http://www.gmu.edu/departments/economics/bcaplan

Econ 816

Spring, 2000

**Week 9:
Optimal Policy; Endogenous Policy Theory, I: Time Consistency**

I. Optimal Policy

A. First part of the course: main positive theories of the economy.

B. Second part: implications for optimal (aka Kaldor-Hicks efficient) policy.

1. Note: Efficiency isn't everything; but as long as it counts at all, it is worth knowing what policies are efficient.

C.
Traditionally, macro policies have been seen as *exogenous*;
policy does what policy-makers want, and there is no theory of what they want
(except perhaps maximize SWF).

D. Note:

1. If policy is really exogenous, figuring out optimal policies makes it possible to actually implement them.

2. If policy is actually endogenous, then figuring out optimal policies makes it possible to confirm the existence of predicted suboptimalities.

E. Understanding efficiency: Just think in terms of minimizing total deadweight costs.

1. Deadweight costs of involuntary unemployment.

2. Deadweight costs of inflation tax.

3. Deadweight costs of expectational errors.

4. Etc.

II. Macro Policy After Rational Expectations (but not Public Choice)

A. Probably the main practical effect of RE was to diminish what people expected macro policy to be able to do.

B.
RE models gained prominence in macro around the same
time that Public Choice theory became influential in public economics. RE questioned the ability of policy-makers
to do things; Public Choice questioned their *desire* to do things; i.e.,
even if policy-makers could "succeed" in the public interest sense of
the word, they might not want to.

C. While the RE has become fairly influential in macro, the PC view of policy-makers as self-interested bureaucrats has been far less so. The PC approach to macro policy will be explored later; for now, we will simply assume that policy-makers are open to (sound) exogenous policy prescriptions.

III. Optimal Fiscal Policy

A. Relatively small literature on optimal fiscal policy.

B. With RE, long decision lags make fiscal policy ineffective stabilization tool.

C. Central fiscal policy conclusion of last two decades: Tax-smoothing welfare dominates "pay-as-you-go" because of:

1. Imperfect consumer credit markets. (Landsburg's fable of jade beach)

2. Non-linear deadweight costs of tax system.

D. Do public choice considerations reverse this conclusion? Hold that thought.

IV. Optimal Monetary Policy, I: What to Target

A. Post-RE, it is generally recognized that in the long-run money only changes nominal variables. The CB may matter for real variables in the short-run, but extended efforts to change real variables will typically just yield bad performance on both real and nominal variables.

1. Caveat: Some empirical evidence that higher inflation has permanent adverse effect on productivity growth. If so, inflation is much worse than standard RE analysis indicates.

B. The rules/discretion debate: anything more to be said? RE can be reconciled with either discretion or rules, but there is much more to say about rules than about discretion.

C. N.B. The same policies may have different effects if one results from rules, the other from discretion. Constant money growth at the CBs discretion may work much worse than a constant money growth rule.

D. N.B. Rules may have varying time horizons (the danger is that a rule with a very long time horizon is hard to distinguish from no rule at all).

E. Interest rates - especially very short-run rates - are by far the most popular target of CBs.

1. Advantages: Stabilizes interest-sensitive sectors; (?) easy for economic actors to understand; very easy to hit.

2. Disadvantages: Indeterminacy problem - depending on level of inflationary expectations, the same nominal interest rate peg could be very expansionary or very contractionary.

F. Money (variety of measures) - briefly popular target, but quickly de-emphasized.

1. Advantages: (?) Transparency; determinacy; easy to hit.

2. Disadvantages: Interest fluctuations; financial innovation requires re-definitions or growing irrelevance; velocity shocks.

G. Inflation - growing popularity.

1. Advantages: transparency; determinacy.

2. Disadvantages: Requires contraction in face of negative supply shocks; not always easy to hit.

3. Sophisticated version - omit food and energy from index to avoid supply shock problems.

H. Nominal GDP - theoretically dominates inflation-targeting, but less popular.

1. Advantages: Determinacy; copes better with supply shocks than inflation targeting.

I. Disadvantages: Opaque; probably difficult to hit.

V. Optimal Monetary Policy, II: The Optimal Rate of Inflation

A.
If monetary policy will not change average
unemployment level, then deadweight macro losses are a function of unemployment
*volatility*,
inflation, and inflation volatility.

B. Many lump together the impact of inflation and inflation volatility. Since these are positively correlated, this is no surprise; but analytically, they are important to distinguish.

C. Similarly, many lump together the redistributive and deadweight impact of inflation, counting both as "costs." These two should be analyzed separately.

D. This generates four "boxes":

1. Redistributive impact of inflation

2. DW costs of inflation

3. Redistributive impact of inflation volatility

4. DW costs of inflation volatility

F. Box #1: Redistributive impact of inflation.

1. Government gets more inflation tax revenue.

2. Non-government redistribution due to menu costs?

3. Other?

G. Box #2: DW costs of inflation.

1. The tax on real cash balances. (With perfectly functional financial markets, this is just reflected in the nominal interest rate).

2. "Shoe leather"/menu costs. (Although this is partly due to inflation volatility).

3. Interaction between inflation and other tax distortions. (E.g. If nominal returns are taxed instead of real returns, then nominal taxes grow as inflation grows).

4. Harm of inflation to productivity growth. (But is this due to volatility?)

5. Other?

H. Box #3: Redistributive impact of inflation volatility

1. Non-government redistribution due to menu costs?

2. Other?

I. Box #4: DW impact of inflation volatility

1. Losses due to imperfect insurance markets (taxes, credit markets, labor markets, etc.)

2. Greater difficulty of long-term contracting.

3. Menu costs?

4. *Productivity growth?

