THE ECONOMETRICS OF MACROECONOMIC MODELLING

The New Keynesian Phillips curve

Hitherto, we have considered, models that have a unique backward solu­tion, given a set of initial conditions. Even though individual variables may be dominated, by unit roots, models defined in terms of differences and cointegration relationships are also asymptotically stable. Models with, forward-looking expectations are not contained by this framework. Recently a coherent theory of price-setting with rational expectations has gained in popularity. In this chapter, we give an appraisal of the New Keynesian Phillips curve model (hereafter NPCM) as an empirical model of infla­tion. The favourable evidence for NPCMs on Euro-area data reported in earlier studies is illusive. The empirical support for the economic forcing variable is fragile, and little distinguishes the performance of the estimated, NPCM from a pure time-series model of the inflation rate. The NPCM can be reinterpreted as a highly restricted (and therefore unlikely) equi­librium correction model. Using that framework, we construct tests based on variable addition and encompassing. The results show that economists should not accept the NPCM too readily, and that specific hypotheses about expectations terms are better handled as potential extensions of existing econometrically adequate models.

7.1 Introduction

The previous four chapters have analysed alternative models of wage-price setting in small open economies. A common underlying assumption has been that all processes are causal or future independent processes, that is, the roots of the characteristic polynomials are on (unit roots) or inside the unit circle. This means that the model can be solved uniquely from known initial conditions. In this chapter, we turn to rational expectations models—systems

where expected future values of endogenous variables enter as explanatory vari­ables, in one or more equations. Rational expectations models yield different types of solutions than causal models. In principle, a solution depends on (all) future values of the model’s disturbances. However, if some of the characteristic roots have modulus less than unity while the others have modulus bigger than unity, saddle-path solutions may exist. Saddle-path solutions are not asymp­totically stable but depend on very specific initial conditions. Assume that the system is initially in a stationary situation A. If a shock occurs that defines a new stationary situation B, there are no stable dynamic trajectories starting from A, due to the lack of asymptotic dynamic stability. The endogenous vari­ables of a macroeconomic model can be classified as state or jump variables. The time derivatives of state variables are always finite. In contrast, and as the name suggests, jump variables can shift up or down to new levels quite instant­aneously (exchange rates and other asset prices are common examples). Jump variables play a key role in saddle-path equilibria. Essentially, if a shock occurs in a stationary situation A, instability is avoided by one or more jump variables jumping instantaneously to establish a new set of initial conditions that set the dynamics on to the saddle path leading to the new stationary situation B. Models with saddle-path solutions are important in academic macroeconomics, as demonstrated by, for example, the monetary theory of the exchange rate and Dornbusch’s (1976) overshooting model. Whether saddle-path equilibria have a role in econometric models of inflation is a separate issue, which we address by considering the New Keynesian Phillips curve.

The New Keynesian Phillips Curve Model (NPCM) is aspiring to become the new consensus theory of inflation in modern monetary economics. This position is due to its stringent theoretical derivation, as laid out in Clarida et al. (1999), Svensson (2000), and Woodford (2003: ch. 3). In addition, empirical evidence is accumulating rapidly. For example, the recent studies of Gall and Gertler (1999) and Gall et al. (2001), hereafter GG and GGL, claim to have found considerable empirical support for the NPCM—using European as well as United States data. Moreover, Batini et al. (2000) derives an open economy NPCM which they have on United Kingdom data with supportive results for the specification. In this chapter, we re-analyse the data used in two of these studies, namely GGL and the study by Batini et al. (2000). The results show that the empirical relevance of the NPCM on these data sets is very weak. We reach this surprising conclusion by applying encompassing tests, where the NPCM is tested against earlier econometric inflation models, as opposed to the corroborative approach of the NPCM papers. In addition we also examine the relevance of the NPCM for Norwegian inflation.[54]

The structure of the chapter is as follows. After defining the model in Section 7.2, we investigate the dynamic properties of the NPCM in Section 7.3. This entails not only the NPCM equation, but also specification of a process for the forcing variable. Given that a system of linear difference equations is the right framework for theoretical discussions about stability and the type of solution (forward or backward), it follows that the practice of deciding on these issues on the basis of single equation estimation is not robust to exten­sions of the information set. For example, a forward solution may suggest itself from estimation of the NPCM equation alone, while system estimation may show that the forcing variable is endogenous, giving rise to a different set of characteristic roots and potentially giving support to a backward solution.

Section 7.4 discusses estimation issues of the NPCM, using Euro-area data for illustration. After conducting a sensitivity analysis of estimates of the model under the assumption of correct specification, we apply several methods for testing and evaluating the specification in Section 7.5. We con­clude that the specification is not robust. In particular, building on the insight from Section 7.3, we show that it is useful to extend the evaluation from the single equation NPCM to a system consisting of the rate of inflation and the forcing variable.

Another strategy of model evaluation is to consider competing theories, resulting in alternative model specifications. For example, there are several studies that have found support for incomplete competition models, giving rise to systems with cointegrating relationships between wages, prices, unemploy­ment, and productivity, as well a certain ordering of causality. In Section 7.5.4 we show that these existing results can be used to test the encompassing implications of the NPCM. This approach is applied to the open economy version of the NPCM of Batini et al. (2000). Finally we add to the existing evidence by evaluating the NPCM on Norwegian data and testing the encom­passing implications. Appendix A.2 provides the necessary background material on solution and estimation of rational expectations models.