Pitfalls of Forward-Looking Monetary Policy by po9383


									                 Pitfalls of Forward-Looking Monetary Policy

                                        By MICHAEL WOODFORD*

   A distinctive feature of the procedures re-                 tion targeting as a regime of discretionary
cently adopted by inflation-targeting central                   policy-making, in which the central bank is
banks is their forward-looking character. Fore-                charged with minimization of a loss function
casts of the economy’s future evolution condi-                 that differs from the true social objective, in
tional upon alternative policies play a central                order to eliminate the Kydland-Prescott infla-
role in the banks’ deliberations, to an extent that            tion bias resulting from discretion. King’s mod-
the procedures adopted are sometimes charac-                   ified loss function changes only the (constant)
terized as “forecast targeting.” This emphasis                 target values for the target variables, and not the
upon the future consequences of policy is un-                  variables themselves that the bank seeks to sta-
surprising in an approach that tries to maintain               bilize; hence, a Markov equilibrium resulting
as transparent as possible a relation between the              from discretionary optimization implies a pol-
banks’ decisions and the ultimate goals of mon-                icy that depends only upon states relevant to the
etary policy; after all, current decisions can still           determination of current or future inflation and
affect the future, but not the past.                           output.
   Nonetheless, common descriptions of how                        Common descriptions of “inflation-forecast tar-
inflation targeting is or should be practiced go                geting” (e.g., Lars E. O. Svensson, 1999) illustrate
too far, in proposing purely forward-looking                   this feature even more clearly. Under such proce-
procedures. I shall argue instead that an optimal              dures, an economic model is used to generate
framework for the conduct of monetary policy                   conditional forecast paths for the target variables
must generally be history-dependent in ways                    from the present onward associated with alterna-
precluded by these simple proposals. This fol-                 tive feasible policies. The bank then chooses
lows from a general feature of the optimal con-                among the candidate forecast paths, either evalu-
trol of a forward-looking system, which is to                  ating them according to a loss function or select-
say, one in which the private sector’s expecta-                ing the path that satisfies some targeting criterion,
tions about future policy are an important de-                 such as a requirement that the forecast of inflation
terminant of the effects of monetary policy.                   at some future horizon equals a target value,
                                                               which may depend upon the output forecast. The
                                                               bank’s current action is then the one required by
     I. Purely Forward-Looking Procedures
                                                               the chosen scenario. The procedure is repeated
                                                               afresh in each decision cycle. Past states obviously
   By a purely forward-looking decision proce-                 cannot affect the action that is chosen, if they
dure for monetary policy I mean one in which                   affect neither the set of scenarios judged to be
the bank’s action at any time is conditioned                   possible nor the criterion used to choose among
solely upon those aspects of the state of the                  alternative scenarios.
world that are relevant for forecasting the sub-                  Other authors have described inflation-
sequent evolution of the bank’s target variables,              targeting policies as rules for setting a short-
which I shall here suppose to be the inflation                  term interest rate as a function of forecasts of
rate and the level of aggregate economic activ-                the future paths of the target variables (raising
ity. Examples of such proposals are common-                    interest rates in proportion to the forecasted
place in the literature on inflation targeting. For             excess of inflation over the target level). Some-
example, Mervyn King (1997) describes infla-                    times the forecast is assumed to correspond to a
                                                               scenario in which the interest rate is left at
                                                               its current level; in other cases it represents
   * Department of Economics, Princeton University,
Princeton, NJ 08544. I thank Julio Rotemberg and Lars
                                                               a forecast of what should happen if the pre-
Svensson for many helpful discussions, and the NSF for         scribed policy rule is followed. In either case,
research support.                                              if the prescribed interest rate is a function only
VOL. 90 NO. 2                            INFLATION TARGETING                                          101

