The Inflation Bias and what to do about it

1. The Inflation Bias and what to do about it Professor Anne Sibert Spring 2012

2. Bad monetary policy in the 1970s and 1980s led to a revolution in central bank design in the 1990s Source: IMF, World Economic Outlook database

3. Examples of Changes in bank legislation • Reserve Bank of New Zealand Act of 1989 binds the Reserve Bank to price stability • Bank of England Act of 1997 imposes an inflation target on the Bank of England • Bank of Japan Act of 1997 orders the pursuit of low inflation

4. This lecture: • Why was monetary policy so bad in the 1970s and 1980s? Why do monetary policy makers cause too much inflation? • The classic model of an inflation bias: the time-inconsistency problem • How can we do to solve the time-inconsistency problem

5. The Phillips Curve Suppose we have the following sequence of events: (1) wage setters choose a fixed nominal wage W; (2) the price level P is observed; (3) firms decide how many workers L to hire. Real wage Labour demand curve W/P Labour L

6. The Phillips Curve Suppose that P1 < P2 < P3. It is seen that higher prices lead to higher employment. Real wage Labour demand curve W/P1 W/P2 W/P3 Labour L1 L3 L2

7. The Phillips Curve • There is a positive relationship between inflation and employment. • The Phillips Curve’s name comes from a 1958 article by William Phillips: Phillips, William (1958), The Relationship between Employment and the Rate of Change of Money Wage Rages in the United Kingdom, 1861-2957, Economica, 25, 283-299. • In 1960 Paul Samuelson and Robert Solow showed a similar correlation between inflation and employment in the United States. They called this relationship a Phillip's Curve. Samuelson, P. and R. Solow (1960), "Analytical Aspects of Anti-Inflation Policy," American Economic Review 50, 177 - 194. • The idea that there is a relationship between inflation and output dates back at least as far as the 1920s when Irving Fisher wrote a paper on the subject. • For many years many economists and policy makers believed that there was a stable relationship between inflation and employment. This led to the Keynesian idea that policy makers could increase employment if they were willing to tolerate higher inflation.

8. Challenges to this View • In the late 1960s Milton Friedman and Edmund Phelps challenged the idea of a stable long-run relationship between employment and inflation. • They argued that workers and firms cared about real wages and that if they believed policy makers were increasing inflation with the intent of increasing employment then they would demand higher nominal wages. • Thus, policy makers could not systematically increase employment by increasing inflation • Stagflation (the simultaneous occurrence of high inflation and high unemployment) in the 1970s lent empirical support to Friedman's and Phelps's criticism. • Today few economists believe that there is a stable long-run Phillip's curve. • See: Phelps, E. (1967), "Phillips Curves, Expectations of Inflation and Optimal Employment over Time," Economica 34, 254--281 and Friedman, M. (1968), "The Role of Monetary Policy," American Economic Review 58, 1-17.

9. The Rational Expectations Revolution • The advent of the rational expectations revolution in the late 1960 and early 1970s led to a new approach to modelling the labour market. • Suppose that wage setters have a preferred employment rate L*. They dislike deviations from this rate. Suppose further that they expect the price level to be Pe and they choose the fixed contractual wage so that L = L* when P = Pe. • When the price is equal to wage setters' expected price, employment is equal to their preferred employment rate L*. However, if the price level is higher than expected, then the real wage is lower than expected and employment is higher than L*. This gives us the expectations-augmented Phillips curve: there is a positive relationship between employment and unexpected inflation. A policy maker can increase employment above L* if and only if he produces inflation that is higher than expected.

10. Why does the policy maker want to increase employment? • One might wonder why a policy maker would want to increase employment above that preferred by wage setters. • One answer is labour market distortions. An example is a tax on wages. • If workers work more than they gain from the extra wages and the economy gains from the extra tax revenue. However each worker views his contribution to aggregate tax revenue to be so relatively tiny that he does not take this into consideration. • Thus, the socially optimal level of employment is higher than rate most preferred by wage setters.

11. Other ways to get an Expectations-Augmented Phillips Curve • In the 1970s academic economists split. One camp was willing to assume that there were nominal rigidities, even though they could not explain why such rigidities arose. These economists were sometimes called salt water economists as they tended to be associated with universities on the east and west coasts of the United States. (MIT, Harvard, Princeton, Stanford) • The other camp insisted that everything in a model be consistent with rational optimising behaviour. These economists were sometimes called fresh water economists because they tended to be associated with universities in the interior of the United States. (Chicago, Carnegie-Mellon, Minnesota, Rochester) • The leading fresh water economist Robert Lucas constructed a model that produced an expectations-augmented Phillips curve even though all prices are perfectly flexible. His result was based on informational asymmetries.

