Eco 225
–
Monetary Economics
Spring 2014/Mello
Stabilization Policy and the Time Inconsistency Problem
(This is a summary of chapter 14 from Mankiw’s Macroeconomics text, 2007)
1. Should policy be active or passive?
Some economists view the economy as naturally unstable and believe that policymakers should engage in active policymaking. On the other hand, some economists view the economy as naturally stable and believe that the best policymaking strategy is to take a hands-off approach.
The first group of economists advocates that policy makers should use monetary and fiscal policy to stabilize the economy in the face of aggregate demand and supply shocks. An active monetary policy rule is a policy rule such that the central bank determines, for instance, a constant growth rate in the money supply plus some variable term that depends on the level of cyclical unemployment (something like
) (
%M uun , where %M is a constant, and u un is cyclical unemployment). In
this case, whenever the economy is in recession (i.e., unemployment above the natural rate) the money supply growth increases faster, and whenever the economy is overheated (i.e., unemployment below the natural rate) the money supply growth increases at a slower pace.
Although policymakers in the federal government view economic stabilization as one of their primary responsibilities1, proponents of the passive policy approach put forth two arguments in favor of hands-off approach: Lags in the implementation and effects of policies, and the Lucas Critique.
In this note, we consider these arguments below. Furthermore, we also discuss the problem of time inconsistency of monetary policy and some monetary policy rules that have been proposed in the literature recently. Finally, as indicated above this note is a
summary of the material in chapter 14 of Mankiw’s Macroeconomics text, 6th
edition, 2007.
2. Lags in the implementation and effects of policies
One issue that makes the practice of economic policy particularly difficult is the temporal lag between the implementation and effects of policies. Mankiw defines two types of lags: (i) the inside lag is the time between a shock to the economy and the policy action responding to that shock; (ii) the outside lag is the time between a policy action and its influence on the economy.
Consider fiscal policy for example. Fiscal packages have to be approved by the President and both houses of the Congress. The legislative process is notoriously slow, which makes the inside lag of fiscal policy long. However, once the fiscal package is approved the impact on the economy of changes in G or T is immediate. That is, fiscal policy has a long inside lag but a short outside lag.
Monetary policy, on the other hand, has a very short inside lag but a long outside lag. Once the central bank decides on a new interest rate the money market adjusts in a
1
matter of hours. However, it is estimated that it takes about six to twelve months for a change in the interest rate to take full effect in the economy. Monetary policy has a long outside lag because it works mainly through the credit channel of the economy, affecting the decision to invest and consume. Typically, investment and consumption adjust slowly to changes in the credit conditions.
Advocates of passive policymaking argue that the long and variable lags make stabilization policy impossible. Advocates of active policymaking say that the long and variable lags require caution when making policy, but that there is still plenty of room for stabilization policy.
3. The Lucas Critique
Economists can estimate econometrically model economies, e.g., an IS-LM model, as a guide to policy making. That is, by using data and appropriate statistical techniques we can obtain numerical estimates for the parameters of an economic model. And, with the parameter estimates we can use the model to predict the effects of monetary and fiscal policy on the economy.
However, according to Robert Lucas, a Nobel prize-winner from the University of Chicago, using econometric estimates of macro models to predict the effects of economic policies can be very misleading. The reason is that econometric models generate their estimates using current and past data, and when the government implements a new policy, individuals change their expectations and therefore make all estimates of the
model’s parameters invalid, since current and past data don’t incorporate the change in
Therefore, because one cannot accurately predict the impact of policy changes in the economy, one should consider adopting a passive policy approach instead of engaging in active policymaking. That is, those who know little should do little.
