**
NBER Reporter: Spring 2002**

Bennett T. McCallum ^{(1)}

The past several years have seen very rapid development in the area of monetary
policy analysis. ^{ (2)}
One welcome aspect is the convergence of approaches used by
academic and central-bank economists. For example, a look at a notable
NBER conference volume ^{ (3)} and/or a special issue of the
Journal of Monetary Economics (Vol.
43, July 1999) suggests that it would be difficult, if not impossible, to identify the author
of almost any article or comment as belonging to one group or the other. A major
stimulus to this convergence, I believe, was John Taylor's exposition of the now-familiar
"Taylor Rule," ^{ (4)} which encouraged academics to focus
on policy rules expressed in terms
of interest-rate instruments (thereby conforming to actual central bank practices) and
encouraged central bankers to think of policy in a more rule-like fashion.

**Mainstream Analysis**

Much of this recent work has used the following approach: the researcher specifies a quantitative macroeconomic model that is intended to be structural (invariant to policy changes) and consistent with both theory and evidence. Then, analytically or by stochastic simulations, he determines how crucial variables such as inflation and the output gap behave on average under various hypothesized policy rules. Normally, rational expectations is assumed throughout. Evaluation of the outcomes can be accomplished by reference to an explicit objective function or left to the judgement (that is, implicit objective function) of the policymaker. Optimal control techniques may or may not be involved.

There is also considerable agreement about the general, broad structure of the
macroeconomic model to be used -- but much disagreement over details. For the
simplest closed-economy analysis a three-equation system is often used, involving just 1)
an optimizing "IS" type of intertemporal spending relation; a price adjustment relation;
and 2) an interest rate policy rule of the general Taylor type. The basic logic of the
analysis is not affected if (1) and (2) are sets of equations representing "sectors" of the
model, rather than single equations. A major development over the past 10-15 years is
the tendency of researchers to use versions of (1) and (2) that are based on optimizing
analysis of individual agents in a dynamic, stochastic setting. Often the price adjustment
relation is based on the work of Calvo and Rotemberg, although there continues to be
much dispute concerning the theoretical and empirical adequacy of this specification.
^{ (5)}
Development of the optimizing or "expectational" IS relationship -- basically a
consumption Euler equation plus some substitutions -- was affected more or less
simultaneously by a number of independent analysts. ^{ (6)}
My own paper with Edward
Nelson was not the first in print, but is arguably the only one to explore the relationship
of the new expectational specification with IS specifications of the traditional type.

**Extensions and Differences**

More generally, my recent work has conformed in large measure to the approach
just outlined. Papers with Nelson appear in both the Taylor volume and the
JME issue
mentioned earlier. ^{ (7)}
The former represents a policy-rule exploration based on an
estimated model that is highly orthodox in most respects; the latter features an extension,
however, that makes the model applicable to a small open economy. We derive import
demand as part of the optimizing behavior of consumer-producer households, with
imports being modelled as intermediate goods used in the production of consumables,
rather than as consumption goods in the manner favored in most of the "new open-economy macro" literature. In a subsequent paper, Nelson and I show that this
alternative formulation is helpful in matching some features of actual exchange rate
behavior. ^{ (8)}

A second way in which my work represents an extension of the basic model
concerns the role of capital. Much of the literature treats the stock of productive capital
as fixed or exogenous. ^{ (9)}
A paper written with Miguel Casares endogenizes capital
investment behavior and explores several issues. ^{ (10)}
Some significant findings are that
capital stock adjustment costs must be included to avoid highly unrealistic behavior
(especially in sticky-price models); that adjustment-cost specifications need to penalize
rapid changes more sharply than with the familiar quadratic cost specification; and that
models with constant capital can provide reasonable approximations for purposes of
monetary policy and business-cycle analysis.

One feature of the literature under discussion is that most models include no
money-demand function and no variable reflecting quantities of any monetary aggregate.
The usual optimizing analysis justifies this omission, however, only if the specification
of the function for transaction costs (which are reduced by holdings of real money
balances) is separable in money and the spending variable. Two recent papers of mine
argue that such separability is implausible; I conduct investigations of the magnitude of
the implied misspecification. ^{ (11)}
My quantitative analysis, based on calibrations intended to
be realistic, indicates that the effects of this misspecification are very small.
^{ (12)} Thus the
usual omission of money perhaps is acceptable, although inappropriate in principle. (The
first of these papers also shows how monetary policy can be effectively expansionary via
an exchange rate channel even with the usual interest rate instrument immobilized by a
"liquidity trap" at its zero lower bound.)

