THE ECONOMETRICS OF MACROECONOMIC MODELLING

# Testing against richer dynamics

In the case of the NPCM, the specification of the econometric model used for testing a substantive hypothesis—forward and lagged endogenous variable— incorporates the alternative hypothesis associated with a mis-specification test (i. e. of residual autocorrelation). Seeing residual correlation as corroborating the theory that agents are acting in accordance with NPCM is invoking a very

strong ceteris paribus clause. Realistically, the underlying cause of the residual correlation may of course be quite different, for example, omitted variables, wrong functional form or, in this case, a certain form of over-differencing. In fact, likely directions for respecification are suggested by pre-existing results from several decades of empirical modelling of inflation dynamics. For example, variables representing capacity utilisation (output-gap and/or unemployment) have a natural role in inflation models: we use the alternative output-gap measure (emugapt). Additional lags in the rate of inflation are also obvious can­didates. As a direct test of this respecification, we move the lagged output-gap (emugapt-i) and the fourth lag of inflation (Apt-4) from the list of instruments used for estimation of (7.14), and include them as explanatory variables in the equation. The results (using 2SLS) are:

Apt = 0.07Apt+i + 0.14u>st + 0.44Apt_ i (0.28) (0.09) (0.14)

+ 0.18 Apt_4 + 0.12 emugapt_i + 0.53 (0.09) (0.05) (0.30)

2SLS, T = 104 (1972(2) to 1998(1)) aIV = 0.28 RSS = 7.52

FAR(i-i)(1, 97) = 2.33[0.13] farch(i-4) (4, 90) = °.80[°.53]

FHETxx (20, 77) = 1.26[0.23]

When compared to (7.14) and (7.15), four results stand out:

1. The estimated coefficient of the forward term Apt+i is reduced by a factor of 10, and becomes insignificant.

2. The diagnostic tests indicate no residual autocorrelation or hetero- skedasticity.

3. The p-value of the Sargan specification test, xt, a, is 0.34, and is evidence that (7.16) effectively represents the predictive power that the set of instruments has about Apt. i0

4. If the residual autocorrelations of the NPCMs above are induced by the forward solution and ‘errors in variables’, there should be a similar auto­correlation process in the residuals of (7.16). Since there is no detectable residual autocorrelation, that interpretation is refuted, supporting instead that the hybrid NPCM is mis-specified.

Finally, after deleting Apt+i from the equation, the model’s interpretation is clear, namely as a conventional dynamic price-setting equation. Indeed, using the framework of Section 7.5.1, the model is seen to correspond to the ICM price equation, with 5{ =0 (and extended with Apt-4 and emugapt-i as explanatory

The full set of instruments is: wst—i, wst—2, Apt—2, Apt—3, Apt—5, and emugapt—2.

variables). We are therefore effectively back to a conventional dynamic markup equation.

In sum, we find that significance testing of the forward term does not sup­port the NPCM for the Euro data. This conclusion is based on the premise that the equation with the forward coefficient is tested within a statistically adequate model, which entails thorough mis-specification testing of the theoretically postulated NPCM, and possible respecification before the test of the forward coefficient is performed. Our results are in accord with Rudd and Whelan (2004), who show that the tests of forward-looking behaviour which Gall and Gertler (1999) and Gall et al. (2001) rely on, have very low power against alternative, but non-nested, backward-looking specifications, and demonstrate that results previously interpreted as evidence for the New Keynesian model are also consistent with a backward-looking Phillips curve. Rudd and Whelan develop alternative, more powerful tests, which exhibit a very limited role for forward-looking expectations. A complementary interpretation follows from a point made by Mavroeidis (2002), namely that the hybrid NPCM suffers from underidentification, and that in empirical applications identification is achieved by confining important explanatory variables to the set of instruments, with mis-specification as a result.

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