The implication of the Lucas Critique is very strong. In particular, it implies that economists can’t use their main tools – economic models – to design and predict the effect of stabilization plans. The importance of expectations in macroeconomics cannot be overstated, and the fact that econometric estimates of economic models cannot capture the change in expectations caused by a change economic policy is also well accepted. But the conclusion that economic models are of limited help in designing stabilization policies is not universally accepted. Advocates of active policymaking acknowledge that the effect of the Lucas Critique is correct in theory, but they argue that its effects are small in practice and, therefore, it does not render economic policy powerless. They argue that the reason why the Lucas critique has a small effect in practice is simple – individuals are not as rational as required by the theory.
One way to settle the debate would be to recur to the historical record. Unfortunately, the problem is that it is not easy to interpret history; more often than not we have more than one interpretation for the same historical event.
Finally, although we saw some arguments in favor of a hands-off approach to economic policy, most governments around the world take an active role in policy making – for better, or for worse.
4. Should policy be conducted by rule or discretion?
an active policy rule is %M 5% (u 5%) , and an example of a passive policy rule is something like %M 5% ). Policy is conducted by discretion if policymakers are free to choose whatever policy they consider appropriate to respond to shocks to the economy.
Why policy might be improved by commitment to a policy rule?
Typically politicians are happy to sacrifice long-run economic gains for short-run political gains – in general, their terms end well before the gains of hard-to-take macroeconomic policies materialize. The Japanese slump in the 1990s provides an example of politicians sacrificing long-run economic gains for short-run political gains. Japanese banks in the 1990s were loaded with non-performing loans, and the correct economic measure was to let failed banks go bust. However, the government avoided at any cost to deal with the problem of the banking sector. No politician in his right mind would advocate a policy action that would cause thousands of job losses, even if the alternative would be to condemn the economy to several years of sluggish growth (and cause the destruction of even more jobs). From a political point of view the best strategy is to delay taking any action. Given that politicians are incompetent and opportunistic, and that the political process can be shady, why should we give politicians power to make economic policy? Maybe the best strategy is to restrain them, and let economic policy be made by economists.
The problem with discretionary policy: the time inconsistency problem
housing in NY persists over time. One reason that may explain this situation is the system of rent controls imposed by the government since the World War II. By law, landlords in NY cannot increase rents except when specifically permitted to do so. This system of rent controls may be constraining the supply of housing units in NY. Why would the system of rent controls affect the supply of new housing units? Advocates of rent controls typically exempt new buildings from the controls. And, they claim that by doing so they won’t discourage the construction of new buildings. Therefore, the supply of new housing units should be unaffected by the rent controls. Is this true?
Consider the following situation. Suppose that the mayor of Smallville impose rent controls on existing buildings but exempt future constructions from rent controls. However, once a new building is constructed and it is ready to be rented out the mayor is tempted to impose rent controls. This way several tenants win, and only one landlord loses. This seems like a good deal for the mayor. The problem with this strategy is that landlords are rational agents and they anticipate the mayor’s strategy. Expecting the mayor to renege on its initial promise of not imposing rent controls on new housing units,
landlords don’t construct new buildings in the first place. The key point here is that landlords know that, once new buildings are constructed, the mayor has an incentive to change his policy and impose rent controls. Unless the mayor provides some way of committing to his initial promise, landlords will not construct new buildings.
The above problem describes what is known as the time inconsistency problem. This situation is considered temporally inconsistent because the mayor has an incentive to renege on his initial promise at a future period. That is, initially the optimal policy from the mayor’s viewpoint is to announce that he will not impose rent controls on new buildings, but at some time in the future his optimal policy is to impose rent controls.
they won’t negotiate with terrorists over the release of hostages, clearly in an attempt to discourage terrorists. But once terrorists hold hostages the government has an incentive to renege on its initial promise and negotiate with terrorists. Knowing this, the terrorists keep coming.
