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5 EL ENFOQUE DEL MARCO LÓGICO
The HMT interest rate rule suggests the Fed's behaviour in formulating monetary policy can be represented by a systematic pattern of reacting to ination and the output gap. But, what exactly is the objective the Fed wants to achieve? Does the Fed have a dual objective of stabilizing prices and output? Or does it have a single objective of maintaining price stability, and only treats the output gap as a leading indicator? (i.e. reacting systematically to output gap as high output gap will lead to high ination). In order to overcome this ambiguity, another approach to understanding central bank behaviour is to formally model a central bank's problem. This approach starts with explicitly specifying the policymakers' loss function and deriving the optimal policy rule that should be followed in order to minimize the specied loss function.
The central banks behaviour in formulating monetary policy is commonly modelled as the solution to the optimal control problem. In their famous paper, which outlines and summarizes recent research in monetary policy, Clarida, Gali, and Gertler (1999) indicate that modelling a central bank's problem in this way has become a standard approach for the literature in this area. This approach is favoured due to its sim- ple, but realistic representation of the real world problems facing policymakers. More importantly, it treats a central bank like any other agent in the economy, which intends to maximize some objective function subject to certain constraints. Similar to the analysis of consumer behaviour, which assumes the observed action is the outcome of the constrained optimization problem of trying to maximize utility subject to a budget constraint, a central bank's problem in conducting monetary policy can also be put in the same perspective. The policymaker's problem can be characterized as using an instrument such as the interest rate, together with knowledge of the evolution of the
economy and the transmission mechanism process, seeking to minimize its loss function by stabilizing the objective variables (such as ination and output).
In this regard, Cecchetti (2000) characterizes a central banks' problem as the solution to a complex control problem similar in structure to the one faced by an aircraft pilot. Given knowledge of the weather and wind, a pilot's objective is to use the aircraft's controls, to y from one place and land safely at the destination point. Similarly, a central bank's objective is to move interest rates, given its knowledge on how the economy evolves, to achieve certain objectives like maintaining steady income growth and stable prices. Hence, the optimal control problem facing central bankers involves minimizing a loss function (consisting of weighted sum of price variability, output variability, nancial variability, etc), subject to the evolution of the state variables (the economic structure describing the paths of output and ination) which act as a policy constraint, using a control rule (the optimal policy rule describing the optimal reaction of a central bank in solving the problem).
In order to understand the framework of a central bank's problem, the rest of this section reviews the general set-up about the application of optimal control problem as a tool to formulate monetary policy. It covers a short description about specication of the loss function, state variables and how to model their movement and the use of optimal rule. However, to minimize repetition, we will not provide in this section any illustration about the mechanics and workings of the optimal control theory framework in modelling a central bank's policy behaviour. We leave that to Chapter 4, where we will illustrate how the optimal control theory is used to represent BNM's policy behaviour.
2.2.1 Specication of a Central Bank's Loss Function
To determine a central bank's policy choice, specication of its preferences is needed. The specied objective function becomes the point of reference for policymakers to evaluate and discriminate all possible policy options at their disposal. As each policy option will generate a dierent policy outcome, the objective function is used as a tool to summarize how consistent each policy outcome is with the policymakers' ultimate aim. This is done by comparing the quantitative result of the objective function for each policy option.
In general, a central bank's objective function can be written in dierent forms, depen- ding on its underlying policy objectives and preferences. Cukierman (1992) provides a detailed discussion of several motivations behind dierent central bank's preferences and objectives. Besides the common objective for monetary policy of achieving price and output stability, Cukierman, argues a central bank's objective in formulating monetary policy could also be motivated by political pressure to ensure a govern- ment being re-elected. A central bank may also have a balance-of-payment motive, an objective to maximize seignorage revenue, or the objective of stabilizing the nancial system. Hence, dierent objectives pursued by central banks will inuence the way the loss function is formulated in the theoretical model.
