Symmetric or Asymmetric Monetary Policy Rules in Different Countries?
Bengt Assarsson1 Department of Economics, Uppsala University Paper to be presented at 10th Annual SNEE European Integration Conference, May 21, 2008 This version May 6, 2008
[email protected]
Abstract This paper discusses and estimates monetary policy rules for a number of countries. The paper departs 2
2
from the conventional symmetric policy objective function L = (π − π T ) + v (Y − Y ) , from which reduced form policy rules can be derived. Since the socially desirable output Y * > Y there is a case for asymmetric policy rules, since a positive output gap is to prefer to a negative gap. I estimate policy rules for 14 inflation and 5 non-inflation targeting countries and test for symmetry. The results show that in the tests of symmetry done in this paper only one country, South Korea, has a significantly asymmetric policy with a smaller weight put on positive output gaps. One country, the UK, has a significantly asymmetric policy with smaller weight put on negative gaps. For the other countries a symmetric policy cannot be rejected.
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The views expressed here is solely the author’s and may only by accident coincide with the views of the Board of Governors (Direktionen) of Sveriges riksbank.
1. Introduction Theoretical monetary policy analysis views central banks as optimizing agents. This view is also used in practice by many central banks or is at least part of the rhetoric or models used by the central banks. In the conventional theory the central bank maximizes (or minimizes) a quadratic objective function (loss function) conditional on private sector behavior. This results in an optimal monetary policy rule, describing the actions of the central bank. Such simple rules (Taylor rules) can also be postulated or estimated empirically and evaluated in general equilibrium models in which the optimal rule in itself may be difficult to derive. In the most common Taylor rule for a central bank using the interest rate as its instrument the arguments used are an output and an inflation gap. For an inflation targeting central bank the inflation gap is the deviation from a set inflation target. Most often a smoother is used (lagged interest rate) that dampens the reactions in the interest rate. Such a simple rule often gives an accurate description of the historical development of the interest rate. Sometimes it also comes close to what some modern dynamic stochastic general equilibrium model considers optimal. A recognized problem with estimated Taylor rules is that the central bank behavior is not identified. The reason is that the estimated parameters are functions of the structural parameters of central bank preferences as well as of the parameters of private sector behavior, i.e. in Phillips curves and aggregate demand curves. Hence, a low weight on the output gap might not reflect low priority on part of the central bank but rather illustrate the behavior of consumers and price setters. Macroeconomic models assume monopolistic firms and frictional labor markets. This means that equilibrium volumes are undesirably low. While a negative output gap lowers welfare a positive gap is socially desirable. Hence, one could suspect that some central banks would raise interest rates less in response to a positive output gap than they would lower the interest rate in response to a negative output gap. In other words, the Taylor might be asymmetric. Since the conventional theory generally does not consider this asymmetry this would be a case in which practice (for some central banks) might be ahead of theory. In this paper I test this symmetry hypothesis. I assume that it is this (optimal) behavior of the central bank that is the sole reason for the asymmetry, i.e. there is no asymmetry in private sector behavior. Then I can identify potential differences between central bank behavior in different countries as well as between different types of policies; inflation targeting vs. non-inflation targeting countries. The next section describes the monetary policy problem and why it is reasonable to depart from an objective function with output and inflation gaps. Section 3 gives a more technical discussion about the objective function and explains the case for an asymmetric objective function/nonlinear policy rule. Section 4 presents data and econometric methods while section 5 gives the empirical results. Finally, there is a concluding section.