Interestingly, the time inconsistency problem also arises in monetary policy. The Fed dislikes both unemployment and inflation, and the Fed prefers individuals to have low inflation expectations so it can face a better short-run inflation-unemployment tradeoff (that is, the Fed likes a Phillips curve that is close to the origin). Thus, the Fed might use the following strategy: announce a low target for the inflation rate to induce individuals to set low inflation expectations in their wages and prices contracts, and then, once they write prices and wages contracts based on low inflation expectations, the Fed implements an expansionary monetary policy (which is inflationary) to reduce the unemployment rate. The problem with this strategy is that individuals understand the
Fed’s incentive to renege on its initial promise of low inflation. Therefore individuals
don’t believe in the Fed’s announcement in the first place, and set high inflation expectations (which mean that the inflation rate will also be high). Because of the time inconsistency problem some economists suggest that the Fed should use policy rules rather than discretion in conducting monetary policy.
Assume that the Fed chooses the inflation rate. Furthermore, assume that the Fed dislikes inflation and unemployment according to the following loss function:
2 )
,
(u u
L (1)
where u is the unemployment rate, represents how much the Fed dislikes inflation relative to unemployment, and is the inflation rate. The Fed’s problem is to choose the inflation rate so as to minimize its loss function. If inflation and unemployment were independent variables this would be a trivial problem (of course, in this case, the best strategy would be to set both variables equal to zero). But we know that the Fed faces a short-run inflation-unemployment trade-off given by the Phillips curve. The Phillips curve can be written as:
)
( e
n
u
u
where 1/ (recall that traditionally we represent the Phillips curve as follows
) ( n e u u
). Consider the optimal inflation rate under a policy rule and under discretion.
Optimal inflation under a policy rule
The Fed announces that it will fix the inflation rate at a low level. As long as the Fed is committed to the announced inflation rate, individuals will believe in the Fed’s announcement and set expectations accordingly. Thus, from the outset we will have
e
, which implies that n
u
u . The optimal inflation rate under a policy rule must be 0
, since the Fed wants to minimize its loss function.
Optimal inflation under policy discretion
inflation rate. Fourth, based on the expected inflation and the actual inflation, the unemployment rate is determined by the Phillips Curve. The Fed’s minimization problem can be written as follows:
( )
, s. t.
(
)
(3)The above problem can be transformed into an unconstrained minimization problem by substituting the Phillips curve into the loss function as follows
( )
(
)
(4)The first-order condition giving the optimal inflation rate is given by
(5)
Rational agents know the Fed’s problem and the Phillips Curve constraint. They know that the Fed chooses inflation equal to , and, therefore, they adjust their expectations accordingly, so we have , which implies that . The striking result is that, as mentioned above, the optimal inflation rate under discretionary policy is greater than the optimal inflation under policy rules. Once we give
the Fed flexibility in making policy, the economy’s inflation rate is greater than when we
tie up the Fed’s hand.
Why can’t the Fed under discretion achieve a zero inflation rate? The Fed can’t achieve zero inflation under discretion because the Fed cannot commit to its initial announcement of low inflation. Individuals are rational and know that if they set low inflation expectations, the Fed has an incentive to renege on its initial announcement of low inflation and promote an expansionary monetary policy (which will be inflationary) to explore the short-run trade-off between inflation and unemployment rate.2
low. This can be achieved by hiring central bankers that dislikes inflation a lot. That is, central bankers with a very high . Note that a conservative central banker can achieve a zero inflation rate just like the outcome of a central banker under a fixed policy rule. This can be easily seen by looking at the optimal inflation rate in equation (5) and noting that it approaches zero if (that is, if ).
5. Monetary Policy Rules
3Suppose that the central bank decided to adopt a policy rule. What policy would that be? There is an ongoing debate in macroeconomics about the optimality of policy rules. We shall study many aspects of this debate along the semester, however, for now
we will follow Mankiw’s text and discuss three policy rules: money supply targeting,
nominal GDP targeting, and inflation targeting.
The simplest monetary policy rule is for the central bank to promote a constant growth rate in the money supply. This rule is associated with Milton Friedman, which was the leading monetarist macroeconomist. Monetarists believe that monetary shocks are largely responsible for shocks in output and prices, and therefore, the best that monetary authorities can do is to promote a stable path for monetary aggregates.
