سیاست های پولی با خطر به اشتراک گذاری خانوارهای ناهمگون و ناقص

This paper considers a sticky-price model with heterogeneous households and financial frictions. Financial frictions lead to imperfect risk-sharing among households with idiosyncratic labor incomes. I study implications of imperfect risk-sharing for optimal monetary policy by documenting its impacts on the monetary transmission mechanism, the inflation–output tradeoff faced by the central bank, the policy objective function, and the resulting targeting rule. The main finding is that while the central bank continues to have the conventional dual mandate — the output gap and inflation stabilization — it should place a greater weight on the later as the degree of financial frictions increases because price stability provides the additional benefit of reducing undesired consumption dispersion.

In reality, workers have heterogeneous labor skills. Consider two types of workers — dentists and carpenters for example. Each type produces a differentiated product and service, which generally results in different labor incomes. In addition, it is not easy for each type to learn a new skill and migrate to another specialty, especially in the short-run. Moreover, various financial frictions may prevent them from sharing their income risks perfectly. In this environment with labor skill/income heterogeneity, this paper studies the implications of imperfect risk-sharing for optimal monetary policy. To the best of my knowledge, most of the literature on optimal monetary policy in standard sticky-price frameworks (also known as New Keynesian (NK) models) either assumes frictionless complete asset markets, or equivalently relies on a ‘fictitious’ representative household that consists of all types of workers. The assumption makes consumption distribution efficient and degenerate at all times, thereby precluding consideration of the policy implications of risk-sharing. This property is in contrast to most empirical analyses that have found risk-sharing is imperfect and thus consumption distribution across households is in general inefficient.2 To consider a range of risk-sharing conditions, this paper introduces frictions in transferring resources between heterogeneous households, which I refer to as “financial frictions”, into an otherwise perfect risk-sharing economy and documents how this affects equilibrium consumption allocation, the monetary transmission mechanism, and the central bank policy objectives. I then examine if monetary policies well-designed under the conventional assumption of perfect risk-sharing (or a representative household) work in a more general environment. I summarize the main results in the subsequent paragraphs. First, this paper demonstrates that the familiar policy prescription, often referred to as “flexible inflation targeting”, that attempts to stabilize two aggregate indices, inflation and the output gap, continues to characterize optimal monetary policy.3 The central bank does not need to pay attention to any other aggregate or disaggregate variables or construct an index to address the inefficiency caused by financial frictions. However, eliminating financial frictions (or assuming perfect risk-sharing) is not a good simplification for evaluating monetary policies. This paper argues that in the presence of financial frictions, stabilizing inflation provides the additional benefit of reducing undesired consumption dispersion. Therefore the central bank should adopt “stronger” inflation targeting. In sum, while the central bank should continue to target inflation and the output gap, it should place a larger relative weight on inflation stabilization. However, in an environment with financial frictions, the ‘cost’ of stabilizing inflation increases as well as the benefit. Imperfect risk-sharing amplifies price stickiness endogenously, reducing the slope of the NK Phillips curve for a given degree of nominal rigidities (Lee, 2012). As a result, under financial frictions the central bank faces a less favorable inflation–output gap tradeoff than in an environment without these frictions. In adjusting the inflation rate, the central bank would have to tolerate a larger deviation of output from its efficient level. In other words, the ‘cost’ of inflation stabilization is higher. Thus “stronger” inflation targeting under financial frictions does not necessarily result in inflation actually being more stable than it would be in an environment without financial frictions. More generally, financial frictions generate macroeconomic as well as microeconomic inefficiencies. On the one hand, in a model with staggered price setting, unstable inflation leads to undesired dispersion of prices/productions across industries. This leads to variation in labor incomes across households, and when risk-sharing is imperfect, inefficient dispersion in household consumption: deviation of the cross-sectional distribution of household consumption from the first-best distribution. On the other hand, financial frictions flatten Phillips curve and hence aggravate inefficiency in macroeconomic dynamics. Stabilizing inflation more would reduce the microeconomic inefficiency in the allocation of household consumption, but the cost of moving inflation closer to the optimal target rate, which is zero in our stylized framework, is greater macroeconomic inefficiency: a larger deviation of output from its efficient level. Therefore the central bank must consider the magnitude of the extra benefit and cost of stabilizing inflation, marginally generated by financial frictions, in the design of optimal monetary policy. Policymakers should stabilize inflation more aggressively only when the extra benefit exceeds the extra cost, or equivalently when the microeconomic effect of financial frictions (consumption dispersion) dominates the macroeconomic effect (output deviation) in affecting household welfare. The paper shows that the microeconomic inefficiency dominates the macroeconomic inefficiency when the degree of financial frictions is sufficiently large (yet in a reasonable range), and argues that this is precisely the situation when financial frictions have potentially significant implications for monetary policy. The finding suggests that the central bank should monitor financial market conditions and shift a weight from the output gap stabilization to inflation stabilization when financial markets do not function well for agents' risk-sharing. The paper proceeds as follows. After discussing the related literatures, I present the model in Section 2. Section 3 then discusses the impacts of financial frictions on the model structural equations. Section 4 shows the impact of financial frictions on the loss function of the central bank that maximizes household welfare and presents the main results on optimal monetary policy. Section 5 summarizes the results and concludes. Related literature I employ a simple variant of a textbook NK model — detailed in Woodford (2003) — as a laboratory for three main reasons. First, NK models have recently become the workhorse for monetary policy analysis, and often serve as the basis for large-scale models used at central banks.4 Second, the basic model is simple enough to show the main results analytically. In this regard, I deliberately avoid using more elaborate sticky-price models.5 Third, Woodford's basic NK model features segmented labor markets across industries, which naturally generates labor income heterogeneity across households who work in different industries. This “industry-specific” labor market specification is widely used in NK literature because not only it is arguably more realistic (at least in the short-run as argued in Woodford (2003) and also at the beginning of this paper) relative to the opposite extreme specification (i.e. common economy-wide factor markets), but also it enhances strategic complementarity in price settings, which improves models' consistency with micro evidence on the frequency of price changes.6 Recently, a growing number of papers examine distributional implications of monetary policy under household heterogeneity, for example Sheedy (2012) and Pescatori (2007). In their models, monetary policy affects wealth distribution since agents hold nominal debt of different amounts.7 Being more focused on financial wealth heterogeneity, however, these studies assumed away labor skill (and income) heterogeneity, precluding any consideration of policy implications of imperfect risk-sharing among heterogeneous workers.8 Curdia and Woodford's (2009) paper is particularly related to this paper, showing a similar result: “flexible inflation targeting” continues to serve as optimal monetary policy (at least approximately) even with certain financial frictions. They construct household heterogeneity by positing two types of households with different time preferences for consumption, one is patient, the other is impatient.9 As a consequence, households have an incentive to transfer their resources although they possess a same labor skill set and their labor incomes are identical. In contrast, this paper assumes households have the same preferences and thus identical impatience to consume, but they produce differentiated goods, which leads to idiosyncratic labor incomes. This paper and Curdia and Woodford (2009) thus complement each other by showing the robustness of flexible inflation targeting to different forms of household heterogeneity and financial frictions. However, since Curdia and Woodford's model excludes the channel through which relative price distortion leads to relative consumption distortion, it shows no extra benefit of stable inflation, and hence there is no motivation for the central bank to place additional importance on inflation stabilization beyond that suggested by the basic NK model. In contrast, the analysis in this paper provides a compelling argument for “stronger” inflation targeting.

