This article discusses the evaluation of programs implemented at multiple sites. Two frequently used methods are pooling the data or using fixed effects (an extreme version of which estimates separate models for each site). The former approach ignores site effects. The latter incorporates site effects but lacks a framework for predicting the impact of subsequent implementations of the program (e.g., would a new implementation resemble Riverside?). I present a hierarchical model that lies between these two extremes. Using data from the Greater Avenues for Independence demonstration, I demonstrate that the model captures much of the site-to-site variation of the treatment effects but has less uncertainty than estimating the treatment effect separately for each site. I also show that when predictive uncertainty is ignored, the treatment impact for the Riverside sites is significant, but when predictive uncertainty is considered, the impact for these sites is insignificant. Finally, I demonstrate that the model extrapolates site effects with reasonable accuracy when the site being predicted does not differ substantially from the sites already observed. For example, the San Diego treatment effects could have been predicted based on their site characteristics, but the Riverside effects are consistently underpredicted.

This article evaluates the usefulness of a nonparametric approach to Bayesian inference by presenting two applications. Our first application considers an educational choice problem. We focus on obtaining a predictive distribution for earnings corresponding to various levels of schooling. This predictive distribution incorporates the parameter uncertainty, so that it is relevant for decision making under uncertainty in the expected utility framework of microeconomics. The second application is to quantile regression. Our point here is to examine the potential of the nonparametric framework to provide inferences without relying on asymptotic approximations. Unlike in the first application, the standard asymptotic normal approximation turns out not to be a good guide.

We apply recent advances in propensity-score matching (PSM) to the problem of estimating the distribution of net income gains from an Argentinean workfare program. PSM has a number of attractive features in this context, including the need to allow for heterogeneous impacts, while optimally weighting observed characteristics when forming a comparison group. The average direct gain to the participant is found to be about half the gross wage. Over half of the beneficiaries are in the poorest decile nationally, and 80% are in the poorest quintile. Our PSM estimator is reasonably robust to a number of changes in methodology.

In this article we introduce a test for the normality assumption in the sample selection model. The test is based on a flexible parametric specification of the density function of the error terms in the model. This specification follows a Hermite series with bivariate normality as a special case. All parameters of the model are estimated both under normality and under the more general flexible parametric specification, which enables testing for normality using a standard likelihood ratio test. If normality is rejected, then the flexible parametric specification provides consistent parameter estimates. The test has reasonable power, as is shown by a simulation study. The test also detects some types of ignored heteroscedasticity. Finally, we apply the flexible specification of the density to a travel demand model and test for normality in this model.

This article analyzes generalized method of moments estimation when the sample is not a random draw from the population of interest. Auxiliary information, in the form of moments from the population of interest, is exploited to compute weights that are proportional to the inverse probability of selection. The essential idea is to construct weights for each observation in the primary data such that the moments of the weighted data are set equal to the additional moments. The estimator is applied to the Dutch Transportation Panel, in which refreshment draws were taken from the population of interest to deal with heavy attrition of the original panel. It is shown how these additional samples can be used to adjust for sample selection.

The optimal reserve price in the independent private value paradigm is generally expressed as a functional of the latent distribution of private signals, which is by nature unobserved. This feature has limited the implementation of the optimal reserve price in practice. In this article, we consider first-price auctions within the general affiliated private values paradigm. We show that the seller's expected profit can be written as a functional of the observed bid distribution. We propose a semiparametric extremum estimator for estimating consistently the optimal reserve price from observed bids. As an illustration, we consider the Outer Continental Shelf (OCS) wildcat auctions.

Statistical matching has been used for more than 30 years to combine information contained in two sample survey files. Rubin (1986) outlined an imputation procedure for statistical matching that is different from almost all other work on this topic. Here we evaluate and extend Rubin's procedure.

This article develops a Bayesian model for the analysis of bidding behavior in final-offer arbitration. Posterior calculations are obtained using a Markov chain algorithm. An example is considered using salary data from Major League Baseball.

A new class of finite mixture discrete choice models, denoted FinMix (fīn miks), is introduced. These arise from the combination of a finite number of core Generalized Extreme Value (GEV) models to achieve more flexible functional forms, particularly in terms of error covariance structures. Example members of the class include combinations of (1) Multinomial Logit (MNL) models with differing scales, (2) multinomial logit with nested MNL models, (3) tree extreme value models with differing preference trees, and so on. Compatibility of FinMix models with utility maximization is easily determined, which permits empirical investigation of the suitability of specific model forms for economic evaluation exercises.

The Parameterized Expectations Algorithm (PEA) is a powerful tool for solving nonlinear stochastic dynamic models. However, it has an important shortcoming: it is not a contraction mapping technique and thus does not guarantee a solution will be found. We suggest a simple modification that enhances the convergence property of the algorithm. The idea is to rule out the possibility of (ex)implosive behavior by artificially restricting the simulated series within certain bounds. As the solution is refined along the iterations, the bounds are gradually removed. The modified PEA can systematically converge to the stationary solution starting from the nonstochastic steady state.

We develop Bayesian methods of analysis for a new class of threshold autoregressive models: endogenous delay threshold. We apply our methods to the commonly used sunspot data set and find strong evidence in favor of the Endogenous Delay Threshold Autoregressive (EDTAR) model over linear and traditional threshold autoregressions.

