Economics Letters 65 (1999) 91–96

Discretionary monetary policy with costly inflation

*Richard Dennis

Australian National University, Economics Program, RSSS, ANU, Canberra, ACT 0200, Australia

Received 27 April 1998; received in revised form 19 April 1999; accepted 4 June 1999

Abstract

This paper considers how an output cost of inflation affects the discretionary inflation bias. We show thatconditions exist under which costly inflation actually increases this inflation bias. 1999 Elsevier ScienceS.A. All rights reserved.

Keywords: Monetary policy; Inflation bias; Time-inconsistency

JEL classification: E31; E52

1. Introduction

Following Kydland and Prescott (1977) it is commonly recognized that through time inconsistencydiscretionary monetary policy can lead to a positive inflation bias. Several authors have addressed thisissue proposing methods to either reduce or eliminate this inflation bias. Rogoff (1985) suggestsappointing an inflation averse central bank governor while Walsh (1995) shows that an optimalcontract for the central bank governor can solve what is essentially a principal agent problem. Otherapproaches rely on the central bank governor either being concerned with their reputation as an‘inflation fighter’ or making the governor deposit a nominal bond that is released only at theconclusion of their contract.

More recently Pearce and Sobue (1997) demonstrate that any inflation bias present is lowered whenthe central bank is uncertain about the strength with which its policy instrument affects inflation.Uncertainty leads policy makers to err on the side of caution, resulting in cautious policy, and a lowerinflation bias.

This paper explores the implications for discretionary monetary policy of costly inflation. Weconsider a Phillips curve where a sub-optimally high inflation rate reduces welfare by permanently

*Tel.: 161-2-6249-2387; fax: 161-2-6249-0182.E-mail address: dennisr@coombs.anu.edu.au (R. Dennis)

0165-1765/99/$ – see front matter 1999 Elsevier Science S.A. All rights reserved.PI I : S0165-1765( 99 )00123-8

92 R. Dennis / Economics Letters 65 (1999) 91 –96

lower real output. Section 2 motivates the case for a non-vertical Phillips curve and describes theeconomic model used to analyze discretionary policy. Section 3 examines how costly inflation effectsthe magnitude of the discretionary inflation bias. Section 4 concludes.

2. Rules versus discretion with costly inflation

Many authors have suggested that there may be a negative relationship between inflation and outputor, alternatively, between inflation and output growth. Feldstein (1982) argues that inflation caninteract with a nominal based tax system raising the cost of capital and lowering investment andoutput. De Gregorio (1993) moots that firms have to hold money balances to purchase capital. Thecost of holding money increases as inflation rises, thus high inflation retards investment, which lowersoutput.

Another common argument is that inflation distorts price signals inducing agents to waste resourcessearching for bargains or otherwise avoiding the effects of inflation (menu costs, shoe leather costs,etc). Similarly, high inflation is generally thought to come hand-in-hand with high inflation variability,or inflation uncertainty. In the face of this uncertainty, Fischer (1993) argues, firms may delay

1investing until the uncertainty is resolved, and this delay lowers output.It is standard in the monetary policy literature (see Walsh, 1998) for the central bank to choose

2inflation to minimize the loss function:

1 l2 2F] ] * GL 5 E (p 2 p*) 1 ( y 2 ky ) , k . 1, l . 0, (1)t t21 t t t2 2

subject to

*y 5 y 1 a(p 2 E p ) 1 u , a . 0. (2)t t t t21 t t

*where p is the inflation rate, p* is the inflation target, y represents (logged) real output, yt t t2represents (logged) potential real output, and u |iid[0, s ] is a supply shock. Finally E is thet t21

mathematical expectations operator conditional upon period t 2 1 information. We assume that periodt 2 1 information includes all variables dated period t 2 1 or earlier as well as the structure of theeconomy.

At this juncture it is useful to ask what is optimal about the inflation target rate p*, or, morefundamentally, why inflation is in the loss function at all? The point to be made is that in the economydescribed by Eq. (2) only unanticipated inflation matters. Anticipated inflation has no effect on theeconomy — even in the short run — making it unclear why the loss function contains inflation.Moreover, with neutral inflation any rate of anticipated inflation is as good as any other; any rate ofinflation is optimal.