12. The Lucas (1972) Model • Lucas argued that firms learn the price of their own good before they learn the aggregate price level. Thus, if they see that their price has gone up, they do not know if it is because demand for their good has gone up, causing an increase in the relative price of their good which would call for an increase in their output, or if it is because there is inflation and all prices have gone up. To the extent that they do not expect inflation they increase their output. Thus, there is a negative relationship between inflation and output. • See Lucas, R. (1972), "Expectations and the Neutrality of Money," Journal of Economic Theory, 4, 103--124. This paper is beautiful, but some find the informational assumptions unappealing

13. Why is Inflation Costly? • Shoe-leather costs: The opportunity cost of holding non-interest bearing money is the nominal interest rate. The higher is inflation, the higher is the nominal interest rate and the more resources households and firms expend to avoid holding money. • Menu costs: If prices change, then menus and other price lists must be updated. • Firms often set prices in advance and keep them unchanged for some time. If not all prices are set simultaneously, then inflation causes relative prices to be distorted. • Inflation makes the currency an inconvenient unit of account; a yardstick is not as useful if its size keeps changing. • Inflation can interact with the tax system in a way that produces distorted or unfair outcomes. For example, in years of high inflation, people may pay capital gains taxes on real capital losses. • Inflation can redistribute income in a way that is regarded as unfair: the sophisticated and relatively wealthy gain at the expense of the poor and the badly educated. • Disinflation is also costly, for most of the same reasons.

14. The Time-Inconsistency Problem Suppose that the monetary policy maker is benevolent and has the same preferences as society. Suppose that society dislikes deviations from the socially optimal level of employment Lo and that it also dislike deviations form zero inflation. Let the society's welfare function be: , where φ > 0 is a parameter that measures the weight that society puts on losses due to deviations of actual employment from their socially optimal level relative to losses due to deviations of inflation from zero. In the above equation it is assumed that optimal inflation is zero. This may seem at odds with real-world central banks that typically aim for low but positive inflation. This, however, is because measured inflation is believed to be significantly higher than actual inflation.

15. Suppose there is an expectations-augmented Phillips curve: where πe is wage setters’ expectation of inflation. Suppose that socially optimal employment is higher than wage setters’ preferred employment: where d > 0 arises from a distortion in the labour market.

16. Society’s Objective Function Putting this together yields . The key feature: Society likes unexpected inflation and dislikes actual inflation.

17. Another story due to Guillermo Calvo • Increasing the money supply produces direct revenue called seigniorage. It also decreases the real value of the government's outstanding debt. This is called an inflation tax. • Both seigniorage and the inflation tax are increasing in unexpected inflation. (Optimal inflation may not be zero because there may be some seigniorage revenue even when inflation is expected.) • It is believed that for most advanced economies (at least in normal times) that (direct) taxation is less distortionary than inflation. But, there is a significant cost associated with administering and complying with the tax code. • For countries with inefficient tax systems or for countries with extraordinary revenue needs it may be optimal to collect some seigniorage or inflation tax. Thus policy makers may like unexpected inflation. • Calvo, G. (1978), "On the Time Inconsistency of Optimal Policy in a Monetary Economy," Econometrica 46, 1411-1428.

18. Optimal Monetary Policy • The timing of events is that wage setters choose a fixed contractual nominal wage based on their expectation of inflation and then the monetary policy maker choose their monetary policy. Thus, monetary policy makers take expected inflation as given and choose actual inflation to maximise social welfare. • It is assumed that the monetary policy maker can perfectly choose inflation. This is untrue but unimportant here.

19. Optimisation: Set the derivative of the objective function with respect to inflation equal to zero: . Note that the second derivative is negative, so the solution is a maximum.

