Prof. Bryan Caplan
Week 9: Endogenous Central Banking: The Public Choice Approach to Money
Public Choice and Money
Time Consistency, I: The Paradox of Discretion
- The traditional modeling assumption: market agents maximize their own utility functions; political agents maximize a social welfare function.
- Implication: Political processes can fail due to lack of ability, but not lack of desire.
- The Public Choice approach: model market and political agents symmetrically as own-U fn maximizers. Don't assume that failed policies are well-intentioned; rather assume that what appear to be policy "failures" are a success given policy-makers' U fns.
- Ex #1: Seigniorage
- Traditional approach: outside forces somehow make money growth high. Or high money growth is necessary for high employment. Or high rate of price growth forces policy-makers to accommodate with high rate of money growth.
- Public Choice approach: money growth is high because the government wants it to be high in order to raise revenue. (Rothbard quote, pp.177-178). Moreover, there is no reason to think that the revenue raised by money creation is allocated to maximize a SWF; far more likely that revenue is used in self-interest of policy-makers.
- Explains a lot about monetary policy in the Third World, and wartime monetary policy everywhere. Not a powerful theory for industrialized countries in peacetime.
- Ex #2: Political Business Cycles
- Traditional approach: If monetary policy can affect output and employment in the short-run, then policy-makers will use this power to smooth fluctuations and compensate for shocks unanticipated by the private sector.
- Public Choice approach: Just because money matters does not mean that it will be used beneficially. Rather it will be used to help keep incumbent in power by raising money supply growth to stimulate the economy during election year. The recession generated by the subsequent monetary tightening is no accident, but a deliberate choice to impose short-run losses when they are least likely to be remembered by the electorate.
- Probably explains a few cases; also helps illustrate the difference between PC with underlying assumption of voter irrationality with later developments.
- (Note Alesina/Rosenthal's contrasting theory of political cycles with RE).
- Ex #3: Tollison on the Great Contraction.
Time Consistency, II: Resolving the Paradox with Reputation
- Time consistency literature that will now be explored is subtly different from Public Choice approach, but also has interesting similarities. In general, the time consistency literature treats policy-makers as SWF function maximizers who are nevertheless untrustworthy and opportunistic.
- Terminological note: "time consistent" is just what macroeconomists call "subgame perfect."
- Reviewing the simplest time consistency model: Suppose that output equals its natural level expectationally, but is a decreasing function of unanticipated inflation: .
- Policy-maker has "opportunistic" LF: , with . Note k>0, so the policy-maker wants to push the output level above its natural level.
- Two steps to solve:
- First, assume policy-maker maximizes V, taking into account the impact of (unexpected) inflation on unemployment.
- Set expected inflation equal to actual inflation, since there are no random variables in this equation.
- Therefore, , yet ! With RE and no random variables, output is always at its natural level, yet inflation is well above zero due to the temptation to use policy to reduce unemployment.
- Why doesn't central bank realize that its policies change expectations? As the model is set up, it doesn't realize this because it isn't true. The model is set up as a one-shot game. Imagine a series of one-shot random meetings between central banks and publics that know nothing about each other.
- Is this a Public Choice theory of money? The problem results from the central bankers' preferences combined with policy discretion- but leads to results even the central bankers don't like.
- But why do central bankers retain discretion? If the answer is something like: "To justify their existence" then this looks a lot more like a standard Public Choice view of bureaucracy.
Time Consistency, Independence, and Compensation
- Much of the paradox of time consistency goes away once one realizes that central banks and the public have repeated interaction with each other.
- With repeat interaction, the public can adopt "punishing" strategies vis-a-vis the central bank. (Note: there is no PD problem here, only a coordination problem).
- Most drastic credible threat sets upper bound on how well reputation constraints CB. So suppose the threat is: if the CB departs from 0 inflation, the public never believes them again.
