CONSERVATIVE CENTRAL BANKS: HOW CONSERVATIVE SHOULD A CENTRAL BANK BE?

, DOI:10.1111/sjpe.12149, Vol. 65, No. 1, February 2018. CONSERVATIVE CENTRAL BANKS: HOW CONSERVATIVE SHOULD A CENTRAL BANK BE? Andrew Hughes Hallett* and Lorian D. Proske** ABSTRACT Using Rogoff s, 1985 model, we determine how inflation averse a central banker should be, given the level of volatility and projected output gap in the economy. We confirm a strong degree of conservatism, almost twice what society would have chosen. But, for a range of developing countries and the OECD, economies that systematically experience higher levels of output volatility would do best to hire a central banker who is more inflation averse than society, but less so than in stable developed economies. Thus, while a conservative central banker remains desirable, the trade-off is with output volatility rather than with the output gap itself. I INTRODUCTION One of the best known results in monetary policy is Rogoff s theory of the conservative central bank [Rogoff, 1985]. This proposition appears in almost every text book on monetary policy and states that inflation will be lower (closer to target) and output more stable if the central bank is designed to have greater inflation aversion than the electorate would have chosen for itself. But just how much more conservative should the central bank be? That question remains unanswered. We provide a formal answer, in both theory and in practice. Using data for the OECD and 15 emerging market economies, we find inflation aversion should nearly double (preferences for output stabilization halve); a result which is attenuated, in poorly managed economies, by the underlying degree of output volatility. II AN OPTIMAL (CONSERVATIVE) CENTRAL BANK We start from the classic objective (loss) function for an independent central bank, extensively used in the central banking literature: Min L ¼ 1 h i 2 ðp t p t Þ 2 þ by ð t kþ 2 ð1þ *George Mason University and University of St Andrews **University of St Andrews 97

98 A. HUGHES HALLETT AND L. D. PROSKE This loss function is divided into the perceived cost of inflation (p t ) deviating from its optimal level p t *, ðp t p t Þ 2 ; and of output y t deviating from a h i h i target level k, by ð t kþ 2 (Alesina and Gatti, 1995). The term b is a known parameter denoting the central bank s aversion to output losses relative to inflation. 1 A value of b = 0 implies strict inflation targeting; it specifies a central bank with the sole goal of minimizing the cost of inflation deviating from its optimal point. If b = 1, the central bank places equal weights on minimizing the deviations of inflation from its optimal value and minimizing any deviations of output from target. Finally, b > 1 refers to a liberal central bank that places more weight on reducing the size of output gap. As is well known, Rogoff (1985) showed that, using a similar loss function, an independent but inflation-averse central bank will result in lower average inflation at the cost of limiting the ability of the central bank to react to output shocks in the economy. But he showed more; he demonstrated that inflation would be reduced more than output volatility increases if the central bank adopts a stronger degree of inflation aversion than society would have chosen for itself. That way the economy is made better-off, on both counts, than under discretionary policies. Rogoff s model uses a Lucas aggregate supply function, where output reacts positively to unexpected inflation, but negatively to adverse shocks. The shocks are randomly distributed with mean zero and variance r 2 e (Alesina and Gatti, 1995): y t ¼ p t p e t þ e t ð2þ 2 In this model, inflation is set after expectations are formed (wages are set before the shock is known). We assume that target inflation p t * is zero, b 0 and k > 0 so that the output target is set above its natural rate in order to offset the inevitable distortions caused by imperfect competition and the imposition of taxes (Alesina and Gatti, 1995). Optimal policies To determine optimal policies for this model, we insert the Phillips curve into the loss function to get: Min L ¼ 1 h i 2 ðp tþ 2 þ bðp t p e t þ e t kþ 2 ð3þ Minimizing (3) with respect to p and solving for rational (private sector) expectations we 1 Relative because, if (1) is written with separate preference parameters on the p and y terms, it can be renormalized (without loss of generality) to the form of (1), with b the ratio of the two separate parameters. This distinction can play a role in the study of the effects of greater transparency. But not here where preference parameters are known: see Demertzis and Hughes Hallett (2007). 2 The unit coefficient on p t p e t is obtained by choice of units. The conclusions that follow are invariant to that choice.

