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Regimes, switching
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Some of the material on this web page is based upon work supported by the National Science Foundation under
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Clickable Table of Contents
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Information
 Research Papers and Software
 Curriculum vitae
 List
of my research papers, alphabetically by title
 Course Materials
 Practical Details
about Viewing, Downloading, File Formats
 Local Links
 Princeton
Department of Economics
 Princeton
University
Discussion papers by myself and
others
Click on the title in the list below to see an abstract. Click on
the title above the abstract to go to a download directory.
 Paper Money (AEA Presidential Lecture))
 Gaps in the Institutional Structure of the Euro Area
 Nobel lecture
 Rational Inattention and Monetary Economics
 Discrete Actions in InformationConstrained Tracking Problems
 Price level determination in general equilibrium
 Government and Central Bank Balance Sheets, Inflation and Monetary Policy
 Fiscal/Monetary Coordination When the Anchor Cable Has Snapped
 Inflation Expectations, Uncertainty and Monetary Policy
 Inflation Expectations, Uncertainty, the Phillips Curve, and Monetary Policy
 Stepping on a Rake: The role of fiscal policy in the inflation of the 1970's
 Interpreting the Macroeconomic Time Series Facts: The Effects
of Monetary Policy
 Models and Their Uses
 Limits to Inflation Targeting
 The Role of Models and Probabilities in the Monetary Policy Process
 Were there regime switches in US monetary policy?, with Tao
Zha
 Stability and Instability in US
Monetary Policy Behavior
 Comments on a paper by Cogley and
Sargent
 Comment on a paper by Sargent, Williams and Zha
 Pitfalls of a Minimax Approach to
Model Uncertainty
 A Simple Model for Study of the
Determination of the Price Level and the Interaction of Monetary
and Fiscal Policy
 A Truly Keynesian Model (Old
paper, posted 10/20/97)
 Bankruptcy Law, Capital
Allocation, and Aggregate Effects: A Dynamic Heterogeneous Agent
Model with Incomplete Markets, by Tao Zha
 Does Monetary Policy Generate
Recessions?, with Tao Zha
 Econometric Implications of the
Government Budget Constraint
 Fiscal Foundations of Price
Stability in Open Economies (Hong Kong FEMES
talk)
 Response to Glenn Rudebusch
 Solving Linear Rational Expectations
Models
 Second Order Accurate Solution of
Discrete Time Dynamic Equilibrium Models
 What Does Monetary Policy Do?,
with Eric Leeper and Tao Zha
 Stickiness
 The Role of Interest Rate Policy in
the Generation and Propagation of Business Cycles: What Has
Changed Since the 30's?
 Whither ISLM
 The Precarious Fiscal Foundations of
EMU
 Projecting Policy Effects With
Statistical Models [1988 publication, with drifting
Phillips Curve model]]
 Drift and Breaks in Monetary
Policy
 Fiat Debt as Equity: Domestic
Currency Denominated Government Debt as Equity in the Primary
Surplus
 Fiscal Consequences for Mexico of
Adopting the Dollar
 A Rational Expectations Framework for
Short Run Policy Analysis [1985 Conference Paper]
 Seattle 8/00 ESWC Comment on papers by
Gali and by Albanesi, Chari and Christiano
 Rational Inattention
 Rational Inattention: a Research Agenda
 Fiscal Aspects of Central Bank
Independence
 Making Macro Models Behave Reasonably
 Tight Money Paradox on the Loose:
A Fiscalist Hyperinflation (by Eduardo Loyo)
 On the Genericity of the Winding Number Criterion for Linear Rational Expectations Models
 Improving Monetary Policy Models
 Comment on Del Negro, Schorfheide, Smets and Wouters(JBES invited paper)
Return to top of page
Return to top of page
Macroeconomics
 Paper Money
 Slides from the January 2013 AEA presidential lecture and a more extended writeup to appear in the April AER.
 Gaps in the Institutional Structure of the Euro Area
 Paper prepared for the Banque de France volume Public Debt, Monetary Policy and Financial Stability. It points out missing institutional structure for
monetaryfiscal coordination in the Euro area and suggests approaches to closing the gaps.
 Nobel Lecture and Slides
 Slow progress toward realization of Haavelmo's research program, with increased understanding of effects of monetary policy along the way.
 Rational Inattention and Monetary Economics
 Paper reviewing the field for the Handbook of Monetary Economics
 Discrete Actions in InformationConstrained Tracking Problems
 A Shannon capacity constraint can easily imply optimality of discretely distributed behavior, even when initial uncertainty is continuously distributed. This
has implications for, e.g., interpreting the time intervals between price changes as indicators for rates of information flow.
