Most economists are projecting a slow recovery in terms of employment. What do historical correlations imply?

In order to investigate this question, I examine the relationship between GDP and nonfarm payroll employment over the 1986-2009 period, which encompasses the “Great Moderation”. Figure 1 illustrates the log GDP and log nonfarm payroll employment series.

Figure 1: Log nonfarm payroll employment (blue, left scale) and log real GDP (red, right scale). NBER defined recession dates shaded gray, assumes last recession ends at 2009Q2. Source: BEA 2009Q3 advance release, and BLS via FREDII.

I estimate the following error correction specification, which includes 4 lags of first differences, using OLS:

Δ nfp_t = 0.54 – 0.069 nfp_t-1 + 0.026 y _t-1 + 0.60 Δ nfp_t-1 + 0.173 Δ y _t-1 + … + 0.00046 time – 0.0000017 time ²

Adj. R² = 0.85 SER = 0.0018, n = 95, DW = 2.02. Breusch-Godfrey LM test, 2 lags, F = 1.84 (p-val = 0.16). HAC robust standard errors. (Nonsignificant coefficients suppressed.)

The long run elasticity of employment with respect to GDP is 0.37, while the short run elasticity is 0.17.

I conduct dynamic simulations (using the regression estimated over the entire sample) for the five years after each recession: 1991Q2-1996Q1, 2002Q1-2006Q4. I also conduct a dynamic forecast for 2009Q3-2010Q4, using the WSJ October mean forecast for GDP growth over that period (discussed in this post) as the right hand side variable.

The results are shown in Figure 2:

Figure 2: Log nonfarm payroll employment (blue) and dynamic simulations from error correction model (red, green, purple). Shaded regions denote forecasting periods. Source: BLS via FREDII, and author’s calculations.

The dynamic simulations initially underpredict nonfarm payroll employment, before overshooting (in the 1990’s) and essentially being on target (in the 2000’s). What does the model imply for the trajectory of employment going forward? The dynamic simulation for the 2009Q3 through 2010Q4 period is shown in Figure 3 (with employment expressed in levels, instead of logs).

Figure 3: Nonfarm payroll employment, SA, in thousands (blue) and dynamic forecast from error correction model (purple), and plus/minus two standard errors (gray lines). WSJ forecast for October 2010 (teal square). Shaded regions denote forecasting periods. Source: BLS via FREDII, WSJ October survey, and author’s calculations.

(Note: for sticklers out there — e.g., juan in comments to this post — what I am conducting here for the 2009Q3-10Q4 period is a conditional forecast, since I am taking the GDP path forecasted by the WSJ survey as given).

I calculate the WSJ forecast for employment by adding the October mean prediction of seventeen thousand per month net job creation to the 2009Q3 figure (literally, this forecast is for October 2010, and should be 17,000 × 12 added to the October employment figure).

Hence, if historical correlations persist, then nonfarm payroll employment will continue to decline through 2010Q2. However, given the imprecision of the estimates, nonfarm payroll employment could begin rising as early as 2010Q2 (the upper gray line).

Of course, not only is there sampling uncertainty; there’s also uncertainty regarding the true model. I’ve imposed cointegration in the estimation procedure (and according to the Johansen maximum likelihood procedure, one can reject the null hypothesis of no cointegration at the 20% level, allowing for deterministic trends in the data). But one could drop that assumption, and assume a relationship in first differences. I estimate:

Δ nfp _t = -0.001 + + 0.687 Δ nfp _t-1 + 0.210 Δ y _t + 0.113 Δ y _t-1

Adj. R² = 0.89 SER = 0.0015, n = 95, DW = 2.05.

Breusch-Godfrey LM test, 2 lags, F = 0.18 (p-val = 0.83). HAC robust standard errors.

The adjusted R² statistic is slightly higher in this ARMAX specification, but of course R² shouldn’t be the key determinant of whether one specification is to be preferred over another. In fact, one might wish to impose the long run cointegrating relationship especially if longer horizon prediction is of central import. Hence, I compare the two (conditional) forecasts in Figure 4.

Figure 4: Nonfarm payroll employment, SA, in thousands, (blue), dynamic forecast from error correction model (purple), dynamic forecast from first differences specification (light green), and from error correction model estimated over 1967Q1-09Q3 period (salmon). WSJ forecast for October 2010 (teal square). Shaded regions denote forecasting periods. Source: BLS via FREDII, WSJ October survey, and author’s calculations.

In this case, job losses taper off, and net job creation occurs in 2009Q3. Or, it could be that the error correction model is correct (cointegration between GDP and employment holds), but the recovery will be more akin to that of the 1970’s and early 1980’s, because of the depth of the downturn. That specification (which would not fit well for the past two recoveries) yields the salmon colored line in Figure 4, and predicts strong job creation in 2009Q2.

James Hamilton says recent output indicators (as of 10/18) are not consistent with a jobless recovery. Paul Ashworth says manufacturing employment has may have [correction added 11/4, 8:45am] already “stabilized”, while Robert Gordon predicts a resumption of employment growth in 2010Q1. David Altig at Macroblog and Mary Daly, Bart Hobijn, Joyce Kwok at SF Fed enumerate the reasons for a slow start in employment growth.

Last 5 posts by Menzie Chinn

• Teaching Macro, after the Great Recession - December 17th, 2009
• How High Do Income Elasticities Have to Be to Explain the Recent Import Drop-off? - December 15th, 2009
• Employment Bounceback? - December 9th, 2009
• Exchange Rate Policies - December 8th, 2009
• The Employment Situation in Graphs - December 4th, 2009