and obtain p ¼ bk b ð1 þ bþ ð4þ EðpÞ ¼ bk ð5þ y ¼ 1 e; implying EðyÞ ¼0 ð6þ ð1 þ bþ One concern might be time inconsistency: a strategy that is optimal at a point of time t 0, may no longer appear optimal at t 1. However, Barro and Gordon (1983) and Rogoff (1985) assume perfect information. Thus, if the central bank tries to surprise the private sector with inflation higher than originally announced in later periods, this can be predicted and the expectation of low inflation rejected. This leaves the central bank with an inflation bias (bk) but the same output growth: a sub-optimal outcome. Thus, time inconsistency may be a problem, but not in this paper because it takes a timeless perspective (Woodford, 2003). Rogoff (1985) argues that this higher-than-optimal inflation rate can be avoided if a credible and independent central banker with preference parameter ^b\b, is appointed before any expectations are formed. Obviously this can be done with ^b ¼ 0. However, that solution is not optimal for society or the private sector since they care about output as well as inflation. This dilemma can be avoided if the central bank looks for an operational rule (^b) that provides smaller losses for society than under pure inflation targeting, 3 EL ð Þ ¼ 1=2 ^b 2 þ b k 2 þ r2 e, when private preferences are defined by ð1þ^bþ 2 ð1þ^bþ 2 b 6¼ 0 but the central bank s policy rule uses ^b ¼ 0; and smaller losses than under discretionary policies when EL ð Þ ¼ 1=2 ^b 2 þ b k 2 þ r2 e is evaluated at ^b ¼ b. It is obvious that the losses can be reduced in the first case if ^b is increased incrementally from zero since that will have a bigger effect on the r 2 e term than the k 2 term. For the same reason, the losses can be reduced in the second case if ^b is decreased below b. In either case, how much the ^b parameter should be modified from b will depend on the ratio of r 2 e to k2. Operating rules HOW CONSERVATIVE SHOULD CENTRAL BANKS BE? 99 The central bank is now in a position to minimize society s expected losses by its choice of priority for inflation vs. output stability. This is the only parameter that remains to be chosen if the central bank is to implement optimal decisions thereafter: 3 This expression for E(L) is obtained by minimizing (2) to obtain the optimizing rules (4) (6). These rules are then inserted into (2), leaving ^b to be chosen in a second stage to obtain the optimal design of central bank. See Hughes Hallett (2004) for details.

100 A. HUGHES HALLETT AND L. D. PROSKE 2 0 12 0 123 Min E L ^b ¼ E4 1 @ 2 ^bk ^b 1 þ ^b ea þ b @ 1 2 1 þ ^b e ka 5 ð7þ To find the optimal choice of ^b, we solve: "!!!# @E 1 ¼ E k @ ^b ð1 þ bþ e ^b ^bk ð1 þ bþ e 1 1 þ b ð1 þ ^bþ 2 e k 2 ð1 þ ^bþ ¼ 0 ð8þ 3k ^b 1 þ ^b 2 þ ^br 2 e br2 e The solution to ð8þ is : 1 þ ^b 3 ¼ 0 ð9þ The denominator in (9) is positive since ^b 0. Hence, the first order conditions for this problem, ^b 1 þ ^b 3k 2 þ ^b b r 2 e ¼ 0, require ^b\b. In other words, society s welfare losses will be minimized by choosing policies that are more inflation averse than society would have chosen for itself; and hence a central bank that prioritizes lower inflation over output stability by more than the private sector would prefer. On the other hand, the larger the output volatility, the closer the optimal ^b will be to electorate s choice of b. To get a more precise solution, take a first-order approximation to ^bð1 þ ^bþ 3 around b. The first-order conditions from (9) now become bð1 þ bþ 3 þ ^b ^b b r 2 b 1 þ 6b þ 9b 2 þ 4b 3 e þ...þ k 2 ¼ 0 ð10þ The optimal solution is then: bð1 þ bþ 3 ^b ¼ b 1 þ 6b þ 9b 2 þ 4b 3 þ r 2 ð11þ e =k2 which is increasing 4 in r2 e. This is easy to calculate given b, r 2 k 2 e, and k. Finally, notice that @ ^b b bð1 þ bþ 3 @r 2 ¼ [ 0: ð12þ e =k2 ½1 þ 6b þ 9b 2 þ 4b 3 þ r 2 e =k2 2 Š Consequently, the larger is r2 e when ^b\b, the closer will ^b approach b from k 2 below as shown in Figure 1 meaning the optimal central bank remains conservative, but less so as output volatility increases relative to the typical output gap. 4 In this paper, we are concerned only with how much ^b should deviate from b. The calculations can be done for any given b.

