Biased Coefficient Estimates Research Articles

Predictive Regressions: A Reduced-Bias Estimation Method

Drinkers and bettors: Investigating the complementarity of alcohol consumption and problem gambling

This paper proposes a measure of the contribution of unequal opportunities to earnings inequality. Drawing on the distinction between “circumstance” and “effort” variables in John Roemer's work on equality of opportunity, we associate inequality of opportunities with five observed circumstances which lie beyond the control of the individual—father's and mother's education; father's occupation; race; and region of birth. The paper provides a range of estimates of the importance of these opportunity‐forming circumstances in accounting for earnings inequality in one of the world's most unequal countries. We also decompose the effect of opportunities into a direct effect on earnings and an indirect component, which works through the “effort” variables. The decomposition is applied to the distribution of male earnings in urban Brazil, in 1996. The five observed circumstances are found to account for between 10 and 37 percent of the Theil index, depending on cohort and allowing for the possibility of biased coefficient estimates due to unobserved correlates. On average, 60 percent of this impact operates through the direct effect on earnings. Parental education is the most important circumstance affecting earnings, but the occupation of the father and race also play a role.

On the upsurge of foreign exchange reserves in India

Predictive Regressions: Method of Least Autocorrelation

Count data models are established to overcome the shortcoming of linear regression model used for trip generation in conventional four step travel demand forecasting. It should be checked if there are overdispersion and excess zero responses in count data to forecast the generation of trips. The forecasted values should also be non-negative ones. The study applies to nonhome based trips at household level to perform efficient analysis on count data. The Poisson model with an assumption of equidispersion has frequently been used to analyze count data. However, if the variance of data is greater than the mean, the Poisson model tends to underestimate errors, resulting in problem in reliability. Excess zeros in data result in heterogeneity leading to biased coefficient estimates for the models. The negative binomial model and the modified count data models are established to consider overdispersion and heterogeneity to improve the reliability. The optimal model is chosen through Vuong test. Model reliability is also checked by likelihood test and accuracy of estimated value of model by Theil inequality coefficient. Finally, sensitivity analysis is performed to know the change of nonhome based trips depending on the change in socio-economic characteristics.

Abstract Standard predictive regressions produce biased coefficient estimates in small samples when the regressors are Gaussian first-order autoregressive with errors that are correlated with the error series of the dependent variable. See Stambaugh (1999) for the single regressor model. This paper proposes a direct and convenient method to obtain reduced-bias estimators for single and multiple regressor models by employing an augmented regression, adding a proxy for the errors in the autoregressive model. We derive bias expressions for both the ordinary least-squares and our reduced-bias estimated coefficients. For the standard errors of the estimated predictive coefficients, we develop a heuristic estimator that performs well in simulations, for both the single predictor model and an important specification of the multiple predictor model. The effectiveness of our method is demonstrated by simulations and empirical estimates of common predictive models in finance. Our empirical results show that some of the predictive variables that were significant under ordinary least squares become insignificant under our estimation procedure.

Much public attention and considerable controversy surround pharmaceutical marketing practices and their impact on physicians. However, views on the matter have largely been shaped by anecdotal evidence or results from analyses with insufficient controls. Making use of a dynamic fixed-effects distributed lag regression model, we empirically assess the role that two central components of pharmaceutical marketing practices (namely, detailing and sampling) have on physician prescribing behavior. Key differentiating features of our model include its ability to (i) capture persistence in the prescribing process and decompose it into own-growth and competitive-stealing effects, (ii) estimate an unrestricted decay structure of the promotional effects over time, and (iii) control for physician-specific effects that, if not taken into account, induce biased coefficient estimates of detailing and sampling effects. Based on pooled time series cross-sectional data involving three drugs, 24 monthly observations, and 74,075 individual physicians (more than 2 million observations in total), we find that detailing and free drug samples have positive and statistically significant effects on the number of new prescriptions issued by a physician. However, we find that the magnitudes of the effects are modest.

The widely used generalized additive models (GAM) method is a flexible and effective technique for conducting nonlinear regression analysis in time-series studies of the health effects of air pollution. When the data to which the GAM are being applied have two characteristics--1) the estimated regression coefficients are small and 2) there exist confounding factors that are modeled using at least two nonparametric smooth functions--the default settings in the gam function of the S-Plus software package (version 3.4) do not assure convergence of its iterative estimation procedure and can provide biased estimates of regression coefficients and standard errors. This phenomenon has occurred in time-series analyses of contemporary data on air pollution and mortality. To evaluate the impact of default implementation of the gam software on published analyses, the authors reanalyzed data from the National Morbidity, Mortality, and Air Pollution Study (NMMAPS) using three different methods: 1) Poisson regression with parametric nonlinear adjustments for confounding factors; 2) GAM with default convergence parameters; and 3) GAM with more stringent convergence parameters than the default settings. The authors found that pooled NMMAPS estimates were very similar under the first and third methods but were biased upward under the second method.

