The effects of small sample bias in Threshold Autoregressive models

This paper investigates Threshold Autoregressive (TAR) models that contain a limited number of observations in some regimes. Simulations show that within the context of the real exchange rate literature, parameter estimates exhibit significant small sample bias even with long time series data. These distortions create substantial power losses in attempting to identify values of coefficients from data.     

When outcome heterogeneously matters for selection: a generalized selection correction estimator

The classical Heckman (1976, 1979) selection correction estimator (heckit) is misspecified and inconsistent, if an interaction of the outcome variable with an explanatory variable matters for selection. To address this specification problem, a full information maximum likelihood (FIML) estimator and a simple two-step estimator are developed. Monte Carlo (MC) simulations illustrate that the bias of the ordinary heckit estimator is removed by these generalized estimation procedures. Along with OLS and ordinary heckit, we apply these estimators to data from a randomized trial that evaluates the effectiveness of financial incentives for reducing obesity. Estimation results indicate that the choice of the estimation procedure clearly matters.     

Testing exclusion restrictions and additive separability in sample selection models

Standard sample selection models with non-randomly censored outcomes assume (i) an exclusion restriction (i.e., a variable affecting selection, but not the outcome) and (ii) additive separability of the errors in the selection process. This paper proposes tests for the joint satisfaction of these assumptions by applying the approach of Huber and Mellace (Testing instrument validity for LATE identification based on inequality moment constraints, 2011) (for testing instrument validity under treatment endogeneity) to the sample selection framework. We show that the exclusion restriction and additive separability imply two testable inequality constraints that come from both point identifying and bounding the outcome distribution of the subpopulation that is always selected/observed. We apply the tests to two variables for which the exclusion restriction is frequently invoked in female wage regressions: non-wife/husband’s income and the number of (young) children. Considering eight empirical applications, our results suggest that the identifying assumptions are likely violated for the former variable, but cannot be refuted for the latter on statistical grounds.     

An MPEC estimator for misclassification models

In this paper, we propose a constrained maximum likelihood estimator for misclassification models, by formulating the estimation as an MPEC (Mathematical Programming with Equilibrium Constraints) problem. Our approach improves the numerical accuracy and avoids the singularity problem. Monte Carlo simulations confirm that the proposed estimator reduces bias and standard deviation of the estimator, especially when the sample is small/medium and/or the dimension of latent variable is large.     

Endogeneity and sample selection in a model for remittances

We estimate a remittance model in which we address endogeneity and reverse causality relationships between immigrants' remittances, pre-transfer income and consumption. In order to take into account the fact that a large share of individuals do not remit, instrumental variable variants of the double-hurdle and Heckit selection models are proposed and estimated by Limited Information ML; semiparametric extensions are considered as robustness checks. Our results for a sample of recent immigrants to Australia show that endogeneity is substantial and that estimates obtained by the methods previously employed in the literature may be misleading if given a behavioral interpretation.     

A new estimator for trade costs and its small sample properties

This paper discusses the estimation of parameters of a traditional transportation model, as it is typically present in so-called Takayama–Judge type spatial price equilibrium models. In contrast to previously used estimation methods, observations of regional prices as well as of trade costs are used in a direct estimation of the first order conditions. The proposed method uses bi-level programming techniques to minimize a weighted least squares criterion under the restriction that the estimated parameters satisfy the Kuhn–Tucker conditions for an optimal solution of the transport model. A penalty function and a smooth reformulation are used to iteratively approximate the complementary slackness conditions. Monte-Carlo simulations are used to trace out some properties of the estimator and compare it with a traditional calibration method. The analysis shows that the proposed technique estimates prices as well as trade costs more precisely than the traditional calibration method. It is suggested to apply the same method to a range of linear and quadratic models.     

Dealing with small sample bias in post-crisis samples

In this paper, we demonstrate that using finite sample correction bootstrapping techniques is advisable in samples that cover less than two complete business cycles, even when high-frequency data seemingly provide a sufficient number of observations to overcome the small sample bias. This is particularly relevant in the current research environment. Because the recent financial crisis is considered as a structural break, research on current problems is often conducted using post-crisis data. That is, the available samples cover only a few years of data, often spanning only one business cycle or even less. We provide ample simulation-based evidence that samples of daily or monthly dynamic data covering periods of this magnitude are prone to a fairly substantial bias. Moreover, we are able to show that standard bootstrap-based bias correction techniques still work in those cases.     

Finite sample bias of the least squares estimator in an AR(p) model: estimation,inference, simulation and examples

This paper shows that the first order bias of least squares estimators of the coefficients of an AR(p) model is important for ‘typical’ macroeconomic time series and proposes a simple to apply method of bias reduction. Biases in individual coefficients often cumulate in the sum with far-reaching consequences for the cumulative impulse response function. This function, being nonlinear in the underlying coefficients, is particularly sensitive to biases when, as is often the case, the shocks are long-lived. Simulations and examples demonstrate some of the magnitudes involved.     

Normality test for multivariate conditional heteroskedastic dynamic regression models

In this paper, we study the Jarque-Bera test for the normality of the innovations of multivariate GARCH models. It is shown that the test is distribution free and its limiting null distribution is a chi-square distribution.     