 Price Level Determination in General Equilibrium
 Slides from a plenary talk at the July 2009 SED meetings in Istanbul. Some overlap with the two slide sets below, but includes new reduced form
VAR evidence on the comovement of long run primary surplus expectations with inflation.
 Government and Central Bank Balance Sheets, Inflation and Monetary Policy
 Slides from the Joe Tiao Lecture at Kansas State University October 27, 2008. The lecture discusses
the relation between fiscal and monetary policy, the conventions that make up "central bank independence",
the central bank balance sheet as the table on which the fiscal/monetary coordination game is played, and
the implications of the recent drastic changes in the US Federal Reserve System's balance sheet.

Fiscal/Monetary Coordination When the Anchor Cable Has Snapped
 An expanded version of the Kansas State talk above.
 Inflation Expectations, Uncertainty and Monetary Policy
 This paper overlaps with the next one. This includes a model in which dispersion of beliefs about monetary policy causes high levels of leverage
and can increase or decrease investment, in an environment where uncertainty about investment, common across agents, has no such effects. This paper does
not include the econometric analysis of the Phillips curve that is included in the one below. The directory includes some slides that describe the
model of dispersed beliefs by itself.
 Inflation Expectations, Uncertainty, the Phillips Curve, and Monetary Policy
 An argument that focusing our attention on even a New Keynesian Phillips curve link between real activity and inflation may be leading
us to miss the most important forms of causal links between monetary policy and inflation.
 Stepping on a Rake: The role of fiscal policy in the inflation of the 1970's
 Fiscal policy was arguably far more unstable than monetary policy during the 1970's and 1980's. This paper gives some informal
evidence that this might be true, and offers a model in which this might have made monetary policy incapable of controlling inflation,
despite retaining the ability to create recessions and, thereby, occasional pauses in inflation. This link
is to a directory that also contains slides from several overlapping and interrelated talks on fiscalmonetary
interactions and the crisis of 20089. The "Rake" paper is the file BOJpresentation.pdf
 Interpreting the Macroeconomic
Time Series Facts: The Effects of Monetary Policy
 A 1991 paper that appeared in the European Economic Review. The paper looks at RMPY VAR's fit to
data from several countries. It notes strong similarities in the impulse responses, and the existence of
what was later called a "price puzzle"  positive interest rate shocks followed by price increases. It
noted that the price puzzles moderated when commodity prices and exchange rates were added to the system.
 Models and Their Uses
 A 1988 paper that appeared in the American Journal of Agricultural Economics. It solves a simple flexprice
RBC model by backsolving and uses the resulting simulated data to generate impulse responses to compare to VAR's fit to
actual data. Though monetary policy has negligible real effects in the model, the observed Granger causal priority of
M to output is reproduced in the simulated data. On the other hand the simulated data imply unrealistic behavior of
prices.

Limits to Inflation Targeting
 Inflation targeting may do more harm than good if there is a
substantial chance that the central bank cannot in fact control
inflation. A prerequisite for central bank control of inflation
is appropriate coordination with or backup by fiscal policy, and
the nature of the required coordination will depend on whether
and how central bank independence from the fiscal authority has
been implemented. These considerations suggest that in those
countries where inflation control has in the past been most
difficult, inflation targeting may be least useful. Where
inflation control has in the past been successful, the benefits
of inflation targeting may have more to do with the associated
changes in the policy process and in the central bank’s
communication with the public than with the inflation target
itself.
 A Simple Model for
Study of the Determination of the Price Level and the Interaction
of Monetary and Fiscal Policy
 A model illustrating the centrality of fiscal policy to price
determination and the dependence of the price level on the
public's beliefs about "off equilibrium path" behavior of policy
makers.
 A Truly Keynesian
Model
 A model that turns the usual ISLM,
expectationalPhillipsCurve "Keynesian" model upside down,
treating expectations as rational and markets as clearing for
assets, while for labor and commodities prices are sticky and
markets don't clear. The result is a model that is arguably
closer to what Keynes had in mind than the standard ISLM
framework.
 Fiscal
Foundations of Price Stability in Open Economies
 This paper, presented at the Hong Kong meeting of the Far
Eastern Region of the Econometric Society on July 24, 1997, is
not yet complete. It displays a simple singlecountry model of
price determination when there is no money, then extends the
model to deal with various versions of how a currency union  a
single monetary authority interacting with multiple fiscal
authorities  might operate. It connects this discussion to the
debates over fiscal criteria for membership in the EMU.
 Does Monetary
Policy Generate Recessions?
 Joint with Tao Zha. This is a nearfinal version of the
paper as it is appearing in Macroeconomic Dyanamics.
Some of the empirical work is partly obsolesced by "What Does Monetary Policy Do?"
