Testing for functional misspecification in regression analysis

Recursive residuals may be used to detect functional misspecification in a regression equation. A simple t-statistic and a related Sign test may be constructed from the residuals. The powers of these tests compare favourably with the Durbin–Watson and other tests commonly used to detect functional misspecification from residuals. In addition the tests are relatively robust to serial correction in an otherwise correctly specified model, and this is a further point in their favour.     

VAR forecasting under misspecification

The paper considers multi-step forecasting of a stationary vector process under a quadratic loss function with a collection of finite-order vector autoregressions (VAR). Under severe misspecification it is preferable to use the multi-step loss function also for parameter estimation. We propose a modification to Shibata's (Ann. Statist. 8 (1980) 147) final prediction error criterion to jointly choose the VAR lag order and one of two predictors: the maximum likelihood estimator plug-in predictor or the loss function estimator plug-in predictor. A Monte Carlo experiment illustrates the theoretical results and documents the empirical performance of the selection criterion.     

Linear prediction of temporal aggregates under model misspecification

This paper aims to demonstrate a possible aggregation gain in predicting future aggregates under a practical assumption of model misspecification. Empirical analysis of a number of economic time series suggests that the use of the disaggregate model is not always preferred over the aggregate model in predicting future aggregates, in terms of an out-of-sample prediction root-mean-square error criterion. One possible justification of this interesting phenomena is model misspecification. In particular, if the model fitted to the disaggregate series is misspecified (i.e., not the true data generating mechanism), then the forecast made by a misspecified model is not always the most efficient. This opens up an opportunity for the aggregate model to perform better. It will be of interest to find out when the aggregate model helps. In this paper, we study a framework where the underlying disaggregate series has a periodic structure. We derive and compare the efficiency loss in linear prediction of future aggregates using the adapted disaggregate model and aggregate model. Some scenarios for aggregation gain to occur are identified. Numerical results show that the aggregate model helps over a fairly large region in the parameter space of the periodic model that we studied.     

Semi-nonparametric estimation and misspecification testing of diffusion models

Novel transition-based misspecification tests of semiparametric and fully parametric univariate diffusion models based on the estimators developed in [Kristensen, D., 2010. Pseudo-maximum likelihood estimation in two classes of semiparametric diffusion models. Journal of Econometrics 156, 239-259] are proposed. It is demonstrated that transition-based tests in general lack power in detecting certain departures from the null since they integrate out local features of the drift and volatility. As a solution to this, tests that directly compare drift and volatility estimators under the relevant null and alternative are also developed which exhibit better power against local alternatives.     

A study of estimator densities and performance under misspecification

The exact density functions of the OLS and 2SLS estimators when exogenous variables are wrongly excluded from the equation being estimated, where two endogenous variables appear in the equation of interest, are presented and tabulated. Misspecification does not appear to alter the relative concentrations of OLS and 2SLS — OLS is always more concentrated — but does change the relative biases with the result that under misspecification OLS may indeed be the superior estimation technique. In addition, misspecification can substantially increase the concentration of both estimators, as well as reducing their biases, therebyyielding an apparent improvement in estimator performance.     

Higher order properties of the wild bootstrap under misspecification

We examine the higher order properties of the wild bootstrap (Wu, 1986) in a linear regression model with stochastic regressors. We find that the ability of the wild bootstrap to provide a higher order refinement is contingent upon whether the errors are mean independent of the regressors or merely uncorrelated with them. In the latter case, the wild bootstrap may fail to match some of the terms in an Edgeworth expansion of the full sample test statistic. Nonetheless, we show that the wild bootstrap still has a lower maximal asymptotic risk as an estimator of the true distribution than a normal approximation, in shrinking neighborhoods of properly specified models. To assess the practical implications of this result we conduct a Monte Carlo study contrasting the performance of the wild bootstrap with a normal approximation and the traditional nonparametric bootstrap.     