20. Rational Expectations Solving yields . There is no uncertainty in this model and is assumed that wage setters know the monetary policy maker’s objective function. They, too can maximise it. It is assumed that their expectations are rational and that π = πe. Substituting into the above equation yields

21. Inflation Bias This is unfortunate. The monetary policy maker chooses π > 0 even though society dislikes inflation and even though it does not increase employment (because it its expected). Society would be better off if the monetary policy maker could commit himself to zero inflation. In this case there would be no increase in employment because the zero inflation is expected, but at least there would be not costly inflation. The problem with this is that if the policy maker announces that he is going to choose π = 0 and this is believed then he should reneg and set .

22. Game in extensive form Expect inflation Don’t expect inflation don’t inflate inflate don’t inflate inflate 2nd best outcome is not subgame perfect Time-consistent ourcome Best outcome for society

23. Inflation Game • No matter whether wage setters choose a contract based on zero inflation or on strictly positive inflation, the monetary policy maker will choose strictly positive inflation. • Knowing this, wage setters should choose a contractual wage based on an expectation of strictly positive inflation. • No promise by the monetary policy maker that it will choose zero inflation is credible. • In game theory jargon the outcome where the monetary policy maker announces that he will set zero inflation, this is believed and the policy maker does indeed choose zero inflation is not subgame perfect. It is based on an incredible announcement.

24. Time-Inconsistency Problem • The monetary policy maker's optimisation problem can be contrasted with that of an engineer trying to control a missile. The following quote is from the Wikipedia article "Trajectory Optimization" and the italics are mine. • For tactical missiles, the flight profiles are determined by the thrust and load factor (lift) histories. These histories can be controlled by a number of means including such techniques as using an angle of attack command history or an altitude/downrange schedule that the missile must follow. Each combination of missile design factors, desired missile performance, and system constraints results in a new set of optimal control parameters. • The flight profile depends on what happened in past. The engineer can use standard control theory techniques to solve his problem. In contrast, the state of the economy depends on what the economic policy maker is expected to do in the futureand standard optimisation techniques do not work. • The seminal work of Kydland and Prescott (1977) discusses this problem, called time inconsistency, and its implications for monetary policy. The model here is due to Barro and Gordon (1983), who popularised the idea of Kydland and Prescott. • See Kydland, F. and E. Prescott (1977), "Rules Rather than Discretion: The Inconsistency of Optimal Plans," Journal of Political Economy 85, 473-491 and Barro, R. and Gordon D. (1983), "A Positive Theory of Monetary Policy in a Natural Rate Model," Journal of Political Economy 91, 589-610.

25. Taxing Capital • The notion of time inconsistency, or the inability of policy makers or others to commit themselves to the optimal plan, appears else where in economics. • It is a standard result in public finance that is less distortionary to tax capital than to tax labour. Even workers should prefer capital taxes to labour taxes. In either case workers bear the burden (either because they pay the tax or because the burden is passed onto them in the form of lower real wages) and capital taxes additionally distort capital formation. • However, once capital is already put into place it is better to tax capital. There are no distortions in this case because capital, unlike labour, cannot be instantly adjusted. • Consider a model where capital is put into place and then the taxes on capital and labour are decided. The optimal outcome requires a government to commit itself to not taxing capital. But owners of capital know that once the capital is in place it will be taxed. So, in making their investment decision they believe capital will be taxed and they invest too little.

26. Commitment • Another example of a time inconsistency problem is that of a firm that would like to borrow. This firm is confronted with two projects: one is risky and one is safe. It would be willing to do either investment if it were able to borrow the necessary funds, but it prefers the risky investment. A bank is willing to lend to the firm if and only if it undertakes the safe project. The optimal outcome if for the firm to commit itself to undertaking the safe project and for the bank to make a loan. But, if the bank cannot itself to undertake the safe project then it will not be able to borrow. The bank will know that once the firm has the money it will undertake the risky project. • The firm and the bank can enter into a legally enforceable contract that requires the firm to invest in the safe project. This commitment device makes the firm and the bank better off. • Unfortunately, it is more difficult for the government to commit itself to a course of action. How does a government bind itself to follow a law, particularly when not following it can make everyone better off?

27. Conservative Central Bankers • One solution to the time-inconsistency problem is to appoint a central banker who does not share society’s preferences. • If you appoint a central banker who cares solely about inflation then he will sets inflation equal to zero and this will be expected. • One problem with this is that it is not always easy to ascertain someone’s preferences. President Eisenhower nominated Earl Warren for Chief Justice of the US Supreme Court in the greatly mistaken belief he would be conservative. Likewise, Pres. George H. W. Bush nominated David Souter in the mistaken belief that he would be conservative.

