Lecture 8 Rules versus Discretion

Anticorruption and the Design of Institutions 2012/13 Lecture 8 Rules versus Discretion Prof. Dr. Johann Graf Lambsdorff

Literature • Barro, R. and D. Gordon (1983), A Positive Theory of Monetary Policy in a Natural Rate Model, The Journal of Political Economy, Vol. 91 (4): 589-610. • Blinder, A. (1998), Central Banking in Theory and Practice: 36-51. • Jarchow, H.-J.: Theorie und Politik des Geldes, Band 1: Geldtheorie, 11. neubearb. und wesentl. erw. Aufl., Göttingen: UTB, 2003. S. 279-303. • Kydlandund Prescott (1977), Rules Rather than Discretion, Journal of Political Economy, Jg. 85: 473-91.

Rational policymaking • Rational economic policymaking was often approached in a technocratic manner: policymakers start by analyzing the functioning of an economic system. This embraces how this system will react to stimuli, which can be controlled by the policymaker. It also embraces finding out societies preferred goals. Once (rational and benevolent) policymakers understand these two issues, they must weigh the costs and benefits of using stimuli and bring these in line with society‘s preferences. • In this perspective, policymaking is the maximizing of a social welfare function (or minimizing a cost function) given the known constraints.

Rational policymaking • Against this widely held view, Kydland and Prescott (1977) argued:“Even if there is an agreed-upon, fixed social objective function and policymakers know the timing and the magnitude of the effects of their actions, discretionary policy, namely, the selection of that decision which is best, given the current situation and a correct evaluation of the end-of-period position, does not result in the social objective function being maximized. The reason for this apparent paradox is that economic planning is not a game against nature but, rather, a game against rational economic agents.” • They state that the social welfare function is not maximized by determining the optimal use of instruments in a given economic situation. The following model for optimal central bank policy helps us understand this argument.

The time inconsistency model • The supply side is characterized by a Philipps-curve: with p: being the rate of inflation; p*: expected rate of inflation (which is formed in the previous period for the current period); : real domestic product; : potential domestic production where labor is employed to an extent that does not induce changes in wages and inflation. For the sake of simplicity we omitted a coefficient preceding the output gap. • In case of rational expectations, economic subjects utilize all available information and know the model. If they are not surprised by unanticipated shocks we obtain: Output gap

The time inconsistency model • Inserting this into the supply side yields: =. The central bank has thus no possibility of influencing production in the long run. • If the central bank, in the short run, manages to set inflation larger than the level that is expected by private agents, production increases above its potential level. • This can be justified by the wage setting process. Wages are negotiated based on expected inflation. • But if inflation increases above this level, employers’ profits increase. This induces firms to increase production.

The time inconsistency model • In our model, the central bank directly controls the inflation rate. This is certainly a simplification. We disregard the problem that inflation is only indirectly controlled by influencing macroeconomic demand by setting the interest rate. • Thus, in our model the central bank can reduce inflation without temporarily reducing macroeconomic demand. • But the central bank faces another major problem: its announcement of zero inflation may not be credible. • Private agents must anticipate inflation well in advance. Lenders, for example, would suffer from inflation unless they well anticipate its magnitude. Should private agents trust the central bank’s announcements? May the central bank have reason to mislead private agents?

The time inconsistency model • In reality we find many reasons why central banks fail to stick to their announcements. Why else are many central banks announcing inflation rates lower than those who are finally achieved? • One reason relates to the government being a net borrower. Unanticipated inflation helps the government reduce its debt. The government also profits from central banks that excessively print money, without giving due consideration to the subsequent risk of inflation. • The central bank may even profit itself from printing money – there are cases of outright corruption among central bankers or the politicians who control central banks.

The time inconsistency model • In 1979 Erwin Blumenthal, who served as an IMF representative in Zaire and was the central bank’s vice governor there, experienced such a case. There was no clear dividing line between the state budget and President Mobutu’s personal account. Equally, the central bank was largely regarded the personal property of the President and his cronies. Blumenthal was repeatedly forced to hand out the central bank’s money for purely private purposes. Once he rejected payment he was threatened with submachine guns to comply with the orders of an army general, Lambsdorff and Schinke (2002). • President Fujimori in Peru embezzled gold reserves from the central bank and transferred them to Japan. The loss in the central bank's net equity must be compensated somehow, for example by printing money and disregarding future inflation.

