This paper discusses specification tests in econometrics, focusing on testing the orthogonality and sphericality assumptions in regression models. The author proposes a general specification test that can be used to detect failures of the orthogonality assumption, which is more critical than the sphericality assumption. The test involves comparing an unbiased estimator with an efficient estimator under the null hypothesis. The test statistic is based on the difference between these two estimators and is distributed as a chi-squared or F distribution under the null hypothesis. The power of the test depends on the noncentrality parameter, which is related to the expected difference between the two estimators. The paper also discusses the application of these tests to error in variables problems, time series-cross section models, and simultaneous equation models. The author emphasizes the importance of these tests in econometric analysis, particularly in situations where efficient estimators are used. The paper also addresses issues related to pretesting and minimum mean square error estimation, and provides examples of how these tests can be applied in practice. The results show that the proposed tests are powerful and can be used to detect misspecification in econometric models.This paper discusses specification tests in econometrics, focusing on testing the orthogonality and sphericality assumptions in regression models. The author proposes a general specification test that can be used to detect failures of the orthogonality assumption, which is more critical than the sphericality assumption. The test involves comparing an unbiased estimator with an efficient estimator under the null hypothesis. The test statistic is based on the difference between these two estimators and is distributed as a chi-squared or F distribution under the null hypothesis. The power of the test depends on the noncentrality parameter, which is related to the expected difference between the two estimators. The paper also discusses the application of these tests to error in variables problems, time series-cross section models, and simultaneous equation models. The author emphasizes the importance of these tests in econometric analysis, particularly in situations where efficient estimators are used. The paper also addresses issues related to pretesting and minimum mean square error estimation, and provides examples of how these tests can be applied in practice. The results show that the proposed tests are powerful and can be used to detect misspecification in econometric models.