A second policy rule that has been advocated is nominal GDP targeting. Under this rule the monetary authority announces a target for the growth in nominal GDP. If the nominal GDP grows faster than the target growth rate, the monetary authority reduces the growth rate of the money supply, if it grows slower than the target growth rate the monetary authority increases the growth rate of the money supply to stimulate aggregate demand. The advantage of nominal GDP targeting is that it allows the monetary policy to adjust to changes in the velocity of money. If indeed the velocity of money changes over
3In this section we don’t discuss interest rate rules, such as Taylor’s rule. Later in the semester we shall
time, and this seems to be the case, this policy rule would deliver greater stability of output and prices than a simple constant growth rate of the money supply.
A third monetary policy rule, and one that is nowadays very popular among several central banks, is the inflation targeting. Under an inflation targeting rule, the monetary authority announces a target for the inflation rate, and adjusts the money supply to hit the target. Like nominal GDP targeting, inflation targeting can accommodate changes in the velocity of money. We shall study in detail all aspects of inflation targeting later in the semester. Finally, we end this section with a question: the above three rules are expressed in terms of nominal variables, why not expressing them in terms of real variables?
6. Conclusion
In this note we discuss whether policy makers should have an active role in stabilizing the economy, or whether a hands-off approach to economic policy is better. Furthermore, we discuss whether they active policymaking should adopt policy rules or use discretion. There are many arguments in favor of a passive policy approach (uncertainty and lags in the implementation of policy), and many arguments in favor of active policy making (none of the arguments in favor of passive policy are, in practice, an impediment to make economic policy; they just imply that policy makers should cautious when making economic policy).
Exercise #1:
(Based on Mankiw, 2002) This question asks you to analyze how an increase in the natural rate of unemployment affects the inflation rate in the light of the time inconsistency problem.
a. In the model we developed above, what happens to the inflation rate when n
u
increases?
b. Suppose now that the central bank’s loss function is given by 2 2 )
,
(u u
L . Find
the optimal inflation rate under discretionary policy.
c. Given your answer in [b], now what happens to the optimal inflation rate when there is an increase in the natural rate of unemployment?
d. As we discussed in class, President J. Carter, in 1979, appointed Paul Volcker, a conservative central banker, to chair the Fed. According to the model developed above, what do you think should have happened to the inflation rate and the unemployment rate after the announcement of the new Fed chairman?
Exercise #2:
Assume that the Fed conducts monetary policy using discretion according to the model developed above. Assume that the Fed’s loss function is given by
2 )
,
(u u
L , and the Phillips curve is given by u un ( e).
a. Find the optimal inflation rate under discretion. Explain why under discretion the Fed cannot obtain a zero-inflation rate.
b. Now suppose that the Fed’s loss function is given by 2 )
,
(u au
L . Furthermore,
if the president is a Democrat, he/she will appoint a central banker with D
a
a . And, if
the president is a Republican, he/she will appoint a central banker with R
a
a , where
R D
a
c. Calculate the optimal inflation rate under discretion using the Fed’s new loss function,
2 )
,
(u au
L .
d. There are presidential elections next year. The probability of a Republican being the president is 70%, and, consequently, the probability of a Democrat being president is 30%. Assume that agents have rational expectations about future inflation and that the Fed conducts monetary policy under discretion as in [c]. Using your answer to [c], calculate the expected inflation for next year as a function of the parameters of the model,
D
a , aR , , and .
e. Given the expected inflation you calculated in [d], use the Phillips curve to describe what happens to inflation and unemployment rate next year if the Democrats win.
f. Given the expected inflation you calculated in [d], use the Phillips curve to describe what happens to inflation and unemployment rate next year if the Republicans win.
g. How does your answers to questions [e] and [f] change if the two parties take turns?