HOW CONSERVATIVE SHOULD CENTRAL BANKS BE? 101 Figure 1. Conservatism with increasing volatility in the output gap. Variances Since lower inflation is obtained at the cost of greater output volatility, it is of interest to see if the extra degree of conservatism called for at the central bank would exaggerate or modify this effect; and hence whether this degree of additional conservatism will increase output or inflation volatility by more in economies with greater output uncertainty. Taking these two questions in turn, inflation volatility is given by (4): VðpÞ ¼^b 2 r 2 e =ð1 þ ^b Þ 2. Hence, @VðpÞ=@^b ¼ 2^b r 2 e =ð1 þ ^b Þ 3 [ 0. Meanwhile, @^b the first term of which is positive; as is the second term since @re, 2 @VðpÞ ¼ @r 2 e @^b ¼ @r 2 e ^b 2 r 2 e ð1þ^b Þ 2 bð1þbþ 3 [ 0 for any given value of k. Consequently, reducing ½1þ6bþ9b 2 þ4b 3 þr 2 e =k2 Š 2 ^b in order to create a conservative central bank will lower inflation volatility as well as average inflation itself. But economies with higher output volatility will find that the optimal degree of conservatism is less, but the degree of inflation volatility more (other parameters equal), than in the developed economies with smaller output volatility. Put another way, the cost of stabilizing or lowering inflation rises as r 2 e (or r2 e =k2 ) rises. This explains why we ease up on the degree of added conservatism in counties with high output instability. There are parallel results for the volatility of output. From (6) we have ðþ @r 2 e Vy ð Þ¼r 2 e =ð1 þ^b Þ 2 and @Vy ¼ 1 ð1þ^b Þ 2 @^b \0 since @^b @r 2 e bð1þbþ ¼ 3 [ @r 2 e ½1þ6bþ9b 2 þ4b 3 þr 2 e =k2 Š 2

102 A. HUGHES HALLETT AND L. D. PROSKE 0. But @Vy ðþ ¼ 2r2 @^b e \0. Hence, reducing ^b to create a conservative central ð1þ^b Þ 3 bank will raise output volatility, our standard result, but less so in economies that have had higher output instability to start with. Summary The existing literature demonstrates that the optimal design of central bank will be more inflation averse than society itself would prefer ð^b \bþ; but has been unable to supply a closed form solution for ^b. The nearest approach is Walsh s (2010) graphical demonstration that a ^b value exists. As a result, it has not been possible to say how far we should reduce b to get to the best design of central bank. Similarly, it has not been possible to say that b ^b is decreasing in output volatility with the implication that ^b varies systematically across economies. Nor has it been possible to study how inflation and output volatilities vary with increasing conservatism. III EMPIRICAL RESULTS All data are taken from World Bank (2016). A sample period of 54 years was used to portray a long-term trend for potential output and estimate the ratio r 2 e for each country. The countries were selected as representative of various k 2 geographical zones and differing economic sizes to illustrate that the results hold for developing countries in general. 5 The OECD was included as a standard developed country comparator. The output gap target, k, was obtained using a standard Hodrick Prescott filter, to give a time-varying (moving average) estimate of potential output at each point. A lambda value of 6.25 was used, recommended by Ravn and Uhlig (2002) for the specific value to be used when dealing with annual data. Finally, the Root Mean Squared Error about the trend was used to calculate r 2 e, the sample standard deviation of the differences between actual and potential output. Comments on these results It is not possible to discern a pattern in terms of size or level of development, except in Nepal and Nicaragua where the degree of output volatility relative to output gap size suggests a mismanaged economy (possibly India also over the wider sample). Most countries had a negative output gap k in 2015, a world-wide slowdown relative to trend. But this is more marked in the OECD area (also in Bangladesh, Malaysia both tied directly into the OECD by trade). It is not true of China, suggesting that China s loose monetary policy during and after the financial crisis may not have been warranted. The high volatility economies, relative to output gap, are Nicaragua, Nepal and possibly India. Here, the r 2 e =k2 ratios are well above unity. 5 Detailed results for the full set of 218 World Bank member economies are available upon request.

