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In the monetary policy literature it is common to assume that trend inflation is zero, despite overwhelming evidence that zero inflation is neither empirically relevant nor a practical objective for central bank policy. We therefore extend the standard New Keynesian model to allow for positive trend inflation, showing that even low trend inflation has strong effects on optimal monetary policy and the dynamics of inflation, output and interest rates. Under discretion, the efficient policy deteriorates and there is no guarantee of determinacy. Even with commitment, targeting non-zero trend inflation leads to substantial welfare losses. Our results serve as a warning against indiscriminate use of models assuming zero trend inflation.

In May 2003 the ECB explicitly announced its view that price stability corresponds to an inflation rate of 2% over the medium term. Unfortunately, most theoretical models in the recent literature say little about how a positive inflation target such as this is likely to affect the optimal short-run stabilization policy of the ECB. Indeed, with few notable exceptions (e.g., Khan et al., 2003; Schmitt-Grohé and Uribe, 2004 and Schmitt-Grohé and Uribe, 2005), the recent literature is typically based on a version of the New Keynesian model that is log-linearized around a zero inflation steady state. This paper aims to solve this inconsistency by addressing the question of how optimal monetary policy is affected by positive trend inflation.1 There are two important reasons why the monetary policy literature has focussed on the zero inflation steady state. The first is analytical convenience. The second is that zero inflation is optimal in a so-called cashless economy (see Goodfriend and King, 2001 and Woodford, 2003). However, quite special theoretical assumptions are needed before optimal steady-state inflation is equal to zero in any framework. We think instead that there are compelling reasons to look at the case of low and positive trend inflation. First, the case of zero inflation is unrealistic in the light of the post-war economic history of industrialized countries. Schmitt-Grohé and Uribe (2004) use the average US GDP deflator growth rate in 1960–1998 to calibrate the steady-state inflation rate to 4.2%. The average inflation rate for European countries in post-war years ranges from about 3% in Germany to almost 10% in Spain (OECD data). Hence, we should study optimal stabilization policy in such an environment. This is even more important if these models are used empirically to assess the behavior of central banks in the post-war period. Second, the practice of many central banks suggests that zero steady-state inflation is not their real target. In other words, zero inflation does not coincide with the concept of “price stability” held by central bankers, as the ECB case illustrates. It is therefore important to check whether results in the existing literature are robust to moderately positive trend inflation levels. This article owes much to the seminal works of Clarida et al. (1999) and Galí (2003), and can be interpreted as a generalization of their findings to the case of positive trend inflation. Indeed, we provide a simple extension of their framework with the main change being an extra equation that arises when the New Keynesian Phillips Curve (NKPC) is generalized. Our model thus encompasses the standard framework, allowing us to find intuitive analytical results for the case of discretionary monetary policy, and develop straightforward comparisons with standard results. Our main finding is that optimal monetary policy is highly sensitive to low levels of trend inflation. In particular, as trend inflation increases we find that monetary policy progressively loses its ability to stabilize inflation. The reason is that trend inflation makes firms more concerned that their prices keep up with the trend in inflation, so they are not eroded in relative terms. The optimal reset price is therefore less affected by the current level of economic activity, the NKPC is flatter, and the current output gap has less effect on current inflation. As a result, under positive trend inflation and optimal discretionary policy we find: (i) the rational expectations equilibrium (REE, henceforth) is not always determinate; (ii) the efficient policy frontier deteriorates substantially. Moreover, under positive trend inflation and optimal commitment policy we have: (i) impulse response functions and gains from commitment are highly sensitive to the level of trend inflation; (ii) interest rate smoothing increases with trend inflation. Finally, our model is able to match the positive empirical correlation between average inflation and inflation variability. As in the standard literature, the monetary authority in our framework controls the nominal interest rate to stabilize inflation and output gap around long-run targets. We therefore ask how the optimal response to shocks is affected when trend inflation assumes empirically relevant values. Our results serve as a warning against the empirical application of existing New Keynesian models, especially versions of the models that cannot explain observed trend inflation. The trend rates of inflation we examine are, however, generally inconsistent with long-run minimization of our assumed loss function. Thus, the true extent and nature of the problem analyzed in this paper will not be known until a model is derived that can predict a positive average rate of inflation. The features that would deliver an endogenously optimal positive long-run inflation are likely to further affect the short-run Phillips curve, and may thus change the results of this paper both quantitatively and qualitatively. At the very least, though, our contribution highlights the need for such a model. Our work is linked to some recent contributions that have appeared in the literature. Khan et al. (2003) show that the optimal long-run inflation rate is actually negative, because a negative rate balances the benefits of following the Friedman rule and the costs of relative price distortions. Schmitt-Grohé and Uribe (2005) perform a similar exercise in a medium-scale model incorporating fiscal policy and many distortions. In contrast, Schmitt-Grohé and Uribe (2004) look at optimal monetary and fiscal policy when treating the level of trend inflation as exogenously calibrated to US post-war data. Our paper is complementary to these works, but differs in two important respects. Firstly, none of the above contributions investigate how optimal monetary policy is affected by changes in trend inflation. Secondly, our framework is sufficiently tractable to deliver many analytic results, whereas the above works rely mainly on numerical results.

With significant levels of post-war inflation in developed countries and central banks typically targeting positive rates of inflation, it is somewhat surprising that the monetary policy literature has taken zero inflation steady-state models as a benchmark. We think it is very important that the main model in the literature is robust to allowing for positive trend inflation level. The contribution we make is to extend the seminal model of Clarida et al. (1999) and Galí (2003) to allow for a generic steady-state inflation rate. The resulting simple framework is tractable and encompasses existing models as a special case. Our main finding is that optimal monetary policy is highly sensitive to the level of trend inflation. In particular, monetary policy becomes less effective at stabilizing the economy once trend inflation increases. This occurs because trend inflation flattens the NKPC and makes inflation less responsive to the output gap. Moreover, under discretion the rational expectations equilibrium is not always determinate and the efficient policy frontier deteriorates substantially. Under commitment, interest rate smoothing increases as trend inflation rises. More generally, impulse responses and gains to commitment are highly sensitive to the level of trend inflation. Our results are naturally sensitive to the assumptions of no indexation and fixed contract length in the standard model. A relaxation of either of these would weaken our conclusions. With respect to the no-indexation assumption, Ascari (2004) shows that indexation reduces the effect that trend inflation has on the NKPC. In the limit, full indexation removes the effect completely. However, we stress that our concern is with low levels of trend inflation such as those observed post-war in developed countries, in which case the sticky price assumption is reasonable. Moreover, (i) in reality we do not observe indexed prices; (ii) we have known that full indexation is not optimal since at least Gray (1976); (iii) the theoretical microfoundations of price indexation schemes are rather questionable; and (iv) the main justification for price indexation in studies such as Christiano et al. (2005) is empirical not theoretical. With respect to the fixed contract length assumption, we find it reasonable to fix the expected duration of prices exogenously for moderate levels of trend inflation. More generally, our results serve as a warning against the use of existing New Keynesian models in empirical analysis of post-war data. It is preferable to work with models such as ours that properly account for trend inflation. However, an issue remains in that the levels of trend inflation we examine are inconsistent with long-run maximization of our assumed loss function. We acknowledge this problem, but see it as highlighting the pressing need for models that endogenously deliver optimal long-run inflation rates that are positive. Such models are likely to have even greater modifications of the short-run NKPC, and may lead to both quantitatively and qualitatively different results.