The theoretical section checks for invertibility of a structural VAR constructed from
a subset of the variables in a larger DSGE, showing that in practice we can find usable
nearinvertibility even where exact invertibility does not hold and that exact match of number of
observables to number of structural shocks may therefore not be necessary.
 What Does Monetary
Policy Do?
 Joint with Eric Leeper and Tao Zha. Presented at the
Brookings Panel on Economic Activity, September 8, 1996. Surveys
recent literature on identifying the effects of monetary policy
using multivariate time series models, and extends the literature
by incorporating standard monetary aggregates and reserves
variables simultaneously. Concludes that the size of monetary
policy effects is uncertain.
 Econometric
Implications of the Government Budget Constraint
 Prepared for a forthcoming volume in honor of Carl Christ.
Explains why the government budget constraint is important even
for models focused on cyclical fluctuations. Examples showing
that high capital taxation can favor investment and that monetary
policy effects can be discontinuously sensitive to small changes
in fiscal policy parameters are worked out in detail.
 Response to Glenn
Rudebusch
 A recent paper by Glenn Rudebusch has criticized
identifiedVAR studies of the effects of monetary policy. The
criticisms are presented not as constructive suggestions, but as
if they show the entire approach is invalid. In fact, most of the
criticisms are either logically incoherent or generic quibbles
about choice of variables, time unit, etc. that are applicable to
any empirical work with time series. This comment attempts to
explain where the errors lie in the paper's comments and to
extract something worthwhile from the rest. It is true, as the
paper asserts at one point, that the time series of estimated
policy shocks is not robust to variations in the identifying
assumptions one finds in the literature. While the paper's
implication that this undermines all or even many of the
conclusions in this literature is incorrect, the point does
deserve more discussion and analysis.
 Solving Linear
Rational Expectations Models
 A computationally robust solution method for linear rational
expectations models is displayed, based on the QZ matrix
decomposition. Any rational expectations model, in continuous or
discrete time, can be solved by this approach. It requires that
the model be cast into firstorder form, but it does not require
that it be reduced so that the number of states matches the
number of equations. It also avoids the artificial requirement
that variables be designated as "jump" variables or not.
(Instead, how expectational error terms enter the system must be
specified  a more general specification.) Matlab code that
implements the approach is in the same directory. The code
automatically determines whether the model satisfies conditions
for existence and uniqueness.
 Second Order
Accurate Solution of Discrete Time Dynamic Equilibrium
Models
 From the first and second derivatives of a set of equations
that may include expectational Euler equations, this algorithm
produces a secondorder accurate expansion of the mapping from
"states" to "controls" and of the dynamics of the states. The
states do not need to be specified explicitly, but the software
allows the user to specify any state vector that seems natural,
reverting to its default method if the user's choice does not
work. The software is all Matlab m files.
 Bankruptcy
Law, Capital Allocation, and Aggregate Effects: A Dynamic
Heterogeneous Agent Model with Incomplete Markets
 By Tao Zha. A general equilibrium model with a continuum of
agents who in steady state have a nondegenerate, continuous,
distribution of net worth. A rare example of numerical solution
of a competitive equilibrium with a nontrivial
infinitedimensional state (the distribution of net worths).
Substantively interesting also, as it shows how, when the only
form of intermediation available is a standard loan contract, the
bankruptcy provisions of that contract are related to welfare in
a nonmonotone way.
 Stickiness
 Presented at CarnegieRochester Conference 11/2122/97 and
now published.
 Price stickiness introduced in the usual Keynesian way to a
dynamic, stochastic general equilibrium model seems to generate
unrealistically strong effects of aggregate demand policy. Price
and wage contracting (explicit, not implicit) can make prices
appear sticky, while creating little or no nonneutralilty of
nominal demand policies. To generate realistic joint stickiness
of quantities and prices as they react to other variables, while
their own time paths remain nonsmooth, seems to require going
beyond conventional categories of macro models with stickiness.
Models with multiple sources of adjustment costs may be able to
match the data if properly formulated. A more promising approach
in the long run may be basing stickiness in the limited
informationprocessing capacity of agents. A sketch of the
implications of such an approach is given.
 The Role of
Interest Rate Policy in the Generation and Propagation of
Business Cycles: What Has Changed Since the 30's?
 The same identification scheme is applied to postwar and
interwar US data. It turns up a surprisingly strong similarity
between periods in the responses to shifts in monetary policy.
There are large differences in the estimated policy reaction
functions, particularly in the faster reactions of policy
authorities to the state of the economy in the postwar period.
Nonetheless, counterfactual simulations show that the depth and
timing of interwar recessions and the great depression would not
have been much affected if the postwar monetary policy reaction
function had been in place. These results must be qualified by
the fact that the methods used do not attribute to monetary
policy any influence on sulien financial panics, whereas in fact
some aspects of monetary policy do affect the likelihood of
panics.
