Nonlinearity in the Canadian and US labor markets: Univariate and multivariate evidence from a battery of tests

The nonlinearity of macroeconomic processes is becoming an increasingly important issue at both the theoretical and empirical levels. This trend holds for labor market variables as well. The reallocation theory of unemployment relies on nonlinearities. At the same time there is mounting empirical evidence of business cycles asymmetries. Thus the assumption of linearity/nonlinearity becomes crucial for the corroboration of labor market theories. This paper turns the microscope on the assumption of linearity and investigates the presence of asymmetries in aggregate and disaggregate labor market variables. The assumption of linearity is tested using five statistical tests for U.S. and Canadian unemployment rates and growth rates of the employment sectoral shares of construction, finance, manufacturing, and trade. An AR(p) model was used to remove any linear structure from the series. Evidence of nonlinearity is found for the sectoral shares with all five statistical tests in the U.S. case but not at the aggregate level. The results for Canada are not clear-cut. Evidence of unspecified nonlinearity is found in the unemployment rate and in the sectoral shares. Overall, important asymmetries are found in disaggregated labor market variables in the univariate setting. The linearity hypothesis was also examined in a multivariate framework. Evidence is provided that important asymmetries exist and a linear VAR cannot capture the dynamics of employment reallocation.