From Peter Hooper, Torsten Slok, Christine Dobridge, “Robust growth needed to avoid jobless recovery,” Deutsche Bank *Global Economic Perspectives* (Dec. 9) [not online]:

Okun’s Law is an empirical regularity that holds that for every one percent decline in GDP growth relative to potential, the unemployment rate will increase by about 1/2 percentage point….To consider the extent to which there may have been some excessive layoffs during the downturn, Charts A1 and A2 show the relationship between changes in employment and changes in real GDP, with GDP lagged one quarter. Both charts show that the change in employment during this recession was noticeably more negative than the standard Okun’s Law regression would predict. On the assumption that historical relationships reassert themselves, we surmise that employment could bounce back more strongly during this recovery…

Below is my version of Figure A2, where I’ve used a sample over 1967q1-09q3

**Figure 1**: Scatterplot of annualized growth rate of q/q nonfarm payroll employment against annualized growth rate of q/q GDP growth, lagged one quarter (blue cirles), and OLS fit (dark blue line). Red circles for 2008q1-09q2, and OLS fit (purple line). Growth rates calculated as log-differences. *Source*: BEA and BLS via FREDII, and author’s calculations.

The idea is that with the lower intercept during the recession period, employment growth will have to compensate later on. This would be represented by an upward shift of the “long term” Okun’s law.

This is in some sense substantiated by the fact that the long run that Okun’s law relationship between employment and lagged GDP growth is even stronger, but with a downshifted intercept, over the 1990q3-09q3 period.

**Figure 2**: Scatterplot of annualized growth rate of q/q nonfarm payroll employment against annualized growth rate of q/q GDP growth, lagged one quarter (blue cirles), and OLS fit (dark blue line). OLS fit for 1990q3-09q3 (pink line). Growth rates calculated as log-differences. *Source*: BEA and BLS via FREDII, and author’s calculations.

Note that implied growth rates are the same only if q/q annualized GDP growth rates exceed approximately 6%.

Some additional observations. First, there are several different Okun’s Law floating around in the literature. Another, perhaps more popular, alternative links the unemployment gap (in percentage points) to the output gap (in percentage gaps) (see here). Second, this set of estimates is partly consistent with the error correction model (ECM) approach adopted in this post. In essence each regression line shown in the figures drops the long term cointegrating relationship between the (log) level of employment and (log) level of GDP.

I’ll observe that while the error correction approach I used in that post can partly accomodate the “bounceback” effect — the deviation from the long term cointegrating relationship adds some extra upward pressure on the growth rate of employment — but doesn’t do so fully. To do that, a threshold ECM would have been necessary.

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