Does high unemployment mean that there’s nothing to worry about in terms of inflation?

Since I’ll be trying to answer this question quantitatively using some equations, I’ll begin with some notation. Let u_t denote the unemployment rate as of the end of a particular quarter t; currently u_t = 9.8 for t corresponding to 2009:Q3. I’ll presume that the question we’re interested in is what sort of inflation rate we should expect over the next two years, and so I’ll let π_t+8 denote the average inflation rate (quoted at an annual rate) over the next 8 quarters as measured by the price index for personal consumption expenditures (data from FRED). Of course at the current time (t = 2009:Q3) we don’t yet know what the value of π_t+8 is going to be– that’s what we’re trying to predict.

One way to come up with a prediction is to look at a regression of the historical values of π_t+8 that we currently know (that is, for t = 1948:Q1 through 2007:Q2) on the historical values of u_t. The results from this regression (with Newey-West standard errors in parentheses) and scatterplot of the raw data are given below.

Each circle corresponds to a particular quarter t between 1948:Q1 and 2007:Q2. Horizontal axis: value of unemployment rate in last month of quarter t. Vertical axis: average PCE inflation rate for two years that came subsequent to quarter t. Upward sloping line is the estimated regression relation.

This is of course a version of the famous Phillips Curve, according to which higher rates of unemployment are supposed to be associated with lower rates of inflation. But there’s just one problem– whereas the Phillips Curve is supposed to slope down, the relation we just estimated slopes up. If a given quarter’s unemployment rate was above average, it’s likely that the subsequent inflation rate was above average as well.

The traditional interpretation of this seemingly anomalous result is that there’s another important component of the Phillips relation that was left out of the above regression, which is expectations of inflation. Particularly for the observations from the 1970s and 1980s, people at the time were expecting inflation to remain high. The traditional argument is that if we could add inflationary expectations as a shift variable to the regression, we would see the anticipated negative relation between unemployment and inflation.

One simple way to try to do this is to add lagged values of inflation to the above relation, that is, include π_t, π_t-1, and earlier values that would have been known as of quarter t, and see what the contribution of unemployment is to that modified regression. Results of that regression when we add the previous 3 years of inflation observations are given below. Note I haven’t reported the individual estimated coefficients on π_t, π_t-1, and π_t-11 because that exceeds our quota for how many numbers can be reported in an Econbrowser entry.

If you allow for the possibility of changing inflation expectations in this way, the result is that the coefficient on unemployment switches from positive to negative, and the negative coefficient is quite statistically significant. In other words, if we’re going to forecast inflation over the next two years on the basis of what inflation has been over the last three years along with the current unemployment rate, the unemployment rate would enter that forecast with a negative sign– higher unemployment causes us to predict lower inflation.

The forecasts of the above regression (in blue) are compared with the actual values (in black) in the top panel below. We don’t know what the actual values after 2007:Q2 are going to turn out to be yet. But the forecast of the model for the average inflation rate between 2009:Q4 and 2011:Q4 is -0.5%.

Top panel: Black line is the value of subsequent average 2-year inflation rate (π_t+8) corresponding to each indicated date t Blue line is the predicted value from the dynamic regression for each indicated date t. Bottom panel: unemployment rate as of last month of indicated quarter t.

Does that mean that deflation is the best forecast given the current high level of unemployment and the recent moderate behavior of inflation? It’s certainly not a crazy forecast, given the historical correlations. But the critical question would seem to be whether the contribution of inflationary expectations in the current situation is adequately captured by the recent observed behavior of π_t.

If for further evidence on inflationary expectations you looked at the gap in yields between nominal Treasuries and TIPS, you’d say inflation expectations remain quite low– currently the 10-year spread corresponds to anu average annual inflation rate under 2% for the next decade.

On the other hand, if your preferred indicator is dollar commodity prices and the sinking exchange rate, the claim that inflationary expectations will remain low is less compelling.

But regardless of where you stand on that question, I believe the Federal Reserve is correct in thinking that high levels of unemployment are a factor that will put downward pressure on inflation over the next two years. The question is how big a pull the dollar and commodities could prove to be in the other direction.

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