RDP 9701: Inflation Regimes and Inflation Expectations 4. Empirical Support

Estimation and testing of the models in the previous section pose a serious econometric challenge that is beyond the scope of this paper. Instead, we show that artificial data generated by the basic model of this paper behave in a manner similar to observed inflation, and that this model may explain certain puzzling properties of the observed data. In addition, we show that the model developed here may be able to explain puzzling features of the evidence on long-run inflation expectations.

Despite the fact that this model does not incorporate any serial correlation of inflation within a regime, nor any serial correlation across regimes, it is capable of explaining much of the observed serial correlation of inflation. Over the sample examined by RR, 1954–1993, the Canadian CPI inflation rate has an estimated dominant autoregressive root of about 0.85, and Augmented Dickey-Fuller (ADF) tests cannot reject a unit root at any significance level. Monte Carlo data generated by Model 1 with the parameters in Table 1 for the same number of observations yield a median dominant autoregressive root of about 0.5, and ADF tests reject a unit root at the 5 per cent level only about 45 per cent of the time. If the model is extended to include an autoregressive lag on inflation of 0.7 (the mean of the within-regime autoregressive parameters estimated by RR) and new Monte Carlo data are generated, the median dominant root increases to 0.82 and the power of the 5 per cent ADF test drops to 15 per cent. For comparison, data generated by a simple autoregression with no regime shifts and a lag coefficient of 0.7 yield a median estimated dominant root of 0.66 and the power of the 5 per cent ADF test is 40 per cent.

In addition to explaining the near unit-root behaviour of inflation over long horizons, a model with regime shifts can also explain the apparent stationarity of inflation over certain shorter horizons. Simply put, within regimes inflation is stationary, therefore one ought to be able to reject nonstationarity in a regime that is sufficiently long-lasting. For example, ADF tests on quarterly US inflation reject a unit root between 1954 and 1966 and also between 1984 and 1996. Regimes of this length are plausible for the United States, as RR estimate only a 10 per cent per year probability of a regime shift (q=0.10) with US data.

The asymmetric distribution of future inflation in these models of regime shifts may explain the asymmetric distribution of survey responses on future inflation expectations. Carlson (1975) and Lahiri and Teigland (1987) present evidence that the distribution of 1-year-ahead inflation expectations across survey respondents is usually asymmetrically distributed. Moreover, the direction of the skewness is identical to that predicted by a regime-shift model for the true distribution of future inflation.^[8] When inflation is higher than its historical average, expectations are skewed negatively. When inflation is lower than its historical average, expectations are skewed positively.

Finally, the asymmetric distribution of future inflation may explain the frequently large discrepancies between surveys of inflation expectations and implied inflation expectations in bond yields. For example, in Canada the inflation premium between nominal and indexed bonds was 3 per cent at year-end 1996, while Consensus Economics' (1996) survey of 10-year-ahead inflation expectations was 2 per cent. The regime-shifting models of inflation presented above and calibrated on Canada yield a 10-year-ahead inflation mean of roughly 4 per cent and a mode (average across years) of roughly 3 per cent. However, if the probability of a regime shift were reduced from 30 per cent to 10 per cent per year – possibly reflecting increased credibility of the Bank of Canada's announced inflation target – then the mean 10-year-ahead inflation rate would drop to around 3 per cent and the mode would drop to below 2 per cent. If survey respondents report the most likely outcome, and bondholders care about the average outcome, then the discrepancy between different measures of inflation expectations would be resolved.^[9]

Footnotes

I am unaware of any research on how the distribution of a variable affects the distribution across individuals of forecasts of that variable. Nevertheless, these results are suggestive. [8]

The professional forecasters surveyed by Consensus Economics presumably are judged by clients on the accuracy of their forecasts. I would like to thank Jeff Dominitz for pointing out that forecasters should report the mean of future inflation if the penalty for forecast errors is proportional to the squared error. They should report something between the mean and the mode if the penalty is proportional to the absolute error. They should report the mode if the penalty is constant for all errors greater than a given magnitude and zero otherwise. In practice, forecasters communicate more to their clients than a simple point forecast. It is common to talk of the forecast being the most likely scenario with unequal upside and downside risks, which would imply a forecast that is closer to the mode than the mean. [9]