Bias in dynamic panel models under time series misspecification

We consider within-group estimation of higher-order autoregressive panel models with exogenous regressors and fixed effects, where the lag order is possibly misspecified. Even when disregarding the misspecification bias, the fixed-effect bias formula is quite different from the correctly specified case though its asymptotic order remains the same under the stationarity. We suggest bias reduction methods under the possible time series misspecification.     

Optimally biased Tullock contests

This paper examines optimally biased Tullock contests. We consider a multi-player Tullock contest in which players differ in their prize valuations. The designer is allowed to impose identity-dependent treatments – i.e., multiplicative biases – to vary their relative competitiveness. The literature has been limited, because a closed-form solution to the equilibrium is in general unavailable when the number of contestants exceeds two, which nullifies the usual implicit programming approach. We develop an algorithmic technique adapted from the general approach of Fu and Wu (2020) and obtain a closed-form solution to the optimum that addresses a broad array of design objectives. We further analyze a resource allocation problem in a research tournament and adapt Fu and Wu’s (2020) approach to this noncanonical setting. Our analysis paves the way for future research in this vein.     

Optimal designs for generalized linear models with biased response

This paper is concerned with the search for locally optimal designs when the observations of the response variable arise from a weighted distribution in the exponential family. Locally optimal designs are derived for regression models in which the response follows a weighted version of Normal, Gamma, Inverse Gaussian, Poisson or Binomial distributions. Some conditions are given under which the optimal designs for the weighted and original (non-weighted) distributions are the same. An efficiency study is performed to find out the behavior of the D-optimal designs for the original distribution when they are used to estimate models with weighted distributions.     

Binary choice models with discrete regressors: Identification and misspecification

This paper explores the inferential question in semiparametric binary response models when the continuous support condition is not satisfied and all regressors have discrete support. I focus mainly on the models under the conditional median restriction, as in Manski (1985). I find sharp bounds on the components of the parameter of interest and outline several applications. The formulas for bounds obtained using a recursive procedure help analyze cases where one regressor’s support becomes increasingly dense. Furthermore, I investigate asymptotic properties of estimators of the identification set. I describe a relation between the maximum score estimation and support vector machines and propose several approaches to address the problem of empty identification sets when the model is misspecified.     

Examining bias in estimators of linear rational expectations models under misspecification

Most rational expectations models involve equations in which the dependent variable is a function of its lags and its expected future value. We investigate the asymptotic bias of generalized method of moment (GMM) and maximum likelihood (ML) estimators in such models under misspecification. We consider several misspecifications, and focus more specifically on the case of omitted dynamics in the dependent variable. In a stylized DGP, we derive analytically the asymptotic biases of these estimators. We establish that in many cases of interest the two estimators of the degree of forward-lookingness are asymptotically biased in opposite direction with respect to the true value of the parameter. We also propose a quasi-Hausman test of misspecification based on the difference between the GMM and ML estimators. Using Monte-Carlo simulations, we show that the ordering and direction of the estimators still hold in a more realistic New Keynesian macroeconomic model. In this set-up, misspecification is in general found to be more harmful to GMM than to ML estimators.     

Determinacy,indeterminacy and dynamic misspecification in linear rational expectations models

This paper proposes a testing strategy for the null hypothesis that a multivariate linear rational expectations (LRE) model may have a unique stable solution (determinacy) against the alternative of multiple stable solutions (indeterminacy). The testing problem is addressed by a misspecification-type approach in which the overidentifying restrictions test obtained from the estimation of the system of Euler equations of the LRE model through the generalized method of moments is combined with a likelihood-based test for the cross-equation restrictions that the model places on its reduced form solution under determinacy. The resulting test has no power against a particular class of indeterminate equilibria, hence the non rejection of the null hypothesis can not be interpreted conclusively as evidence of determinacy. On the other hand, this test (i) circumvents the nonstandard inferential problem generated by the presence of the auxiliary parameters that appear under indeterminacy and that are not identifiable under determinacy, (ii) does not involve inequality parametric restrictions and hence the use of nonstandard inference, (iii) is consistent against the dynamic misspecification of the LRE model, and (iv) is computationally simple. Monte Carlo simulations show that the suggested testing strategy delivers reasonable size coverage and power against dynamic misspecification in finite samples. An empirical illustration focuses on the determinacy/indeterminacy of a New Keynesian monetary business cycle model of the US economy.     

