سیاست های پولی تحت عدم قطعیت مالی

Monetary policy may play a substantial role in mitigating the effects of financial crises. In this paper, I suppose that the economy occasionally but infrequently experiences crises, where financial variables affect the broader economy. I analyze optimal monetary policy under such financial uncertainty, where policymakers recognize the possibility of crises. Optimal monetary policy is affected during the crisis and in normal times, as policymakers guard against the possibility of crises. In the estimated model this effect is quite small. Optimal policy does change substantially during a crisis, but uncertainty about crises has relatively little effect.

The recent financial crisis and subsequent recession have illustrated how developments in credit and financial markets may be transmitted to the economy as a whole. However prior to the crisis, the baseline models for monetary policy analysis had no direct way to model such developments. The potential importance of financial factors was recognized in the literature, but financial factors were not present in the most widely used models for policy analysis. One interpretation of this state of affairs is that in “normal times” financial market conditions are not of primary importance for monetary policy. In such times, policy focuses on the consequences of interest rate setting for inflation and output, reacting primarily to shocks which directly affect these variables. However the economy may occasionally enter “crisis” periods when financial frictions are of prime importance and shocks initially affecting financial markets may in turn impact the broader economy. The transitions between normal and crisis period may be difficult to predict, and a crisis may be well underway before its effects become apparent in the broader economy. In this paper I develop methods to provide guidance in assessing and responding to such financial uncertainty. In this paper, I focus on monetary policy design when occasional crisis episodes impact on the transmission mechanism. Importantly, we do not consider financial stability policy, which may have distinct objectives (financial stability, appropriately defined) and instruments (bank supervision and regulation, liquidity provision to banks, and so on). In our setting, monetary policy always has as its objective the stabilization of inflation around a target and economic activity around a target of a sustainable level, and sets a nominal interest rate as its instrument. Crises impact the ability of monetary policymakers to attain these objectives, as they introduce additional shocks and factors which affect inflation and output. Importantly, we take crises here as exogenous, reflecting financial market developments beyond the control of monetary policy. Thus we focus on how monetary policy may mitigate the effects of such crises, and how uncertainty about financial crises affects the appropriate monetary policy response. This paper encapsulates a stylized reading of the developments in monetary policy analysis over the past decade. By the mid-2000s there had been influential work showing that larger New Keynesian models were able to successfully confront the aggregate data. In particular, the work of Christiano et al. (2005) and Smets and Wouters (2003) showed that such theoretically based models were able to fit aspects of the data comparable to VARs. Such models incorporated a host of real and nominal frictions, but did not discuss financial factors. In addition, there was a growing literature on monetary policy analysis under uncertainty, some of which used these larger scale models.1 This literature considered the implications for policy of model uncertainty, including uncertainty about the specifications and parameterizations of the models, and the types of nominal rigidities. But again financial factors were notably (in hindsight) absent. Of course, the seminal contributions of Bernanke and Gertler (1989), Kiyotaki and Moore (1997), and Bernanke et al. (1999) were recognized. There was also ongoing work on financial frictions in monetary policy, including work by Christiano et al. (2003) and Gertler et al. (2007) among others. But the “consensus” policy models had not yet incorporated these frictions. The turmoil of the past several years has naturally spurred interest in models of financial frictions and the interaction of real and financial markets more broadly. In hindsight, it is clear that the much of the previous literature on monetary policy analysis missed a big source of uncertainty: uncertainty about financial sector impacts on the broader economy. Under one reading, this was simply an omission, and monetary policymakers should have been more focused on financial factors throughout. In this paper we suggest another interpretation, namely that there may be significant variation over time in the importance of financial shocks for monetary policy. In normal times, defaults and bank failures are rare, sufficient liquidity is provided for businesses, and monetary policy focuses on responding to shocks to inflation and output. However in crisis periods, defaults and bank failures increase, liquidity may be scarce, and shocks to the financial sector may impact the transmission of monetary policy. I assume that the economy switches stochastically between such “normal times” and “crisis” regimes, and consider the design of monetary policy in an environment where policymakers and private sector agents recognize the possibility of such switches. As a model of “normal times” I use a small empirical New Keynesian model. In particular, I use a version of the model of Lindé (2005), which adds some additional exogenous persistence in the form of lagged dynamics to the standard New Keynesian model. For the model of crises, I use a version of the model of Curdia and Woodford (2009b), which is a tractable extension of the standard New Keynesian model to incorporate financial frictions. As in the standard model, the key equilibrium conditions of the model include a log-linearized consumption Euler equation (governing aggregate demand) and a New Keynesian Phillips curve (reflecting price setting with nominal rigidities). However the allocative distortions associated with imperfect financial intermediation give rise to a spread between borrowing and lending interest rates, and a gap in the marginal utility between borrowers and lenders. These factors only matter for inflation and output determination in a crisis, and an exogenous Markov chain governs the switches of the economy between normal and crisis periods. Importantly, I focus on a simple specification of the model where the key interest rate spread is exogenous. I first suppose that crises