 Whither
ISLM
 ISLM inhibits attention to expectations in macroeconomics,
going against the spirit of Keynes's own approach. This can lead
to mistaken policy conclusions and to unnecessarily weak
responses to classical critiques of Keynesian modeling. A
coherent Keynesian approach, accounting for endogenous
expectations, implies very strong effects of monetary and fiscal
policy and leads to greater attention to the role of the
government budget constraint in making the effects of monetary
policy conditional on prevailing fiscal responses, and vice
versa.
 The Precarious
Fiscal Foundations of EMU
 After a brief overview of the fiscal theory of the price
level, we consider insights it provides into monetary policy
formation under certain kinds of deflationary and inflationary
stress. Then we consider how the institutions of the EMU are
equippedor unequippedto deal with such stress. The
conclusion is that fiscal institutions as yet unspecified will
have to arise or be invented in order for EMU to be a long term
success.
 Projecting
Policy Effects With Statistical Models
 Paper presented at the August 1988 Latin American Meetings of
the Econometric Society in San Jose, Costa Rica. Later published
in Revista de Analisis Economico (Santiago, Chile). The
promise of then newly developing statistical methods for policy
analysis is discussed. A model of policy makers who continually
reestimate a timevaryingparameters Phillips Curve wtihout
correctly modeling expectations shows that such policy makers may
stay nearly all the time near the optimal policy attainable by
policymakers who know the true economic structure. The version
here omits some graphs, but includes new, clearer versions of the
graphs related to the Phillips curve model.
 Drift and Breaks
in Monetary Policy
 US monetary policy behavior since 1948 is modeled as
nonlinear, changing over time according to a hidden Markov chain
pecification. Though the estimated Markov chain model implies
large shifts in the form of the policy reaction function, its
improvement in fit over a simple linear model comes almost
entirely from its allowance for persistent heteroscedasticity. A
linear model that allows such heteroscedasticity fits almost as
well. The shifts in policy regime that are uncovered are not
unidirectionalthey oscillate, with a given state seldom
persisting more than a few years. The paper discusses how these
results mesh with attempts to interpret this period through the
Lucas critique and natural rate models.
 Fiat
Debt as Equity: Domestic Currency Denominated Government Debt as
Equity in the Primary Surplus
 Fiat debt is more closely analogous to privately issued
equity than to privately issued debt, as it implies no promise to
pay anything except future issues of governmentpaper. This has
implications for optimal fiscal policy and implies problems with
the issue of large amounts of foreigncurrency or indexed
debt.
 Fiscal
Consequences for Mexico of Adopting the Dollar
 Fiat government debt  debt that promises to pay only
governmentissued paper  is much more closely analogous to
equity issued by private firms than to debt issued by private
firms. Indexed government debt, or government debt denominated
in foreign currency, is analogous to privately issued debt. A
decision to dollarize, in the sense of converting all debt to
dollardenominated debt and committing to issue only
dollardenominated debt in the future, involves many of the same
considerations that arise in corporate finance when a firm
decides between equity and debt finance. From this perspective,
the paper argues that dollarization has a number of drawbacks.
It should not be expected to lower the interest costs of public
borrowing, indeed it is likely to raise it. It does not
automatically generate pressures for greater fiscal
responsibility, and indeed may create incentives in the opposite
direction. It has ambiguous implications for the stability of
the financial system, in part because it reduces the range of
assets available to the private sector in trading risk, but also
because it leaves the government less able to intervene
supportively in financial crises.
 Seattle
8/00 ESWC Comment on papers by Gali and by Albanesi, Chari and
Christiano
 Macroeconomists have developed a common terminology and set
of modeling tools, despite differences over policy. But are we
also developing a common set of "incredible" but "standard"
assumptions that for some purposes lead us astray?

Pitfalls of a Minimax Approach to Model Uncertainty
 A minimax approach to robustness may be useful, but not if it
is taken to offer a substitute for assessing probabilities. And
the monetary policy models to which these methods have recently
been applied are structured so as to extinguish all but very high
order effects of model uncertainty.
 Rational
Inattention
 Suppose agents are "rational", but can process information
only at a finite rate? If agents have finite Shannon capacity,
they cannot react arbitarirly quickly and precisely to market
signals. This leads to well defined dynamic optimization problems
whose solutions differ systematically from those of the usual
dynamic stochastic optimization setups. The results are
intutitively appealing in some respects and account for some
observed patterns in time series data. New version, 6/28/01
 Rational Inattention: a Research Agenda
 Promise and pitfalls of work that attempts to apply the idea of modeling economic behavior as reflecting finite Shannon capacity of economic agents. To the linearquadratic models of "Implications of Rational Inattention" are added a set of simple twoperiod savings models with nonLQ objective functions. These show that the framework can accommodate bounded budget sets, that analytic solutions are available for a few (but only a few) cases beyond LQ, and that numerical solutions are possible for more general cases.