In 1999 surprise inflation was created by a central banker himself in Brazil. Francisco Lopes headed the Brazilian Central Bank as a governor for only three weeks. Upon his appointment he devalued the Brazilian currency, the Real, by eight percent. Such a devaluation increases import prices and, thus, inflation. Before the devaluation, Lopes gave advance notice of the new exchange rate to several private Brazilian banks, enabling them to profit from the “unexpected move” (BBC, April 14, 1999). Furthermore, a few days after the devaluation, Lopes sold dollars at favorable prices to the same banks. A Brazilian weekly news magazine quoted Salvatore Cacciola, an owner of one of the banks, as saying that he had a paid informant within the central bank. This informant would alert him to important events, such as changes of the interest rates or currency movements (BBC, April 26, 1999). A raid on Lopes’ house by the Brazilian police revealed several documents showing that Lopes, while working as a public servant, had maintained close connections to a private consulting firm and had more than $1.5 million in a foreign bank account (BBC, April 26, 1999). One year later, in February 2000, Lopes was charged with fraud (BBC, February 3, 2000) and with maintaining a foreign bank account that he had not declared to the tax office or the central bank (BBC, January 20, 2001). This event is reported in Schinke (2006).

The time inconsistency model • But even benevolent central banks may have reason to depart from their announcement. This is best investigated by considering the central bank‘s cost function. The central bank dislikes inflation and deviations of production from its desired level. It weights the latter by l, its employment preference: • We call central bankers with a small l “conservative”. Those with a large l are called “populist”. The domestic product which is preferred by society and the central bank alike is denoted by (). It is larger than potential production and the difference is denoted by z:

The time inconsistency model • A plausible reason relates to unemployment aid. This aid implies that individual costs of unemployment are lower than social costs. In an extreme case where unemployment pay equals the regular salary an individual would not suffer from unemployment, while society at large would have to bear the full burden. • This cost function assumes that desired inflation is zero (otherwise a nonzero target rate for inflation would have to be considered). • The cost function entails another plausible assumption: A mixture of two “evils”, unemployment and inflation, is preferred to being hit excessively by only one “evil”. For this reason the two terms are squared, expressing increasing marginal disutilities.

The time inconsistency model • The game is played by letting private agents act first. They determine expected inflation. These expectations are used to sign labor contracts. In case of high expected inflation, high increases in wages are negotiated. If low levels of inflation are expected, moderate wage increases result. The central bank acts in the final period by fixing the true level of inflation. t Private agents expect inflation. Wages are negotiated Central bank fixes inflation.

The time inconsistency model • Inserting for z and the supply function into the cost function yields: • The central bank takes p* as given, because it is determined at the beginning of the game. • For the solution of the game three cases must be distinguished: • Rule • Cheating • Discretion

The time inconsistency model Rule • The central bank announces price stability (p=0) and the private agents believe in this announcement, (p*=0). • Due to p=p* the supply side implies that production equals its potential level, . • Costs for the central bank amount to:

The time inconsistency model Cheating • When determining actual inflation the central bank observes that expected inflation is given. All wages are already fixed and will not react to the central bank’s choice. • The central bank will minimize its costs. A cost minimum requires: • Assuming that private agents trusted the central bank (p*=0), we obtain: • The central bank will thus fix the following inflation rate:

The time inconsistency model • In spite of its announcement of price stability the central bank chooses a positive rate of inflation. • Production increases to the following level: • Due to surprise inflation the central bank is thus able to increase production and lower unemployment towards a level preferred by society. The costs amount to • These costs are lower as compared to the rules based solution:

The time inconsistency model

The time inconsistency model Discretion • Rational private agents will anticipate the central bank’s temptation to cheat. • This will increase their expected level of inflation. But by how much? Rational private agents know the central bank‘s calculus and the model. They thus know that the central bank maximizes according to • Solving for p yields the central bank’s reaction function, • Inflation, p, thus increases with expected inflation and z.

