Small sample bias in conditional sum-of-squares estimators of fractionally integrated ARMA models

This paper considers estimation of the parameters for the fractionally integrated class of processes known as ARFIMA. We consider the small sample properties of a conditional sum-of-squares estimator that is asymptotically equivalent to MLE. This estimator has the advantage of being relatively simple and can estimate all the parameters, including the mean, simultaneously. The simulation evidence we present indicates that estimation of the mean can make a considerable difference to the small sample bias and MSE of the other parameter estimates.     

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.     

Asymptotic distribution of least squares estimator and a test statistic in linear regression models

This paper presents a fairly general and sufficiently weak condition on the observation matrix for the asymptotic normality of the least squares estimator of coefficient vector in a linear regression model. The asymptotic distribution of a statistic for testing the nullity of coefficient vector is also considered.     

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.     

Deriving conditional and unconditional marginal effects in log earnings equations estimated by Heckman's procedure

Although the Heckman approach has often been used in empirical analysis, the marginal effects, necessary to interpret the effect of the regressors on the dependent variable, appeared to be overlooked. Using the Heckman approach, general expressions are derived for calculating the conditional and unconditional marginal effects. Based on a sample of Brazilian women, the conditional and unconditional return to education are calculated for the logarithm of earnings equation estimated by Heckman's procedure, comparing them to the marginal effect of education obtained without correcting for selectivity bias. The same analysis is carried out for a discrete variable ‘black’.     

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.     

Estimating gravity equation models in the presence of sample selection and heteroscedasticity

Gravity models are widely used to explain patterns of trade. However, two stylized features of trade data, sample selection and heteroscedasticity challenge the estimation of gravity models. We propose a two-step method of moments (TS-MM) estimator that deals with both issues. The Monte-Carlo experiments show that the TS-MM estimates are resistant to various combinations of sample selection and heteroscedasticity. Moreover, the TS-MM estimator performs reasonably well even when the data generating process deviates from the TS-MM assumptions. We revisit the world trade in 1990 to illustrate the usefulness of the proposed model, with emphasis on the identification of the extensive margin of trade.     

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.     

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.     

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.     

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.     

Dynamic conditional score models: a review of their applications

ABSTRACT

In this paper, applications of dynamic conditional score (DCS) models are reviewed and those models are discussed in relation to classical time series models from the literature. DCS models are robust to outliers, which improves their statistical performance compared to classical models. Three applications are presented in order to compare the statistical performances of DCS and classical models in three very different contexts: (i) The QAR (quasi-autoregressive) plus Beta-t-EGARCH (exponential autoregressive conditional heteroscedasticity) model is presented, which is a score-driven expected return plus volatility model. This model is used for daily returns on the DAX (Deutscher Aktienindex) equity index for the period of January 1988 to December 2017. (ii) The score-driven local level and seasonality plus Beta-t-EGARCH model is presented, which is used for daily AFN/USD (Afghan Afghani/United States Dollar) currency exchange rates for the period of March 2007 to July 2017. (iii) The Seasonal-t-QVAR (quasi-vector autoregressive) model is presented, which is a score-driven multivariate dynamic model of location. For this model, monthly US inflation rate and US unemployment rate are used for the period of January 1948 to December 2017. For all applications, the statistical performance of each DCS model is superior to that of a corresponding classical alternative.     

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.     

Modelling land development processes using a sample selection regression

Land value tax has been thoroughly scrutinized as a potential tool in mitigating urban sprawl. However, most studies that have measured the impact of land value tax on land development have focused mainly either on purely new development on vacant land, or on land development on partially developed land such as subdivision development. This study tries to incorporate these two types of residential development conceptually and empirically to make an accurate assessment of the impact of land value tax on land development.     

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.     

On the asymptotic bias and mean squared error of an improved estimator for coefficients in linear regression

An estimator for regression coefficients of Kadiyala (1984) is considered. It is proved that the estimator is asymptotically unbiased. The asymptotic weak mean squared error of the estimator is also derived and it is proved that, under certain conditions, the estimator dominates a general class of estimators given by Vinod and Ullah (1981).