The modified Okun's law for Canada. Model validation

 In our previous post, we revisited and validated our version of Okun’s law for the USA with new GDP and unemployment data for the years between 2010 and 2019. The revised model accurately describes the new data and three quarters of 2020, i.e. the original model is validated. In order to reach the best fit between the measured and predicted unemployment rates, we introduced a structural break in 2010 as related to the change in real GDP definition. 

In this post, we apply the same approach to Canada and start with the CPI and GDP deflator difference, which is used to reveal definitional breaks in the dGDP estimates. Obviously, such breaks in the dGDP creates breaks in the real GDP per capita estimates, and thus, in the statistical estimates associated with our model. One needs to find such breaks and allow the model to compensate for corresponding disturbances. At this stage, we ignore well-known steps in the unemployment rate estimates (see, TP-66 – CPS Design and Technology) related to the change in the population controls after the decennial censuses, e.g. the 2010 census. Such steps could be accurately compensated by dummy variables. More efforts are needed to investigate this problem and find the years when such steps were introduced in the labor force statistics.

 In the upper panel of Figure 1, we present the evolution of the cumulative inflation (the sum of annual inflation estimates) as defined by the CPI and dGDP between 1962 (we use the OECD data for the unemployment rate since 1961) and 2018. Both variables are normalized to their respective values in 1961. From the very beginning, the dGDP curve is above the CPI one and this configuration we interpret as economic underperformance. Another indicator of underperformance is the average annual increment of the real GDP per capita (from the Maddison Project Database) of $533 (2011 prices) compared to $643 in the USA – the biggest trade partner. In the middle panel, the inflation rates are shown for both variables. In the lower panel, we present the fit between the CPI and the dGDP cumulative inflation curves after correction of the latter in 1962 (coefficient 0.8), 1977 (0.8*1.4=1.12) and 2003(0.8*1.4*0.77=0.86). There was a period between 1977 and 2003 when the CPI grew faster than the dGDP.

  

Figure 1. Upper panel: The evolution of the cumulative inflation (the sum of annual inflation estimates) as defined by the CPI and dGDP between 1961 and 2018. Both variables are normalized to their respective values in 1961.  Middle panel: The dGDP and CPI inflation estimates. Lower panel: The fit between the CPI and the dGDP cumulative inflation curves after correction of the latter in 1962, 1977 and, 2003 (see text).   

 

In our model, we are looking for breaks near the years and obtain the following intervals and coefficients: 

du_p = -0.270dlnG + 1.130, 1977>t≥1970

du_p = -0.281dlnG + 0.303,  2000≥t≥1978     

du_p = -0.280dlnG + 0.505,  2009≥t≥2001              

du_p = -0.350dlnG + 0.180,           t≥2010     (1)

 

where du_p – one-year change in the (OECD) unemployment rate, G – real GDP per capita (2011 prices). The break years are slightly different from those estimated from the inflation curves in Figure 1. This is likely due to the higher sensitivity of the predicted unemployment rate to the coefficients in (1). The cumulative inflation curves in the upper panel of Figure 1 are both synchronously corrected in many revisions through their whole length. The estimates of the unemployment rate are obtained in the Current Population Surveys and represent independent estimates. The unemployment values are also corrected in the revisions to unemployment definition and when new population controls estimated after the decennial censuses. The original estimates cannot be changed but rather synchronously corrected. The rate of unemployment is an independent economic variable consisting of independent measurements. The predicted rate of unemployment depends on the integral value of the real GDP per capita. This makes the predicted value to be very sensitive to the GDPpc evolution. In other words, the current prediction, u_p, depends on the initial value, u(t₀), and the whole path of the GDPpc between t₀ and the current time. This is 49 years for Canada and 68 for the USA. The new readings of the unemployment rate and GDPpc (2011 to 2019) validate the model, which links the change in the rate of unemployment and the relative growth rate of the real GDP per capita in Canada.

 

Figure 2. Upper panel: The measured rate of unemployment in Canada between 1970 and 2019, and the rate predicted by model (1) with the real GDP per capita published by the MPD and the unemployment rate reported by the OECD. Middle panel: The model residual: stdev=0.62%. Lower panel: Linear regression of the measured and predicted time series. Rsq. = 0.87.