A Comparison of Methods for Analyzing Health-Related Quality-of-Life Measures

A so-called hierarchical recursive least-squares (HRLS) algorithm was suggested in a recent letter in an attempt to reduce the computational burden and improve the convergence rate of the classical RLS algorithm. The discussion of HRLS in the original letter, however, has several unclear points; in particular no clear explanation was offered for the good simulation results reported. In this letter we provide some analysis of the HRLS to determine when this algorithm may be expected to work or fail. It turns out that the input to the channel must be a white sequence, otherwise HRLS may yield grossly biased estimates of the channel FIR coefficients.

When data are censored, ordinary least squares regression can provide biased coefficient estimates. Maximum likelihood approaches to this problem are valid only if the error distribution is correctly specified, which can be problematic in practice. We review several semiparametric estimators for the censored regression model that do not require parameterization of the error distribution. These estimators are used to examine changes in black-white earnings inequality during the 1960s based on censored tax records. The results show that there was significant earnings convergence among black and white men in the American South after the passage of the 1964 Civil Rights Act.

International relations scholars make frequent use of pooled cross-sectional regression in which N dyads over T time points are combined to create NT observations. Unless special conditions are met, these regressions produce biased estimates of regression coefficients and their standard errors. A survey of recent publications in international relations shows little attention to this issue. Using data from the period 1951–92, we examine the consequences of pooling for models of militarized disputes and bilateral trade. When pooled models are reestimated to allow for stable but unobserved differences among dyads, the results are altered in fundamental ways.

Correlated response data often arise in longitudinal and familial studies. The marginal regression model and its associated generalized estimating equation (GEE) method are becoming more and more popular in handling such data. Pepe and Anderson pointed out that there is an important yet implicit assumption behind the marginal model and GEE. If the assumption is violated and a nondiagonal working correlation matrix is used in GEE, biased estimates of regression coefficients may result. On the other hand, if a diagonal correlation matrix is used, irrespective of whether the assumption is violated, the resulting estimates are (nearly) unbiased. A straightforward interpretation of this phenomenon is lacking, in part due to the unavailability of a closed form for the resulting GEE estimates. In this note, we show how the bias may arise in the context of linear regression, where the GEE estimates of regression coefficients are the ordinary or generalized least squares (LS) estimates. Also we explain why the generalized LS estimator may be biased, in contrast to the well-known result that it is usually unbiased. In addition, we discuss the bias properties of the sandwich variance estimator of the ordinary LS estimate.

Two algorithms for producing multiple imputations for missing data are evaluated with simulated data. Software using a propensity score classifier with the approximate Bayesian bootstrap produces badly biased estimates of regression coefficients when data on predictor variables are missing at random or missing completely at random. On the other hand, a regression-based method employing the data augmentation algorithm produces estimates with little or no bias.

Selecting a subset of predictors from a pool of potential predictors continues to be a common problem encountered by applied researchers in education. Because of several limitations associated with stepwise variable selection procedures, the examination of all possible regression solutions has been recommended. The authors evaluated the use of Mallow's Cp and Wherry's adjusted R 2 statistics to select a final model from a pool of model solutions. Neither the Cp nor the adjusted R 2 statistic correctly identified the underlying regression model any better and was generally worse than the stepwise selection method, which itself was poor. Using any of the model selection procedures studied here resulted in biased estimates of the authentic regression coefficients and underestimation of their standard errors. The use of theory and professional judgment is recommended for the selection of variables in a prediction equation.

Self-reported health status is often measured using psychometric or utility indices that provide a score intended to summarize an individual's health. Measurements of health status can be subject to a ceiling effect. Frequently, researchers want to examine relationships between determinants of health and measures of health status. Regression methods that ignore the presence of a ceiling effect, or of censoring in the health status measurements can produce biased coefficient estimates. The Tobit regression model is a frequently used tool for modeling censored variables in econometrics research. The authors carried out a Monte-Carlo simulation study to contrast the performance of the Tobit model for censored data with that of ordinary least squares (OLS) regression. It was demonstrated that in the presence of a ceiling effect, if the conditional distribution of the measure of health status had uniform variance, then the coefficient estimates from the Tobit model have superior performance compared with estimates from OLS regression. However, if the conditional distribution had non-uniform variance, then the Tobit model performed at least as poorly as the OLS model.