of the forecasts, such a decision procedure is        Euler equation. The first relation determines t
purely forward-looking.                               given xt, inflation expectations (Et t 1), and an
                                                      exogenous cost shock ut. The second determines
         II. Why Optimal Policy Must                  xt given Et xt 1, the expected real rate of return
             Be History-Dependent                     (determined by the central bank’s instrument it
                                                      and by Et t 1), and exogenous variation in the
   It might seem that the property just identified     Wicksellian “natural rate of interest” r n. I assume
is a simple consequence of optimization, and          that social welfare requires the minimization of
thus wholly desirable. In particular, one might       the expected value of a discounted sum of period
suppose that, in the case of a social objective       losses of the form
that is additively separable over time, familiar
principles of dynamic programming imply that          (1)          Lt      t     x   x2
                                                                                      t   i 2
                                                                                          i t
optimal policy at any point in time should de-
pend only upon state variables that determine         for some weights x          0, i       0.
constraints upon possible paths of the target             In this simple model, conditional forecasts in
variables from that time onward. However, such        period t of the paths of the target variables from
principles apply only to the control of a system      that period onward depend only upon the exog-
in which the target variables evolve according        enous state vector st , describing information at
to laws of motion that are purely backward-           t about the current and future values of the
looking. When, instead, private-sector expecta-       exogenous disturbances u t j , r n j . Thus any
tions of the economy’s future path are among          determinate equilibrium resulting from a purely
the determinants of the current values of target      forward-looking procedure makes i t , t , and x t
variables (as in almost any model of the mon-         functions solely of st . If the disturbances are
etary transmission mechanism derived from op-         Markovian, this means a function only of the
timizing behavior), such a conclusion is              current disturbances u t and r n.t
incorrect (Woodford, 1999a).                              Except in the special case that i        0 and
   The reason is simple. In general, forward-         there are no cost shocks, an optimal equilibrium
looking behavior implies that more desirable          requires these variables to be functions of
responses of the target variables (inflation and       lagged disturbances as well. For example, in the
output) to a shock can be achieved if it can be       case of a transitory cost shock, a forward-
arranged for private-sector expectations about        looking procedure results in an equally transi-
the future paths of the target variables to adjust    tory increase in inflation and decrease in output,
in the right way in response to the shock. How-       with both variables expected to return to their
ever, this can occur (when the private sector has     average values once the disturbance is past.
rational expectations) only if subsequent             However, an optimal commitment would in-
central-bank policy does in fact change as a          volve a negative output gap that returns to zero
result of the past shocks in such a way as to         only slowly, so that the initial burst of inflation
bring about the alternative evolution that it was     is expected to be followed by a period of dis-
desired that people would expect. However, an-        inflation; when i         0, this eventually returns
ticipation by the private sector that the central     the price level to its original trend path (Clarida
bank will apply a purely forward-looking pro-         et al. 1999; Woodford, 1999b). This expectation
cedure at later dates precludes such adjustment       of subsequent disinflation mitigates the effects
of expectations at the earlier date.                  of the adverse cost shock, by restraining price
   The history-dependence of optimal policy can       increases during the period of the shock.
be usefully illustrated in the context of a simple        Similarly, in the case of a transitory increase
optimizing model of the monetary transmission         in the natural rate of interest, a forward-looking
mechanism, analyzed by Richard Clarida et al.         procedure results in an equally transitory
(1999) and by Woodford (1999a), among others.         increase in the nominal interest rate. When
In this model, inflation t and the output gap xt         i      0, an optimal commitment instead in-
(output relative to its efficient level) are deter-    volves a more persistent increase in the nominal
mined by a pair of structural relations, consisting   interest rate (Woodford, 1999a). This results in
of an aggregate supply curve and an intertemporal     a larger response of long rates (which restrain
102                                  AEA PAPERS AND PROCEEDINGS                                    MAY 2000