1Further arguments regarding the costs of inflation can be found in De Gregorio (1993) and Stockman (1991).Alternatively, the Tobin effect suggests that inflation may not always be detrimental for output, Tobin (1965).

2We use this loss function because it is standard in the literature and because we want to explore the consequences ofcostly inflation for the inflation bias in the context of the core literature. An alternative approach might have used a utilitybased loss function following Cubitt (1993) or Ireland (1997).

R. Dennis / Economics Letters 65 (1999) 91 –96 93

In light of these arguments, and the literature on costly inflation discussed above, we respecify the(inverted) Phillips curve as

*y 5 y 1 a(p 2 E p ) 2 f(p ) 1 u , a . 0 (3)t t t t21 t t t

where f(p ), f 9 5 b $ 0, represents the output cost associated with anticipated inflation. We assumet

that f(p ) equals zero at p*. It is in this sense that p* is an optimal inflation rate — it eliminates anyt

effect of anticipated inflation on output. A linear Taylor series approximation to f(p ) about p* givest

f(p ) 5 f(p*) 1 b(p 2 p*). (4)t t

Imposing f(p*) 5 0 and substituting (4) into (3) generates the Phillips curve

*y 5 y 1 a(p 2 E p ) 2 b(p 2 p*) 1 u . (5)t t t t21 t t t

3. Discretionary inflation bias

Substituting (5) into (1) and maximising, while holding inflation expectations constant, yields theinflation equation

*(k 2 1)(a 2 b )lyt]]]]]]p 5 p* 1 . (6)t (1 2 (a 2 b )lb )

The second term on the RHS of (6) represents the inflation bias. If we had used the Phillips curve (2)*in place of (5), then the inflation bias would be (k 2 1)aly . There are several points we can maket

about the magnitude and sign of the inflation bias when anticipated inflation is costly.

*1. When b 50 the bias collapses down to (k 2 1)aly : the costless inflation case.t

2. Depending on a and b the inflation bias can be either positive or negative. When b 50 theinflation bias is strictly non-negative.

3. When b 5a the output cost of anticipated inflation completely offsets any benefits to surpriseinflation and the inflation bias equals zero.

4. In the limit as b →`, the inflation bias→0 from below.5. If b .a, then the inflation bias with costly inflation must be smaller than the inflation bias without

the output cost.

The inflation bias under costless inflation equals that for costly inflation when

(a 2 b )]]]]]] 5 a.(1 2 (a 2 b )lb )

2This occurs when b 5 0, (a l 2 1) /al, which we denote b and b , respectively. The first of these1 2

roots, b , produces the familiar result that, if b 50, Eq. (5) collapses to Eq. (2). With the second root,1

b , note that the denominator al is always positive, implying that b will be positive or negative2 2

94 R. Dennis / Economics Letters 65 (1999) 91 –96

2depending on whether a l 2 1 is greater or less than zero. Given our theoretical assumption that b is2non-negative the only economically interesting case is that where a l 2 1 $ 0.

To examine how the inflation bias changes with b we differentiate it with respect to b, holding allelse constant. Evaluating this derivative at b 50 gives

≠(bias) 2U]]] ] *5 (k 2 1)l(a l 2 1)y . (7)b 50 t≠b

2When a l 2 1 . 0, the slope of the bias equation is positive at b 50, and conversely negative if2

a l 2 1 , 0.Similarly, the derivative of the bias with respect to b, evaluated at b , equals2

2 *(1 2 k)(a l 2 1)y≠(bias) t]]] ]]]]]]5 . (8)U b 5b 22≠b (1 2 (a 2 b )lb )

Clearly the denominator of (8) is positive. Consequently, because k . 1, we have the result that at2 2

b 5 b the derivative is positive if a l 2 1 , 0 and negative if a l 2 1 . 0.2

Therefore, we can make two further observations about the inflation bias.

21. If a l 2 1 , 0, then so too is b , and the only economically interesting point where the biases are2

equal is at b 50. The slope of the bias function is negative at b 50 indicating that the bias withcostly inflation is less than that where inflation is costless for all b .0.

