zone -many
Ifo WES 0.52 0.77 0.26 0.26 0.48 0.40
other surveys 0.49 - 0.43 - - 0.43
RE approach 0.62 0.65 0.67 0.52 0.70 0.61
Notes: As some of the papers cited in table 2.13 of appendix F only report standard errors for the deep parameters of the Phillips curve (β, θ, ω), but not for γf, we resorted to a non-parametric statistical significance test, the Wilcoxon rank-sum test, for testing whether our γf’s are significantly lower than those in the RE (= rational expectations) literature. The results, which are available from the authors upon request, show that the null hypothesis that the median of the RE estimates is lower than our estimates can be rejected at the 5% level for all countries except France.
Table 2.6: Summary of estimates for γf
the beginning of the 1990s whereas most of the other studies begin in the 1960s or 1970s. Most of the countries in our sample, however, underwent one or even more significant changes in their monetary policy strategy. As the monetary policy regime that is in force plays a crucial role for the estimated behavioral parameters, it is likely that these models suffer from instabilities that cannot be accounted for by GMM techniques. Unfortunately, stability of the results is rarely discussed in these papers.
Note, however, that a shorter sample size cannot explain why γf in these studies tends to be systematically higher than in our study. A further argument against this explanation are the results of other studies listed in table 2.12 using US survey data. While their samples range from the 1960s to 1999 or later, which roughly corresponds to to the time span covered by most rational expectations studies, the average point estimates for γf are close to ours.
Second, the above findings are consistent with some recent papers questioning the appropriateness of the rational expectations approach. The Phillips curve model is typically estimated by replacing expectations with actual realizations and by deriving orthogonality conditions that may be used to estimate the parameters of the model with GMM. These moment conditions are derived on the assumption that expectations are rational, i.e. that the expectation-induced ‘errors in variables’
must be orthogonal to the information set available to the agents at the time the expectations are formed. Rudd and Whelan (2005), however, argue that GMM estimates may overstate the degree of forward-looking behavior if the instrument set includes variables that directly cause inflation but are omitted from the hybrid model specification. Thus, the error term of the estimation equation is no longer a pure rational expectations error. As a consequence estimates for γf will be biased upwards as long as both, πt+1 and its instruments, are correlated with the omitted variable. According to Mavroeidis (2005) the mis-specification of the Phillips curve
model can alternatively be interpreted as a failure of rationality. Irrespective of the source for the violation of the orthogonality conditions, he shows that the model is weakly identified, which introduces a bias in the GMM estimation in favor of a hybrid specification with apparently dominant forward-looking behavior.
The use of survey data avoids this problem as there is no need to specify the expectation formation process and expectations can be taken as exogenous.
Section 2.2.2 shows in detail that a Phillips curve relationship can be derived for a wide range of expectations formation processes. The only assumption that is made, is that the law of iterated expectations holds. Rational expectations can be considered as a special case. According to this theoretical model, which serves as a basis for the econometric part of the paper, agents are considered to be forward-looking if they do not simply extrapolate past inflation rates into the future, but use additional information when they reset prices. This does not necessarily mean that expectations have to be rational. They can be anything else except purely backward-looking (i.e. Etπt+1 = πt−1), which would lead to perfect multicollinearity, and hence to problems in the OLS estimation. In section 2.3.1 we showed that inflation expectations from the CESifo WES are far from being rational. In addition, we ran some simple regressions of expected inflation on past inflation, which indicate that survey expectations contain information way beyond past inflation rates.12 In section 2.4 the behavior of forward-looking agents is then approximated by the survey expectations of the CESifo WES. Under the assumption that these are an accurate measure of ‘true’ expectations, we estimated the share of forward-looking agents using the subjective expectations HNKPC and showed that there is a role for forward-looking behavior. Given the theoretical set-up this result holds irrespective of the information content of the survey expectations.
The advantage of the survey data approach is that its results are more reliable than those obtained from the GMM approach. On the one hand, there is no need for instruments. Appendix 2.D shows at length that the estimations of the HNKPC do not suffer from a violation of the OLS assumptions. Ruling out weak instruments we re–estimate the Phillips Curve by TSLS and find that, in particular, endogeneity of the regressors can be rejected. On the other hand, the OLS estimation has the advantage that the results are robust despite the relatively short sample size. A CUSUM of squares test, which is presented in appendix 2.E, yields satisfactory results for the stability of the estimated parameters. It is well known that the small sample properties of GMM estimations are very poor, meaning that estimators are often found to be biased, widely dispersed and sensitive to the normalization of the orthogonality conditions as well as to the choice of the instruments (see for
12Specifically, we find thatπt−1only explains between 16% (for Germany) and 56% (for France) of the variation of expectations ¯Ftπt+2. These results are not shown in the paper, but available from the authors upon request
why we did not apply the rational expectations GMM approach to a shorter sample (starting for example in 1993) in order to find out whether the identified gap between the estimates for γf are due to the sample size or due to the proxy for inflation expectations and the related estimation methodology.