Charles M. Beach

A MAXIMUM LIKELIHOOD PROCEDURE FOR REGRESSION WITH AUTOCORRELATED ERRORS

The widely used Cochrane-Orcutt and Hildreth-Lu procedures for estimating the parameters of a linear regression model with first-order autocorrelation typically ignore the first observation. An alternative maximum likelihood procedure which incorporates the first observation and the stationarity condition of the error process is proposed in this paper. It is similar to the Cochrane-Orcutt procedure, and appears to be at least as computationally efficient. This estimator is superior to the conventional ones on theoretical grounds, and sampling experiments suggest that it may yield substantially better estimates in some circumstances.

Distribution-Free Statistical Inference with Lorenz Curves and Income Shares

The paper considers the problem of statistical inference with estimated Lorenz curves and income shares. The full variance-covariance structure of the (asymptotic) normal distribution of a vector of Lorenz curve ordinates is derived and shown to depend only on conditional first and second moments that can be estimated consistently without prior specification of the population density underlying the sample data. Lorenz curves and income shares can thus be used as tools for statistical inference instead of simply as descriptive statistics.

Joint Confidence Intervals for Income Shares and Lorenz Curves

In a recent paper, Beach and Davidson [1983] extended the principles of statistical inference to Lorenz curves and income shares by establishing the (asymptotic) distribution and covariance structure of a vector of Lorenz curve ordinates corresponding to a set of quantile abscissae. One can thus use the Lorenz curve and income shares, no longer just as descriptive devices for summarizing distribution information, but now also as analytical tools for comparing alternative distributions and carrying out conventional statistical inference on them. It would clearly be desirable, however, to extend and complement this work by providing a method for computing a set of joint confidence intervals about these income shares and for illustrating graphically a joint confidence band about a set of estimated Lorenz curve ordinates. The present paper provides a new and simple technique for doing this. When analyzing differences between sets of income shares or Lorenz curves, one typically wants to elicit more detailed information than is provided by a standard joint chi-square test on the overall set of shares. That is, when the hypothesis of two sets of shares being the same is rejected, we generally want to know further which particular differences in shares are different from zero, and of these nonzero differences which are positive and which negative (Savin [1980]). A natural way of providing such information is through multiple comparison procedures developed in this paper. In a recent work, Richmond [1982] has developed a general method of finding multiple comparison intervals that is particularly suited to the present problem and in this situation appears to dominate other conventional alternatives. In contrast, for example, to Scheff&s S-projection method, Richmonds approach focuses on a set of primary points of interest (income shares) among a more general set of points (including the Lorenz curve ordinates) and optimizes the joint confidence interval lengths on this primary set of points. Since estimated Lorenz curve ordinates are built up from underlying income shares, these shares (perhaps further supplemented) are natural choices for the primary set. The method, however, also provides a joint confidence band that geometrically bounds the set of Lorenz curve ordinates (and interpolated segments between them). The present

Maximum Likelihood Estimation of Singular Equation Systems with Autoregressive Disturbances

Maximum likelihood estimation of equation systems with first-order autocorrelation should, in principle, take into account the first observation and associated stationarity condition. In the general case, this leads to computational difficulties compared with conventional procedures, which perhaps explains the failure of the latter to incorporate the initial observation. However, in a special case where the autoregressive process has only one parameter, which is widely used for single equation systems such as demand systems, taking the first observation into account is no more difficult than ignoring it. The paper presents empirical results of estimating a demand system with Canadian data which suggest that maximizing the full likelihood function can yield very different and more reasonable estimates than maximizing the conventional one.

Impacts of the Point System and Immigration Policy Levers on Skill Characteristics of Canadian Immigrants

This paper examines how changes in immigration policy levers actually affect the skill characteristics of immigrant arrivals using a unique Canadian immigrant landings database. The paper identifies some hypotheses on the possible effects on immigrant skill characteristics of the total immigration rate, the point system weights and immigrant class weights. The “skill” characteristics examined are level of education, age, and fluency in either English or French. Regressions are used to test the hypotheses from Canadian landings data for 1980–2001. It is found that (i) the larger the inflow rate of immigrants the lower the average skill level of the arrivals, (ii) increasing the proportion of skill-evaluated immigrants raises average skill levels, and (iii) increasing point system weights on a specific skill dimension indeed has the intended effect of raising average skill levels in this dimension among arriving principal applicants.

Toward Improving Canada's Skilled Immigration Policy: An Evaluation Approach

Canada’s approach to immigration faces major challenges, and requires reform if Canada is to meet the international competition for skilled immigrants, according to a new policy study. In the Policy Study, the authors assess the strengths and weaknesses of the current point system used to screen new arrivals, identify the policy levers that affect the attributes and success rates of new arrivals, and break new ground by providing a tool to measure those impacts.The past two and a half decades have seen a marked worsening in the adjustment process of new immigrants, as their earnings levels have dropped significantly relative to Canadian-born workers, say the book’s authors. The earnings gap between Canadian- and foreign-born workers has widened, and the catch-up interval between the earnings of immigrants and Canadian-born workers has lengthened. These results have come at the cost of fewer human resources and skills available to the Canadian economy, a potential threat to social cohesion, and the likely loss of skilled immigrants who choose to return home or move on to another country.

Statistical inference for decile means

Abstract This paper provides a simple set of formulas to compute standard errors, variances, and covariances for a set of decile mean incomes. This facilitates the statistical implementation of the Rank Dominance criterion for comparing two income (or wealth) distributions.

A longitudinal analysis of earnings change in Canada

This paper examines trends in earnings, using tax-based longitudinal data from the last two decades and synthetic cohort analysis.

Inequality and polarization of male earnings in the United States, 1968-1990

Abstract In this paper we examine trends in inequality and polarization of U.S. male earnings using recently developed techniques of statistical inference to test for distributional changes. We find that earnings inequality of male paid workers increased between 1968 and 1990. Decile mean real earnings fell in deciles 1–7 and rose in deciles 9 and 10 over this period. Changes in the distribution of earnings may be characterized by a decline of the “middle” and increased polarization. A combination of trend and cyclical factors appears to drive changes in the middle-class shares and polarization shares and the effect of the cyclical factors varies between the 1970s and 1980s.

Long-Run Inequality and Short-Run Instability of Men'S and Women'S Earnings in Canada

This paper examines the variability of workers’ earnings in Canada over the period 1982–2006. We decompose the total variance of workers’ earnings into a ‘permanent’ component between workers and a ‘transitory’ earnings instability component over time for given workers. We then investigate the statistical relationships between these components and indicators for the business cycle. The most marked change in earnings variances in Canada since 1982 is the general rise in total earnings variance, which is essentially driven by a quite dramatic rise in long-run earnings inequality. The patterns across age categories of the two variance components are almost opposite. Long-run earnings inequality generally rises with age, but earnings instability is seen to generally decline with age, so that earnings instability is markedly highest among entry age workers. Unemployment rate effects are positive on almost all variance measures, while higher unemployment is associated with widened long-run earnings differentials and greater short-run earnings instability.