are observable, so the main source of uncertainty is over the future state of the economy. I then consider the case where agents must infer the current state of the economy from their observations, so uncertainty and learning about the current state become additional considerations. Thus even in normal times, the optimal policy differs from the prescriptions of a model without such crises. The optimal policy under uncertainty reflects the possibility that the economy may transit into a crisis in the future, as well as the uncertainty about whether the economy may already have switched into such a state. Thus the results imply variation over time in the policy response to shocks to real and financial factors, with learning about the state of the economy potentially playing a role in moderating fluctuations. The policy analysis in this uses the approach of Svensson and Williams, 2007b and Svensson and Williams, 2007a. There we have developed methods to study optimal policy in Markov jump-linear-quadratic (MJLQ) models with forward-looking variables: models with conditionally linear dynamics and conditionally quadratic preferences, where the matrices in both preferences and dynamics are random.2 In particular, each model has multiple “modes,” a finite collection of different possible values for the matrices, whose evolution is governed by a finite-state Markov chain. In our previous work, we have discussed how these modes could be structured to capture many different types of uncertainty relevant for policymakers. Here I put those suggestions into practice, by analyzing uncertainty about financial factors and the transmission of financial shocks to the rest of the economy. In a first paper, Svensson and Williams (2007b), we studied optimal policy design in MJLQ models when policymakers can or cannot observe the current mode, but we abstracted from any learning and inference about the current mode. Although in many cases the optimal policy under no learning (NL) is not a normatively desirable policy, it serves as a useful benchmark for our later policy analysis. In a second paper, Svensson and Williams (2007a), we focused on learning and inference in the more relevant situation, particularly for the model-uncertainty applications which interest us, in which the modes are not directly observable. Thus, decision makers must filter their observations to make inferences about the current mode. As in most Bayesian learning problems, the optimal policy thus typically includes an experimentation component reflecting the endogeneity of information. This class of problems has a long history in economics, and it is well-known that solutions are difficult to obtain. We developed algorithms to solve numerically for the optimal policy. Due to the curse of dimensionality, the Bayesian optimal policy (BOP) is only feasible in relatively small models. Confronted with these difficulties, we also considered adaptive optimal policy (AOP). 3 In this case, the policymaker in each period does update the probability distribution of the current mode in a Bayesian way, but the optimal policy is computed each period under the assumption that the policymaker will not learn in the future from observations. In our setting, the AOP is significantly easier to compute, and in many cases provides a good approximation to the BOP. Moreover, the AOP analysis is of some interest in its own right, as it is closely related to specifications of adaptive learning which have been widely studied in macroeconomics (see Evans and Honkapohja, 2001 for an overview). Further, the AOP specification rules out the experimentation which some may view as objectionable in a policy context. 4 In this paper, I apply our methodology to study optimal monetary-policy design under what I call “financial uncertainty.” Overall, I find that in the estimated model the optimal monetary policy does change substantially during a crisis, but uncertainty about crises has relatively little effect. In crises, it is optimal for the central bank to cut interest rates substantially in response to increases in the interest rate spread. However the size of this response is nearly the same in our MJLQ model as in the corresponding constant coefficient model. In addition, the possibility that the economy may enter a crisis means that even in normal times policy should respond to interest rate spreads. But again, this effect is fairly negligible. These results seem to rely on two key factors: the exogeneity of the interest rate spreads and the rarity of crises. In regard to the first point, policy cannot affect spreads in our model, so responding to interest rate spreads in normal times has no effect on the severity of crises. If policy could affect spreads, then there may be more of a motive for policy to react before a crisis would appear, as stabilizing interest spreads may make crises less severe. On the second point, note that by responding to spreads in normal times policymakers are effectively trading off current performance for future performance. The greater the chance of transiting into a crisis, the larger the weight that the uncertain future would receive in this tradeoff. As crises are sufficiently rare, there is little reason to sacrifice much current performance. Policymakers are typically able to react sufficiently strongly once crises do arrive, so there is little reason to alter policy in advance of the crisis. Our conclusions are certainly model-specific, and as we have noted, they rely on the exogeneity of interest rate spreads. Certainly during the crisis most central banks rapidly expanded their balance sheets, making asset purchases as a means of providing liquidity to financial markets and attempting to reduce interest rate spreads. In this paper I focus on interest rate policy solely, treating liquidity policy as a separate issue. Curdia and Woodford (2009a) show that in their model, as used in this paper, liquidity policy can indeed be viewed as a separate instrument which need not affect interest rate policy. But in general there may be broader interactions, with liquidity policy imposing costs, such as political pressure associated with the central bank holding a broader array of assets, which could affect future interest rate policy. Such issues are clearly relevant for the current policy environment, but are outside the scope of this paper. The paper is organized as follows: Section 2 presents the MJLQ framework and summarizes our earlier work. Section 3 then develops and estimates our benchmark model of financial uncertainty, while Section 4 analyzes optimal policy in the context of this model under different informational assumptions. Section 5 presents some conclusions and suggestions for further work.

