The cumulative growth gap since January 2011 between the US and Wisconsin coincident indices was 2.2% in December. The forecast indicates a continued widening to 2.8% in six months time.
Figure 1 depicts the log coincident indices for Wisconsin and the US.
Figure 1: Log coincident indices for Wisconsin (blue) and US (gray), and levels implied by leading indices for 2014M06. NBER defined recession dates shaded gray. Source: Philadelphia Fed, NBER, and author’s calculations.
Reader Ed Hanson wonders about the predictive characteristics of the leading indices produced by the Philadelphia Fed. Figure 2 depicts the actual and forecasted six-month growth rates for Wisconsin.
Figure 2: Actual six-month growth rate (non-annualized) in WI coincident index (blue) and corresponding leading index (red). NBER defined recession dates shaded gray. Source: Philadelphia Fed, NBER, and author’s calculations.
A regression of the actual six-month growth rate on the forecasted yields the following results:
Table 1: Unbiasedness test.
Note that the leading index appears to be an unbiased predictor of actual six-month growth rates, since the point estimate of the slope coefficient is 1.001, with a Newey-West robust standard error of 0.058; hence one would not reject a null hypothesis of a unit coefficient. The adjusted R2 is 0.84 — in other words 84% of the variation of the six-month growth rate around the mean is explained by the leading index. Note that this is not a “real time” analysis, as the coincident series are the revised, rather than initial, figures, and one might wish to compare the forecasts to the initial.
The leading index for the United States shares the same characteristics of unbiasedness; the adjusted-R2 is 0.93.
Has the behavior of the Wisconsin index changed over time? The log ratio (WI/US) rose from 1982 to a peak in 2000 before descending. Estimating the relationship between the (log) WI coincident index and the (log) US coincident index using dynamic OLS (6 leads and lags of the first differenced right hand side variable, 2001M01-13M12) and a dummy taking a value of one from 2011M01-2013M12 yields a cointegrating coefficient of 0.507, and the coefficient on the dummy is 0.021, significant at the .0002 level using Newey-West standard errors. Literally interpreted, Wisconsin economic activity is 2% lower than usual, starting from 2011M01.
This is not a conclusive finding; using a different specification, sample period, or estimation method would likely lead to a different finding.
Update, 2/8 noon Pacific: Reader Ed Hanson still contends that Wisconsin economic performance has improved since 2011M01. He writes:
What we mainly disagree with, the Walker policies have began the change back toward superior economic performance. I say it has, and comparing the performance of Wisconsin from 2001 until 2011, with Wisconsin after 2011, supports my position. In addition, Walker policy of reduced taxation, both personal and business, since 2013 will accelerate economic performance.
Since Mr. Hanson is not persuaded by a coefficient on a dummy variable, I have undertaken another analysis, which conditions on US economic activity, and lagged WI economic activity. I estimate a error correction model over the 2001M01-2010M12 period:
Table 2:Error correction model, WI and US economic activity.
Where LCOINWI (LCOINUS) is the log coincident index for Wisconsin (United States), “D” indicates first difference. Note the high adjusted-R2, Q(6) and Q(12) statistics fail to reject the no-serial correlation null, as does the Breusch-Godfrey LM (2 lags) test.
The implied long run cointegrating coefficient is approximately 0.50; that is a 1 percent increase in the US coincident index is associated with a 0.5 percent increase in the Wisconsin index, over the 2001M01-2010M12 period.
I use this error correction model to forecast out of sample (2011M01-2013M12), conditioning on actual US economic activity. The forecast is shown in Figure 3, with plus/minus two standard errors, compared against the actual.
Figure 3: Log actual WI coincident index (blue), forecast (red) and plus/minus two standard errors (pink). Forecast based on error correction model (Table 2). Dashed vertical line at beginning of Walker administration. NBER defined recession dates shaded gray. Source: Philadelphia Fed, NBER and author’s calculations.
Notice that the actual Wisconsin index under-performs the forecasted (what we would call the counterfactual, if the usual economic relationship between the US and WI economies prevailed into 2013) by a significant amount — by up to 2.5% (log terms) earlier in 2013, and 1.9% as of 2013M12. The fact that the blue line (actual) is outside of the plus/minus two standard error bands suggests that the under-performance did not happen by accident, at conventional significance levels.