28. Central Bank Independence • Making the bank operationally independent does not necessarily solve the time-inconsistency problem. If the central bank shares the government’s preferences, it will have a time-inconsistency problem as well. • However, Bernanke et al (1999, p. 25) argue that central bankers are apt to be more inflation averse than the government, saying that this, “… may be the result of ‘tough’ central bankers … or it may just be that their professional backgrounds and socialization make central bankers relatively hawkish on inflation.”

29. Inflation Targets • Either appointing conservative central bankers or imposing a legally binding inflation target on the central bank has the problem that it will cause the central bank not to react to or not react enough to stochastic shocks that are realised after nominal wages are set but before monetary policy is made. • Such shocks provide a stabilisation role for a central bank. Any commitment device that removes the inflation bias may be at the expense of the central bank being able to respond to these shocks.

30. What if the central bank has a stabilisation role? • Suppose that the timing of events is • Wage setters chose the fixed nominal wage • A shock shifts the labour demand curve • The monetary policy maker chooses inflation • The monetary policy maker has better information than the private sector (because he chooses his action later) and he can use this information to offset the shock: the central bank has a stabilisation role.

31. Suppose that the expectations-augmented Phillips curve is: where θis a shock to labour demand that has mean zero and variance σ2. Then society’s objective function becomes . The central bank takes expected inflation as given and it knows the shock. Maximising with respect to inflation yields . The wage setters do not know the shock. They have rational expectations and their expectation of inflation is the statistical expectation. Thus, and . Society’s expected welfare is If instead, society appointed a conservative central banker who always chose zero inflation, then expected welfare would be .

32. Society is better off with a conservative central bank if and only if Rogoff (1985) showed that if the government could precisely pick the preferences φ* of the central banker then it should pick one who was more conservative than society (that is φ*< φ), but not one who cares solely about inflation. See Rogoff, K. (1985), “The Optimal Degree of Commitment to an Intermediate Monetary Target,” Quarterly Journal of Economics 100, 1169-1189. It is hard to believe that the government can precisely gauge someone’s preferences. Rogoff’s model led to a sizable academic literature on the trade-off between central bank credibility and the ability of the central bank to stabilise. This literature probably puts too much emphasis on the central bank’s stabilisation role. In reality, uncertainty is not captured in one readily observable variable. The state of the economy is extremely difficult to observe, describe and interpret. Moreover, making monetary policy is difficult. Milton Friedman and the monetarist school, however, famously questioned even a short-run stabilisation role for monetary policy, claiming that there are long, variable and uncertain lags between the implementation of monetary policy and when its effects occur and that these lags cannot be easily predicted. Central banks cannot “fine tune” the economy. At most, they can offset some large and observable shocks.

33. Walsh Contracts • Walsh (1995) proposes that the government should enter into a contract with the monetary policy maker who has a stabilisation role. • The contract imposes a linear penalty on a central bank in excess of its target and pays a reward for inflation below target. • If the contract is written properly, society gets the optimal outcome. There is no inflation bias and the central bank stabilises the shock to the labour demand curve. • See Walsh, C. (1995), “Optimal Contracts for Central Bankers,” American Economic Review 85, 150-67.

34. Problems • This only works if it is credible that the government will enforce the contract. But the time-inconsistency problem arises precisely because policy makers are not credible. Giving the government the responsibility for monitoring the central bank and punishing deviations merely shifts the time-inconsistency problem from the central bank to the government. • This solution requires the unrealistic assumption that the government knows the exact preferences of the central banker. • Probably for these reasons, real-world examples of Walsh contracts are hard to find.

35. Escape Clauses • Lohmann (1992) suggests that in normal times monetary policy should be made by an independent central banker who is more conservative than society. • If a large shock occurs the government should threaten to override the central bank if it does not stabilise. • Requires that the government knows the preferences of the central banker. It must be believed that the government will intervene in extraordinary times but refrain from intervention in normal times.

36. Real World Examples • The New Zealand government is allowed to override the central bank and the central bank is allowed to accommodate the first-round effect of a shock on prices in “extreme economic circumstances”. • The UK Treasury is allowed to instruct the Bank of England on monetary policy for a limited time.

37. Reputation Models Consider a simpler objective function for society: /2. The central bank chooses This is expected and .

