## Friday, October 12

### GDP, GDI and Okun

Yesterday, I noted that the recent jump in real gross domestic product (GDP) did not appear to be driving a fall in the unemployment rate, as would be expected under Okun's rule.  I wondered  whether real gross domestic income (GDI) - GDP adjusted for changes in the terms of trade - would provide a better explanation for the unemployment rate. To help answer that question I have completed a series of simple linear regressions.

First, however, a quick recap: Okun's rule can be expressed as a relationship between GDP growth and the change in the unemployment rate. While the Okun co-efficient varies from country to country, at its simplest the Australian data suggests that GDP typically needs to be growing faster than three per cent each year for the unemployment rate to decline year-on-year.

Because the GDI data is only available back to 1986, I have limited my all of my regression models to the available data since that date (the charts span the same period). I have also looked at the data in terms of quarterly changes (comparing the current quarter with the previous quarter) and through-the year changes (comparing this quarter with the same quarter last year).

The first case I looked at was GDP v unemployment rate on a quarterly basis. The R output from my regression model is in the grey box below. You can skip the grey box if this is not your thing. In summary, it says that while this regression model is statistically significant at the 5 per cent level, it only explains 10 per cent of the variance in the data.

Analysis of Variance Table

Response: dlm$UR.qtly.growth.dif Df Sum Sq Mean Sq F value Pr(>F) dlm$GDP.qtly.growth   1 1.1321 1.13207  12.724 0.0005517 ***
Residuals           102 9.0753 0.08897
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Call:
lm(formula = dlm$UR.qtly.growth.dif ~ dlm$GDP.qtly.growth, na.action = "na.exclude")

Residuals:
Min       1Q   Median       3Q      Max
-0.53668 -0.19291 -0.01702  0.13009  1.16620

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)          0.10929    0.04725   2.313 0.022720 *
dlm$GDP.qtly.growth -0.16160 0.04530 -3.567 0.000552 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.2983 on 102 degrees of freedom Multiple R-squared: 0.1109, Adjusted R-squared: 0.1022 F-statistic: 12.72 on 1 and 102 DF, p-value: 0.0005517  My second case was GDI v unemployment rate on a quarterly basis. Again, we have a regression model that is statistically significant at the 5% level. This model, however, explains 20 per cent of the variance in the data. Analysis of Variance Table Response: dlm$UR.qtly.growth.dif
Df Sum Sq Mean Sq F value    Pr(>F)
dlm$GDI.qtly.growth 1 2.0870 2.08704 26.215 1.445e-06 *** Residuals 102 8.1203 0.07961 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Call: lm(formula = dlm$UR.qtly.growth.dif ~ dlm$GDI.qtly.growth, na.action = "na.exclude") Residuals: Min 1Q Median 3Q Max -0.54498 -0.20640 -0.04825 0.15066 0.92417 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 0.13064 0.04083 3.20 0.00183 ** dlm$GDI.qtly.growth -0.16019    0.03129   -5.12 1.45e-06 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2822 on 102 degrees of freedom
Multiple R-squared: 0.2045, Adjusted R-squared: 0.1967
F-statistic: 26.22 on 1 and 102 DF,  p-value: 1.445e-06


My third model was GDP v unemplotyment rate on an annual basis. Again, statistically significant at the 5 per cent level. This model explains some 48 per cent of the variance.

Analysis of Variance Table

Response: dlm$UR.tty.growth.dif Df Sum Sq Mean Sq F value Pr(>F) dlm$GDP.tty.growth   1 42.787  42.787  96.787 < 2.2e-16 ***
Residuals          102 45.092   0.442
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Call:
lm(formula = dlm$UR.tty.growth.dif ~ dlm$GDP.tty.growth, na.action = "na.exclude")

Residuals:
Min       1Q   Median       3Q      Max
-1.70934 -0.44203 -0.02494  0.51764  1.43543

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)         1.25296    0.15237   8.223 6.69e-13 ***
dlm$GDP.tty.growth -0.41343 0.04202 -9.838 < 2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.6649 on 102 degrees of freedom Multiple R-squared: 0.4869, Adjusted R-squared: 0.4819 F-statistic: 96.79 on 1 and 102 DF, p-value: < 2.2e-16  The final model is GDI v the unemployment rate on a through the year basis. Again, we have a valid regression, this time one that explains 56 per cent of the variance in the data. Of note: the gradient of the TTY-GDI model (-0.303) is not as steep as the gradient of the TTY-GDP model (-0.413). However, the average requirement for an unemployment rate that is falling over the year is a GDI through the year rate of 3.5 per cent. Analysis of Variance Table Response: dlm$UR.tty.growth.dif
Df Sum Sq Mean Sq F value    Pr(>F)
dlm$GDI.tty.growth 1 49.720 49.720 132.9 < 2.2e-16 *** Residuals 102 38.159 0.374 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Call: lm(formula = dlm$UR.tty.growth.dif ~ dlm$GDI.tty.growth, na.action = "na.exclude") Residuals: Min 1Q Median 3Q Max -1.64366 -0.40215 0.00907 0.42876 1.34243 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 1.07347 0.11829 9.075 9.05e-15 *** dlm$GDI.tty.growth -0.30252    0.02624 -11.528  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.6116 on 102 degrees of freedom
Multiple R-squared: 0.5658, Adjusted R-squared: 0.5615
F-statistic: 132.9 on 1 and 102 DF,  p-value: < 2.2e-16


Conclusion: for Australia at least, on both a quarterly basis and an annual basis, the GDI growth rate appears better at explaining changes in the unemployment rate than the GDP growth rate.

Caveat: I should admit to being a little troubled by the through the year regression models. I suspect the R-squared is over stated, as the sequential observations are not independent of each other (they include a 9 month period in common). Data points six months apart have a six month period in common. And you can do the math for data points that are nine months apart.

The next chart has the underlying data for the two through-the-year scatter plots.

GDP is currently growing at a rate that should see the unemployment rate decline. GDI is more lacklustre, growing at a much slower rate, which on average would see the unemployment rate grow.

#### 1 comment:

1. Great post.

Another idea - most econometric specifications of the Okun relationship use a 1Q to 2Q lag of GDP, to account for the lagged response in actual hiring. My guess is you'll find a stronger relationship for both of these tests with the lag.