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Statistical Inference on the Canadian Middle Class

Department of Economics and CIREQ, McGill University, Montréal, QC H3A 2T7, Canada
AMSE-GREQAM, 5 Boulevard Maurice Bourdet, CS 50498, CEDEX 01, 13205 Marseille, France
Econometrics 2018, 6(1), 14;
Received: 25 December 2017 / Revised: 2 February 2018 / Accepted: 8 March 2018 / Published: 13 March 2018
(This article belongs to the Special Issue Econometrics and Income Inequality)
Conventional wisdom says that the middle classes in many developed countries have recently suffered losses, in terms of both the share of the total population belonging to the middle class, and also their share in total income. Here, distribution-free methods are developed for inference on these shares, by means of deriving expressions for their asymptotic variances of sample estimates, and the covariance of the estimates. Asymptotic inference can be undertaken based on asymptotic normality. Bootstrap inference can be expected to be more reliable, and appropriate bootstrap procedures are proposed. As an illustration, samples of individual earnings drawn from Canadian census data are used to test various hypotheses about the middle-class shares, and confidence intervals for them are computed. It is found that, for the earlier censuses, sample sizes are large enough for asymptotic and bootstrap inference to be almost identical, but that, in the twenty-first century, the bootstrap fails on account of a strange phenomenon whereby many presumably different incomes in the data are rounded to one and the same value. Another difference between the centuries is the appearance of heavy right-hand tails in the income distributions of both men and women. View Full-Text
Keywords: middle class; Canada; bootstrap middle class; Canada; bootstrap
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Davidson, R. Statistical Inference on the Canadian Middle Class. Econometrics 2018, 6, 14.

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