Data snooping occurs when a given set of data is used more than once for purposes of inference or model selection. When such data reuse occurs, there is always the possibility that any satisfactory results obtained may simply be due to chance rather than to any merit inherent in the method yielding the results. This problem is practically unavoidable in the analysis of time-series data, as typically only a single history measuring a given phenomenon of interest is available for analysis. It is widely acknowledged by empirical researchers that data snooping is a dangerous practice to be avoided, but in fact it is endemic. The main problem has been a lack of sufficiently simple practical methods capable of assessing the potential dangers of data snooping in a given situation. Our purpose here is to provide such methods by specifying a straightforward procedure for testing the null hypothesis that the best model encountered in a specification search has no predictive superiority over a given benchmark model. This permits data snooping to be undertaken with some degree of confidence that one will not mistake results that could have been generated by chance for genuinely good results.

This paper examines the consequences and detection of model misspecification when using maximum likelihood techniques for estimation and inference. The quasi-maximum likelihood estimator (QMLE) converges to a well defined limit, and may or may not be consistent for particular parameters of interest. Standard tests (Wald, Lagrange Multiplier, or Likelihood Ratio) are invalid in the presence of misspecification, but more general statistics are given which allow inferences to be drawn robustly. The properties of the QMLE and the information matrix are exploited to yield several useful tests for model misspecification.

INTRODUCTION THE METHOD OF INSTRUMENTAL VARIABLES (IV), proposed independently by Reiersol [15] and Geary [4], is one of the most useful classes of estimation techniques available to econometricians. The method is particularly useful in the context of errors-in-variables and simultaneous equation problems, and it ineludes ordinary least squares (OLS), two-stage least squares (2SLS) (Klein [9]), three-stage least squares (3SLS) (Madansky [12]) and certain full-information maximum likelihood estimators (Hausman [7]) as special cases. To date, the definitive theoretical treatment of the instrumental variables method is that of Sargan [16]. Important contributions have also been made by Brundy and Jorgenson [!, 2]. However, this work has not established the properties of IV estimators for all of the kinds of data analyzed by economists. Sargan's work is appropriate for data which are stochastic processes of the kind considered by Koopmans, Rubin, and Leipnik 10] in their study of dynami

[This paper examines the consequences and detection of model misspecification when using maximum likelihood techniques for estimation and inference. The quasi-maximum likelihood estimator (OMLE) converges to a well defined limit, and may or may not be consistent for particular parameters of interest. Standard tests (Wald, Lagrange Multiplier, or Likelihood Ratio) are invalid in the presence of misspecification, but more general statistics are given which allow inferences to be drawn robustly. The properties of the QMLE and the information matrix are exploited to yield several useful tests for model misspecification.]

This paper presents a parameter covariance matrix estimator which is consistent even when the disturbances of a linear regression model are heteroskedastic. This estimator does not depend on a formal model of the structure of the heteroskedasticity. By comparing the elements of the new estimator to those of the usual covariance estimator, one obtains a direct test for heteroskedasticity, since in the absence of heteroskedasticity, the two estimators will be approximately equal, but will generally diverge otherwise. The test has an appealing least squares interpretation

This paper is a revised version of a paper originally en.titled "Asymptotic Properties of Nonlinear Weighted Least Squares Estimators with Independem not Identically Distributed Regressors." In Section 2, the strong consistency of a class of weighted least squares (WLS) estimators is proven under general conditions, as well as the strong consistency of weighted least squares with estimated weights (EWLS). Conditions which ensure asymptotic normality of the estimators are provided in Section 3, and a general statistic for testing hypotheses is given. In Section 4, consequences of misspecification are discussed and a test for misspecification is given. Section 5 contains a summary and concluding remarks. As should be expected, the condi- tions obtained are natural extensions of those found in the fixed regressor case. Also, the unconditional covariance matrix of the parameter estimates has a more general form than the usual conditional covariance matrix

We show that quasi-maximum likelihood (QML) estimators for conditional dispersion models can be severely affected by a small number of outliers such as market crashes and rallies, and we propose new estimation strategies (the two-stage Hampel estimators and two-stage S-estimators) resistant to the effects of outliers and study the properties of these estimators. We apply our methods to estimate models of the conditional volatility of the daily returns of the S&P 500 Cash Index series. In contrast to QML estimators, our proposed method resists outliers, revealing an informative new picture of volatility dynamics during typical daily market activity.

This paper provides general conditions which ensure consistency and asymptotic normality for the nonlinear least squares estimator. These conditions apply to time-series, cross-section, panel, or experimental data for single equations as well as systems of equations. The regression errors may be serially correlated and/or heteroscedastic. For an important special case, we propose a new covariance matrix estimator which is consistent regardless of the presence of heteroscedasticity or serial correlation of unknown form. We also give some new tests for model misspecification, based on the information matrix testing principle

The authors provide a convergence theory for adaptive learning algorithms useful for the study of learning by economic agents. Their results extend the framework of L. Ljung previously utilized by A. Marcet-T. J. Sargent and M. Woodford by permitting nonlinear laws of motion driven by stochastic processes that may exhibit moderate dependence, such as mixing and mixingale processes. The authors draw on previous work by H. J. Kushner and D. S. Clark to provide readily verifiable and/or interpretable conditions ensuring algorithm convergence, chosen for their suitability in the context of adaptive learning. Copyright 1994 by The Econometric Society.

[This paper develops a simulation model to study the income distribution effects--total and factorial-of optimum restrictions on the flows of factors and products across national boundaries. Imposing both optimum tariffs and optimum taxes on factor flows allows an increase in national income that is much larger than the sum of the two effects evaluated separately. Often there are large shifts in the incomes of factors even though total income changes only slightly.]