This paper develops a modified version of the Sargan (1958, Econometrica 26(3): 393-415) test statistic of overidentifying restrictions, and shows that it is numerically equivalent to the test statistic of Hahn and Hausman (2002, Econometrica 70(1): 163-189) up to a sign. The modified Sargan test is constructed such that its asymptotic distribution under the null hypothesis of correct specifica...

The conventional Sargan (1958) / Hansen (1982) test of overidentifying restrictions and the Tilting Parameter test of Imbens, Spady and Johnson (1998) are compared in the context of the AR(1) dynamic panel data model using Monte Carlo experiments. Interestingly, the size properties of the former are found to be superior in this setting. Nevertheless, the Sargan / Hansen test is found to have no...

Mendelian randomisation (MR) estimates causal effects of modifiable phenotypes on an outcome by using genetic variants as instrumental variables, but its validity relies on the assumption of no pleiotropy, that is, genes influence the outcome only through the given phenotype. Excluding pleiotropy is difficult, but the use of multiple instruments can indirectly address the issue: if all genes re...

This paper considers specification testing for instrumental variables estimation in the presence of many instruments. The test is similar to the overidentifying restrictions test of Sargan (1958) but the test statistic asymptotically follows the standard normal distribution under the null hypothesis when the number of instruments is proportional to the sample size. It turns out that the new tes...

An alternative to the Engle-Granger tests is the Cointegration Regression Durbin-Watson (CRDW) test of Sargan and Bhargava (1983). The test involves a simple regression of one variable on the other, and the standard Durbin-Watson test on the residuals. Recall the null for the DW test is that the residuals form a nonstationary random walk, whereas the alternative hypothesis is that the residuals...

This article surveys J. D. Sargan’s work on instrumental variables (IV) estimation and its connections with the generalized method of moments (GMM). First the modeling context in which Sargan motivated IV estimation is presented. Then the theory of IV estimation as developed by Sargan is discussed. His approach to efficiency, his minimax estimator, tests of overidentification and underidentific...

SINCE THE ESTIMATOR PROPOSED in the paper is based on a simple conditional moment restriction, standard approaches to specification testing are available (e.g., the Sargan–Hansen test of overidentifying restrictions). However, as in any application, it is helpful to think about specific directions of misspecification and to construct tests accordingly. As an example, note that an implication of...

Empirical econometric findings are often vindicated by supplementing them with the p-values of Sargan–Hansen tests for overidentifying restrictions, provided these exceed a chosen small nominal significance level. It is illustrated here that probability such reject instrument validity may barely levels, even when instruments seriously invalid, whereas minor invalidity can severely undermine inf...

This paper gives a test of overidentifying restrictions that is robust to many instruments and heteroskedasticity. It is based on a jackknife version of the overidentifying test statistic. Correct asymptotic critical values are derived for this statistic when the number of instruments grows large, at a rate up to the sample size. It is also shown that the test is valid when the number instrumen...