expenditure and hence prices despite the distur-      period t to seek to minimize an objective that
bance), without requiring a sharp increase in         adds terms of the form 1,t 1 t             2,t 1 x t to
short rates. As a result, it is possible to simul-    the expected discounted sum of terms L t j for
taneously achieve lower volatility of inflation,       j     0. Here the coefficients i,t 1 are deter-
the output gap, and the short-term nominal in-        mined as part of the bank’s period-t 1 decision
terest rate.                                          cycle and then taken as given parameters of the
   Purely forward-looking procedures forfeit          bank’s objective in its period-t decision cycle.
these gains from desirable responses of inflation      A discretionary procedure of this kind has a
expectations and interest-rate expectations to        Markov equilibrium in which inflation and out-
exogenous shocks. In addition, purely forward-        put evolve as under the optimal commitment,
looking approaches more easily result in inde-        and the coefficients i,t 1 are set equal to La-
terminacy of equilibrium. In the model sketched       grange multipliers associated with that optimi-
above, an exogenously specified nominal inter-         zation problem.
est-rate process results in price-level indetermi-       This approach represents a relatively general
nacy; a determinate equilibrium requires a            solution to the problem of making optimal pol-
sufficient degree of dependence (of the right          icy consistent with a discretionary optimization
sort) of the central bank’s interest-rate operating   procedure. However, the practicality of the pro-
target upon endogenous variables, such as in-         posal may be doubted. Since the coefficients
flation and output (Woodford, 1999a). Further-           i,t 1 result from the central bank’s calcula-
more, an operational procedure must make the          tions when choosing period-t 1 policy, they
interest rate a function of variables that are        respond to no endogenous variables (not chosen
exogenous or predetermined at the time that the       by the bank itself) determined in period t 1
interest rate is chosen (Svensson and Woodford,       and so will be a function solely of the history of
1999). In the case of a purely forward-looking        exogenous disturbances. Such a procedure once
procedure, this means a function solely of the        again implies an interest-rate reaction function
exogenous state st , as no predetermined endog-       that leads to indeterminacy (Svensson and
enous variables are relevant for forecasting the      Woodford, 1999).
target variables. But such a procedure necessar-         On both grounds one might therefore prefer
ily leads to indeterminacy of the paths of both       an alternative approach, in which the modified
inflation and output.                                  loss function involves no time-varying coeffi-
                                                      cients, but instead a period loss function that
   III. Examples of History-Dependent Policy          depends upon lagged as well as current values
                                                      of the target variables. In this case, discretionary
   There are a variety of ways in which a deci-       policy is history-dependent because the bank’s
sion procedure for monetary policy might in-          loss function is history-dependent (even though
corporate the sort of history-dependence              the true social loss function is not). The implied
required for an optimal regime. As Svensson           reaction function will make the nominal interest
and Woodford (1999) stress, these include             rate a function of lagged endogenous vari-
history-dependent variants of inflation-forecast       ables— dependence of which sort is necessary,
targeting procedures. For example, a forecast-        though not sufficient, for determinacy of
targeting procedure that amounts to discretion-       equilibrium.
ary optimization can nonetheless be sufficiently          For example, David Vestin (1999) shows that
history-dependent, if the loss function that the      discretionary optimization results in more nearly
central bank seeks to minimize is modified in a        optimal responses to cost shocks (in the above
way that introduces history-dependence.               model, with i 0) if the central bank is charged
   A particularly straightforward approach is to      with stabilization of the price level rather than the
incorporate into the bank’s loss function terms       inflation rate, even though the true social loss
that represent the value, at earlier dates, of hav-   function is that shown in equation (1). The pro-
ing people anticipate different subsequent paths      posed loss function is history-dependent, in that it
of the target variables (Svensson and Woodford,       effectively depends upon the cumulative sum of
1999). For example, in the simple model above,        inflation rates over all past periods, rather than
one might instead direct the central bank in          only upon the current period’s inflation rate. This
VOL. 90 NO. 2                                                  INFLATION TARGETING                                           103