2. The Monetary Policy Problem Government policies, whether tax, fiscal, social, monetary, aim at affecting resource allocation or distribution one way or the other. Money facilitates transactions in the economy but comes at a cost. The opportunity cost of money is the nominal interest rate foregone. Hence, the higher the interest rate, the higher the cost of holding money. Since the cost of producing money is negligible it seems as if a zero interest rate would optimize money holdings – the so called Friedman rule. In view of the
Fisher equation this sets long run inflation to minus the real interest rate, deterrent for many. But in a frictionless world this seems as the ultimate and simple monetary policy. However, macroeconomic theory acknowledges several frictions, among which rigidities in nominal prices and wages are regarded as most important. When the economy is hit by an aggregate shock some nominal prices and wages respond slowly while yet other prices may respond quickly. Apparently, relative prices change and affect the resource allocation, which becomes then suboptimal. This suboptimal allocation is the result of the price rigidities. The resource allocation would be left unaffected (and possibly optimal) in the case of perfect price and wage flexibility.2 So, the monetary policy problem is twofold: •
determine the optimal rate of interest (rate of inflation)
•
reduce the resource allocation problems associated with nominal price and wage rigidity
using an appropriate monetary policy instrument, such as the short term interest rate now used in many countries (interest rate policy). One can also view this as deciding upon a normal rate of interest consistent with the optimal rate of inflation – i.e. zero in the Friedman case above – and changing this interest rate up and down so as to mitigate the allocation problems associated with price and wage rigidities. This description of the problem seems far from the rhetoric exercised by the monetary authorities in many countries, even though it is standard in the literature, e.g. in Woodford’s book. There are differences among central banks in their effort to communicate their policies. Most central banks have explicit inflation targets and do not stress their role in stabilizing the real economy. Rather, as in Woodford’s book, it is (implicitly) assumed that a central bank with inflation target fulfils the role above. The concept of “flexible inflation targeting” as put forward by e.g. (Svensson and Woodford 2004; Svensson 2006; Woodford 2007) has also been applied by e.g. the central banks in Norway and Sweden. By this is meant a policy in which the central bank acknowledges the tradeoff between the inflation target and some real target and put some weight on the real target as well. Technically, this is formulated as a social welfare, or loss, function to be optimized by the central bank. There is a widespread consensus about this setup but less so about the details, for instance what are the optimal targets, how to measure these, and so forth.
3. Defining the Social Loss Function The legislation underlying monetary policy in many countries is based on a lexicographic preference ordering3, while economic theory most often postulates a quadratic loss function. This loss function can be used to derive an optimal policy rule for the central bank, taking account of optimizing private 2
This description is similar to Woodford, M. (2003). Interest and Prices. Foundations of a Theory of Monetary Policy. Princeton and Oxford, Princeton University Press.
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This is clear from, for instance, the Swedish legislation: ”The target for monetary policy shall be to maintain a fixed value of money. This target is outspoken in the law. As an authority under the parliament the Riksbank shall also, without setting the target of price level stability aside, support the targets for economic policy in general with the purpose of achieving balanced growth and high employment level.” See Finansdepartementet (1997). Riksbankens st„llning. Stockholm, Regeringskansliet, Finansdepartementet.. The Riksbank has interpreted ”maintain a fixed value of money” as 2 percent inflation as measured by the Consumer Price Index.