The time inconsistency model • Rationality now assumes that private actors will not make systematic errors when anticipating the level of inflation. Since there are no stochastic shocks, this implies that they will not err: p=p*. Inserting this into the reaction function yields • Due to a lack of central bank credibility private agents and the central bank bias upwards the level of inflation (“inflation bias“). • This inflation bias is the higher the higher the central bank‘s preference for employment, l, and the more desired production exceeds potential production, z. • Due to p=p* production equals its potential level, .

The time inconsistency model

The time inconsistency model • Graphically the equilibrium is reached where both, the supply curve and the isocost-curve intersect with the -curve and have the same slope. • The costs in the discretionary solution are given by: • As expected, inflation has increased relative to the cheating solution: • Costs are also higher as in “rules”:

The time inconsistency model • To conclude, economic policy should not be carried out by determining an optimal use of instruments in specific situations. • Instead, politics should strive to impose rules on its own conduct. • Politics must strive to make these rules binding, so that decision makers can sustain the temptations when they arise. • This viewpoint is parallel to that of Ulysses and the Sirens. Ulysses was curious to hear the Sirens' songs but mindful of the danger. He ordered his men to stop their ears with beeswax and ties himself to the mast of the ship. He orders his men not to pay attention to his cries while they pass the Sirens. He anticipated his irrational behavior and bound himself to a commitment mechanism (i.e. the mast) to survive.

The time inconsistency model • Problems of time inconsistency not only arise with central bank policy. • Taxation is another widely used example. Investors are sometimes promised preferential taxation in an attempt to attract their capital. Once these commit their capital, the advantages from increased capital are reached. Suddenly it is no longer optimal to stick to ones promise of reduced taxation. • The same also applies to issues of regulation, for example on environmental issues. • Investors value the governments announcements on its future policy when assessing the attractiveness of a country. But along with their content, they focus on the credibility of these announcements.

Repeated play and reputation • In reality, the central bank’s temptation to surprise with a high level of inflation may be less severe, (Blinder 1998). • But this may relate to the fact that most central banks already operate under conditions that ameliorate our problem. • One such condition is that central banks operate repeatedly with private agents and thus can establish a reputation of trustworthiness. • In order to better understand the resulting game, we must investigate the impact of repeated play. • Current inflation is likely to impact on expected inflation in subsequent periods. The short term gains from reduced unemployment would then be seen against the long term losses from increased expected inflation.

Repeated play and reputation • A first theoretical conclusion is that this disciplining effect arises only if there is no final period (or if private agents do not know when there might be one). • Imagine such a final period (t=n). In this period the central bank will minimize its costs because it does not care about future expectations. This will be anticipated by private agents who expect p*=p=pD. We obtain the simple discretionary solution in the final period. • Since the result for the last period is already fixed, the central bank obtains no incentive to try to influence the last period‘s expectations. Why then should it abstain from a surprise inflation in the penultimate period (t=n–1)? Indeed, it will also act according to its reaction function and minimize costs. Private agents will anticipate this again. By backward induction we observe that the discretionary solution is obtained in all periods.

Repeated play and reputation • There are straightforward implications for the design of institutions: Central banks and similar institutions should not be confronted with a final period. This can be practically achieved by allowing continuity in the pursuit of its obligations. • First, employment contracts with central bankers should last for a long term. • Second, there should be overlapping time horizons for the central bankers’ employment contract. This introduces the continuity necessary for the central bank’s tasks and avoids end period problems that would arise if a complete cohort of central bankers leaves office. • If, indeed, end period problems are overcome, we can model the central bank’s problem as one with an infinite time horizon.

Repeated play and reputation • In case of an infinite time horizon the central bank‘s incentive to cheat with p*=0 is: • Cheating once induces private agents to disbelief in future announcements of the central bank. They will expect p*=pD and the central bank will act accordingly by setting p=pD. This future inflation bias goes along with increasing costs: • These costs arise in the future. Their present value depends on the degree to which central banks discount future costs (r) and the length (s) by which private agents sanction the central bank‘s malfeasance by disbelieving in its announcements.

