## Saturday, March 24, 2012

### What is with inflation expectations? Analysis from Cleveland Fed Data

After working with TIPS data in a previous post, I became more interested in the relationship between inflation expectations and actual inflation over time.  Generally, as per a paper by Mankiw, Reis, and Wolfers, inflation expectations can be highly contentious, with uncertainty among Economists especially high in times of crisis.  However, even though the data suggests that inflation expectation are well correlated with past inflation, the hypothesis of rational expectations and inflation predictions is a bit more uncertain.  In the Mankiw et al. study, the short term predictions of the Michigan, Livingston, and Survey of Professional Forecasters seemed reasonably accurate; how does this accuracy carry over to longer term measures of inflation expectation?

However, since the TIPS data does not go back very far, I used the Cleveland Fed's inflation expectation data instead.  And as per some comparative analysis between the two measures, the Cleveland Fed data can be more descriptive in times of major change, which is when the stability of expectations is the most important.  From the CPI data, I calculated the actual inflation over the future timeframe of the expectation, and then associated this inflation rate with each month's inflation expectation data starting from January 1982.  Thus, for the 5-Year inflation expectation data for January 1982, the actual inflation was the average annual inflation from January 1982 to December 1986.  These two numbers formed a point.  I then took 60 of these points (five years), and used them to calculate a Pearson's r-value, a measure of the correlation between the two values.  For example, the set of data beginning with a point in January 1982 includes the inflation data from December 1992 to make the last calculation for actual inflation.  The movements of the different correlations are plotted below:

What is immediately apparent is that the stability of the relationship changes with time.  During the second half of the 80's, expectations matched reality quite well, with an r-value of over 0.9 for the 5 year expectation data.  This seems to match the rational expectations proposition that the expectation should be the reality.  However, beginning with the 90's, the correlation between inflation expectations and actual inflation became more negative.  What is striking is that the correlation kept on going down, reaching almost -0.8 with the 5 year expectation.  The correlation is consistent with the r value of about -0.73 with the TIPS data, lending credibility to the fact that Cleveland Fed predictions are theoretically robust.

What is more interesting than the correlations are the slopes; an increase in expected inflation predicts how much of an increase in actual inflation over the future period?  The data is graphed below.  A value of 1 means that for every percentage point increase in inflation expectations in a period, the actual inflation in the corresponding term is 1 percentage point higher.

Before looking at the actual numbers, what should we expect the slope to be?  In a world of perfect rational expectations, in which $\pi_t = \pi_{t-1}^{e} + \epsilon$, the slope should be one.  Although there may be error, the expectation should, on average, match reality.  In the world of an inflation targeting central bank (with or without rational expectations), the slope should be 0, as actual inflation should always gravitate towards a constant.  This analysis of central banks is supported by comparisons between US (non-inflation targeting) and UK and Swedish (inflation targeting) central banks.  Below are both the time series of the slopes, as well as box and whisker plots showing the distributions of the slopes.

As can be seen from the time series, the slopes don't stay constant.  Rather, they jump around, with the 1-Year slope value substantially more volatile than the 5 or 10 year slopes.  In spite of this, the median of the slopes do lie around zero.  However, their distributions are skewed right, with the outliers mostly coming from the mid 1980's to the early 1990's time period, which was the time after the brunt of the Volcker disinflation.  The amazing convergence of measures at that time suggest it has something to do with people adjusting to a new monetary regime.  It is as if, in the transition to the fight against inflation, people were able to accurately predict the new stable regime, creating the high correlation as people lowered their expectations of inflation.  Later, as the regime became stable, the correlation became weaker as noise gained a proportionally larger effect.

But then what explains the negative slopes in more recent times?  One interpretation is that they're statistical anomalies: the 1 year data goes much farther and, while it does have a few blips into negative slope, they revert back to mildly positive relatively quickly.  Given this volatility, we will have to wait for more data to try to evaluate the impact of the regime on inflation and their expectations.