Lonnie Magee

Alternative Transformations to Handle Extreme Values of the Dependent Variable

Abstract Transformations that could be used to reduce the influence of extreme observations of dependent variables, which can assume either sign, on regression coefficient estimates are studied in this article. Two that seem reasonable on a priori grounds—the extended Box—Cox (BC) and the inverse hyperbolic sine (IHS)—are evaluated in detail. One feature is that the log-likelihood function for IHS is defined for zero values of the dependent variable, which is not true of BC. The double-length regression technique (Davidson and MacKinnon 1984) is used to perform hypothesis tests of one transformation against the other using Canadian data on household net worth. These tests support the use of IHS instead of BC for this data set. Empirical investigators in economics often work with a logged dependent variable (taking the natural logarithm of a data series is, of course, a special case of BC) to reduce the weight their particular estimation procedure might otherwise attach to extreme values of the dependent v...

R 2 Measures Based on Wald and Likelihood Ratio Joint Significance Tests

Abstract Two methods are suggested for generating R 2 measures for a wide class of models. These measures are linked to the R 2 of the standard linear regression model through Wald and likelihood ratio statistics for testing the joint significance of the explanatory variables. Some currently used R 2s are shown to be special cases of these methods.

Transforming the Dependent Variable in Regression Models

A scale-invariant family of transformations is proposed which, unlike the Box-Cox transformation, can be applied to variables that are equal to zero or of either sign. Two Lagrange Multiplier tests are derived for testing the null hypothesis of no dependent variable transformation against the alternative of a transformation from this family. These tests do not require explicit specification of the transformation and are related to the RESET test. We discuss a model that uses a particular case of this transformation, based on sinh-1, in some detail. Monte Carlo results are given, and an empirical example is provided.

The Education Premium in Canada and the United States

In the United States the education premium - the ratio of the earnings of university graduates to the earnings of high school graduates - has risen sharply in the last 20 years. Some economists and policymakers presume the same fact holds in Canada. Since so much of modern growth theory and micro- and macroeconomic policy turns on the education premium, it is important for social scientists and policymakers to know what has actually happened to the education premium. This paper argues that based on available evidence over the last 20 years the premium has been constant or has fallen in Canada.

On the use of sampling weights when estimating regression models with survey data

Abstract In this paper it is argued that when the population regression coefficient is of interest, the use of sampling weights can be desirable in regression models with complex survey data. A two-step ML estimator is proposed as an alternative to OLS and weighted least squares. Specification tests are given. The ML estimator does well in simulations, including several cases where it is based on a misspecified model. The specification tests are effective in selecting the best estimator. As an example, the methods are used to estimate the returns to education using data from the Canadian Survey of Consumer Finances.

Canadian Wage Inequality over the Last Two Decades

We study the dispersion of wages of full-time full-year workers over two decades controlling for both education and experience. Applying non-parametric statistical methods we find statistically significant and large increases in inequality for males with low levels of education and experience coexist with more modest changes in inequality for those with average education and experience, and with actual declines in inequality for older, more experienced workers with a university degree. These relative patterns tend to be similar for females though with a stronger tendency towards inequality in each education-experience category. Given the recent focus in this debate on the issue of polarization, we also show graphs of the actual distributions of wages and analyze these to conclude that the groups experiencing increased dispersion do display what is commonly known as polarization though it would be an exaggeration to claim that the jobs in the middle of the distribution have vanished.

Computing Kernel-Smoothed Conditional Quantiles from Many Observations

Abstract Quantiles of a variable Y conditional on another variable X, when plotted against X, can be a useful descriptive tool. These plots give a quick impression of the functional form of the relation between X and the location, spread, and shape of the conditional distribution of Y. If several Y are observed for each X, then sample quantiles could be calculated for each X. The resulting quantile plot may be quite noisy, however, and smoothing across X may be desired. This article presents an algorithm that calculates kernel-smoothed conditional quantiles with a cross-validation choice of bandwidth for X. It is computationally feasible for large data sets when X assumes a small number of values since it requires only one pass through the full data set. The cross-validation does not require a pass through the data because of simplifications arising from the L 1 loss function being based on absolute values. The technique is illustrated by plotting the conditional quantiles of the net wealth of a sample of...

Kernel Smoothed Consumption-Age Quantiles

In earlier work, the authors explored life-cycle consumption profiles of Canadian married couple families. That research concluded that the common presumption in simulation models of upward-sloping consumption-age profiles accompanied by dissaving in retirement could not be supported in Canadian data. Here, the authors continue to explore the shape of the consumption-age profile by nonparametric techniques they have developed. These techniques allow them to estimate profiles in a manner that does not depend on assumptions about functional form. In particular, the authors estimate the median and other quantiles of the consumption distribution conditional on age. Broadly speaking, the authors confirm their earlier results.

Improving survey‐weighted least squares regression

The weighted least squares (WLS) estimator is often employed in linear regression using complex survey data to deal with the bias in ordinary least squares (OLS) arising from informative sampling. In this paper a ‘quasi-Aitken WLS’ (QWLS) estimator is proposed. QWLS modifies WLS in the same way that Cragg’s quasi-Aitken estimator modifies OLS. It weights by the usual inverse sample inclusion probability weights multiplied by a parameterized function of covariates, where the parameters are chosen to minimize a variance criterion. The resulting estimator is consistent for the superpopulation regression coefficient under fairly mild conditions and has a smaller asymptotic variance than WLS.

AN EDGEWORTH TEST SIZE CORRECTION FOR THE LINEAR MODEL WITH AR(1) ERRORS

T. J. Rothenbergs (1984) Edgeworth test size correction for the linear model with a nonscalar covariance matrix is applied to the special case of AR(1) errors. Simulations show that the correction reduces the overrejection that is commonly encountered in this model, although substantial overrejection remains when the original amount is large. When the regressors are autocorrelated and collinear (for example, two trended regressors) there is not nearly as much overrejection when testing a single restriction as there is when the model contains only one autocorrelated regressor. Copyright 1989 by The Econometric Society.