Non-Linearity in the Canadian and US Labour Market: Univariate and Multivariate Evidence from a battery of tests.

The non-linearity of macroeconomic processes is becoming an increasingly important issue both at theoretical and empirical level. This trend holds for labour market variables as well. Reallocation theory of unemployment relies on non-linearities. At the same time there is mounting empirical evidence of business cycles asymmetries. Thus the assumption of linearity /non-linearity becomes crucial for the corroboration of labour market theories. This paper turns on the microscope on the assumption of linearity and investigates the presence of asymmetries on aggregate and disaggregate labour market variables. The assumption of linearity is tested using five statistical tests for the US and Canadian unemployment rates, growth rates of the employment sectoral shares of construction, finance, manufacturing and trade sectors. An AR(p) model was used to remove any linear structure from the series. Evidence of non-linearity is found for the sectoral shares with all five statistical tests in the US case but not in the aggregate level. The results for Canada are not clear-cut. Evidence of unspecified non-linearity is found in the unemployment rate and in the sectoral shares. Overall important asymmetries are found in disaggregated labour 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.