38. Other outcomes • If actual and expected inflation are zero then the payoff is • If expected inflation is zero and actual inflation is φ then the payoff is . • If expected inflation is φ and actual inflation is zero then the payoff is . • Note that .

39. Infinite-Horizon Game • In reality the monetary policy scenario does not occur just once, it occurs over and over. • Suppose it is repeated an infinite number of times. Suppose that society and the monetary policy maker’s discount factor is φ • Suppose wage setters expect zero inflation in the first period and zero inflation thereafter as long as inflation has always been zero. If they ever observe inflation of φ then they expect inflation of φ forever after. • What would the monetary policy maker do?

40. Equilibrium with zero inflation • Either the monetary policy maker chooses zero inflation forever. Or, there is some period where he chooses inflation of is φ. After that, inflation of is φ is expected so he chooses inflation of is φ forever after. • The monetary policy maker will choose zero inflation forever if • This is true if . • If society cares enough about the future then there is an equilibrium with zero inflation.

41. Problems with this • This is not the only equilibrium. An obvious equilibrium is where wage setters expect inflation of φ every period and the monetary policy maker chooses φ every period. • There could be an equilibrium where actual and expected inflation is φ in odd periods. In period zero expected inflation is zero and expected inflation is zero in even periods if actual inflation has always been zero in even periods and is φ if it has ever been φ in an even period. Actual inflation is zero in even periods. • Along with too many equilibria, zero inflation forever might be attained by different threats. It might occur if wage setters threat to play non-cooperatively forever if they ever see a deviation. A threat to play non-cooperatively for N>1 periods may also work.

42. A finite horizon • Suppose that the game is played a finite number T times. • In period T the wage setters have no credible threat do deter the monetary policy maker from inflation is φ and this is expected. • In period T-1 the wage setters have no credible threat because their only credible strategy in T is to expect φ. So in T-1 actual and expected inflation is φ. Things unravel backward. The only equilibrium is actual and expected inflation of φ each period. • But, people are probably not that rational. If the monetary policy game were repeated 100 times you might get cooperation for much of the time.

43. Hawks and Doves • Suppose that a fraction of all policy makers are hawks who only care about inflation and always choose zero inflation. A fraction are doves who maximise social welfare. • Suppose that the monetary policy game is played twice. If a dove inflates in period zero he is known to be a dove and expected inflation is in period one. But, if he chooses zero inflation, then wage setters are not sure if he is a hawk or a dove. In period one the dove inflates.

44. Bayes Rule Suppose that wage setters believe that doves choose zero inflation in period zero with probability p*. Then if the see zero inflation in period zero, they believe the monetary policy maker is a dove with probability = = = =

45. Let be the probability that a dove chooses zero inflation in period zero. Ignoring terms that do not depend on , his payoff is . • The dove takes P as given and maximises this objective function to find p. • In equilibrium, the beliefs of wage setters are consistent: Thus, p* = p.

46. Equilibrium where doves always inflate • If doves always inflate and wage setters see that period zero inflation is zero, they will believe that the policy maker is a dove with probability zero. • The doves objective function is • This is maximised at p = 0 (doves always inflate) if • So if there is an equilibrium where hawks and doves separate. Hawks choose zero inflation in period zero and doves choose strictly positive inflation in period zero.

47. Equilibrium were doves never inflate in period zero • If doves never inflate (p = 1) and wage setters see zero inflation they will believe that the policy maker is a dove with probability 1 – ρ. • The doves objective function is . • This is maximised at p = 1 if is . • If there is an equilibrium where hawks and doves pool. No policy ever inflates in period zero.

48. One other outcome • If then doves are indifferent and randomise. • This is the case when . • This occurs when

49. Another Solution: Peg the Exchange Rate • One strategy for insuring low inflation is for a government to peg its currency to the currency of a country that can be counted on to pursue low inflation. • It is a central result in the theory of international finance that if a country is to maintain a fixed exchange rate, it cannot follow an independent monetary policy. • As long as the country maintains its peg, it must follow the less inflationary country’s monetary policy.

50. Why it might work • As long at it has enough foreign reserves to buy back its monetary base it is always possible for a country with a fixed exchange rate to maintain its peg. • Policy makers may be able to commit to pursuing the monetary policy necessary for maintaining a fixed exchange rate, at least for a while, because devaluations can cause severe economic disruption and are not a career-enhancing move for the policy maker involved.