سیاست های پولی تجارت آف در مدل برآورد اقتصاد باز DSGE

This paper studies the trade-offs between stabilizing CPI inflation and alternative measures of the output gap in Ramses, the Riksbank׳s estimated dynamic stochastic general equilibrium (DSGE) model of a small open economy. Our main finding is that the trade-off between stabilizing CPI inflation and the output gap strongly depends on which concept of potential output in the output gap between output and potential output is used in the loss function. If potential output is defined as a smooth trend this trade-off is much more pronounced compared to the case when potential output is defined as the output level that would prevail if prices and wages were flexible.

In this paper, we use an estimated open economy model to study the trade-off between stabilizing CPI inflation and the output gap, and trade-off depends on alternative definitions of the output gap. Specifically, we compare variance trade-offs under optimal monetary policy and under an estimated instrument rule. We do this analysis in Ramses, the main model used at Sveriges Riksbank for forecasting and policy analysis. Ramses is a small open-economy dynamic stochastic general equilibrium (DSGE) model estimated with Bayesian techniques and is described in Adolfson et al., 2007a and Adolfson et al., 2008. The notion that alternative definitions of the output gap can have important implications for the conduct of monetary policy is visualized in Fig. 1, which depicts one statistical and three model-based output gaps in Sweden 1997–2007.1 As expected, the correlation is highest between the statistical HP-filtered output gap and the model trend output gap (where the trend is the model׳s unit-root technology shock). Even so, the upper panel of the figure demonstrates that the correlation between the routinely used statistical HP-filtered output gap and all three model based gaps is well below unity, and that their variances are also clearly different.2 By implication, adhering to one of these measures should have non-trivial implications for monetary policy.We define optimal monetary policy as a central bank that minimizes an intertemporal loss function under commitment. We assume that the central bank adopts a quadratic loss function that corresponds to flexible inflation targeting and is the weighted sum of three terms: the squared inflation gap between the 4-quarter CPI inflation and the inflation target, the squared output gap (measured as the deviation between output and potential output), and the squared quarterly change in the central banks policy rate. To get an idea about how inefficient the empirically estimated rule is compared with optimal policy and about the policy preferences implied by the estimated rule, we compare the optimal policy with policy following the estimated instrument rule. The definition of potential output is important since this latent variable is used to compute the output gap (the difference between output and potential output) in the loss function. A conventional measure of potential output is a smooth trend, such as the result of a Hodrick–Prescott (HP) filter. A second definition of potential output, promoted in the recent academic literature, is defined as the level of output that would prevail if prices and wages were flexible, see for instance Woodford (2003) and Galí (2008). This latter measure of potential output is in line with the work of Kydland and Prescott (1982), since it incorporates efficient fluctuations of output due to technology shocks. Using an approach similar to ours, subsequent work by Justiniano et al. (2013), and Edge et al. (2008) present measures of potential output for the US economy within closed-economy frameworks. Justiniano et al. (2013) study the inflation and output stabilization trade-off in the US using an estimated DSGE model. They find that the gap between optimal output (maximizing the household׳s utility function) and potential output (the fully competitive equilibrium) is virtually zero once they treat the observed high-frequency movement in wages as measurement errors rather than variations in workers’ market power. Therefore, they conclude that inefficient movements in US output could have been eliminated without increasing price and wage inflation. To the extent that the welfare function is a good representation of the actual monetary policy objectives, they find that the historical conduct of monetary policy – as described by an estimated interest rate rule – has not performed well. We extend their analysis to an open-economy setting by using an estimated DSGE model with trade channels. By comparing the upper and lower panels in Fig. 1, we see that open economy aspects matter importantly for the computed output gaps.3 Another important difference is that we build on the recent empirical results in Galí et al. (2011), and assume that observed movements in real wage represent variations in workers׳ market power. Finally, and as mentioned above, we do not use the model׳s welfare function, but model the monetary policy objectives directly. Our analysis focuses on the variance trade-off the central bank is facing under various specifications of the loss function, comparing the different output-gap definitions. Results for the estimated instrument rule are also reported. The efficient variance frontiers are computed with a given weight on interest-rate smoothing. As a benchmark, we use a weight of 0.37 on the squared changes in the nominal interest rate in the loss function.4 However, it turns out that the volatility of the nominal interest rate in this case heavily violates the zero lower bound (ZLB) of the interest rate. Therefore, we also follow the suggestion by Woodford (2003) and Levine et al. (2008) and investigate to what extent the efficient variance frontier is affected by increasing the weight on the squared interest rate in the loss function, in order to limit the volatility of policy rates and thus ensure a low probability of the nominal interest rate falling below zero. In addition, we quantify to what extent the estimated instrument rule can be improved by optimizing the response coefficients of the simple instrument rule to minimize the loss function. Finally, we examine how different sets of shocks (technology, markup, preference, and foreign shocks) affect the variance trade-offs faced by the central bank for different definitions of the output gap in the loss function. Our main findings are as follows. First, the stationary productivity shocks create a sharp trade-off between stabilizing CPI inflation and stabilizing the output gap when trend output is computed with a smooth trend. The estimated model assigns a dominant role to shocks to total factor productivity as a driver of business cycles in Sweden in order to explain the fact that the correlation between GDP growth and CPI inflation is about −0.5 for the years 1950–2007. Productivity shocks have also been shown by ALLV (2007b) to play a key role for understanding the episode with low inflation and high output growth in Sweden 2003–2006 (at least for policy under a simple instrument rule). Second, using an output gap in the loss function where potential output is defined as the level of output under flexible prices and wages improves the policy trade-off, but the trade-off still remains significant for some shocks, notably labor supply shocks (which are isomorphic to wage markup shocks) and price markup shocks. The specification of potential output in the output-gap definition is of key importance for the transmission of stationary technology shocks: if potential output is defined as trend output, the output response after a technology shock will be substantially smaller than if potential output is specified as the level of output under flexible prices and wages.5 A labor shock, on the other hand, creates a trade-off between inflation and output-gap stabilization regardless of which output-gap definition is used. Third, we find that the estimated instrument rule is clearly inefficient relative to optimal policy. Our analysis documents that most of this ineffectiveness is driven by the fact that the estimated policy rule responds very inefficiently to fluctuations induced by foreign shocks. Fourth, optimizing the coefficients in the simple instrument rule closes about half the distance relative to optimal policy. Finally, limiting the volatility of the short-term nominal interest rate shifts out the variance frontiers somewhat, but the conclusions regarding the trend output gap and the flexible price-wage output gap are – at least in our approximative approach – robust to introducing this constraint.6 The outline of the paper is as follows: Section 2 presents the model and very briefly discusses the data and the estimation of the model. Section 3 illustrates the variance trade-offs the central bank is facing under different output-gap definitions and attempt to examine their origins. Finally, Section 4 presents a summary and some conclusions. Online Appendices contain some technical details. More technical details are reported in Adolfson, Laseen, Linde and Svensson, ALLS henceforh, (2008).