sector behavior. Alternatively and in practice, Taylor rules can be estimated and actual central bank behavior be evaluated in terms of a loss function. Central bank legislation typically favors price level stability, though the rhetoric as well as actual behavior of many central banks seems to take account of the real sector as well. A typical loss function would be 2
2
L = (π − π T ) + v (Y − Y ) ,
(1)
where π T is the inflation target, Y is potential GDP and v is the relative weight put on output gaps. A central bank using (1), unless v=0, violates lexicographic preferences, since (1) implies invoking a tradeoff between inflation and output deviations. Hence, there seems to be a wedge between legislation and actual behavior in many countries which to some extent seems unhealthy and problematic, particularly as it comes to evaluating the policy. Sometimes it is argued that the rate of interest should be included in the loss function. The reason is that the higher the nominal interest rate, compared to some risk-free rate, the higher the social cost of money. This cost would be at the lowest when the interest rate is zero, according to the BaileyFriedman rule. The discussion of optimal monetary policy has its origins in (Bailey 1992; Friedman 2006). They argued that when a government has access to lump-sum taxation to finance its expenditure, the optimal monetary policy should adopt a rule (later called the Friedman rule) that generates a zero interest rate, corresponding to a zero inflation tax. The logic is straightforward. Because there is a wedge between the private marginal cost of holding money (which is the nominal interest rate) and the social marginal cost of producing money (which is approximately zero), a positive nominal interest rate generates social losses. Thus, to achieve optimum, the monetary authorities should set the nominal interest rate to zero in order to eliminate the private opportunity costs. (Chari, Christiano et al. 1996) and (Correia and Teles 1996) provide a general conclusion whereby the validity of the Friedman rule crucially depends on the property of consumers' preferences and the role of money for producing transaction services. In the case lump-sum taxation is unavailable the optimal nominal rate of interest might be some positive number, since then the inflation tax can reduce the excess burden imposed by other taxation. Hence, an alternative loss function should include the deviation of the nominal interest rate from some risk-free rate of interest, such as in 2
2
L = (π − π T ) + v (Y − Y ) + ( i − 0 ) , 2
(1’)
where the risk-free interest is assumed to be zero as in the Bailey-Friedman case. It is straightforward to derive a policy rule using (1) and substituting a Phillips curve for π and an aggregate demand curve for Y . The linear curves and the quadratic form (1) yields a linear policy rule, as illustrated in Diagram 1, where the left out demand curve is in the interest rate/output ( i , Y ) space. The point A illustrates the equilibrium in which the targets (π T , Y ) in (1) are fulfilled. The diagram also illustrates
Y as the maximum long run attainable output level given the existing institutions – such as monopolized firms and labor unions – and Y * as the level of output that maximizes welfare. Clearly, it is Y rather than Y * that is commonly referred to in the literature though Y * is the more relevant concept in (1). If the monetary authorities were to aim at Y * , however, then the inflation target would not be credible and hence an inflation bias would occur. This is illustrated in the diagram as the distance AD, where D is the point at which the authorities aims at Y * and actual and expected inflation is above target, i.e. monetary policy lacks credibility.
Instead of announcing an incredible target the central bank can use different weights on the real variable depending on the output gap being positive or negative. In other words, the central bank would raise the interest rate by less if the output gap is positive compared to lower the interest rate if the output gap is negative. The reason of course is that welfare is raised temporarily if Y < Y ≤ Y * but lowered in the case Y > Y . A simple generalization of the loss function could then look something like 2
2
2
L = (π − π T ) + v1 (Y − Y )Y >Y >Y * + v2 (Y − Y )Y Y > Y α v 1
(3a)
−1
1 * T i = in + η α + (π − π ) + α (Y − Y ) for Y < Y ≤ Y α v 2
(3b)
and v1 > v2 . This could be simplified to the reduced form * i = in + a1 (π − π T ) + b1 (Y − Y ) for Y > Y > Y
(4a)
* i = in + a2 (π − π T ) + b2 (Y − Y ) for Y < Y ≤ Y
(4b)
in which the hypothesis of asymmetric response could be tested. The form (4) lacks dynamics usually introduced into Taylor rules. A very simple form is * it = k + λ it −1 + a1 (π t − π T ) + b1 (Yt − Yt ) + ε 1t for Yt > Yt > Yt
(5a)
* it = k + λ it −1 + a2 (π t − π T ) + b2 (Yt − Yt ) + ε 2 t for Yt < Yt ≤ Yt
(5b)
k = π T + r , where r is the real or 1− λ natural rate of interest. ε 1 and ε 2 are i.i.d. stochastic errors in the policy process. We could merge (5a)-(5b) into for which we could derive the normal rate of interest as in =
it = k + λit −1 + a1 (π t − π T )
Yt >Yt >Yt*
+ b1 (Yt − Yt )Y >Y >Y * + a2 (π t − π T ) t
t
t
Yt
