Model Specification Tests Against Non-Nested Alternatives

Non-nested hypothesis tests provide a way to test the specification of an econometric model against the evidence provided by one or more non-nested alternatives. This paper surveys the recent literature on non-nested hypothesis testing in the context of regression and related models. Much of the purely statistical literature which has evolved from the fundamental work of Cox is discussed briefly or not at all. Instead, emphasis is placed on those techniques which are easy to employ in practice and are likely to be useful to applied workers.Cox test, nonnested hypotheses, J test, specification tests, nonnested hypothesis test

Double-Length Artificial Regressions

Artificial linear regressions often provide a convenient way to calculate test statistics and estimate covariance matrices. This paper discusses one family of these regressions, called "double-length" because the number of observations in the artificial regression is twice the actual number of observations. These double-length regressions can be useful in a wide variety of situations. They are easy to calculate, and seem to have good properties when applied to samples of modest size. We first discuss how they are related to Gauss-Newton and squared-residuals regressions for nonlinear models, and then show how they may be used to test for functional form and other applications.artificial regression, double-length regression, DLR, Gauss-Newton regression, functional form

The Case Against JIVE

We perform an extensive series of Monte Carlo experiments to compare the performance of two variants of the "Jackknife Instrumental Variables Estimator," or JIVE, with that of the more familiar 2SLS and LIML estimators. We find no evidence to suggest that JIVE should ever be used. It is always more dispersed than 2SLS, often very much so, and it is almost always inferior to LIML in all respects. Interestingly, JIVE seems to perform particularly badly when the instruments are weak.two-stage least squares, LIML, JIVE, instrumental variables, weak instruments

Convenient Specification Tests for Logit and Probit Models

We propose several Lagrange Multiplier tests of logit and probit models, which may be inexpensively computed by artificial linear regressions. These may be used to test for omitted variables and heteroskedasticity. We argue that one of these tests is likely to have better small-sample properties, supported by several sampling experiments. We also investigate the power of the tests against local alternatives. The analysis is novel because we do not require that the model which generated the data be the alternative against which the null is tested.binary response model, LM test, logit, probit

Bootstrap Inference in a Linear Equation Estimated by Instrumental Variables

We study several tests for the coefficient of the single right-hand-side endogenous variable in a linear equation estimated by instrumental variables. We show that all the test statistics--Student's t, Anderson-Rubin, Kleibergen's K, and likelihood ratio (LR)--can be written as functions of six random quantities. This leads to a number of interesting results about the properties of the tests under weak-instrument asymptotics. We then propose several new procedures for bootstrapping the three non-exact test statistics and a conditional version of the LR test. These use more efficient estimates of the parameters of the reduced-form equation than existing procedures. When the best of these new procedures is used, K and conditional LR have excellent performance under the null, and LR also performs very well. However, power considerations suggest that the conditional LR test, bootstrapped using this new procedure when the sample size is not large, is probably the method of choice.bootstrap test, weak instruments, anderson-rubin test, conditional LR test, wald test, instrumental variables

Inflation and the Savings Rate

This paper examines two explanations of the observed positive relationship between inflation rates and saving rates in Canada and the United States. Several models are estimated using quarterly time series data from both countries, and the best of these are subjected to a variety of tests. One of the two explanations appears broadly consistent with the data. The observed relationship arises primarily because, in times of inflation, measured income and measured savings overstate the corresponding real and perceived quantities.inflation, savingsinflation, savings, income, wealth, mismeasurement

Bootstrap Confidence Sets with Weak Instruments

We study several methods of constructing confidence sets for the coefficient of the single right-hand-side endogenous variable in a linear equation with weak instruments. Two of these are based on conditional likelihood ratio (CLR) tests, and the others are based on inverting t statistics or the bootstrap P values associated with them. We propose a new method for constructing bootstrap confidence sets based on t statistics. In large samples, the procedures that generally work best are CLR confidence sets using asymptotic critical values and bootstrap confidence sets based on LIML estimates.weak instruments, bootstrap, confidence sets, CLR test, LIML

Bootstrap Tests of Nonnested Linear Regression Models

The J test for nonnested regression models often works badly as an asymptotic test, but it generally works very well when bootstrapped. We provide a theoretical analysis of the J test which explains both of these phenomena. We also propose a modified version of the test which works even better than the ordinary J test when bootstrapped. Using our theoretical results to make simulation much faster, we obtain extremely accurate Monte Carlo results which demonstrate just how well the bootstrapped tests perform.J test, Nonnested hypothesis test, Bootstrap, Regression

Improving the Reliability of Bootstrap Tests

We first propose procedures for estimating the rejection probabilities for bootstrap tests in Monte Carlo experiments without actually computing a bootstrap test for each replication. These procedures are only about twice as expensive as estimating rejection probabilities for asymptotic tersts. We then propose procedures for computing modified bootstrap P values that will often be more accurate than ordinary ones. These procedures are closely related to the double bootstrap, but they are far less computationally demanding.Double Bootstrap, Monte Carlo, Specification Test, Bootstrap P Value, Bootstrap Test

Critical Values for Cointegration Tests

This paper provides tables of critical values for some popular tests of cointegration and unit roots. Although these tables are necessarily based on computer simulations, they are much more accurate than those previously available. The results of the simulation experiments are summarized by means of response surface regressions in which critical values depend on the sample size. From these regressions, asymptotic critical values can be read off directly, and critical values for any finite sample size can easily be computed with a hand calculator. Added in 2010 version: A new appendix contains additional results that are more accurate and cover more cases than the ones in the original paper.unit root test, Dickey-Fuller test, Engle-Granger test, ADF test