RDP 2016-08: The Slowdown in US Productivity Growth: Breaks and Beliefs Appendix F: Including Multiple Observed Wage Series in Estimation

Our baseline model includes a single observed wage series – hourly compensation in the total economy. In contrast, Justiniano et al (2013) (whose approach we follow closely) use an additional wage series – average hourly earnings of production and non-supervisory employees – and include measurement error to account for the observed differences between the two series. When we estimate our model using this series we continue to find strong evidence of a break in steady-state productivity growth, and of a substantial gap between the break occurring and agents' expectations adjusting. However, the size of the break is somewhat larger, and it occurs around 10 years later, than in our baseline model. In this appendix, we explain our decision to include only a single observed wage series.

Over our estimation sample, the mean of the two wage series is substantially different.^[17] The mean of the hourly compensation series is 1.25 per cent in quarterly terms compared to 1.05 per cent for the hourly earnings series. The differences are even more striking after accounting for inflation – the earnings data imply that real wages did not increase at all between 1973 and 1996, while according to the compensation series, real wages increased by around 25 per cent.

Including the earnings series as an additional observable variable alters the estimation results in three ways. First, as Justiniano et al (2013) note, it reduces the estimated standard deviation of the model's wage mark-up shocks, implying a smaller trade-off between stabilising inflation and stabilising the output gap. Second, it reduces the estimated inflation target. In our baseline model, the mean of the estimated inflation target is 0.63 per cent in quarterly terms. When we include earnings as an observable variable this parameter decreases to 0.28 per cent.

To understand why the inclusion of earnings lowers the estimated inflation target, consider the following decomposition of the growth of nominal wages:

where is the growth rate of nominal wages, is the steady-state growth rate of real wages, is the steady-state inflation target, is the growth rate of the deviation of nominal wages from their steady state. A lower estimated inflation target allows the model to match the low observed growth rate of hourly earnings with smaller deviations of nominal wage growth from its steady state.^[18]

The third way in which including the earnings series as an additional observable variable affects the result is by shifting the estimated date of the break in steady-state TFP growth from the early 1970s to the early 1980s. This shift helps the model to match the observed path of real earnings which, after stagnating during the 1970s, decreased during the 1980s.

We find the results for the model that does not include the earnings series as an observable variable to be more plausible. Taken literally, the model that includes earnings implies that the Federal Reserve has an inflation target of just 1 per cent in annualised terms and that inflation has been above target for almost the entire estimation sample, including for much of the period since 2008. This is at odds with most descriptions of Federal Reserve policy over recent decades. The date of the break in steady-state productivity growth in the model that includes earnings is also difficult to reconcile with the observed behaviour of productivity. Moreover, as Champagne et al (2016) discuss, the earnings measure restricts coverage to a particular group of workers whose average earnings have grown less than those of the rest of the US workforce. It therefore may be an undesirable series to use to uncover trends in long-run growth.

Footnotes

Champagne, Kurmann and Stewart (2016) discuss the conceptual differences between alternative US wage measures. [17]

Of course, this also implies larger deviations of inflation from its steady state. However, because of the persistence of the model's inflation target shock, the model requires relatively small shocks to achieve this path of inflation. [18]