 Fiscal
Aspects of Central Bank Independence
 Central Bank independence from fiscal pressures depends on
the Treasury's acceptance of the idea that seignorage revenue
fluctuates for monetary policy reasons and is not subject to
Treasury budget control. Support for this convention in practice
seems to depend on the Bank's not requiring injections of funds
from the Treasury. There are differing balance sheet strategies
for ensuring this, and actual Central Banks show wide variation
in their balance sheet compositions that seem to correspond
roughly to the institutional foundations for Bank
independence.

Comment on a paper by Cogley and Sargent
 Comment on an NBER Macro Annual paper. The paper is a
technically sharp and innovative descriptive analysis of US
monetary and macroeconomic time series. It reaches substantive
conclusions using informal identifying assumptions. The comment
finds quite a bit to disagree with in the paper.
 Comment on a paper by Sargent, Williams and Zha
 Slides from a comment on their AER paper on the history of US inflation. The comment
suggests skepticism about the results, because they imply policy makers used estimated Phillips curves which, unlike any that
were actually used historically, predicted that unemployment would oscillate widely in the absence of precise stabilizing policy actions.
Also, the model simulations show extreme oscillatory out of sample behavior unlike any seen in sample.
 Stability
and Instability in US Monetary Policy Behavior
 A monetary policy reaction function is estimated, allowing
for several possible patterns of time variation in both its
coefficients and its disturbance variances. A clear improvement
in fit over a fixedparameter linear model is found. The
strongest effect on likelihood is from time variation in
variances, but there are also improvements in fit from allowing
coefficient variation. The variation is estimated as evolving in
a stochastic, repeating pattern, not as evolution from one style
of policy at midcentury and a new style in the 90’s. The
“regime shifts” that are estimated to occur do not
last very long, and appear to reflect temporary shifts in the
level of policy activism, not systematic improvement.
 A Rational
Expectations Framework for Short Run Policy Analysis
 Final version published in New Approaches to Monetary
Economics, William Barnett and Ken Singleton, editors,
Cambridge University Press 1987. The usual formulation of the
Lucas critique of econometric policy evaluation is internally
contradictory. There is no logical difficulty in supposing that
policy makers are offered a menu of time paths for the economy
conditioned on choices of policy variables, and that they then
choose the path they like best. This is not just an
approximation for small variations in policy, but the logical
form of any policy evaluation, including changes in "rule". It
is the consideration of policy changes cast as deterministic,
onceforall changes in policy rule that can be accurate only as
an approximation useful for a limited range of cases.
 Were there regime switches in US monetary policy?
 A multivariate model, identifying monetary policy and allowing for simultaneity and regime switching in coefficients and variances, is confronted with US data since 1959. The best fit is with a model that allows
time variation in structural disturbance variances only. Among models that allow for changes in equation
coefficients also, the best fit is for a model that allows coefficients to change only in the monetary policy rule.
That model allows switching among three main regimes and one rarely and briefly occurring regime. The three
main regimes correspond roughly to periods when most observers believe that monetary policy actually differed, and
the differences in policy behavior are substantively interesting, though statistically illdetermined. The
estimates imply monetary targeting was central in the early 80's, but also important sporadically in the 70's.
The changes in regime were essential neither to the rise in inflation in the 70's nor to its decline in the 80's.
This paper replaces an earlier draft titled "Macroeconomic Switching". There is a second paper, giving
methodological details, in the directory reached from this link.
 The
Role of Models and Probabilities in the Monetary Policy
Process
 The primary models in use as part of the policy process in
central banks are deeply flawed, both from the point of view of
econometric analysis and from the point of view of economic
theory. "Subjective" approaches to forecasting play a major role
in policy formation in every central bank, and data on the
forecasting record of FRB nonmodel forecasts shows that they are
excellent forecasts by several measures. Academic research on
econometric method and on macroeconomic theory has not provided
much guidance for model builders who need to contribute to policy
analysis in real time. Policy discussion at central banks uses
the language of Bayesian decision theory  putting postsample
probabilities on models, generating probability distributions for
future values of variables that reflect uncertainty about
parameter values and subjective judgment, weighing expected
losses of alternative courses of action. But the standard toolkit
of econometrics does not connect to this way of thinking about
probability. There is some reason to hope for improvement before
long.
