سیاست پولی بهینه در اقتصاد تعمیم یافته تیلور

In this paper, we use the generalized Taylor economy (GTE) framework to examine the optimal choice of inflation index. In this otherwise standard dynamic stochastic general equilibrium (DSGE) model, there can be many sectors, each with a different contract length. In the GTE framework with an empirically relevant contract structure, a simple rule under which the interest rate responds to economy-wide inflation gives a welfare outcome nearly identical to the optimal policy. This finding suggests that it may not be necessary for a well-designed monetary policy to respond to sector-specific inflations.

The optimal choice of an inflation-index is an important question for policy makers. This paper aims to address this issue in a model that accounts for the heterogeneity in contract lengths we observe in empirical data. To accomplish this we have used the generalized Taylor economy (GTE) ( Dixon and Kara, 2007 and Dixon and Kara, 2010). The GTE generalizes the simple Taylor model to allow for a distribution of contract lengths in different sectors. 1 An additional advantage of the GTE framework is that it is general enough to represent any distribution of contract lengths, including the one generated by the Calvo model. Dixon and Kara (2007) find that the GTE with a distribution of contract lengths based on the data set of Bils and Klenow (2004) tracks the US data well. In this paper, we extend the GTE framework by assuming that each sector is subject to sector-specific productivity shocks. We then consider the design of welfare-maximizing inflation-targeting monetary policy rules in a setting where there are multiple sectors, each with a different contract length. We examine the monetary policy implications of alternative assumptions regarding the distribution of contract lengths and explore how to assign weights to different sectors in an optimal inflation index for a central bank to target (i.e. sectoral inflation-targeting). We then compare the performance of the aggregate inflation targeting relative to the sectoral inflation-targeting rule and ask if it is really necessary for a well-designed monetary policy to respond to sector-specific inflation rates. For this purpose, in our model we derive a utility-based objective function of a central bank by following the procedure described in Rotemberg and Woodford (1998). In doing so, we illustrate the challenge facing the central bank in an environment in which there are many sectors. In particular, we show that welfare in the GTE depends on the variances of the output gap and on the cross-sectional price dispersion. We find that in the GTE framework, in the presence of sector-specific shocks and nominal rigidities, it is impossible for the central bank to simultaneously stabilize all the objectives; as a result, the first-best allocation cannot be achieved. We then employ Lagrangian methods to determine the optimal policy and use it as a benchmark to evaluate the performance of alternative simple rules. A main finding of this paper is that in a model with an empirically relevant distribution of contract lengths, a simple rule under which the interest rate responds to economy-wide inflation gives a welfare outcome close to the optimum, which suggests that it may not be necessary for a well-designed monetary policy to respond to sector-specific inflations. Before we turn to a description of the GTE model, we briefly review the literature on this topic. A rapidly growing literature assesses the question of which inflation index a central bank should target in models that allow for two sectors, such as those studied by Woodford (2003, pp. 435–443) and Aoki (2001), or with two countries such as that studied by Benigno (2004). These studies find that targeting economy-wide inflation is not optimal. Instead, they suggest a sectoral inflation targeting rule that puts more weight on the sector in which there is a longer contract. Benigno (2004, p. 295) evaluates the gains from pursuing a sectoral inflation targeting rule at around 0.02% of consumption. This result is consistent with the one we obtain with simple two-sector GTEs. We suggest, however, there is a limitation in studies like these which use models that have only two sectors. Clearly, generating a more realistic case requires going beyond the simple case of two-sector economies. Indeed, we find that in the GTE with an empirically relevant distribution of contract lengths the gains from pursuing sectoral inflation targeting are smaller than what two sector-economies suggest and are virtually zero. In general, we believe that the GTE may be better at capturing the environment facing a central bank. The remainder of the paper is organized as follows. Section 2 presents the model and Section 3 describes equilibrium dynamics. Section 4 derives a welfare function for a central bank based on the representative household's utility function. Section 5 characterizes the optimal policy and Section 6 analyses the implications of various assumptions regarding the distribution of contract lengths and compares the performance of alternative simple inflation-targeting rules. Section 7 summarizes our conclusions

When examining the implications of the heterogeneity of contracts lengths on optimal monetary policy design, the standard approach is to consider economies in which there are only two sectors. But more realistic analysis requires considering economies with many sectors, each with a different contract length and modelling the distribution of contract lengths using empirical data. The purpose of this paper has been to investigate the implications of ignoring the heterogeneity of contract lengths on the optimal choice of inflation index. To accomplish this we have used the generalized Taylor economy (GTE) framework to analyze the design of monetary policy rules in an economy where there can be many sectors with different contract lengths. We have generalized the analysis of Rotemberg and Woodford (1998) and have derived a utility-based objective function of a central bank to provide a benchmark for evaluating the performance of alternative inflation-targeting monetary policy rules in an economy in which there are many sectors with different contract lengths. We have then compared the performance of two alternative policy rules. The first is the sectoral inflation-targeting rule under which the nominal interest rate reacts to the appropriately weighted average of the inflation rates in different sectors. The second is the aggregate inflation-targeting rule under which the nominal interest rate targets aggregate inflation. Two results emerge from the analysis in this paper. First, the results suggest that in a model that assumes an empirically relevant distribution of contract lengths, the performance of an aggregate inflation-targeting scheme closely approximates the performance of a sectoral inflation-targeting rule in which an appropriately weighted average of sectoral inflation rates is targeted. However, a two-sector model suggests that the welfare gain is larger. The main difference between the rules is that aggregate inflation targeting rule requires a larger deviation of output from potential to control price stability. Higher volatility in the output gap when aggregated inflation is targeted leads to a larger deterioration in social welfare in two-sector models than in a model with a distribution. This is because, for a given mean, the presence of long-term contracts in an economy with a wider range of contracts leads to a higher degree of price dispersion. Increased price dispersion makes it more important to control price stability, reducing the importance of the output gap term in the central bank loss function. Therefore, higher volatility in the output gap under the aggregate inflation-targeting scheme is less costly in a multi-sector economy. Second, if the central bank adopts a sectoral inflation-targeting rule, then the optimal rule does not necessarily place the largest weight on the inflation rate in the sector where the contract length is the longest. In two-sector economies, the optimal weights that sectors receive in the optimal inflation index depend on the contract length in that sector as well as the sector's share. The intuition is simple: if there are only a few firms with long contracts, the behavior of these firms simply does not matter significantly for optimal policy. Although this finding may seem obvious, the existing literature commonly claims that the sector with the longest contract receives the largest weight in the optimal inflation index because of the simplifying assumption that sectors have equal sizes. In a model with a distribution of contract lengths, the optimal weights sectors receive depend on the shape of the distribution. The experiments reported in the paper suggest that if a distribution looks like a geometric distribution (i.e. a longer duration corresponds to a smaller share of the sector), then the sector with the longest contracts receives the greatest weight. On the other hand, if there is a hump-shaped distribution, then the longest-contract sector does not receive the greatest weight. In this case, the sectors in which prices are sticky but have a large weight in the sectoral index receive a larger weight than the longest-contract sector. This sensitivity makes it difficult to generalize results of optimal weights when there is a distribution of contract lengths. The results suggest that central banks may still prefer to follow the aggregate inflation-targeting rule rather than the sectoral inflation targeting rule. Such a rule is easier to implement, since this rule does not require to measuring all sectoral characteristics and since it closely approximates the performance of the sectoral inflation-targeting.