Skill supply and biased technical change

This article contributes to the debate on skill-biased technical change by studying the dynamics of skill supply and wage inequality in an endogenous growth model with ability-biased technical progress. Due to a discouragement effect, rising within groups inequality reduces incentives to become educated for ordinary-ability workers. This mechanism generates a non-monotonic relationship between the growth rate and skill supply driving wage inequality upward during periods of accelerating technical change. This theoretical explanation is consistent with the apparent ambiguous relationship between the relative skill supply and inequality in the last decades in several OECD countries.     

Biased recommendations from biased and unbiased experts

When can you trust an expert to provide honest advice? We develop and test a recommendation game where an expert helps a decision maker choose among two actions that benefit the expert and an outside option that does not. For instance, a salesperson recommends one of two products to a customer who may instead purchase nothing. Subject behavior in a laboratory experiment is largely consistent with predictions from the cheap talk literature. For sufficient symmetry in payoffs, recommendations are persuasive in that they raise the chance that the decision maker takes one of the actions rather than the outside option. If the expert is known to have a payoff bias toward an action, such as a salesperson receiving a higher commission on one product, the decision maker partially discounts a recommendation for it and is more likely to take the outside option. If the bias is uncertain, then biased experts lie even more, whereas unbiased experts follow a political correctness strategy of pushing the opposite action so as to be more persuasive. Even when the expert is known to be unbiased, if the decision maker already favors an action the expert panders toward it, and the decision maker partially discounts the recommendation. The comparative static predictions hold with any degree of lying aversion up to pure cheap talk, and most subjects exhibit some limited lying aversion. The results highlight that the transparency of expert incentives can improve communication, but need not ensure unbiased advice.     

Nonparametric methods for paired samples

The small sample and asymptotic properties of nonparametric tests for paired sampled are examined. Linear rank statistics are compared with the paired t-test and the Wilcoxon-signed-rank test in simulation studies. From a minimax point of view the linear rank statistics turn out to be the best. Moreover, it is illustrated that the Wilcoxon-signed-rank test should not be used if it is not clear that the differences of the pairs have a symmetric distribution.     

On length biased dynamic measure of past inaccuracy

In the present communication we introduce a length biased past inaccuracy measure between two past lifetime distributions over the interval (0, t). Based on proportional reversed hazard model characterization problem for the length biased inaccuracy measure has been studied. An upper bound to the weighted past inaccuracy measure has also been derived, which reduces to the upper bound obtained in case of weighted past entropy.     

Asymmetric control limits for small samples

When designing control charts, it is usually assumed that the measurement in the subgroups are normally distributed. The assumption of normality implies that the control limits for a chart for sample averages will be symmetrical about the centerline of the chart. However, the assumption of an underlying normal distribution of the data may not hold in some processes. If the measurements are asymmetrically distributed then the decision maker may choose different actions. One thing that can be done is to consider the degree of skewness. If the nature of the underlying distribution is skewed, then the traditional Shewhart individuals chart may not be valid. This paper presents a technique for constructing appropriate asymmetric control limits when the distribution of data cannot be assumed to be a normal distribution. Meanwhile, it proposes a skewness correction method for the generated Burr, lognormal and exponential distributions. Some numerical calculations are generated for n  =  2, 3, 4 by using MATLAB.     

Model selection in random effects models for directed graphs using approximated Bayes factors

With the development of an MCMC algorithm, Bayesian model selection for the p ₂ model for directed graphs has become possible. This paper presents an empirical exploration in using approximate Bayes factors for model selection. For a social network of Dutch secondary school pupils from different ethnic backgrounds it is investigated whether pupils report that they receive more emotional support from within their own ethnic group. Approximated Bayes factors seem to work, but considerable margins of error have to be reckoned with.