 Making Macro Models Behave Reasonably
 Using the idea of generalized dummy observations, we extend the
methods of Del Negro and Schorfheide, who have proposed a way to use a dy
namic stochastic general equilibrium (DSGE) model to generate a prior distribu
tion for a structural vector autoregression (SVAR). The method proposed here is
more explicit and systematic about the prior's assertions about the SVAR identi?
cation, and it provides a mechanism for varying the tightness of the prior across
frequencies, so that for example the long run properties of the DSGE can be as
serted more con?dently than its shortrun behavior.
 Comment on Del Negro, Schorfheide, Smets and Wouters (JBES invited paper)
 Comment on a paper presented at the August 2006 Joint Statistical Meetings in Seattle and published in the Journal of Business and Economic Statistics. The paper extends the Del Negro and Schorfheide approach to connecting beliefs about parameters of a behavioral DSGE to a prior on coefficients of a structural VAR. The comments argue that and explain why this is a good idea, then suggest some directions in which the particular methods used in the paper might be improved.
 Tight Money Paradox on the Loose:
A Fiscalist Hyperinflation
 An unpublished classic by Eduardo Loyo. Hyperinflation is usually interpreted as a result of the monetary financing o
serious fiscal imbalances. Here, a fiscalist alternative is explored, in which inflatio
explodes because of the fiscal effects of monetary policy. Higher interest rates cause th
outside financial wealth of private agents to grow faster in nominal terms, which i
fiscalist models calls for higher inflation. If the monetary authority responds to highe
inflation with sufficiently higher nominal interest rates, a vicious circle is formed. Th
model is particularly advantageous for hyperinflations in which most of the fiscal actio
concentrates in the interest bill on public debt and debt rollover, rather than seigniorag
or primary budget deficits. Brazil in the late 1970s and early 1980s serves as a motivatin
case.
 On the Genericity of the Winding Number Criterion for Linear Rational Expectations Models
 In a recent paper Onatski derives a new criterion for existence and
uniqueness of solutions of rational expectations models. Specialized to finite order models, the criterion is an improvement on the usual rootcounting criterion, but shares its main defect  there are models on which it gives the wrong answer.
Onatski argues that the models where the winding number gives the right answer
are "generic"  an open, dense subset of the space of all models. This could give
a mistaken impression. A sequence of models for which the new criterion works
that converges in Onatski's metric to a model on which the criterion does not work
shows increasingly bizarre solution behavior as the limit is approached. In a metric
that treats models with very different solution behavior as very far apart, the sequence is divergent, not convergent. Models on which the winding number gives
the wrong answer will not in fact be extremely uncommon in economics, and they
are not in any substantively meaningful sense close to nicely behaved models for
which the winding number gives the right answer.
 Improving Monetary Policy Models
 If macroeconomic models are to be useful in policymaking, where uncertainty is pervasive, the models must be treated as probability models, whether formally or informally. Use of explicit probability models allows us to learn systematically from past mistakes, to integrate modelbased uncertainty with uncertain subjective judgment, and to bind databased forecasting together with theorybased projection of policy effects. Yet in the last few decades policy models at central banks have steadily shed any claims to being believable probability models of the data to which they are fit. Here we describe the current state of policy modeling, suggest some reasons why we have reached this state, and assess some promising directions for future progress.
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Finance
 Empirical
Implications of ArbitrageFree Asset Markets
 (joint with S. Maheswaran) The result that asset prices in
arbitragefree asset markets follow stochastic processes
equivalent to a martingale process is almost empty of predictive
content in discrete time, but in continuous time it implies
restrictions on observed behavior of prices. We derive such
restrictions and present a convenient class of stochastic
processes in which these restrictions can be violated. Such
processes are also not semimartingales and therefore provide
examples of what is excluded when analysis starts from the
assumption that asset prices follow semimartingale processes.
This paper appeared in Models, Methods and Applications of
Econometrics, Peter C. B. Phillips, ed., Basil Blackwell
1993
 MartingaleLike
Behavior of Asset Prices
 This is a 1990 paper that was never published in a journal.
In good part it is superseded by "Empirical Implications of
ArbitrageFree Asset Markets," (with S. Maheswaran) above.
However, its different approach is of some independent interest.
This paper shows how regularity conditions on the behavior of the
price process, together with absence of arbitrage, imply that
econometric tests of the martingale hypothesis on asset prices
will tend to accept it when the data are at small time
intervals. The paper includes a somewhat nonstandard derivation
of the existence of a "market probability measure".
 The Futility of CostBenefit Analysis for Data Dissemination
 A nearfinal draft of Chapter III of Natural Gas Data Needs in a Changing Regularory Environment, a 1985 publication of the
National Academy of Sciences, National Research Council, Committee on National Statistics. I drafted this chapter. It explains why the
apparently reasonable idea of applying costbenefit analysis to government programs founders when applied to data dissemination programs.