- Revise the CBs LF to give it an infinite horizon, with a period discount factor of b
- To be a credible punishment strategy, the CBs loss from always cooperating must be less than its loss from defecting once, then being punished eternally. Formally,
- These three payoffs are given by:
- (Inflation in every period is 0; y-y*=-k in every period).
- It is then possible to solve for the critical value of b
. If b
is large enough, then a reputational solution is possible - though hardly necessary. In particular, in a world with noise "trigger strategies" are not a very good idea.
Time Consistency and the Gold Standard (from Bordo and Kydland)
- What is the advantage of CB independence? Rogoff's paper notes that central bankers are normally selected from the "conservative" elements of society.
- "Conservative" can be economically interpreted as "high disutility of inflation."
- Interesting result: Time consistency problem can be solved by giving independent authority to a person who dislikes inflation more than most people dislike it.
- Simplest case: In one-shot game, what must the weight on the inflation variable in the loss function be to get a 1st-best equilibrium?
- Note: Change loss function to ; then equilibrium inflation is (ak/b).
- Therefore: Pick b to be as large as possible.
- More complex case: What if there are supply shocks that it is desirable for the CB to compensate for? Then bnormal<b*<¥
- Empirical evidence on CB independence: More CB independence associated with substantially lower inflation, but NOT associated with unemployment rate, real growth, or other real variables. Data actually seem fairly consistent with simple model without supply shocks. If more CB independence eventually makes real performance worse, then it seems hard to find examples of countries that have that much CB independence.
- Alternate strategy: Instead of putting inflation-averse people in charge of monetary policy, just base their compensation on performance. To formally model supply shocks: , with everything else the same as the simple model.
- Then , so , and with RE .
- If you want to eliminate inflation bias, but allow accommodation of shocks, then the optimal reaction function would be: .
- How could a contract induce the CB to implement the optimal policy? Make inflation-contingent payment, so that CB now wants to: .
- Implies: , so . Then if you set , !
- Therefore, the optimal contract is: . With the right incentive scheme, discretion leads CB to first-best result.
- PC critique of optimal contracts?
- The gold standard provided the primary solution to the time consistency problem in earlier periods.
- Note Bordo and Kydland's revisionist concept of rules. For B&K, a rule is a way to bind policy over time, rather than anything "impersonal and automatic."
- Even with a weaker gold standard, the need to deflate later to compensate for inflation now removed most of the incentive for opportunism. One-shot gain balanced out by later need to contract, even without reputational effects.
- During gold standard period, defection was more likely to involve inflation for expropriation than inflation for employment-expansion. But the time consistency problem is analogous.
- Gold standard worked as a contingent rule: countries did suspend payment during big wars and similar emergencies, but for over a century there was a credible implied promise to return at parity. Analogous to allowing limited discretion for supply shocks.
- But isn't there also a "peaceful intentions" credibility problem that a non-contingent gold standard could help solve on the international level? I.e., if countries precommit to make it difficult to raise war revenue, won't that make mutually advantageous disarmament easier?
- The contingent rule of the gold standard also made emergency finance cheaper, since creditors could anticipate repayment would not be eroded by inflation.
- Other important aspects:
- Core vs. periphery countries.
- Inflation (non-)persistence.
- Gold standard as a rule was extremely credible (for some countries) for a long period. Consider:
- Resumption after Napoleonic wars.
- Resumption after WWI.
- Contrast with:
- ABC countries of Latin America.
- Southern European countries.
- How does the classical gold standard compare to other solutions to the time consistency problem?
- Why did the gold standard cease to be credible from the inter-war period on?
- How would a non-contingent gold standard compare - in stability and as a solution to the time consistency problem?
- A tale of reverse causality: how could going off the gold standard cause wars? How could peace treaties become more credible if participants make it difficult to get emergency tax revenue? (Do you need additional assumptions on conquest and defense technology?)
- Is there an analogy between "dollarized" economies and an economy on a non-contingent gold standard?
- Is there any way to combine Public Choice and time consistency on a deeper level?
- Is there any way to use PC in a policy-relevant way (in monetary policy and/or more generally)?