A simple IID test for autoregressive conditional duration models

We propose using the rank-based variance ratio test as an easy-to-implement test for testing the independent and identically distributed assumption of autoregressive conditional duration (ACD) models. We apply the proposed test to duration data of five stocks and get the same conclusions as previous studies.     

A sample selection model for prepared food expenditures

The factors affecting household expenditures on four types of prepared food products from a sample selection model estimated using a two-step method are explored. Results suggest that several variables affect household expenditures on various prepared food products. Factors examined are presence of children, number of earners, region, household size, seasonality, age, race, education, and income.     

Second order bias of quasi-MLE for covariance structure models

For covariance structure models, the QMLE second-order bias is derived and compared with EL and GMM. Surprisingly, QMLE and EL have the same second-order bias if QMLE and GMM(EL) are equally first-order efficient. Other examples favoring QMLE are given.     

A comparison of bias approximations for the two-stage least squares (2SLS) estimator

We consider the bias of the two-stage least squares (2SLS) estimator in linear instrumental variable regression with only one endogenous regressor. By using asymptotic expansion techniques, we approximate the 2SLS coefficient estimation bias under various scenarios regarding the number and strength of instruments.     

A small sample test for non-nested regression models

Optimal redistributive tax-subsidy schemes are devised leading to maximum unweighted and class-weighted balanced growth per capita consumption levels in the two-class neoclassical model. A subsidy, and, if workers are numerically dominant, a tax are required in each respective case.     

Equilibrium selection in bargaining models

This paper examines evolutionary equilibrium selection in bargaining models. We show that random best-response and continuous best-response learning dynamics give rise to (different) simple sufficient conditions for identifying outcomes as stochastically stable. This allows us to characterize the implications of these dynamics in simple bargaining games.     

Nonparametric lag selection for nonlinear additive autoregressive models

The lag selection procedure based on the final prediction error (FPE) is investigated when the additive structure is a priori known in the nonparametric autoregression. The consistency of the lag selection is proved, followed by the finite sample simulation results.     

The effects of optimism bias in teams

This article imports a behavioural perspective into a team context to study the effort-coordination problem among agents. Specifically, we investigate how the presence of optimism bias impacts the severity of the free-rider problem, the organizational structure of the team and the compensation contracts offered to agents in equilibrium. The results indicate that all agents become more reluctant to exert effort and the team welfare decreases when some of its agents are optimistic, suggesting that optimism aggravates the free-rider problem in teams. Appointing a team leader makes all agents work harder, and the team benefits more by having the optimistic agent as its leader. These findings are in sharp contrast to the effects of overconfidence as identified in the literature. It is advisable to pay the optimistic agents less than the rational agents. Encouragingly, optimistic agents can learn about their own bias in the long run, leaving their team without too much detriment of optimism.     

Analysis of electricity prices for Central American countries using dynamic conditional score models

In this paper, we compare the performance of dynamic conditional score (DCS) and standard financial time-series models for Central American energy prices. We extend the Student’s t and the exponential generalised beta distribution of the second kind stochastic location and stochastic seasonal DCS models. We consider the generalised t distribution as an alternative for the error term and also consider dynamic specifications of volatility. We use a unique dataset of spot electricity prices for El Salvador, Guatemala and Panama. We consider two data windows for each country, which are defined with respect to the liberalisation and development process of the energy market in Central America. We study the identification of a wide range of DCS specifications, likelihood-based model performance, time-series components of energy prices, maximum likelihood parameter estimates, the discounting property of conditional score, and out-of-sample forecast performance. Our main results are the following. (i) We determine the most robust models of energy prices, with respect to parameter identification, from a wide range of DCS specifications. (ii) For most of the cases, the in-sample statistical performance of DCS is superior to that of the standard model. (iii) For El Salvador and Panama, the standard model provides better point forecasts than DCS, and for Guatemala the point forecast precision of standard and DCS models does not differ significantly. (iv) For El Salvador, the standard model provides better density forecasts than DCS, and for Guatemala and Panama, the density forecast precision of standard and DCS models does not differ significantly.     

The bias of some estimators for panel data models with measurement errors

The paper deals with the (asymptotic) bias in the estimation of regression slope coefficients from panel data observed with error. Unobserved individual and time specific heterogeneity is also assumed. The estimators considered include: the standard ‘within’ and ‘between’ estimators, and estimators based on differences over time. It is shown that in terms of bias, there may be a trade-off between the effect of heterogeneity and of measurement errors. The paper also shows that in situations where the number of observations of each individual is finite (and in practice often small), changes in the correlograms of the measurement error and of the latent exogenous variable may substantially affect the relative bias of the different estimators of the slope coefficient.     

Antithetic variates to estimate the simulation bias in non-linear models

This paper describes a Monte Carlo experiment, which makes use of antithetic variate sampling, to get an accurate estimate of the deterministic simulation bias in the non-linear Klein—Goldberger model. The computational efficiency is more than 500 times greater than in case of simple random sampling.