There are a few ways in which my work differs from much of the current
research, though. One is its emphasis on the difficulty of measuring the "output gap"
variable that appears in price-adjustment and Taylor-rule equations, that is, the
percentage difference between current output and its "potential" or "natural-rate" value.
Papers written with Nelson and on my own argue that ignorance of the reference value is
not a matter of simple measurement error, but rather a conceptual uncertainty that is
likely to be long-lasting. ^{ (13)}
In such circumstances, it is dangerous to respond strongly to
measures of the output gap, as some analysts have recommended. A second difference is
that we occasionally use monetary-base or exchange-rate instruments, rather than the
usual short-term interest rate.

A methodological paper argues strongly for the general approach to policy
analysis outlined at the start of this report. ^{ (14)}
It emphasizes that structural models are
necessary for policy analysis and that so-called "structural VARs" do not qualify -- their
relationships are not designed to have the necessary policy invariance. More
controversially, the paper argues that vector-autocorrelation functions, not impulse
response functions, should be emphasized in model diagnostics (to avoid the need for
highly questionable identification assumptions). A starting point for the discussion is
that policy analysis needs to focus on the systematic portion of monetary policy, not
policy "shocks," since the latter account for a very small fraction of movements in
interest rate instruments in actual economies.

**Rational Expectations Indeterminacies**

A substantial portion of my recent work has been devoted to the contention that
one small but prominent strand of the recent literature is misguided. This strand features
rational expectations "indeterminacies" that occur under various conditions pertaining to
policy-rule design. In several papers, I have emphasized that the aberrations in question
reflect multiple (real) solutions of the "bubble" or "sunspot" type, not purely nominal
indeterminacies of the sort discussed in the classic monetary writings of Lange, Gurley
and Shaw, Johnson, and especially Patinkin. ^{ (15)}
I argue that there are several reasons to
believe that the multiple-solution indeterminacies represent mathematical curiosities that
are of no relevance for actual policymaking. One reason featured in my most recent
papers is that the solutions involving problematic results are not E-stable or (therefore)
adaptively learnable, as explained in the extensive theoretical contributions of Evans and
Honkapohja. ^{ (16)}
By contrast, the unique minimum-state-variable solution (defined in
several of my papers ^{ (17)})
exists, is learnable, and is perfectly well-behaved in the
analytical settings under discussion. Applications of this analysis pertain to the "fiscal
theory of price level determination," as well as warnings against monetary rules based on
expected future inflation rates ^{ (18)}
and suggestions of liquidity traps generated by global
indeterminacy under Taylor rules. ^{ (19)}

All of these warnings are, I suggest, spurious. My position on these indeterminacy issues is admittedly idiosyncratic, but could therefore be of greater value if correct.

1. McCallum is a Research Associate in the NBER's Program on Monetary Economics and the H. J. Heinz Professor of Economics at Carnegie Mellon University.

2.
For useful reviews, see R. Clarida, J. Gali, and M. Gertler, "The Science of Monetary Policy: A New
Keynesian Perspective," *Journal of Economic Literature*, 37 (December 1999), pp. 1661-1707;
and M. Goodfriend and R.G. King, "The New Neoclassical Synthesis and the Role of Monetary Policy,"
*
NBER Macroeconomics Annual 1997*, Cambridge, MA: MIT Press, 1997, pp. 231-83. A more historical perspective is taken in B.T. McCallum, "Recent Developments in Monetary Policy Analysis: The Roles of
Theory and Evidence,"
NBER Working Paper No. 7088,
April 1999, and *Journal of Economic Methodology,* 6 (2) (1999), pp. 171-98.

3.
J.B. Taylor, ed., *Monetary Policy Rules*, Chicago: University of Chicago Press, 1999.

4.
J.B. Taylor, "Discretion versus Policy Rules in Practice," *Carnegie-Rochester Conference Series on
Public Policy*, 39 (December 1993), pp. 195-214.

5.
This issue, and others involving model specification, is discussed briefly in B.T. McCallum, "Should
Monetary Policy Respond Strongly to Output Gaps?"
NBER Working Paper No. 8226,
April 2001, and *American Economic Review*, 91 (May 2001), pp. 258-62.

6.
Notable publications include M. Woodford, "Price Level Determinacy Without Control of a Monetary
Aggregate," *Carnegie-Rochester Conference Series on Public Policy*, 43 (December 1995),
pp. 1-46; W. Kerr and R. G. King, "Limits on Interest Rate Rules in the IS Model," *Federal Reserve
Bank of Richmond Economic Quarterly,* 82 (Spring 1996), pp. 47-75; and B.T. McCallum and E. Nelson,
"An Optimizing IS-LM Specification for Monetary Policy and Business Cycle Analysis,"
NBER Working Paper No. 5875,
January 1997, and *Journal of Money, Credit, and Banking*, 21 (3, 1) (August 1999, pt. 2), pp. 296-316.