Methodology

Econometrics for Policy Analysis: Progress and Regress
 Slides from a talk at the Rotterdam conference commemorating the 100th birthday of Jan Tinbergen.
The talk looked at developments in empirical macroeconomic modeling since the time of Tinbergen and
Haavelmo, finding signs both of advance and retreat. A paper that expands on these slides is also available, in a directory with another paper that is a more recent discussion of some of the same issues.
 Macroeconomics and
Methodology
 Appeared in the Journal of Economic Perspectives. How
economics is and isn't like a science, or a priesthood.
Applications of these ideas to the state of econometrics and to
the controversy over Real Business Cycle school methodology.
 Loss Functionbased Evaluation of DSGE Models
 (by Frank Schorfheide)In this paper we propose a Bayesian econometric procedure for the evaluation and comparison of DSGE models. Unlike in many previous econometric approaches we explicitly take into account the possibility that the DSGE models are misspecified and introduce a reference model to complete the model space. Three loss functions are proposed to assess the discrepancy between DSGE model predictions and an overall posterior distribution of population characteristics that the researcher is trying to match. The evaluation procedure is applied to the comparison of a standard cashinadvance (CIA) and a portfolio adjustment cost (PAC) model. We find that the CIA model has higher posterior probability than the PAC model and achieves a better insample time series fit. Both models overpredict the magnitude of the negative correlation between output growth and inflation. However, unlike the PAC model, the CIA model is not able to generate a positive real effect of money growth shocks on aggregate output. Overall, the impulse response dynamics of the PAC model resemble the posterior mean impulse response functions more closely than the responses of the CIA model.
 Remarks on Bayesian
methods for macro policy modeling
 One incomplete paper and two sets of notes taken from seminar slides. They discuss problems and prospects
for use of Bayesian methods in macro policy modeling. There is specific discussion of the work of Smets and
Wouters along this line. There is also some general discussion of the pitfalls of Bayesian model comparison
methods.
 Understanding NonBayesians
 A chapter written for the Oxford University Press Handbook of Bayesian Econometrics, but withheld from publication there because of the Draconian copyright agreement
that OUP insisted on  forbidding posting even a late draft like this one on a personal web site. The paper discusses the essential distinctions between Bayesian and
frequentist approaches to inference, then takes up examples of models and estimators that are widely used, or seem useful, but that are thought of as "nonBayesian". It also
takes up the special problems of inference in highdimensional parameter spaces, arguing that there are indeed special problems, that they emerge clearly in Bayesian approaches,
and that they emerge just as strongly, but less clearly, in frequentist approaches.
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Econometrics
 Comment on Angrist and Pischke
 Comment on a paper by Angrist and Pischke, questioning their broad claims for the value of "design based econometrics".
 Bayesian Methods in Applied Econometrics, or, Why Econometrics Should Always and Everywhere Be Bayesian
 Slides from the Hotelling lecture, presented June 29, 2007 at Duke University.
 On an Example of Larry Wasserman
 Examples where likelihoodbased inference inevitably leads to bad
estimators that are clearly worse than estimators that cannot be derived from a
likelihoodbased approach are rare, possibly because they do not exist. A recent
textbook contains what is meant to be exactly such an example. More careful con
sideration shows that the example is one where Bayesian methods work very well
indeed, better than the nonBayesian method that is proposed in the book. Work
ing through to this conclusion provides useful insights into the pitfalls of inference
in highdimensional parameter spaces. The example is very close to "propensity score" methods
in econometrics.
 VAR Tools
 Programs in R and matlab to compute estimates of reduced form VAR's, optionallly using Bayesian priors formed from dummy observations. The programs will compute integrated posteriors (for model comparison) and will compute impulse response functions.
 Generalized Dummy Observations
 In the standard normal linear regression model, Theil's dummy observation idea may seem to be a matter
of notation  just another way to specify a conjugate prior. But in more complicated models, or where we
have prior notions about nonlinear functions of parameters, dummy observations are a distinct, and often
convenient and intuitively appealing, approach to specifying a prior. Examples are priors on structural
coefficients in simultaneous equations, on Markov transition matrices, and on VAR impulse responses.
 Thinking About
Instrumental VAriables
 This is not a paper, just notes from a talk that is primarily
a survey of existing results, illustrated with example
calculations. We take a decisiontheoretic view on the question
of how to use instrumental variables. Since prior beliefs play an
inevitably strong role when instruments are possibly ``weak'', or
when the number of instruments is large relative to the number of
observations, it is important in these cases to report
characteristics of the likelihood beyond the usual IV or ML
estimates and their asymptotic (i.e. secondorder local)
approximate standard errors.
 Using a
Likelihood Perspective to Sharpen Econometric Discourse: Three
Examples (pdf file. 171k)
 (Formerly, "Why Are Econometricians So Little Help?")
