Canzoneri, Cumby, and Diba (2007) argue that model-generated and ex-post observed rates are generally uncorrelated and move into opposite directions in response to a change in the monetary policy instrument. Assuming that the way the household forms expectations does not change over time (i.e. estimate one VAR over the entire sample), the size and the sign of the correlation coefficient should not change between subsamples.8 As this section shows, this is not the case. The moderate correlation for nominal rates and the low correlation for real rates estimated over the full sample horizon could be due to averaging. For this reason, the following step splits the sample into two subsamples. The first comprises an episode called the Great Inflationwhereas the second subsample looks at the last 30 years. It includes the so-calledGreat Moderation, the recent financial crisis and beyond. Differences over the sample horizon could
8Looking at smaller subsamples means that the series, estimated using the full-sample VAR is split at several points and compared with observed rates within this period.
1.4 The Importance of the Sample Horizon | 21
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 -0.15
-0.1 -0.05 0 0.05
0.1 Real Fuhrer
Real Federal Funds Rate
1970 1980 1990 2000 2010
-0.2 -0.15 -0.1 -0.05 0 0.05
1970 1980 1990 2000 2010
-0.05 0 0.05 0.1
Real Abel Real Federal Funds Rate
1970 1980 1990 2000 2010
-0.15 -0.1 -0.05 0 0.05
Figure 1.3.Model-Implied Rates vs. Ex-Post Observed Rates (annualized)
Notes:The figure’s first column shows the development of ex-post observed real interest rates (dashed) compared to rates predicted from the VAR and the DSGE model (solid) for the Fuhrer (2000) and Abel(1990,1999) preference specification. The second column calculates the spread, i.e. the difference between model rate and the data and sets and highlights period when the US has been in a recession as classified by the NBER.
be either due to a change in the way agents form expectations or because the macroeconomic environment has changed tremendously. This chapter focuses on the later and thus assumes that the estimated coefficients of the VAR are time-constant. The following subsections motivate and discuss the choice of these subsamples.
1.4.1 Great Inflation
Meltzer (2005) describes the high inflation period from the mid-1960’s to the mid-1980’s with inflation rates varying between two and 15 percent as the []...“the climactic monetary event of the last part of the 20th century.” Siegel (1994) even calls it “[]...the greatest failure of American macroeconomic policy in the postwar period”. During this period, the Bretton-Woods system which had been established during World War II collapsed, two oil-price shocks caused severe damage and the economy suffered from four recessions. In addition, macroeconomic theory and the way policy makers thought about monetary policy started to change as a consequence of outcomes of this episode. Finally, this period provides the biggest spread between model and
data, as the right half of Figure 1.2 shows. Furthermore, the spread seems to be positive on average, whereas it appears to be negative on average for the later part of the sample.
The following Table 1.4 displays sample moments and correlation from 1969 to 1982. Model Table 1.4.Ex-post Observed and Model-Implied Nominal Interest Rates, 1969-1982
Time period: 1969-01-01 to 1982-10-01 Rates computed from models
Data CRRA Fuhrer (2000) Abel (1999)
Real Rates
Mean 0.016 0.0097 0.0015 0.0013
St. deviation 0.032 0.031 0.037 0.028
Min -0.035 -0.052 -0.13 -0.062
Max 0.11 0.06 0.065 0.045
corr(Data,Model) 1 0.0061 -0.05 0.0072
Nominal Rates
Mean 0.087 0.078 0.07 0.069
St. deviation 0.039 0.024 0.034 0.021
Min 0.035 0.0076 -0.035 0.0019
Max 0.18 0.13 0.14 0.11
corr(Data,Model) 1 -0.41 -0.24 -0.41
and data are far from being positively correlated as the correlation coefficients are close to zero for real and negative, in the range of -0.30 to -0.13 for nominal rates. Upon other explanations as e.g. the high inflation period, the Federal Reserve’s behavior in response to shocks could be an explanation for the switch of the sign of the correlation coefficient. If agents had been surprised a lot by the Fed’s policy but their expectations had been based on a version of the models revisited above, the huge spread between model and data appears to be quite natural.
The next section will cast a closer look upon that hypothesis using narrative policy evidence provided by Romer and Romer (2004).
1.4.2 Great Moderation and Beyond
The second subsample includes the years from 1983 to 2017. It comprises the years of theGreat Moderation, a term coined by Stock and Watson (2002) and former Federal Reserve chairman Ben Bernanke.9 This period has seen a reduction in the volatility of Real GDP and inflation relative to the 1970’s as Table 1.1 showed. Moreover, both nominal interest and real rates and inflation exhibited some trend decline. Monetary policy fought high inflation rates by respond-ing aggressively to inflationary shocks (as argued in Clarida, Galí, and Gertler (2000), Boivin
9Bernanke referred to this in a speech at the meeting of the Eastern Economic Association, Washington, DC on February 20, 2004.
