The Stock and Watson (2007) model is a benchmark in forecasting inflation.
According to the Stock and Watson (2007) model, most of the current increase in core PCE price inflation is estimated from stochastic volatility shocks. Nevertheless, the trend of the model (which is its forecast of future inflation) has increased in recent quarters and reached 3.0% in 2022:Q1. Overall, the model suggests upside risks around the Fed staff medium-term forecast.
Why the Stock and Watson (2007) model is relevant
The Stock and Watson (2007) model is a popular model in academic and policy circles. The literature (Stock and Watson (2016)) has shown that its forecast is a hard-to-beat benchmark, despite the relative simplicity of the model.
Policymakers often refer to Stock and Watson (2007) and seem to have in mind its updated predictions when looking ahead. For instance, last week Chicago Fed President Evans referred to the Stock and Watson model in his speech at the 2022 US Monetary Policy Forum, and former Fed Vice Chair Clarida mentioned it as something he used to track (Clarida’s speech was a conversation over lunch at the Monetary Policy Forum so there is no record of it).
Here is what Chicago Fed President Evans said last week referring to the increase in inflation since last year (link to the full speech here): “These swift relative price increases didn’t look monetary in nature. The inflation path certainly didn’t follow the hallmark characteristics of the Friedman–Phelps narrative or many other models in which monetary accommodation slowly generates inflation. This encompasses inflation paths generated by movements along the Phillips curve (including a possible steeper one), excessive money growth, or even an erosion of Fed credibility. Instead, the spike in prices looks more like a volatility shock of the kind in the models of Stock–Watson and Cogley–Sargent. Those statistical models don’t come with economic labels for these shocks, but economic factors that could fall into this category can include the following: an abrupt increase in demand for goods to replace lost consumption of in-person services; an unusually large and swift fiscal response quickly fueling stronger demand for goods; and a sharp collapse of just-in-time supply chains under the weight of this outsized flow of goods.”
Given the renewed attention by policymakers, we have set up the Stock and Watson (2007) model and run it. Please, find below a brief description of the model, the results, and our comment.
The Stock and Watson (2007) model
The Stock and Watson (2007) model is an unobserved component model with stochastic volatility (UC-SV). This class of models are also called “state-space models” or “dynamic factor models”.
In Stock and Watson (2007), inflation (pi(t)) is modeled as a sum of an unobserved trend (tau(t)) plus a noise term (eta(t)). Formally, the model is expressed by:
The model has three key features: (i) inflation is modeled as a univariate process (that is, slack or supply-side shocks are not explicitly modelled and they do not play any role), (ii) the trend component is specified as a random walk so the latest estimated value is also the forecast of the model, and (iii) the variance of the error terms varies over time according to an autoregressive process. The general idea of the model is that periods of relatively low and stable inflation are followed by periods with high volatility. Nevertheless, periods of high volatility do not necessarily translate into a regime-shift if the trend (tau(t)) remains stable.
The model has become very popular and remains a benchmark because it forecasts future inflation (average inflation over 1-3 year horizon) more accurately than a variety of other benchmarks (Stock and Watson (2016)).
Results
We have run the Stock and Watson (2007) model* on core PCE price data (QoQ a.r.). Our sample spans from 1960:Q1 to 2022:Q1 (for the current quarter we have used our nowcast: +5.5% a.r.). The figure below shows the extracted trend (tau(t)) and the 90% confidence intervals.
The model correctly captures the inflationary period (1970s) and the following disinflationary period (1980s). The estimated trend converges around 2 percent in the middle of the 1990s, briefly goes above 2 percent just before the great financial crisis, and falls below 2 percent after 2009.
The model estimates that the unobserved trend has picked up in recent quarters and reached 3.0% in 2022:Q1 (for the record: stopping the estimation in 2021:Q4 results in a trend estimated at 2.7%). The 90% confidence intervals (the gray area in the figure below) are estimated at 1.72 – 4.36.
Note: the figure shows the extracted trend (tau(t)) from the unobserved component model. The Y-axis is expressed in percent. The shadowed area indicates the 90% confidence intervals.
* Following Chan (2013), we have run a version of the unobserved component model of Stock and Watson that produces a smoother version of the estimated trend. The reason is that (as shown by Chan (2013)) this version has a lower root mean squared forecasting error.
Comment
The Stock and Watson (2007) model is a univariate model. As such, the estimated trend depends only on the behavior of core inflation itself. The downside of univariate models is that they are quite sensitive to the incoming data, although in the case of Stock and Watson (2007) the stochastic volatility feature can absorb part of the shocks. In any case, the model information set contains nothing about Covid or the narrative of the incoming data. For this reason, the models results should be interpreted cautiously right now.
In our view and estimates, Chicago Fed President Evans is right when saying that “the spike in prices looks more like a volatility shock of the kind in the models of Stock–Watson and Cogley–Sargent”. However, even net of volatility shocks, the trend of the model has increased notably in recent quarters and it is now at a level comparable to the beginning of the 1990s. For this reason, in our view, the recent increase in inflation cannot be attributed only to volatility shocks. Indeed, the more persistent component signals that inflation might moderate going forward but possibly remain above target. Please note that the model results are very close to the mean of the set of trend models we maintain (see here for latest update) so going forward we will continue to rely on our set of models, although we will run Stock and Watson if needed.
Finally, because the current level of the trend is also the model forecast of future inflation, the results of the model suggest upside risks around the Fed staff forecast (which assumed an underlying trend at 2 percent, as per the December 2021 FOMC minutes).