is desirable, as it implies that an inflationary shock                     responses to cost shocks are optimal. The tar-
should cause anticipation of lower inflation in                            geting criterion is history-dependent in that (3)
subsequent periods, to an extent that the price                           involves x t 1 . Note that if the efficient level of
level is expected to eventually return to its original                    output is a deterministic trend, and          , this
level.                                                                    rule corresponds to nominal GDP-growth tar-
   Similarly, Henrik Jensen (1999) shows that a                           geting, as proposed by Jensen; however, the
nominal GDP growth target can be preferable to                            latter rule is fully optimal only in this special
discretionary minimization of the true social                             case.
loss function (“inflation targeting”) in a similar                            In the more general case that i 0, Marc P.
model. This makes the period loss function de-                            Giannoni (1999) shows that the optimal target-
pend upon lagged output as well as the current                            ing criterion instead takes the form
values of target variables. Specifically, low out-
put in the previous period leads the central bank
to choose low output and/or deflation in the                               (4)        it    i
                                                                                          1 t 1       2   it   1    it   2
current period. As a result, a transitory cost
shock results in a more persistent contraction of                                                 t       x    xt   xt   1
output, lowering overall inflation and output
variability as discussed above.
   Finally, Woodford (1999a) shows that more                              for appropriately chosen coefficients 1 , 2 , ,
nearly optimal equilibrium responses to fluctu-                              x     0. The optimal values of these coeffi-
ations in the natural rate of interest (in the                            cients depend upon the coefficients of the struc-
model with i          0) result from discretionary                        tural equations and of the loss function (4), but
optimization if the central bank’s period loss                            they are completely independent of all parame-
function is given by                                                      ters specifying the shock processes. Again this
                                                                          condition determines a unique nonexplosive
(2)    L cb
                  t           x   x2
                                   t         it   it       1
                                                                          equilibrium corresponding to the optimal
for an appropriate choice of        0, rather than                            The targeting criterion (4) provides a rule for
by the true social loss function (1). Such an                             setting the central bank’s interest-rate instru-
“interest-rate smoothing” objective induces the                           ment that is in the spirit of the “Taylor rule.”
sort of gradual adjustment of the interest rate                           But it differs from John B. Taylor’s (1993)
that characterizes responses under the optimal                            classic formulation in involving additional
commitment.                                                               history-dependence: interest rates respond to
   The appeal of such modified central-bank                                the growth rate of the output gap rather than to
objectives depends, of course, upon the expec-                            its level, and the coefficients 1 , 2      0 imply
tation that a discretionary optimizer will not                            inertial interest-rate dynamics. It is interesting
efficiently achieve its official aims. An appeal-                           to note that both of these departures from Tay-
ing alternative involves commitment to the                                lor’s formulation characterize at least some
achievement of a specific targeting criterion.                             econometric estimates of actual Fed reaction
Introducing history-dependence is especially                              functions (e.g., John P. Judd and Glenn D.
straightforward under such an approach; one                               Rudebusch, 1998).
simply needs a targeting criterion that depends                               This example indicates that an optimal tar-
upon past values of the target variables, as well                         geting criterion need not involve forecasts for
as their current and future values.                                       periods beyond the one for which interest
   For example, in the case that i 0, Wood-                               rates are being set. In this case, private-sector
ford (1999a) shows that a policy that ensures                             anticipation of subsequent central-bank action
that inflation satisfies the targeting criterion                            substitutes for preemptive actions by the cen-
                                                                          tral bank. However, the optimality of this rule
(3)           t       x   /        xt   xt   1         0                  under an arbitrary information structure de-
                                                                          pends upon the absence of intrinsic dynamics
(where is the slope of the short-run Phillips                             in the model’s structural equations; more gen-
curve) suffices to ensure that the equilibrium                             erally, an optimal targeting criterion will
104                                AEA PAPERS AND PROCEEDINGS                             MAY 2000

involve forecasts, as in Svensson (1999).            nal of Monetary Economics, June 1997,
Even so, an optimal procedure will not gen-          39(1), pp. 81–97.
erally be purely forward-looking, but will         Svensson, Lars E. O. “Inflation Targeting as a
instead have to involve backward-looking             Monetary Policy Rule.” Journal of Mone-
elements of the kind illustrated here.               tary Economics, June 1999, 43(3), pp. 607–
                                                   Svensson, Lars E. O. and Woodford, Michael.
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                                                     flation-Forecast Targeting.” Mimeo, Prince-
Clarida, Richard; Galı, Jordi and Gertler, Mark.
                     ´                               ton University, 1999.
  “The Science of Monetary Policy: A New           Taylor, John B. “Discretion versus Policy Rules
  Keynesian Perspective.” Journal of Eco-            in Practice.” Carnegie–Rochester Conference
  nomic Literature, December 1999, 37(4), pp.        Series on Public Policy, December 1993, 39,
  1661–1707.                                         pp. 195–214.
Giannoni, Marc P. “Does Model Uncertainty          Vestin, David. “Price-Level Targeting versus In-
  Imply Caution? Robust Optimal Monetary             flation Targeting in a Forward-Looking
  Policy in a Forward-Looking Model.”                Model.” Mimeo, Stockholm University,
  Mimeo, Princeton University, 1999.                 1999.
Jensen, Henrik. “Targeting Nominal Income          Woodford, Michael. “Optimal Monetary Policy
  Growth or Inflation?” Mimeo, University of          Inertia.” National Bureau of Economic Re-
  Copenhagen, 1999.                                  search (Cambridge, MA) Working Paper No.
Judd, John P. and Rudebusch, Glenn D. “Tay-          7261, August 1999a.
  lor’s Rule and the Fed: 1970 –1997.” Eco-                . “Commentary: How Should Monetary
  nomic Review (Federal Reserve Bank of San          Policy Be Conducted in an Era of Price Sta-
  Francisco), 1998, (3), pp. 3–16.                   bility?” in New challenges for monetary pol-
King, Mervyn. “Changes in UK Monetary Pol-           icy. Kansas City, MO: Federal Reserve Bank
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