آیا توابع واکنش های پولی، سیاست های نامتقارن است؟: نقش غیر خطی در منحنی فیلیپس

This paper investigates the implications of a nonlinear Phillips curve for the derivation of optimal monetary policy rules. Combined with a quadratic loss function, the optimal policy is also nonlinear, with the policy-maker increasing interest rates by a larger amount when inflation or output are above target than the amount it will reduce them when they are below target. Specifically, the main prediction of our model is that such a source of nonlinearity leads to the inclusion of the interaction between expected inflation and the output gap in an otherwise linear Taylor rule. We find empirical support for this type of asymmetries in the interest rate-setting behaviour of four European central banks but none for the US Fed.

For the most part, derivations of optimal rules for the conduct of monetary policy have taken place in a linear–quadratic (L-Q) framework, stemming from the combination of a quadratic objective function for the policymaker and a linear dynamic system describing the economy; cf., inter alia, Taylor 1993 and Taylor 1999, Svensson (1997) and Clarida 1998 and Clarida 2000. When the policy instrument is a short-term interest rate, this combination leads to a linear reaction function (Taylor rule) whereby central banks adjust nominal interest rates proportionally to inflation and output deviations from their targets. There are, however, at least three good motives to challenge the L-Q paradigm underlying linear Taylor rules. First, it has been recognised for some time that the short-run inflation-output trade–off may be nonlinear. For instance, convexity may arise under the traditional Keynesian assumption that nominal wages are flexible upwards but rigid downwards, giving rise to a quasi-convex AS schedule; cf. Baily (1978). More recently, Akerlof et al. (1996) have further elaborated on this argument claiming that even a downward-sloping Phillips curve (in the inflation–unemployment space) might hold in the long run at very low rates of inflation due to the existence of money illusion on the part of the workers when there is a price stability. Conversely, Stiglitz (1997) argues in favour of a concave relationship when the output gap is negative on the grounds that firms operating under monopolistic competition may exhibit increasingly greater willingness to reduce prices under weak demand to avoid being undercut by rival firms. Orphanides and Wieland (2000) is, to our knowledge, the first paper to consider this type of nonlinearity in the derivation of optimal reaction functions. In particular, they allow for a zone-linear Phillips curve where inflation is essentially stable for a range of output gaps and changes outside this range, providing in this way a good theoretical rationale for inflation-zone as opposed to inflation point-targeting behaviour by central banks. From an empirical viewpoint, Latxon 1995 and Latxon 1999, Álvarez-Lois (2000), Gerlach (2000) and others have presented evidence in favour of a convex shape for several European countries and the US whereby the inflationary tendencies of capacity constraints on prices imply a considerably steeper Phillips curve when the output gap is positive than when it is negative. In every case, the derived implication is an asymmetric response of inflation with respect to the output gap. Secondly, there is a growing body of research that departs from the standard assumption of a quadratic loss function by acknowledging the possibility that central banks may have asymmetric preferences with respect to inflation and/or output gaps. For example, given that some central bankers are supposed to be accountable to elected political officials, Cukierman (1999) points out that they may have greater aversion to recessions than to expansions. Under these asymmetric preferences, an inflation bias à la Barro–Gordon emerges even when the policy-maker targets the natural output level rather than a larger level. By contrast, Mishkin and Posen (1997) argue that a deflation bias might be a more likely outcome, since independent central banks often tend to deny the possibility that an expansionary monetary policy stance can reduce cyclical unemployment, and report some favourable evidence to this viewpoint for the Bank of Canada and the Bank of England. Clarida and Gertler (1997), in turn, have tested formally for the null hypothesis of symmetry and found evidence against it for the Bundesbank. More recently, Orphanides and Wieland (2000), Ruge-Murcia (2002), Dolado et al. (2002), Surico (2002) and Cukierman and Muscatelli (2002) have analysed the implications for the derivation of interest-rate reaction functions of assuming asymmetric preferences with respect to inflation and/or output by the policy-maker. In particular, Dolado et al. (2002) find that, in the absence of certainty equivalence, when the central banker associates a larger loss to positive than to negative inflation deviations, uncertainty induces a prudent behaviour by the monetary authorities which is reflected by the inclusion of the conditional variance of inflation as an additional argument in the Taylor rule. Allowing as well for asymmetric preferences as regards the output gap, Cukierman and Muscatelli (2002) provide