5. Expectational errors get more severe - could lead to larger deviations from natural unemployment rate.

6. Other costs emphasized by Leijonhufvud: diversion of resources to the inflation-guessing sector; political replacement of markets; multiple monetary standards; more?

7. Other?

V. The Case for Zero Inflation, Deflation, and Moderate Inflation

A. Why zero?

B. Reduces inflation tax, but does not eliminate (unless nominal rates fall to 0 too).

C.
Substantial reduction in menu costs for __goods__. (But note: with increasing labor
productivity, zero inflation can still entail big menu costs for labor).

1. Question: Which is better from this perspective? Hitting zero on the un-quality-weighted inflation index, or zero on a Boskin-corrected inflation index?

D.
Reducing the deadweight costs of __other__ parts
of the tax code.

1. Intertemporal allocation distorted by taxation of nominal interest.

2. Capital stock distorted by taxation of nominal return.

3. Housing stock distorted by deductibility of nominal mortgage interest payments.

E. Feldstein's calculation: compare the one-time cost of disinflation with the PDV of the infinite-horizon benefits of disinflation.

1. One-time cost: 5% of GDP

2. PDV of benefits: 35% of GDP

F. Why not just use indexation of capital income, or abolish capital taxes?

G. Why deflation?

H. Friedman's case for deflation: even zero inflation is probably too high, since nominal interest rates will remain positive, implying a positive tax on real balances.

1. Can get the same result by simply paying interest on cash.

I. Indeterminacy problems of zero nominal interest rate; same problems from payment of market rate of interest on cash.

J. Selgin's productivity norm and deflation - a form of nominal GDP targeting to economize on labor market's menu costs and account for supply shocks.

K.
Note on Friedman's optimality rule: Productivity
norm is closer to Friedman than zero inflation rule, but Friedman's rule
actually requires deflation in *excess* of productivity growth.

L. Why moderate inflation?

M. ADP (only argument that touches on level of unemployment rather than just the volatility).

N. Makes it possible to actually drive real interest rates below zero.

VI. Conclusions on the Optimal Inflation Rate

A. Unemployment level - Probably the same for all policies within plausible ranges. ADP effect exists but probably doesn't appear even with mild deflation.

1. ADP is a plausible argument against Friedman's deflation rule.

B. Unemployment volatility - Productivity norm/nominal GDP target beats out zero-inflation or stable inflation target.

C. Inflation - Friedman's rule wins on inflation tax grounds; the more the prescription deviates from Friedman's rule, the greater these inefficiencies become.

D. Inflation volatility: Productivity rule/nominal GDP target seems to do worse than zero-inflation/stable inflation target, but consider effects of contractionary response to supply shocks.

E. Main point in favor of ZIG: it's more focal.

F.
Overall: If inflation/inflation volatility genuinely
*causes*
lower productivity growth, then getting low and stable inflation is very
important. Otherwise, all of these
policies are probably close to optimal.

G. Other opinions?

VII. Time Consistency, I: The Paradox of Discretion

A.
While the PC approach to macro policy has had
limited influence, a different approach with a similar flavor has been more
influential. **Time consistency literature**
treats policy-makers as SWF function maximizers who are nevertheless *untrustworthy*
and *opportunistic*.

1. Terminological note: "time consistent" is just macroeconomists' synonym for "subgame perfect."

B.
Simplest time consistency model: Suppose that output equals its natural level
expectationally, but is a decreasing function of __unanticipated__
inflation: _{}.

C.
Policy-maker has "opportunistic" LF: _{}, with _{}. Note k>0, so the
policy-maker wants to push the output level above its natural level.

D. Two steps to solve:

1.
First, assume policy-maker minimizes V, taking into
account the impact of (unexpected) inflation on unemployment. _{}

2. Set expected inflation equal to actual inflation, since there are no random variables in this equation.

E.
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.

F.
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.

G. 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.

1. 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.

H. Time consistency often used to explain failure of discretionary policy in the '70's - and around the world in high inflation countries today. Does this make sense?

VIII. Time Consistency, II: Resolving the Paradox with Reputation

A. Much of the paradox of time consistency goes away once one realizes that central banks and the public have repeated interaction with each other.

B. 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).

C. 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.

D.
Revise the CBs LF to give it an infinite horizon,
with a period discount factor of b: _{}

E.
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, _{}

F. These three payoffs are given by:

1.
_{} (Inflation in every
period is 0; y-y*=-k in every period).

2.
_{}

3.
_{}

G.
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.

IX. Time Consistency, Independence, and Compensation

A. What is the advantage of CB independence? Rogoff's paper notes that central bankers are normally selected from the "conservative" elements of society.

1. "Conservative" can be economically interpreted as "high disutility of inflation."

2. Interesting result: Time consistency problem can be solved by giving independent authority to a person who dislikes inflation more than most people dislike it.

B.
Simplest case: In one-shot game, what must the
weight on the inflation variable in the loss function be to get a 1^{st}-best
equilibrium?

1.
Note: Change loss function to _{}; then equilibrium inflation is (ak/b).

2. Therefore: Pick b to be as large as possible.

C.
More complex case: What if there are supply shocks
that it is desirable for the CB to compensate for? Then b^{normal}<b*<¥.

D. 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.

1. Explanations?

E. Alternate strategy: Instead of putting inflation-averse people in charge of monetary policy, just base their compensation on performance.