7.
B.T. McCallum and E. Nelson, "Performance of Operational Policy Rules in an Estimated Semi-Classical
Structural Model,"
NBER Working Paper No. 6599,
June 1998, and J.B. Taylor, ed., *Monetary Policy Rules*, Chicago: University of Chicago Press, 1999; and B.T. McCallum and E. Nelson, "Nominal Income Targeting in an Open-Economy Optimizing Model,"
NBER Working Paper No. 6675,
August 1998, and *Journal of Monetary Economics*, 43 (3) (June 1999), pp. 553-78.

8.
B.T. McCallum and E. Nelson, "Monetary Policy for an Open Economy: An Alternative Framework with
Optimizing Agents and Sticky Prices,"
NBER Working Paper No. 8175,
March 2001, and *Oxford Review of Economic Policy,* 16 (Winter 2000), pp. 74-91.

9.
This practice is not universal, of course. Notable exceptions include R.G. King and A. Wolman,
"Inflation Targeting in a St. Louis Model of the 21st Century," Federal Reserve Bank of St. Louis Review
78 (May/June 1996), pp. 83-107; and T. Yun, "Nominal Price Rigidity, Money Supply Endogeneity, and
Business Cycles," *Journal of Monetary Economics*, 37 (April 1996), pp. 345-70.

10. M. Casares and B.T. McCallum, "An Optimizing IS-LM Framework with Endogenous Investment," NBER Working Paper No. 7908, September 2000.

11.
B.T. McCallum, "Theoretical Analysis Regarding a Zero Lower Bound on Nominal Interest Rates,"
NBER Working Paper No. 7677,
April 2000, and *Journal of Money, Credit, and Banking*, 32 (November 2000, pt. 2), pp. 870-904; and B.T. McCallum, "Monetary Policy Analysis in Models Without Money,"
NBER Working Paper No. 8174,
March 2001, and *Federal Reserve Bank of St. Louis Review*, 83 (July/August 2001), pp. 145-60.

12. This finding is consistent with the econometric analysis of P.N. Ireland, "Money's Role in the Monetary Business Cycle," NBER Working Paper No. 8115, February 2001.

13. B.T. McCallum and E. Nelson, "Timeless Perspective vs. Discretionary Monetary Policy in Forward-Looking Models," NBER Working Paper No. 7915, September 2000; and B.T. McCallum, "Should Monetary Policy Respond Strongly to Output Gaps?" NBER Working Paper No. 8226, April 2001. Also relevant in this regard is A. Orphanides, "The Quest for Prosperity without Inflation," ECB Working Paper Series 2000-15, March 2000.

14.
B.T. McCallum, "Analysis of the Monetary Transmission Mechanism,"
NBER Working Paper No. 7395,
October 1999, and *The Monetary Transmission Process: Recent Developments and Lessons for Europe*, Deutsche Bundesbank, eds., Palgrave Publishers, 2001.

15.
B.T. McCallum, "Issues in the Design of Monetary Policy Rules,"
NBER Working Paper No. 6016,
April 1997, and J.B. Taylor and M. Woodford, eds., *Handbook of Macroeconomics*, North Holland: Elsevier Science, 1999; B.T. McCallum, "Indeterminacy, Bubbles, and the Fiscal Theory of Price Level
Determination,"
NBER Working Paper No. 6456,
March 1998, and *Journal of Monetary Economics*, 47 (February 2001), pp. 19-30; B.T. McCallum, "Monetary Policy Analysis in Models Without Money,"
NBER Working Paper No. 8174,
March 2001; and B.T. McCallum, "Inflation Targeting and the Liquidity Trap," NBER Working Paper No. 8225,
April 2001. For references and a summary of the earlier literature see H.G. Johnson, "Monetary Theory and Policy," *American Economic Review*, 52 (June 1962), pp. 325-84.

16.
Most notable of many publications is G.W. Evans and S. Honkapohja, *Learning and Expectations in
Macroeconomics*, Princeton: Princeton University Press, 2001. Also see J. Bullard and K. Mitra,
"Learning About Monetary Policy Rules," forthcoming in the *Journal of Monetary Economics*.

17.
B.T. McCallum, "Role of the Minimal State Variable Criterion in Rational Expectations Models,"
NBER Working Paper No. 7087,
April 1999, and *International Tax and Public Finance*, 6 (4) (November 1999), pp. 621-39.

18.
First noted by M. Woodford, "Nonstandard Indicators for Monetary Policy: Can Their Usefulness Be
Judged from Forecasting Regressions?" in *Monetary Policy*, N.G. Mankiw, ed., Chicago:
University of Chicago Press, 1994.

19.
For example, J. Benhabib, S. Schmitt-Grohe, and M. Uribe, "The Perils of Taylor Rules," *Journal of
Economic Theory*, 96 (January 2001), pp. 40-69.

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