Nonlinear regime-switching behavior and structural change are often perceived as competing alternatives to linearity. In this article we study the so-called time-varying smooth transition autoregressive (TV-STAR) model, which can be used both for describing simultaneous nonlinearity and structural change and for distinguishing between these features. Two modeling strategies for empirical specification of TV-STAR models are developed. Monte Carlo simulations show that neither of the two strategies dominates the other. A specific-to-general-to-specific procedure is best suited for obtaining a first impression of the importance of nonlinearity and/or structural change for a particular time series. A specific-to-general procedure is most useful in careful specification of a model with nonlinear and/or time-varying properties. An empirical application to a large dataset of U.S. macroeconomic time series illustrates the relative merits of both modeling strategies.

We analyze the modifications that occur in indirect inference when a nuisance parameter is not identified under the null hypothesis. We develop a testing procedure adapted to this simulation-based estimation method, and detail its use for detecting the threshold effect in threshold moving average models with contemporaneous and lagged asymmetries. In contrast to existing threshold models, these models allow taking into account the presence of asymmetric effects of current and lagged random shocks. We use them to measure the persistence of shocks to U.S. output.

This article develops a new method to evaluate revealed preference separability conditions. In contrast to previous studies, our results generally find weak separability, even when datasets have some measurement error. In addition, revealed preference and weak separability appear robust to measurement error, different price distributions, and alternative preference settings. Measurement error generally results in relatively few violations of revealed preference or weak separability.

There has recently been renewed research interest in the development of tests of the rank of a matrix. This article evaluates the performance of some asymptotic tests of rank determination in reduced rank regression models together with bootstrapped versions through simulation experiments. The bootstrapped procedures significantly improve on the performance of the corresponding asymptotic tests. The article also presents a Monte Carlo exercise comparing the forecasting performance of reduced rank and unrestricted vector autoregressive (VAR) models in which the former appear superior. The tests of rank considered here are then applied to construct reduced rank VAR models for leading indicators of U.K. economic activity. These more parsimonious multivariate representations display an improvement in forecasting performance over that of unrestricted VAR models.

This article builds on the existing literature on (stationarity) tests of the null hypothesis of deterministic seasonality in a univariate time series process against the alternative of unit root behavior at some or all of the zero and seasonal frequencies. This article considers the case where, in testing for unit roots at some proper subset of the zero and seasonal frequencies, there are unattended unit roots among the remaining frequencies. Monte Carlo results are presented that demonstrate that in this case, the stationarity tests tend to distort below nominal size under the null and display an associated (often very large) loss of power under the alternative. A modification to the existing tests, based on data prefiltering, that eliminates the problem asymptotically is suggested. Monte Carlo evidence suggests that this procedure works well in practice, even at relatively small sample sizes. Applications of the robustified statistics to various seasonally unadjusted time series measures of U.K. consumers' expenditure are considered; these yield considerably more evidence of seasonal unit roots than do the existing stationarity tests.

This article considers consistent testing the null hypothesis that the conditional mean of an economic time series is linear in past values. Two specific tests are discussed, the Cramér–von Mises and the Kolmogorov–Smirnov tests. The particular feature of the proposed tests is that the bootstrap is used to estimate the nonstandard asymptotic distributions of the test statistics considered. The tests are justified theoretically by asymptotics, and their finite-sample behaviors are studied by means of Monte Carlo experiments. The tests are applied to five U.S. monthly series, and evidence of nonlinearity is found for the first difference of the logarithm of the personal income and for the first difference of the unemployment rate. No evidence of nonlinearity is found for the first difference of the logarithm of the U.S. dollar/Japanese Yen exchange rate, for the first difference of the 3-month T-bill interest rate and for the first difference of the logarithm of the M2 money stock. Contrary to typically used tests, the proposed testing procedures are robust to the presence of conditional heteroscedasticity. This may explain the results for the exchange rate and the interest rate.

Minimum t statistics to test for a unit-root are available when the form of break under the alternative evolves according to the crash, changing growth, and mixed models. It is shown that serious power distortions occur if the form of break is misspecified, and thus the practitioner should use the mixed model as the appropriate alternative in empirical applications. The mixed model may reveal useful information regarding the location and form of break. The maximum F statistic for the joint null of a unit-root and no breaks is shown to have greater and less erratic power compared to the minimum t statistic. Stronger evidence against the unit-root is found for the Nelson-Plosser series and U.S. Postwar quarterly real gross national product.

Two methods of identifying cointegrating vectors are commonly used: linear restrictions and the nonlinear method of Johansen's maximum likelihood procedure. That the linear method can produce invalid estimates while the Johansen approach always produces valid estimates has been recognized in several recent articles. Because all Bayesian studies to date have used linear restrictions, this article presents a Bayesian method for obtaining estimates of cointegrating vectors that will always be valid. In addition, it also presents an approach for evaluating the validity of linear restrictions.

Tests for business cycle asymmetries are developed for Markov-switching autoregressive models. The tests of deepness, steepness, and sharpness are Wald statistics, which have standard asymptotics. For the standard two-regime model of expansions and contractions, deepness is shown to imply sharpness (and vice versa), whereas the process is always nonsteep. Two and three-state models of U.S. GNP growth are used to illustrate the approach, along with models of U.S. investment and consumption growth. The robustness of the tests to model misspecification, and the effects of regime-dependent heteroscedasticity, are investigated.