Within a small open economy framework, this paper has examined how the trade-offs between stabilizing CPI inflation and alternative measures of the output gap depend on the conduct of monetary policy. We have shown that it matters substantially which output-gap definition the central bank uses in its loss function. Depending on whether it is the trend output gap (between output and trend output) or the unconditional output gap (between output and unconditional flexprice potential output, the hypothetical output level that would prevail if prices and wages were entirely flexible and had been so forever) that is included in the loss function, the central bank faces different trade-offs between stabilizing inflation and the output gap. According to our analysis, the trade-off between stabilizing inflation and the output gap is more favorable for the unconditional output gap than for the commonly used trend output gap. However, abandoning the trend output gap in favor of the unconditional output gap would also be associated with an increase in the variance of output since unconditional potential output fluctuates more than trend output due to the fact that stationary but persistent technology shocks are important to explain business cycle fluctuations in the Swedish economy. On the other hand, because the trade-off between output-gap stabilization and inflation stabilization is more favorable for unconditional output gaps than for trend output gaps, abandoning the trend output gap in favor of the unconditional output gap should be associated with lower inflation variability.23 The sensitivity of the results when limiting the volatility of short-term nominal interest rate was also examined. While we acknowledge that our approach to address the effects of imposing the zero lower bound is a crude approximation and should therefore be treated with grain of salt, our results do suggest that this assumption has similar implications for optimized simple instrument rules and optimal policy. In future work, it would be of interest to extend our analysis to other small open economies (e.g. Canada). It would also be of interest to allow for financial frictions and a more developed banking sector in the model. Finally, it would be of interest to study the influence of monetary transmission lags (i.e. assume that firms and households make current period pricing and consumption decisions before the central bank adjust interest rates following Christiano et al., 2005) and allow for imperfect information about the state of the economy.