This paper has illustrated how to formulate and analyze monetary policy with uncertainty about the impact of the financial sector on the broader economy. We have found that uncertainty about financial crises causes substantial changes in optimal monetary policies, but such changes are mostly due to the crises and not the uncertainty. In our estimated model, crises are infrequent, exogenous events and so policy in normal times is affected relatively little by the possibility of crises. In addition, even if crises are not directly observable, they are relatively easy to detect, so uncertainty and learning about the state of the economy play a relatively minor role. We find that policy should indeed by tailored to crises, but that such considerations are largely independent of how policy should be conducted in normal times. Of course, these conclusions are specific to the particular model that we analyze. In addition, even in the context of this model, the dimensions of uncertainty we consider are rather limited. Policymakers and private agents know the form and severity of crises, and they know the expected frequency and durations of crisis episodes. Thus we certainly understate the degree of uncertainty that policymakers face. We have carried out some preliminary exercises analyzing uncertainty about the duration of crises, which we implemented by having separate crisis modes of different persistence, and uncertainty about the severity of crises, implemented by having separate crisis modes with different values for the key parameters governing the financial frictions. While these increased the impact of uncertainty, the effects were rather minor. More important is likely to be a broader role for financial frictions. While the version of the model of Curdia and Woodford (2009b) that we use is a simple staring point, it incorporates financial frictions in a limited way. Most prominently, we have focused on a version of the model where the key credit spread is exogenous. Curdia and Woodford develop a more general version in which this spread evolves endogenously and is dependent on the level of private borrowing, which in turn depends on interest rates. The role of monetary policy in mitigating crises may be larger when policymakers have some control over interest spreads. More broadly, the model abstracts from investment, which is a key channel in the financial accelerator model of Bernanke et al. (1999). In their model financial frictions entail an important role for business balance sheets, which in turn makes aggregate net worth a key state variable. More recent work by Christiano et al. (2009), includes many of the real and nominal frictions studied by Smets and Wouters (2003) and Christiano et al. (2005), along with the financial frictions of Bernanke et al. (1999) embedded into an explicit banking sector. The financial frictions play a more prominent role in the transmission mechanism in these models, and so the policy reactions to financial variables may be even more crucial in such settings. There are many related issues which can also be addressed using our approach. For example, while we focused on uncertainty about the impact of financial frictions, there is also uncertainty about the type of frictions which best describes the economy. We could embed some of the models just discussed as alternative possible modes. The types of frictions – real, nominal, and financial – and their interactions vary substantially across these models, and thus policy implications may differ substantially as well. Finally, one important aspect of the current crisis has been that policymakers have engaged in “unconventional” policies, including purchases of a broad range assets and direct lending to the private sector. The models of Curdia and Woodford (2009a) and Gertler and Karadi (2009) allow for such additional channels of policy response. By embedding such models in our setting we can analyze how these unconventional instruments should be used in an uncertain environment, and how they would interact with the more conventional policies. In all of these cases, the MJLQ approach provides a simple and flexible way of structuring and analyzing optimal policy under uncertainty. By appropriately specifying the structure, the MJLQ framework can provide guidance to policymakers on how to deal with the broad forms of uncertainty they face.