evidence showing that central banks in some G7 economies develop a precautionary demand for expansions and for low inflation once credibility building and disinflation have been achieved. Lastly, there is a third source of nonlinearity which stems from uncertainty regarding the NAIRU or the trend growth rate of productivity. As Meyer et al. (2001) have shown, in periods of heightened uncertainty about the NAIRU (like the second half of the 1990s in the US following the IT-induced productivity acceleration), an optimal updating rule of the NAIRU leads to a nonlinear interest-rate policy according to which policy-makers are more cautious about adjusting interest rates in response to small output gaps than in a standard linear Taylor rule but more aggressive when they reach a certain threshold. In view of these arguments, our goal of this paper is to extend the available evidence on the presence of asymmetric features in monetary policy rules. Specifically, our focus is restricted to the first source of nonlinearity. To this end, we re-examine the analytical implications of assuming a nonlinear short-term inflation–output trade-off in the derivation of such rules and provide some empirical evidence consistent with this nonlinearity. By assuming a quadratic functional form for the effects of the output gap in an accelerationist Phillips curve we obtain a modified Taylor rule which only differs from the conventional linear specification in that it includes an interaction between expected inflation and the output gap as an additional term in the Euler equation. This simple device allows us to capture the asymmetric response of the interest rate to inflation and output gaps which turns out to be optimal in this framework. 1 Our results echo those recently derived by Schaling (1999) in a more restricted set-up than ours. Deriving this modified policy rule for the specific model considered here, together a cross-country empirical analysis supporting the usefulness of the proposed approach, is the contribution of the paper to the literature. Our empirical approach relies upon testing for the statistical significance of the interaction term in the estimation of two types of models. First, we consider an Euler equation specification, in line with the influential approach by Clarida et al. (1998) to capture the performance of a policy rule in describing the evolution of a continuously adjusted short-term interest rate, like (say) an overnight interest rate. Second, we consider an ordered probit model which, as pointed out by Dolado and Marı́a-Dolores (2002), is a useful modelling strategy to analyse the determinants of decisions concerning adjustments in interest rates which only take place irregularly and in discrete increments, as is the case of discount rates. The proposed methodologies are applied to estimate the interest rate-setting behaviour of three European central banks (Banque de France, Bundesbank and Banco de España), the US Federal Reserve and the (surrogate) European Central Bank (ECB) over different sample periods. The rest of the paper is organised as follows. Section 2 reviews the basic theory behind derivation of the optimal interest-rate reaction function under a nonlinear Phillips curve in a simple model along the lines of Svensson (1997). With this illustrative model in mind, we derive the main features of the nonlinear policy rule which serves as a benchmark for the empirical section. Section 3 presents the empirical results obtained from applying the two econometric methodologies described above to five central banks. Finally, Section 4 concludes.

In this paper we search for asymmetries in the policy responses of five central banks to inflation and output gaps. We have argued that such responses can arise when the Phillips curve underlying the derivation of the optimal policy rule is nonlinear. To test for the existence of such asymmetric features we use two empirical approaches. The first one is based on the estimation of a Euler equation which allows for the interaction between expected inflation and the output gap while the second relies on the estimation of an ordered probit model to capture the discrete nature of changes in discount rates, allowing again for the interaction term. We find significant evidence of nonlinearity in the policy rules of four European central banks after the 1980s, in the sense that they have tended to intervene with more virulence when inflation and output move above their target than what a linear Taylor rule would predict. However, that is not the case for the Fed, where a linear Phillips curve cannot be rejected. These contrasting results between European countries and the US can be interpreted by the fact that the convexity of the Phillips curve relies upon the existence of labour market rigidities and that those are much more severe in the former than in the latter. In sum, the results in this paper seem to confirm the hypothesis that there are nonlinearities in the operating procedures of central banks when setting a short-term interest rate to control monetary policy. Taking them into consideration may turn out to be helpful for financial market analysts when they forecast the evolution of interest rates on the basis of the already very popular usage of Taylor rules.