions depend on the assets and moments included in the estimation.
• The document poses this interpretation issue but does not offer a technical explanation or solution.

Tags

# J-test and Empirical Model Performance of Conditional and Unconditional Estimations (as for example in Cochrane (1996))


# J-test and Empirical Model Performance of Conditional and Unconditional Estimations (as for example in Cochrane (1996))












Take for example the Consumption-based model with a power utility function estimated by Cochrane in his paper "A Cross-Sectional Test of an Investment-Based Asset Pricing Model" (1996). The following refers to table 7 and figure 6.

When we use GMM to estimate the unconditional model, where we only use the base assets as moment conditions and conduct a J-test to test, if the pricing errors are close enough to zero, the model cannot be rejected, although of its poor empirical performance. We can see that for example by plotting the exspected returns against the predicted returns.

In contrast, if we use the base assets and additionally managed portfolios, a conditinal estimation, the J-test clearly rejects the model, which is also supported by the poor preditcions.

Now, it is very unclear to me why this is the case. How can it be that the J-test cannot reject the unconditional estimation, despite the poor performance but the conditional estimation?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.