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This paper analyzes the optimal behavior of the Central Bank in an economy characterized by balanced growth. We show how trend-growth affects the dynamics of inflation, the preferences of a welfare-maximizing Central Bank and optimal monetary policy. In particular, we show that the optimal monetary policy response to cost-push shocks is not invariant to trend growth, and that countries with lower trend growth have substantially higher incentives to commit to simple rules, both from a welfare and price-stability perspectives.

Modern dynamic macroeconomic theory, both in the original real business cycle version and in the more recent New Keynesian framework, views business cycles as fluctuations around a constant linear trend, which are produced by short-run, persistent shocks of various nature. The trend is meant to capture the “balanced growth property” of the neoclassical growth model, according to which, when technology is represented by a constant returns production function with labor augmenting technical progress, macroeconomic variables like output, consumption and the stock of physical capital display a similar average rate of growth over sufficiently long periods of time. Although trend growth is an essential characteristics of dynamic macroeconomics, however, theoretical models usually abstract from it and set it to zero.1 New Keynesian models, in particular, tend to focus on monetary policy and on the tradeoff between inflation and short-run deviations of output from its potential level, without worrying about the long-run evolution of potential output. Is this an innocuous simplification? Indeed, the recent debate on monetary policy suggests that the question of how Central Banks should respond to technological progress is an important issue. Until the burst of the “dot.com” bubble and the recent financial crisis, the ability of monetary policy to accommodate the impressive growth in productivity that occurred during the period of the New Economy, was praised as a very important achievement of the Greenspan’s Fed.2 Recently Orphanides, 2000, Orphanides, 2001, Orphanides, 2002 and Orphanides, 2003 has argued that the “great inflation” of the 1970s can be explained by the failure of the Federal Reserve to understand the productivity slowdown that characterized the US economy in those years. According to this hypothesis, that challenged the traditional interpretation provided by Barro and Gordon (1983) the over-expansionary policy undertaken by the Fed was due to the underestimation of the output gap rather than to the unwillingness of the Fed to fight inflation in order to avoid a recession.3 In light of these considerations, in this paper we study the relationship among trend growth, inflation dynamics and monetary policy within an otherwise standard New Keynesian model, in which productivity follows a trend-stationary process. Are the implications of the standard Dynamic New Keynesian (DNK) model affected by trend growth? Should the Central Bank explicitly consider the rate of productivity growth in formulating monetary policy? Should a Central Bank behave differently in countries (or time periods) characterized by low productivity growth than they should when the productivity growth is very fast? We find that once trend growth is allowed for, it affects the slope of the Phillips curve and the preferences of a welfare maximizing Central Bank. Moreover, trend growth is also important for the design of optimal monetary policy: when trend growth is high and cost-push shocks are very persistent, optimal monetary policy requires a lower sterilization of these shocks. Interestingly, this effect becomes most important under commitment. Indeed, trend-growth affects the inflation elasticity to expectations by affecting the effective discount factor, and we show that this effect can be quantitatively sizable. This channel makes the equilibrium under commitment – in which monetary policy is able to affect expectations – more sensitive to trend growth than the one under discretion – in which expectations are, instead, taken as given. Specifically, we show that the lower the rate of productivity growth, the greater the improvement in the tradeoff a Central Bank obtains by committing to a simple policy rule, and therefore the stronger the incentive to commit to such simple rule. Moreover, we find that also the gains from commitment, both in terms of inflation stability and welfare, are a decreasing function of trend growth. In the calibration exercise we perform at the end of the paper we show that these effects may be relevant from a quantitative point of view. The paper is structured as follows. Section 2 discusses the modeling of trend growth in DSGE models. Section 3 describes the theoretical model and the effects of trend growth on the dynamic system. Section 4, then, derives our main results in terms of implied inflation dynamics and optimal monetary policy, providing also a quantitative assessment. Section 5 finally summarizes and concludes.

This paper analyzes optimal monetary policy in an economy characterized by balanced growth where the dynamics of labor productivity is described by a trend-stationary process. We show that differences in trend growth have important implications for the short-run dynamics of inflation. A low rate of productivity growth implies a higher marginal rate of substitution between current and future consumption. Accordingly, the lower is productivity growth, the larger are the effects of inflationary expectations on current inflation and the smaller are the effects of current marginal costs. Monetary policy is evaluated through a welfare criterion, derived as a second-order approximation of consumers’ utility. We show that a lower trend growth of labor productivity implies a higher concern about relative inflation stabilization. We first derive optimal monetary policy under discretion. If the cost-push shock is sufficiently persistent relative to the degree of price rigidity, a discretionary policy in an economy characterized by slower growth in productivity requires a lower sterilization of the cost-push shock. We then show that if the Central Bank pre-commits to a state-contingent rule, it can achieve an improvement in the policy tradeoff, and that this improvement is greater the lower is the trend growth in productivity. Moreover, in economies with lower trend growth a committed Central Bank should respond more aggressively to inflation than in economies with higher productivity growth, especially in response to highly persistent cost-push shocks. Finally, we show that if the Central Bank is unable to credibly commit to a state-contingent rule when productivity growth is slow, its policy produces higher inflation instability and a dead-weight loss in social welfare. The gains that a Central Bank obtains from committing to a simple policy rule, both in terms of inflation stability and welfare, turn out to be quite relevant from a quantitative point of view. All this suggests that trend growth is quite important for an optimizing Central Bank: the lower the growth rate of productivity the stronger the incentive to adhere to simple policy rules.