1.4 The Importance of the Sample Horizon | 23
and Giannoni (2006) or Lubik and Schorfheide (2004) among others). The years of the finan-cial crisis orGreat Recessionare included into the subsample on purpose, as both interest rates and consumption follow a similar trend decrease since the 1980’s and are thus rather positively correlated. Between 2008 to 2015, when the effective Federal Funds rate hit the ZLB, i.e. is lower than 0.25%, the shadow rate calculated from the model by Wu and Xia (2016) has been used instead of the Federal Funds rate. Furthermore, Figure 1.2 supports the argument to dis-tinguish these two episodes as mean and variance of the spread are smaller on average over the last 30 years. In contrast to the first subsample, the second one shows a strong positive
Table 1.5.Ex-post Observed and Model-Implied Nominal Interest Rates, 1983-2017
Time period: 1983-01-01 to 2017-01-01 Rates computed from models
Data CRRA Fuhrer (2000) Abel (1999)
Real Rates
Mean 0.0092 0.0035 -0.00056 -0.0041
St. deviation 0.031 0.019 0.022 0.017
Min -0.053 -0.07 -0.077 -0.071
Max 0.08 0.048 0.058 0.038
corr(Data,Model) 1 0.38 0.2 0.38
Nominal Rates
Mean 0.036 0.03 0.026 0.022
St. deviation 0.034 0.025 0.025 0.023
Min -0.029 -0.072 -0.05 -0.073
Max 0.11 0.091 0.1 0.081
corr(Data,Model) 1 0.62 0.49 0.63
correlation that ranges from 0.5 to 0.6 for nominal and a moderate one between 0.2 and 0.35 for real rates. Table 1.5 displays the respective results.
1.4.3 What’s driving the correlation
I conclude this section with an alternative way to think about the surprisingly distinct results for correlation coefficients between model and data at different points in time. For a given sample or subsample period, the calculated correlations coefficients report the ratio of the model’s and the data’s covariance over the product of the sample variances. In any case, this involves some sort of averaging over theentire(sub)sample. Using a correlation coefficient, augmented with a weighted, two-sided rolling window, reveals that the correlation centered around a specific date or point is far from being always negative in earlier and always positive in later years.10 Figure 1.4 depicts this sequence of correlations within an eight quarter window, and illustrates
10Appendix A.3 provides the formula used to obtain smoothed correlation coefficients.
1970 1980 1990 2000 2010 -0.04
-0.02 0 0.02 0.04 0.06
1970 1980 1990 2000 2010
-0.05 0 0.05
Level
1970 1980 1990 2000 2010
-1 -0.5 0 0.5
1970 1980 1990 2000 2010
-0.5 0 0.5
Correlation
Figure 1.4.Smooth Correlation and Smooth Mean of Interest Rate and Model Rate
Notes:The figure shows the smoothed correlation and smoothed mean of observed interest- and model-implied rates using a eight-year rolling window. Appendix A.3 provides the exact formulas.
that the rolling-window correlation is much more volatile than expected. Furthermore, big re-versals of the series of correlation coefficients seems to take place around NBER recession dates which underlines the hypothesis that the business cycle plays an important role in explaining the divergence of model and data. In addition, the sample average over the rolling-window cor-relation coefficients does not coincide with the coefficients calculated in Tables 1.2, 1.4 or 1.5.
To understand, where the volatility, inherent in Figure 1.4 comes from, I cast a closer look on the smoothed, weighted means, used to calculate the rolling correlation. A similar pattern as in Figure 1.2 emerges. The model is not too bad in capturing the long-term trend movements, but it fails at predicting business cycle movements.
Using a standard HP-filtering approach to separate trend and cyclical component of both model-implied and observed rates, reveals that the cyclical components of the model and the data are negatively correlated. From the Consumption Euler equation we know that cyclical components should be highly positively correlated. In contrast to that, the size of the correlation coefficient for the trend components is close to the one calculated in the replication of Canzoneri, Cumby, and Diba (2007)’s results. Moreover, the cyclical component of the spread between model and data is negatively correlated with the cyclical component of both real and nominal interest rates. This confirms the result of Canzoneri, Cumby, and Diba (2007) that monetary expansions over the business cycle are associated with a wider discrepancy between model and data. The following table visualizes this result using the HP-Filter and the Baxter-King-Filter.
Results for the later are robust to findings using the HP-Filter. The filtered data comprises the