The NK research programs have provided an important lesson on why inflation stabilization is important. Inflation generates a distortion in relative prices, which results in an inefficient allocation of resources across industries and/or sectors. This paper took one step further and considered the possibility that relative price distortion creates another distortion in relative consumption because household risk-sharing is not as ideal as frictionless complete market models suggest. In this environment, heterogeneous households' imperfect risk-sharing due to financial frictions increases both the benefit and cost of stabilizing inflation. When the degree of financial frictions is sufficiently large, however, the extra benefit dominates the extra cost, and this is precisely the situation when financial frictions may play an important role in designing optimal monetary policy. The result suggests that the central bank should monitor financial market conditions and place an even greater emphasis on inflation stabilization when financial markets do not function well for agents' risk-sharing. There are clearly other important channels by which household heterogeneity and financial frictions are relevant for macroeconomic dynamics and monetary policy.30 This paper focused on one specific channel and thus deliberately used a highly stylized model to make the main points in the simplest way possible. Consequently, while the exercise in this paper suggests that the extent of risk-sharing may have non-trivial implications for monetary policy, it is not designed to offer a strong quantitative statement. Instead, my results encourage further quantitative investigation with more realistic and elaborate models such as the ones in Christiano et al. (2005) or Smets and Wouters, 2003 and Smets and Wouters, 2007. Gornemann et al. (2012) are taking a significant step forward in this direction.