How much of the US employment shortfall is due to trend factors?
One of the central puzzles following the financial crisis and the ensuing Great Recession has been the sluggish growth in employment during the recovery which began in June 2009, given the growth rate of output (the growth rate of output is understandably low, given our knowledge of recoveries in the wake of balance sheet/financial crises). Our analysis is related to the issue of whether structural unemployment has risen in the wake of the Great Recession.
In a new paper coauthored by Laurent Ferrara and Valérie Mignon, we estimate a log-levels version of Okun’s law, so that we can specify a decomposition of employment between trend and cyclical factors. Following up on intuition laid out here and here, we implement an error correction model with nonlinear short run dynamics. While it is possible to interpret the trend factors as structural in nature, it is also possible to view our trend component in a purely statistical context.
Relying on a non-linear error-correction specification over the 1950-2012 period, we find:
- If one does not account for the long-term relationship between GDP and employment, then we overestimate employment by a substantial amount.
- A standard error-correction model is able to reproduce the general evolution of employment, but underpredicts the decline in employment during the recession, and therefore over-predicts employment during the recovery.
- Using an innovative non-linear smooth transition error-correction model (STECM), we better reproduce stylized facts associated with the business cycle.
- The nonlinear model estimated over the 1950-2007 period produces ex post historical simulation results that indicate employment is still on average 1.05% below its potential level after the recession. Some share of this mis-prediction might be attributable to structural factors.
Predicting Employment using and Error Correction and Differences Model
Assume a long run cointegrating relationship between log private nonfarm payroll employment and log real GDP:
empt = β0 +β1yt
One can estimate this relationship using a first differences specification, a first differences specification with lags, and a (linear) error correction model, over the 1950-2007 period, and then forecast out assuming knowledge of the right hand side variables. The error correction model incorporates one lag of the first differences.
Figure 5 from Chinn, Ferrare and Mignon (2013): Conditional forecasts of log-employment stemming from linear models. Note: Conditional forecasts stemming from the model in differences (red), the model in differences with dynamics (dotted red) and the ECM (blue). Observed values are presented in the dark line.
Notice that neither first differences specifications fit the data very well. While the static first differences specification broadly matches the contours of actual employment, it overpredicts by a wide margin. By contrast, the dynamic first differences specification hits actual by 2012Q3, but missing completely the dip to trough in 2010Q1. The error correction model fits better, but still overpredicts on the order of 3% in log terms.
A Nonlinear in Dynamics Error Correction Model
Given the shortcomings of these linear models, we considered a smooth transition error correction model, wherein the short run dynamics vary depending upon the state of the business cycle (in this case, lagged GDP growth).
Where LEMP is log private employment, LGDP log real GDP, G denotes the transition function, γ is the slope parameter that determines the smoothness of the transition from one regime to the other, c is the threshold parameter, and Z denotes the transition variable. The smooth transition function, bounded between 0 and 1, takes a logistic form given by:
G(c, γ, Zt) = [1 + exp( - γ(Z t - c))]-1
Zt = 0.5 × (Δ LGDPt-2 + Δ LGDPt-3)
Details and references for the procedure are provided in this post. The results of estimating this over the 1950-2007 period are given y:
Most of the time, the economy is in regime 1, with regime 2 in effect usually right at the end of a recession. Estimating this model out of sample yields the following forecasts.
Figure 6: Conditional forecasts of log-employment stemming from linear and non-linear error-correction models. Note: Conditional forecasts stemming from the linear ECM (blue) and the non-linear ECM (green). Observed values are presented in the dark line.
The extent of mis-prediction is now much reduced. Employment is over-predicted by only about 1%.
One is tempted to conclude that the gap represents the extent of employment that is reduced by structural factors. One could do that, although the first point to recall is that the mis-prediction incorporates both structural factors (say demographic trends, skills mismatch, other policies that affect the benefit of work versus leisure) as well as model uncertainty.
In order to try to determine the source of the 1% overprediction, we estimated the nonlinear model over the entire 1950-2012Q3 sample, and then predicted employment. In this in-sample assessment, the over-prediction declines to 0.6%, suggesting that at least some noticeable share (perhaps around half?) of the 1% out-of-sample over-prediction is due to factors other than a rise in structural factors. However, this conjecture awaits further investigation.
Note that we have allowed only nonlinearities in short run dynamics. We have retained a constant employment-output elasticity over the long run. Had we allowed for time variation in the long run relationship, we might very well have obtained different results. However, the theory to validate the application of the smooth transition methods to integrated variables doesn’t yet exist, to our knowledge.