HOW CONSERVATIVE SHOULD CENTRAL BANKS BE? 103 The surprisingly low volatility in Zambia reflects the dominance of copper revenues in that economy, which again ties it into the OECD. Specific results Equation (11) implies a minimum value of 0.550 for ^b if b = 1 (or 0.25 if b = 0.5) at r 2 e =k2 0. Hence the results in the last two columns of Table 1 show Rogoff s conservative central bank result at work. China behaves very similarly to the OECD; as do Brazil, Malaysia, Uruguay, Zambia, and (to some extent) Bangladesh, Malaysia, Costa Rica, and Ghana. The optimal ^b values effectively halve society s choice of b everywhere except for Nepal and Nicaragua where ^b is about ⅓ smaller because output volatility is so high relative to k. This is true whether b =1or b = ½. Hence, the Rogoff effect is strong but stable across countries. It is only attenuated in exceptional cases (Figure 2). There are other exercises that could be done: to illustrate the positive effect of output volatility on the variance of inflation (demonstrated in section II) across countries; the decline in inflation variability as output volatility declines in a given economy 6 ; to show how inflation aversion declines as output volatility declines over time. The first two are not part of the conservative central bank hypothesis as such. For the third, there has been no systemic, as opposed to episodic, declines in output variability over time. These exercises are better left to another study with a different focus. Table 1 Optimal values for ^b in the OECD and Emerging Market Economies, 2015 k 2 2015 r 2 e r 2 e =k2 ^b if b = 1 ^b if b =½ $tn China 0.059260 0.00633 0.1068 0.552 0.246 India 0.000645 0.00096 1.4890 0.581 0.295 Brazil 0.110986 0.00722 0.0650 0.551 0.252 OECD 340.5528 8.74390 0.0257 0.550 0.251 $bn Bangladesh 24.897 4.4124 0.1772 0.554 0.256 Malaysia 74.288 6.4751 0.0872 0.552 0.253 Nepal 0.0320 0.0972 3.0359 0.609 0.328 Guatemala 0.4261 0.4339 1.0182 0.572 0.252 Uruguay 18.431 2.0083 0.1090 0.552 0.283 Costa Rica 1.9322 0.4528 0.2343 0.555 0.258 Nicaragua 0.0181 0.0936 5.1601 0.642 0.358 Kenya 0.8388 0.9442 1.1257 0.574 0.286 Zambia 9.0465 0.6411 0.0709 0.551 0.253 Uganda 1.0222 0.2564 0.2509 0.556 0.259 Malawi 0.1022 0.1125 1.1005 0.573 0.285 Ghana 8.7587 2.1349 0.2437 0.555 0.259 6 For example, from the date an economy adopts inflation targeting and an independent central bank (Caputo and Herrera, 2017). In fact, section 2 suggests output variability would rise in such cases; implying inflation targeting is a substitute for conservatism.

104 A. HUGHES HALLETT AND L. D. PROSKE 0.66 0.64 Nicaragua 0.62 Nepal 0.6 0.58 Guatemala Kenya Malawi India 0.56 Uganda BangladeshGhana Zambia Malaysia China Brazil Costa Rica OECD 0.54 0 1 2 3 4 5 6 Figure 2. Decreasing Rogoff conservatism with volatility in the output gap (b = 1). IV CONCLUSIONS This paper has demonstrated that the optimal conservatism parameter, ^b, depends on the ratio of output variability to potential output. The higher the output variance, the larger ^b should be and the less inflation averse the central bank relative to society. Nevertheless, these results remain in line with Rogoff s proposition: an optimal level of conservatism that is almost twice that which society would have chosen for itself. The trade-off, less conservatism vs. higher output volatility, is weaker (conservatism less by 17%) but particularly pertinent for developing countries. References ALESINA, A. and GATTI, R. (1995). Independent central banks: low inflation at no cost. American Economic Review, 85, pp. 196 200. BARRO, R. J. and GORDON, D. B. (1983). Rules, discretion and reputation in a model of monetary policy. Journal of Monetary Economics, 12, pp. 101 21. CAPUTO, R. and HERRERA, L. (2017). Following the leader? The relevance of the fed funds rate for inflation targeting countries. Journal of International Money and Finance, 71, pp. 25 52. DEMERTZIS, M. and HUGHES HALLETT, A. (2007). Central bank transparency in theory and practice. Journal of Macroeconomics, 29, pp. 760 89. HUGHES HALLETT, A. (2004). A central bank for all seasons? The lower inflation at no cost proposition under conditions of political uncertainty. Macroeconomic Dynamics, 8, pp. 207 25. RAVN, M. and UHLIG, H. (2002). On adjusting the Hodrick-Prescott filter for the frequency of observations. Review of Economics and Statistics, 84, pp. 371 6. ROGOFF, K. (1985). The optimal degree of commitment to an intermediate monetary target. Quarterly Journal of Economics, 100, pp. 1169 89. WALSH, C. E. (2010). Monetary Theory and Policy, 3rd edn. Cambridge, MA: MIT Press. WOODFORD, M. (2003). Interest and Prices: Foundations of a Theory of Monetary Policy. Princeton, NJ: Princeton University Press. World Bank (2016). Data. The World Bank (available at: http://data.worldbank.org). Date of receipt of final manuscript: 11 September 2017