Diagnostic tests for models based on individual data: A survey

Abstract

This paper surveys the growing literature on diagnostic testing of models based on unit record data. We argue that while many of these tests are produced in a Lagrange multiplier framework they are often more readily derived, and more easily applied, if approached from the conditional moment testing view of Newey (1985) and Tauchen (1985). In addition we propose some new tests based on comparisons of parametric estimators with nonparametric estimators which are consistent under certain forms of misspecification. To illustrate the utility of the tests we employ them in the examination of some existing published studies.

Censored Data and Truncated Distributions

“…5 Several approaches have been devised, including a Hausman test that compares the robust LAD estimator to the tobit/normal estimator [Melenberg and van Soest (1996)], LM tests Jarque (1981, 1982)] and conditional moment tests [Nelson (1981), Chesher and Irish (1987) and Pagan and Vella (1989)]. The LM and conditional moment and LM tests require a set of residuals that contain information about the distributionand nonnormality in particular.…”

“…where i is a column of ones and D is N×K+3, where each row contains (Pagan and Vella (1989) propose a variety of similar conditional moment tests for the tobit model.) Skeels and Vella (1999) have examined the behavior of this test in an extensive Monte Carlo study.…”

Comparing Securitized and Balance Sheet Loans: Size Matters

“…See also Cox and Snell (1968), Pagan and Vella (1989), and Greene (2000, pp. 916-917) for discussions of generalized residuals.…”

Sectoral border effects and the geographic concentration of production

“…She applies the Tobit estimator (Tobin 1958) because the dependent variable is censored to zero (5% of the total) in her data set. 4 However, given the inconsistency of the Tobit estimator when non-normal and/or heteroskedastic errors occur (Pagan and Vella 1989) and that the bias of OLS is increasing in the percentage of censored observations (Goldberg 1981, Ruud 1986, the choice between Tobit and OLS must entail weighing the pros and cons of Tobit with respect to OLS given Tobit's likely inconsistency. Indeed, given such a small percentage of censored observations and heteroskedastic and/or non-normally distributed residuals, it is likely that the bias of the OLS estimator is less than the Tobit's; OLS might still be the right choice.…”