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fitting quality. Consequently, the factor analysis and the identification are focused on the two-factor model.

In what concerns to the factor loadings (Figure 3.15a and b), the first factor - less persistent and volatile - is relatively more important for the short end of the curve, while the second assumes that role in the long end of the curve.51

The results already presented illustrate two ways of assessing the identification problem. A third one, as previously mentioned, is to analyse the correlation between the factors and the variables with which they are supposed to be related - the real interest rate and the expected inflation - including the analysis of the leading indicator properties of the second factor concerning the inflation rate.

The comparison between the unobservable factors, on the one hand, and a proxy for the real interest rate and the inflation rate, on the other hand, shows (in Figure 3.16a-d) that the correlation between the factors and the corresponding economic variables is high. In fact, using ex-post real interest rates as proxies for the ex-ante real rates, the correlation coefficients between one-month and three-month real rates, on the one side, and the first factor, on the other side, are around 0.75 and 0.6 respectively in the shorter and in the longer sample.52 Using the identified models, that correlation coefficient decreases to 0.6 and 0.7 in the shorter sample, respectively using the models in (3.55) and (3.56), while

51 Excluding the identified two-factor models for the shorter sample.

52 This finding contrasts with the results in Gerlach (1995) for Germany, between January 1967 and January 1995. However, it is in line with the conclusion of Mishkin (1990b) that US short rates have information content regarding real interest rates.

Term to maturity (in months)

F1 non-id.

F2 non-id. ■

0 0

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