Walsh (2003) claims it is standard practice in the literature to assume a central bank's preference is represented by an objective function that consists of target variables like ination, output and stabilizing (smoothing) interest rates. The benet of low and stable ination to an economy is well known and documented. Among others, the cost of ination to an economy is high and entails signicant social losses. Hence, the primary objective of the monetary policy adopted by many central banks around the world is to stabilize ination at a level low enough that it becomes irrelevant to household and rm decision-making.
The role of output stabilization in the loss function is to ensure the economy always operates at or near its full potential. The benet of an economy operating at its full potential is straightforward. For example, operating below potential means resources are redundant. Social welfare, as a whole, can be improved by utilizing these idle resources. Similarly, the notion that ination is created by excess demand (demand pull ination) is related to the fact that an economy is operating beyond its potential level. The capacity constraint to produce this additional demand will be translated into upward price pressure. In addition, a central bank also wants to minimize output volatility in order to promote further economic growth. Ramey and Ramey (1995) present evidence that in a broad group of 95 countries, there is a strong negative correlation between output volatility and growth.
Many empirical studies have shown that the interest rate movement is highly correlated with its past value. This observation has caused many to include interest rate smoothing in a central bank's loss function. While the reason for including price and output stability is intuitive, the rationale for including an interest rate smoothing objective
in a central bank's loss function is more controversial and has been discussed in many papers. See among others Lowe and Ellis (1997) and Sack and Wieland (2000) for detailed discussion and a literature review on this area. For example, central banks smooth interest rates to maintain nancial stability (Cukierman (1992)), to enhance credibility by minimizing policy reversal (Goodhart (1999)) or just a reection of a central bank's cautious attitude to information and model uncertainty (Clarida, Gali, and Gertler (1999)).
The loss function central banks try to minimize is commonly written in a quadratic form. There are three main reasons for this. The rst is to incorporate a cen- tral bank's preference to stabilize its objective variable around a certain target. For example, Walsh (2003) argues that most central banks have a desire to minimize output and ination uctuations. In conducting monetary policy, central banks always prefer output to be near its natural level. This will ensure an economy operates at near full employment, as operating below full capacity is inecient, while operating above capacity puts upward pressure on price levels. Likewise, central banks always try to keep ination close to its target level. Hence, specifying the loss function in a quadratic form will generate a role for a stabilization policy that is absent when the loss function is specied in a quasi-linear form . The second reason for the popular use of a quadratic loss function is theoretical. Woodford (2003) (Chapter 6) shows that, under certain conditions, the quadratic central bank's loss function can be shown to originate from the second order approximation to the expected utility of the economy's representative household. Hence, it can be argued that a central bank's objective function in formu- lating monetary policy is not done on an ad-hoc basis, but is instead chosen based on a public welfare consideration. The last reason for the preference of using quadratic form is its mathematical convenience. A quadratic loss function, together with a linear specication for the economic structure, results in an optimal decision rule that is also linear. This simplies the computation and estimation burden of the theoretical and empirical exercise.
2.2.2 State Variables and Modelling of the Economy
As the name suggests, state variables describe the state or existing condition of the system. In the context of monetary policy formulation, they are macroeconomic
variables that provide information on the condition of the economic system at a point in time. The three most common state variables central banks monitor very closely are ination, output and the level of interest rates. These variables are closely monitored not only for their importance for central banks' policy objectives, but also due to their information content in summarizing the overall condition of an economic system. For example, an economic system that produces a large output gap or has an ination rate above its targeted level, give signals that it is currently overheating or operating beyond its optimal level. Similarly, interest rates that are persistently high indicate a tight money market condition; or that agents' ination expectations are on the upward trend. After doing an assessment on the overall state of the system, policymakers will consider the appropriate policy action to rene the current condition of the economic system. In the example given here, the central bank's reaction would be to raise its policy instrument (short-term interest rate) to slow down aggregate demand with the objective of steering the system towards its optimal path.
