# Another Attempt At Estimating September Payrolls

### Another Attempt At Estimating September Payrolls

Today’s September employment report from the Labor Department has been postponed and rescheduled (maybe) for release down the road. The source of the delay, of course, is the ongoing shutdown of the federal government, courtesy of the budget battle in Congress. As a result, the official data remains a mystery at the moment, but that doesn’t stop us from considering the published numbers from other sources in an effort to develop some perspective on last month’s labor market profile. For instance, this week’s updates on the manufacturing and services sectors from the Institute for Supply Management offer useful proxies for inferring the hard data on payrolls. In particular, the employment components in the ISM Manufacturing and Non-Manufacturing reports are especially valuable.

Consider how the two ISM employment indexes compare with the monthly percentage changes in private non-farm payrolls in recent history, as shown in the first chart below. Visual inspection suggests there’s a relatively tight connection between this trio. Several statistical tests also tell us there’s a fairly close link here. For example, the multiple R-squared measure for all three data sets is a high 0.76 (1.0 would be a perfect fit) in the monthly numbers going back to 1997, which is the earliest date for the ISM non-manufacturing employment series.

The relationship suggests that we can use the two data points in the September ISM reports to estimate what today’s private payrolls release would have revealed if it had been published. Let’s create a simple model based on regressing the monthly percentage changes in private employment against the monthly index values of the two ISM employment series, which together represent a guesstimate of the trend in the nation’s labor market. Based on the historical relationship between all three series, the September ISM employment numbers imply that private payrolls increased 175,000, or moderately higher than the previously reported 152,000 advance for August.

All forecasts are wrong, of course, but some are useful, as the saying goes. With that in mind, let’s review the fitted values in our model, which we’ll call R-2 (a regression model with 2 variables for predicting private payrolls). Not surprisingly, the R-2 model falls short of perfection. But a crucial test for any prediction model is measuring how the residuals—the errors—stack up through history. Assuming we used this model in past years to predict private payrolls, here’s how R-2 fared relative to the actual data that was reported each month. Clearly, the model suffers errors, as every forecasting model does. But note too that the errors tend to bounce around the zero mark with a fair amount of randomness (a zero value would indicate that the prediction matches the actual data). The random behavior of the errors is an encouraging sign for thinking that the R-2 model, through time, will provide a relatively reliable guide for projecting the monthly change in private payrolls. By contrast, if the errors had a history of trending, up or down, that would be a warning that our model was deeply flawed. But that’s not the case here and so we have what appears to be a fairly useful model for anticipating private payrolls.

On that note, I’ll be adding R-2 to the payrolls previews that make monthly appearances on The Capital Spectator, including the latest edition in yesterday’s post. As for estimating when the government shutdown will end, well, that’s one of those mysteries that just can’t be modeled. Why? The key variable—politics—is hopelessly inscrutable.

This piece is cross-posted from The Capital Spectator with permission.