Repeated play and reputation • The central bank will stick to its promise of zero inflation if • This implies: • Apparently, this is achieved with l and s being large and r being small. If we assume the special case of s=1, private agents would sanction the central bank only once and afterwards again believe in an announcement of zero inflation. We obtain:

Repeated play and reputation • With r being small, future losses are little discounted and thus larger. This induces the central bank to avoid future sanctions by private agents. • Suggestions have been made that this discount rate is lower for independent central banks. Political actors can boost their chances of being reelected by increasing employment during the electoral campaign. Inflation would thus increase during electoral cycles – and they are difficult to reduce afterwards. For politicians r is rather large during elections. Independent central bankers would act less myopic. • With s being large, malfeasance is heavily sanctioned and thus becomes unattractive. There are apparent conclusions of this finding for the design of institutions. Environments with a good memory for past misbehavior appear better in deterring malfeasance.

Repeated play and reputation • The result for l is paradox. Shouldn‘t a large preference for employment increase the central bank‘s temptation to cheat? Indeed, it does so but it also increases the future costs of malfeasance. This impact on the future costs is even higher. • An employment preferring central banker is aware of the high future costs of his malfeasance and more deterred to avoid cheating. • This is comparable to a self-help group of anonymous alcoholics. Those engaging in such a group are well aware of the temptation to drink. While the temptation is higher for them, they suffer heavier from malfeasance. One drink alone is likely to put them back on the slope to addiction. Rational behavior thus induces them to strictly avoid any alcohol.

Repeated play and reputation • The likelihood of drunk driving is thus lower for such an alcoholic. Parents seeking someone to drive back their children after a party may have good reason to entrust their offspring to such an alcoholic rather than anyone else. • Our results, however, are valid only for a central banker who is aware of the future sanctions that follow his malfeasance. • If a populist central banker disbelieves in the private agents sanctions, he would not be deterred from surprise inflation. The deterrence effect is thus restricted to central bankers who accept our model.

Stochastic Supply Shocks • The model has been deterministic. In reality, shocks are likely to hit the economy. • The central bank may stochastically err in setting the inflation rate. It aims at a certain level but misses this level. For example, after aiming at p=pD import prices drop suddenly or macroeconomic demand declines and produce p=0. As long as private agents observe the shocks, the impact on the model are minor. We do not further investigate this here. • Another type of shock relates to the supply side. These shocks are problematic for the central bankers because they confront him with a dilemma. Should he stick to his rigid rules or prefer some flexibility that is responsive to the shock?

Stochastic Supply Shocks A Negative Supply Shock

Stochastic Supply Shocks • Should we worry about shocks? They might be good or bad! • Indeed, we should care about shocks: inflation and the output gap enter the cost function with quadratic terms. Extreme deviations are particularly bad. In case of a large shock, the desire to balance one disutility with another may become stronger. • Imagine Ulysses and the Sirens again. His strict commitment helped him survive. But what would have been the outcome if his ship sank? His solution of tying himself to the mast would turn out to be dreadful and he may have preferred to somewhat cope with the Sirens instead.

Stochastic Supply Shocks • The game is played only once. A shock, w, is normally distributed with expected mean E(w)=0 and variance V(w)=s2 . If w>0 inflation rises. This is equal to saying that production drops. • The game is played according to the following sequence: t Private agents expect inflation Wages are negotiated Nature determines shock Central bank fixes inflation

Stochastic Supply Shocks • If the central bank is strictly bound by a rule (p=0), it cannot recognize the shock‘s impact on production. • We obtain pR =p*=0 and • The variance of production is determined by: • Since we obtain • To see this, observe that and E(w)=0.

Stochastic Supply Shocks • For the costs we obtain: • For expected costs we obtain due to pR=p*=0: • Due to and E(w)=0 • As compared to the deterministic model costs increased due to the shock because situations of reduced production are particularly painful (variations of production enter the costs function in squared form).

Stochastic Supply Shocks • In case of discretionary policy the central bank observes the shock, w, prior to determining its policy. It will minimize: • A cost minimum requires: • The central bank sets inflation according to: • On average the following inflation rate can be expected:

Stochastic Supply Shocks • Due to rational expectations private agents know this calculus of the central bank. They cannot be systematically misled and expect inflation equal to the mean inflation set by the central bank, p*= E(p). This implies: • Inserting this into the central bank’s calculus, we obtain: • Inflation in case of discretion is thus:

Stochastic Supply Shocks • From this we can determine production. Due to p-p*=l/(1+l)·w: • Variance of production is: • This is smaller than s2. This reveals that the impact of shocks on production is dampened in case of a discretionary policy.