This paper investigates the matching of job searchers with vacant jobs: a key component of the dynamics of worker reallocation in the labour market. The job searchers may be unemployed, employed or not in the labour force and we estimate matching or hiring functions including all three groups. We show that previous studies, which ignore both employed job seekers and unemployed job seekers who are considered to be out of the labour force, produce biased estimates of the coefficients of interest. By considering only unemployment outflows into jobs and ignoring interdependencies with other flows, these studies overlook an important aspect of job matching. Our estimates on Australian data support a more general approach and produce models that dominate those proposed previously. We find that concentrating on the aggregate matching function alone does not reveal the full extent of the interaction across job searchers. Indeed, we find that job searchers from the three groups do not receive a fair share of hires: there appears to be segmentation of hiring opportunities which may be explained by a form of ranking of applicants. Together these results demonstrate that the disaggregate worker flows and their interdependence are key features on the labour market and should be included in studies of the hiring process.

I. INTRODUCTION In a recent issue of this journal Fremling and Lott [1996] present a novel explanation of why forecasts can be biased, casting considerable doubt on applicability of rational expectations. Their argument is based on some individuals making specification errors (which in a misuse of econometric terminology they call errors) when formulating economic models, omitting relevant explanatory variables from estimation of economic relationships. This causes these individuals to produce biased coefficient estimates, so that when coefficient estimates are averaged to obtain corresponding coefficients in aggregate or individual forecasting relationship, aggregate/representative coefficients are biased. This in turn creates prediction bias, offering an explanation for why empirical evidence tends not to support rational expectations. Unfortunately, Fremling and Lott's presentation of their argument is misleading. In particular, they lead readers to believe that phenomenon they identify results in aggregate/representative coefficient estimates biased toward zero, and they lead readers to believe that this causes underprediction. The purpose of this note is to show that although these results are possible, Fremling and Lott's argument does not guarantee this - it is also possible for coefficient estimates to be biased away from and/or that overprediction could result. II. BIAS TOWARD ZERO Throughout their paper Fremling and Lott suggest that their argument shows that coefficient estimates of an relationship between variables or of a representative are biased toward zero. Bias towards zero appears in title of their paper; first sentence of their abstract talks of downward biases in that are equivalent to public underestimating strengths of true relationships; in summarizing their analytical result they state (p. 279) there should be a bias toward for 'representative' estimate; on p. 280 they claim that the importance of argument lies in that bias created by identification errors is always negative; and in contrasting their theory to rational expectations they conclude on p. 283 that our theory predicts that if mistakes occur, they will involve, as evidence indicates, systematic underestimates of relationship. Fremling and Lott's explanation of this phenomenon rests on reasonable assumption that some people make specification errors when estimating relationships, omitting relevant explanatory variables. Suppose, for example, P depends on M and F, as in macroeconomic modeling example in section V of Fremling and Lott's paper, so that we predict [Delta]P by [Delta][P.sup.*] = [[Alpha].sup.*][Delta]M + [[Beta].sup.*][Delta]F where [[Alpha].sup.*] and [[Beta].sup.*] are ordinary least squares estimates of corresponding parameters [Alpha] and [Beta]. Adopting usual statistical assumptions, as noted by Fremling and Lott in their footnote 4, p. 278, if everyone estimates this relationship by regressing [Delta]P on [Delta]M and [Delta]F, or representative relationship will have unbiased coefficient estimates. Fremling and Lott claim that if some people estimate this relationship omitting AM, in effect estimating [Alpha] by zero, they will cause aggregate/representative relationship to have a coefficient estimate biased toward zero. This is their result shown in equation (3) on p. 279. Unfortunately, in reaching this result Fremling and Lott have violated one of their own assumptions, namely that, as noted in their footnote 5, p. 279, specification errors are random. They have forgotten to account for those individuals who estimate this relationship by omitting [Delta]F. These individuals could create upward-biased estimates of a that could cause aggregate/representative estimate of [Alpha] to be biased away from zero! …

Empirical labor market studies often do not include controls for family and income structure. Because these variables are significantly correlated with many of the variables commonly included, such as education, estimated coefficients are subject to omitted variable bias. We demonstrate how omission of family and income variables can lead to statistically biased coefficient estimates on nonfamily variables and can lead to false inferences by examining labor force attachment of workers who have lost their previous job. The traditional variables most biased by the omission of family and income characteristics are education, displacement age, and predicted pre-displacement wages. As an indication of the extent of the bias, we calculate expected labor force participation rates for single women, married women, and married men using the average characteristics for each group using both the biased and unbiased coefficients. We find a 50 percent reduction in the extent to which market-oriented opportunities explain the differences in observed labor force attachment between married women and men when family characteristics are included relative to when they are not.