This is a long, technical/wonkish academic-style post – skip if not interested!
In a recent note (here), Bloomberg U.S. Chief Economist Anna Wong, argues that the recent immigration shock “feels like stagflation”. The claim is based on an FRB-US simulation run by Wong herself in which a shock to the labor force lowers the output gap (on impact) but raises price and wage inflation. In this note, we show that Wong’s results depend on a controversial technical assumption: running FRB-US under the so-called “model-consistent” expectations for price and wage setters, rather than under the standard “VAR-consistent” expectations. When the model is run under more realistic assumptions, the positive supply shock of the labor market generates a slowdown in wage growth, a more intuitive result, consistent with micro101.
If the reader has questions, please direct them to our FRB-US specialist: Tilda Horvath (tilda.horvath@underlyinginflation.com). Tilda has programmed FRB-US at the Board and managed the model for almost 20 years. We remind the reader that we run ad-hoc scenarios using FRB-US free of charge. Do not be shy.
Replicating Wong’s results
Figure 1 shows our replica of Wong’s results. Specifically, we took the current baseline of FRB-US and constructed a scenario by raising the level of the labor force by about 4mln people. As in Wong’s, Figure 1 shows the difference between the baseline and the constructed scenario for the output gap, the unemployment rate, and the ECI. While the trajectory of the labor force shock influences a bit the results, we were able to reproduce Wong’s findings: the output gap falls on-impact but then increases, the unemployment rate does the opposite, and price and wage inflation accelerates.
Ok.. but then, what is the issue? The issue is that Wong obtained her results setting the model expectations to “model-consistent” (or “MC”) for price and wage setters, instead of “VAR-consistent” expectations. As explained in the next section, the main difference between the two expectation regimes is the assumption of “who knows what and when”. Wong’s assumption (“MC” expectations) is that at time “t” financial markets and the wage and price setters know with perfect foresight the size and timing of all future shocks. On the other hand, under “VAR-consistent” expectations, the agents’ information set stops at time “t-1”.
On top of the above, Wong considers the SEP-consistent database as the “FRB-US forecast”. As explained in the past -see here– the publicly available FRB-US dataset -the so-called “SEP-consistent database”- is made-up by the Fed staff to interpolate the latest SEP, and it is really not the “true” model forecast. Indeed, in the publicly available SEP-consistent database the default option is “MC” expectations but as explained below, this is not reasonable when forecasting. This is one of the reasons why taking the publicly available FRB-US database (and setups) as it is might not be a good idea.
Figure 1. Replicating Wong’s results in FRB-US
Note: the figure shows the behavior of the output gap, the unemployment rate, and ECI wage growth following a 4mln shock to the level of the labor force (bottom-right panel). “Hourly compensation” refers to the “Employment Cost Index” (or ECI). The output gap, the unemployment rate, and the ECI wage growth are calculated as the difference between the constructed scenario (4mln shock to the labor force) and the current FRB-US baseline. The y-axis scale is “percent” for all charts, excluding for the labor force for which it is “millions of people”. The ECI wage growth shows the YoY percent change. The scenario was constructed following Wong’s BB note, and assuming “MC” expectations for price and wage setters.
A technical dive into the FRB-US expectations
The role of expectations in FRB-US is crucial. As mentioned above, there are two options in FRB-US: running the model under (i) “VAR-consistent expectations” (or backward looking), and (ii) under “model-consistent (MC) expectations” (or forward looking). The main difference is the modeler’s assumption about the information available to the agents at time “t”. Indeed, one can either assume that (i) all agents are backward-looking, or (ii) they are forward-looking, or (iii) a combination of (i) and (ii) according to the variable/sector of interest. In theory, for some variables (i.e. financial variables) it is reasonable to assume a forward-looking behavior, while for other variables (i.e. real-side variables) it is reasonable to assume a backward-looking behavior.
Not only, but there is an additional technical aspect which is important. When someone runs a forecast from the current quarter to “m” quarters ahead, under “VAR-consistent” expectations it requires an m-quarter simulation. On the other hand, running this m-quarter experiment under “MC” expectations requires extending the simulation period well beyond m quarters of interest. The standard criterion for determining the total length (m+n) of an “MC” simulation is that extending the length by an additional period has negligible effects on the relevant solution values through quarter m. For FRB-US “MC” simulations, the value of n that satisfies these criteria is likely to be at least 120 quarters, subject to the requirement that both fiscal and monetary policy be set in the extension period in a manner consistent with the movement of the extended FRB-US solution toward a steady-state equilibrium.
The main point is that Wong has derived her results by assuming that wage and price setters know everything about the future (and a very distant one in FRB-US.. that is, 120 quarters!). However, when assuming that wage and price setters have limited (or no) information about the future, Wong results do not hold.
Wong’s results under “VAR-consistent” expectations
Under a more realistic expectation generating process, a positive labor supply shock is not stagflationary. Figure 2 shows the results in FRB-US assuming the same shock of Figure 1 but under the standard “VAR-consistent” FRB-US expectations process. Unsurprisingly, a large positive supply shock on the labor market lowers (ECI) wage growth “on impact”, that is for about 8 quarters. This is a more intuitive result, and the opposite of what Wong claims. Eventually, the output gap becomes positive and wage growth recovers following a positive aggregate demand shock.
The reader can now understand why Wong got her results. In fact, under “MC” expectations, at time “t” when the positive supply shock occurs, the (agents in the) model already knows that the output gap will turn and stay positive in the future. Therefore, there is no reason for wage growth to decelerate today; in fact, wage growth can already accelerate today under “MC” expectations in anticipation of the future aggregate demand shock. But again, this result is not driven by the shock itself today. Instead, it is driven by the wage setter expectations component under the “MC” option: the agents in the model “knows everything about the future” and act accordingly today.
Figure 2. Replicating Wong’s shock in FRB-US under “VAR-consistent” expectations
Note: the figure shows the behavior of the output gap, the unemployment rate, and ECI wage growth following a 4mln shock to the level of the labor force (bottom-right panel). “Hourly compensation” refers to the “Employment Cost Index” (or ECI). The output gap, the unemployment rate, and the ECI wage growth are calculated as the difference between the constructed scenario (4mln shock to the labor force) and the current FRB-US baseline. The y-axis scale is “percent” for all charts, excluding for the labor force for which it is “millions of people”. The ECI wage growth shows the YoY percent change. The scenario was constructed assuming “VAR-consistent” expectations for price and wage setters.
Conclusion
Choose wisely what set of assumptions you accept. We stop here because this note is already long enough, but we could provide many more details. Having said so, we have one recommendation to you. Everyone can have an answer on Bloomberg. Everyone can have a chart with two lines and some sensationalistic view on a social media. We are not in that business. Our work is to provide answers under the most plausible assumptions, and we do not have to sell a firm view. We are here to explain in details how models work, and we are basically the only one at this level on the street. We know, it can be tedious, and it requires a huge effort. But we will never work differently. Choose wisely who you listen to.