The dynamics of the state variables are assumed to follow a certain form of structure, which essentially describes the mechanical operation of the economic system. This will form the constraint to the central bank's optimization problem. There are two general approaches to construct these constraints. The rst approach constructs the simple structural equations like the IS and Phillips Curve functions on an ad-hoc basis to t the data. This method was popularized by Rudebusch and Svensson (1999) and was used in other subsequent work, among others by Favero and Rovelli (2003), Ozlale (2003), Soderstrom, Soderlind, and Vredin (2005) and Dennis (2004, 2006). Another approach to represent the operation of the economy is to develop a dynamic stochas- tic general equilibrium (DSGE) model. The main attractiveness of DSGE models is that they are derived from rst principles. This approach overcomes the limitation of structural modelling in treating parameters to be time invariant, or as popularly known in the literature as the Lucas critique (Lucas (1976)). Obviously, for this reason, DSGE models are seen as powerful tools that provide a coherent framework for policy discussion and analysis. Among examples of work that apply this approach and use it to analyze central banks' policy behaviour are Devereux, Lane, and Xu (2006), Justiniano and Preston (2006) and Kam, Lees, and Liu (Forthcoming). In this thesis, we adopt both approaches to model the Malaysian economy and later use them to analyze BNM's policy behaviour.
2.2.3 The Control Variable and Optimal Instrument Rule
The control variable in this optimal control problem is the instrument a central bank uses to execute its monetary policy. It operates to steer the economic system by aecting the movement of the state variables (output and ination). After knowing the overall set-up and operation of the system, how should a central bank use its control instrument to steer the economic system towards achieving its specied objectives? The solution to a central bank's optimal control problem is to set its control variable according to the optimal rule. It is mathematically derived to minimize the specied loss function, given the knowledge of the economic structure. The optimal rule serves as the `decision rule' or `optimal reaction function' to policymakers in determining the correct value of ne-tuning the economic system needs in order to ensure the objective variables are moving on the desired path.
In this regard, most of the recent literature derives the optimal decision rule for the control variable in the form of an interest rate rule. Depending on the way the optimal control problem is constructed, the corresponding optimal interest rate rule derived from this optimization problem may have a dierent form than the HMT interest rate rule. To dierentiate between these two classes of interest rate rule, the HMT-type interest rate rule is sometimes known as the `simple interest rate rule' while the optimal interest rate rule is known as the `complex interest rate rule'.
This distinction leads to another strand of research in the literature which class of interest rate rules perform better and hence should be favoured by central bankers? This strand of research compares the performance of the optimal interest rate rule vis-à-vis the simple HMT-type interest rate rule across dierent economic models. See among others Taylor (1999b), Levin, Wieland, and Williams (1999, 2003), Batini, Harrison, and Millard (2001) and Orphanides and Williams (2007) for examples and results of these comparisons. The general conclusion of the research in comparing the performance of simple and complex rules is that the simple interest rate rule performs better on average than the complex rule when each of them is used across dierent economic models. This result is not surprising. As mentioned earlier, the optimal interest rate rule is mathematically derived from a specic model that forms a central bank's optimization problem, hence making it model-specic. The optimal interest rate rule only works best in a model where it is originally assumed.
In contrast, the simple HMT-type interest rate rule is more robust to model misspeci- cation. Since the HMT interest rate rule is not derived from any economic model, but instead originates from the attempt to describe the systematic behaviour of central bankers in formulating monetary policy, the HMT rule has implicitly incorporated the best practice principle that central bankers around the world should follow in setting policy instruments. Perhaps, besides its simplicity, the robustness of the HMT rule is the main property that has contributed to its popularity. Even though it is not expli- citly derived to solve the optimization problem by formally considering the economic structure and a central bank's loss function, the notion of setting interest rates by reacting systematically to ination and output gap; and adhering to Taylor's Principle, are the general code-of-conduct that lead to a favourable economic outcome.