We study large-sample properties of likelihood ratio tests of the unit root hypothesis in an autoregressive model of arbitrary, finite order. Earlier research on this testing problem has developed likelihood ratio tests in the autoregressive model of order one, but resorted to a plug-in approach...

This paper extends the statistical inference approach developed in Beach (2016) to look at income changes over different regions of an income distribution. Specifically, it looks at relative-mean earnings (RME) ratios and mean earnings levels for lower earners, middle-class (MC) workers and...

This paper looks at changes in employment and relative wages of near higher earnings (NHE) workers between middle-class (MC) and higher earners (HE) in Canada over 2000-2015. An approach is also forwarded for evaluating these changes in terms of underlying demand and supply factors. It is found...

This paper assesses whether the economy of East Germany is catching up with the West German region in terms of welfare. While the primary measure for convergence and catching up is per capita output, we also look at other macroeconomic indicators such as unemployment rates, wage rates, and...

We calculate numerically the asymptotic distribution functions of likelihood ratio tests for fractional unit roots and cointegration rank. Because these distributions depend on a real-valued parameter, b, which must be estimated, simple tabulation is not feasible. Partly due to the presence of...

In an important generalization of zero frequency autoregressive unit root tests, Hylleberg, Engle, Granger, and Yoo (1990) developed regression-based tests for unit roots at the seasonal frequencies in quarterly time series. We develop likelihood ratio tests for seasonal unit roots and show that...

This paper provides tables of critical values for some popular tests of cointegration and unit roots. Although these tables are necessarily based on computer simulations, they are much more accurate than those previously available. The results of the simulation experiments are summarized by...

This paper offers a tool box of disaggregative measures of distributional change, including population shares, income shares, quantile mean incomes and relative mean incomes of different income groups. It highlights median-based measures along with quintiles and deciles. It also offers formulas...

This paper applies the tool box measures of disaggregative income inequality characterization and the statistical methodology of Beach (2021) to percentile-based distribution statistics such as quintile income shares and decile means typically published by official statistical agencies. It...

This paper uses distribution-free formulas for the asymptotic variances of sample quantile income shares - as typically published by statistical agencies as measures of the distribution of income inequality - to calculate how large a survey sample must be in order to estimate a more refined...