22. If a l 2 1 . 0, then there are two economically interesting points at which the biases are equal.For b [ [b , b ] the bias with costly inflation is higher than that for costless inflation. As b1 2

3increases above b the opposite result prevails.2

2 2Of interest here is the fact that when a l 2 1 . 0, for all b [ [0, (a l 2 1) /al] the inflation biasactually increases despite the fact that this inflation bias has a permanent output cost. The inflationbias rises when a and l are large and b is small. This is the case where the monetary authority placesa large weight on output stabilization and gains a large benefit from surprise inflation. If thepermanent cost of inflation is small then the monetary authority is prepared to incur this cost, but tooffset the lost output due to the inflation cost the monetary authority must create a greater inflationsurprise than it otherwise would. Consequently, the inflation bias is greater in this case than it wouldbe if inflation were costless.

Fig. 1 graphs the inflation bias (as a percent of potential output) under hypothesized values for a,2and k, for two values of l as b changes. The solid line has a l 2 1 , 0 while the dashed line has

2a l 2 1 . 0.

To examine whether anticipated costs of inflation are likely to have any material impact on the sizeof the inflation bias we parameterize the f(p ) function using estimates from Fischer (1993). Table 4t

4of Fischer (1993) presents an estimate for b of 0.046 using panel estimation. Taking b 50.046,l50.5 (inflation receives twice the weight of output in the loss function), k51.02, and a 52.5 gives

3 2Here we further assume that a l , 4 to rule out discontinuous jumps in the bias as b increases.4Details of the sample period and countries included to generate this estimate are available in Fischer (1993).

R. Dennis / Economics Letters 65 (1999) 91 –96 95

Fig. 1. Inflation bias. Alpha51.5, k51.02.

96 R. Dennis / Economics Letters 65 (1999) 91 –96

an inflation bias of 0.025% of potential when inflation is not costly and a bias that is approximately0.026% of potential when inflation is costly. In this example the presence of an output cost of inflationactually raises the inflation bias by about 4%. While small this increase in inflation is neverthelessnoteworthy, given the plausibility of the underlying parameters.

4. Conclusions

In this paper we have extended the standard ‘rules versus discretion’ model to include the casewhere anticipated inflation has a permanent output cost. When inflation is costly we have shown thatthe inflation bias associated with discretionary policy is generally smaller than that when inflation iscostless. Interestingly, if the marginal cost of inflation is large enough the inflation bias can even benegative. Finally, we have also shown that for some parameter values the presence of costly inflationactually increases the size of the bias. Interestingly, using an estimate of the cost of anticipatedinflation we have presented an example where the inflation bias actually increases.

Acknowledgements

I would like to thank participants of the ANU, RSSS, Tuesday seminar series and an anonymousreferee for their comments. The usual caveat applies.

References

Cubitt, R., 1993. Welfare and monetary precommitment in an economy with menu costs and unionized wage setting. Bulletinof Economic Research 45 (1), 7–17.

De Gregorio, J., 1993. Inflation, taxation, and long-run growth. Journal of Monetary Economics 31 (2), 271–298.Feldstein, M., 1982. Inflation, tax rules and investment: some econometric evidence. Econometrica 50 (4), 825–862.Fischer, S., 1993. The role of macroeconomic factors in growth. Journal of Monetary Economics 32, 485–512.Ireland, P., 1997. Sustainable monetary policies. Journal of Economic Dynamics and Control 22, 87–108.Kydland, F., Prescott, E., 1977. Rules rather than discretion: the inconsistency of optimal plans. Journal of Political

Economy 85 (3), 619–637.Pearce, D., Sobue, M., 1997. Uncertainty and the inflation bias of monetary policy. Economics Letters 57, 203–207.Rogoff, K., 1985. The optimal degree of commitment to an intermediate monetary target. The Quarterly Journal of

Economics, November.Stockman, A., 1991. Anticipated inflation and the capital stock in a cash-in-advance economy. Journal of Monetary

Economics 8, 387–393.Tobin, J., 1965. Money and economic growth. Econometrica 33 (4), 671–684.Walsh, C., 1995. Optimal contracts for central bankers. The American Economic Review, March.Walsh, C., 1998. Monetary Theory and Policy, MIT Press, Cambridge, MA.