Stochastic Supply Shocks • This advantage, however, comes at a cost: average inflation increases due to an increased inflation bias. • Another downside effect is that variation of inflation has increased. While it was zero in case of a rules-based policy, variation of inflation now amounts to l/(1+ l).w. • Strict rules avoid the inflation bias. But they also disallow a more flexible reaction towards supply shocks. Shocks would impact completely on production, without any dampening reaction. • There is a trade off between credibility (rules) and flexibility (discretion). • Which policy to prefer can be revealed by comparing expected costs.

Stochastic Supply Shocks • In case of discretion we obtain: • Inserting yields: • Due to E(w)=0 we obtain:

Stochastic Supply Shocks • Comparing this to the costs of rules yields that discretion is preferable if: • Simplifying this, we obtain: • Discretionary policy should be preferred in case of • a high variance of supply shocks, (s2 is large) • a low preference for employment (l is small), • a small difference between desired and potential production (z is small).

Optimal Design of Central Bank Policy • As we observed, rules are preferable with respect to containing inflation. • Discretion is preferable with respect to stabilizing production. • Is there some optimal policy in between these two extreme cases? • In research four different variants have been discussed: • A flexible rule • Incentive contracts for central bankers • A moderately conservative central banker • Rules with exceptions

Optimal Design of Central Bank Policy • A flexible rule for the central bank would be: • ais the long-term desired value for inflation. • bis the central bank‘s flexible reaction towards shocks (w > 0). • Both parameters can be determined so as to minimize costs. • We assume that the flexible rule is binding and announced upfront. Apparently, we then obtain p*=a. • Inserting this and the flexible rule into the cost function, it follows:

Optimal Design of Central Bank Policy • Partial differentiation yields: • The optimal flexible rule is thus: • This allows to achieve long-term price stability. At short sight, deviation from price stability are allowed so as to dampen supply shocks. Production would be equal to the discretionary value: • With inflation being zero on average, total costs are lower than in both previous solutions: strict rules or strict discretion.

Optimal Design of Central Bank Policy • Such a solution, however, faces practical problems: How should private agents distinguish between a central bank that cheats and one that reacts to a shock? Maybe it cannot! How can the central bank commit to such a flexible rule, if nobody can observe its adherence to the rule? • One attempt could be that the central bank upfront identifies various observable shocks and determines its quantitative reaction to these shocks. But supply shocks may range from natural catastrophes, oil price shocks, sudden technological innovations to warfare. Determining upfront how to react to such crises is not an easy task. • Apart from that, determination of the output gap may contain a high degree of discretion. Whether a drop in production is due to a shortage in demand or a decrease in supply is commonly disputed. • A central bank may use its discretion to cheat and private agents may therefore disbelieve in its announcements.

Optimal Design of Central Bank Policy • An optimal solution can also be achieved by providing incentives to central bankers. A government that seeks to approach the optimal solution would confront a central banker with a penalty in case of excessive inflation. • Assume this penalty to be Kp=2lzp. The cost function of the central bankers is then modified to: • A cost minimum requires: • This simplifies to: • Taking expectations on both sides, we observe that and

Optimal Design of Central Bank Policy • The solution thus equals that of the flexible rule. The impact of shocks on production are dampened and inflation is allowed to vary. • The advantage of this solution is that private agents do not have to verify the magnitude of a shock. Even if the magnitude of a shock is known only to the central bank, the central bank does not obtain an incentive to cheat. • A disadvantage is that central bankers commonly earn less than private bankers. Punishing central bankers would not be feasible, as they prefer to quit. Another problem is that the contract would be exercised by the government. But the government faces the same (or in case of a forthcoming election even a larger) incentive to cheat. Why should a government punish a central banker for an action that it considers to be optimal? Due to these incentives the government may fail in committing to exercising such a contract.

Lecture 8 Rules versus Discretion