 This paper discusses a number of areas of inference where
dissatisfaction by applied workers with the prescriptions of
econometric high theory is strong and where a likelihood approach
diverges strongly from the mainstream approach in its practical
prescriptions. Two of the applied areas are related and have in
common that they involve nonstationarity: macroeconomic time
series modeling, and analysis of panel data in the presence of
potential nonstationarity. The third area is nonparametric kernel
regression methods. The conclusion is that in these areas a
likelihood perspective leads to more useful, honest and objective
reporting of results and characterization of uncertainty. It also
leads to insights not as easily available from the usual
perspective on inference.
 Error Bands for
Impulse Responses
 Joint with Tao Zha. We show how correctly to extend known
methods for generating error bands in reduced form
VAR’s to overidentified models. We argue that the
conventional pointwise bands common in the literature should be
supplemented with measures of shape uncertainty, and we show how
to generate such measures. We focus on bands that characterize
the shape of the likelihood. Such bands are not classical
confidence regions. We explain that classical confidence regions
mix information about parameter location with information about
model fit, and hence can be misleading as summaries of the
implications of the data for the location of parameters. Because
classical confidence regions also present conceptual and
computational problems in multivariate time series models, we
suggest that likelihoodbased bands, rather than approximate
confidence bands based on asymptotic theory, be standard in
reporting results for this type of model.
 Bayesian
HillClimbing Software
 Old FORTRAN code for minimizing a function whose evaluation
is expensive. At each iteration, a Bayesian posterior mean for
the surface shape conditional on points already sampled is
constructed and the minimum of this is found. This minimum is
then used as a trial point for a new function evaluation. A
version of the program exists that takes account of the fact that
the expected improvement is raised at points far from points
already sampled, by the fact that there is high uncertainty in
such regions. There seems to be no particular performance
advantage for this program over, say, quasinewton with BFGS
update. But one gets an estimate at every function evaluation of
the shape of the function, which may be useful.
 Optimization
Software
 Matlab programs that solve nonlinear equations and minimize
using quasiNewton with BFGS update. The programs are somewhat
more robust, apparently, than the stock Matlab programs that do
about the same thing. The minimizer can negotiate discontinuous
"cliffs" without getting stuck.
 Bayesian Methods for
Dynamic Multivariate Linear Models
 Joint with Tao Zha. Computationally feasible methods for
using Bayesian priors with VAR models, both reducedform and
identified.
 Inference
For Multivariate Time Series Models With Trend
 Flatprior estimates of time series models that condition on
initial observations, especially of multivariate time series
models, have a strong tendency to attribute implausible
explanatory power to initial conditions. This point is
illustrated with examples. It is argued that this is the source
of the wellknown bias toward stationarity in conventional
estimates of such models, and that the remedy is formulation of
reference priors, specific to the application at hand, that
reflect the prior implausibility of models that generate
elaborate "trend" predictions from initial conditions.
 Adaptive
MetropolisHastings, or Monte Carlo Kernel
Estimation
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Course Materials
By clicking these course names you in some cases reach ftp sites
containing miscellaneous course materials. Since this site began
only in the Fall of 1996, the older courses may have very
incomplete sets of materials. In other cases you reach a document
that gives a syllabus/reading list with links to other course
materials.
 Econometric Modeling
 Advanced modeling methods. The first half for 2014 will consider hierarchical Bayes methods for large crosssections and panel data and structural VAR's
 Money and Banking (ECO342)
 An undergraduate course, assuming calculus and previous coursework in macroeconomics. Models of price
determination. Monetary and financial institutions. Financial stability. Monetary policy for economic stability.
Financial regulation.
 Speculative
Bubbles and Financial Panics (Eco315, part 2)
 An undergraduate course, assuming previous work in macroeconomics. Combines
historical reading and discussion about financial bubbles and
panics with examination of mathematical models of them. The
models may provide insight into what kinds of asset market
behavior are to be expected in wellfunctioning markets, how they
can be distinguished from pathological behavior, and what, if
anything, ought to be done to control or curtail the pathological
behavior.
 Econometric Theory I (517)
 The firstyear, firstsemester graduate econometrics course.
 Time Series
(513)
 We discuss the general definition of a stochastic process and
a variety of specific cases: ARMA, trigonometric, continuous or discrete
time, stationary or nonstationary, large model, small model, structural and
nonstructural. We also consider inference for each model type we discuss.
The emphasis will be on Bayesian inference, with some discussion of similarities
and differences between Bayesian and samplingtheory approaches.
 Econometrics III
(552b)
 This course covers linear regression, generalized least
squares, generalized method of moments, simultaneous equations,
and Kalman filtering, among other topics. It is meant as a
highlevel introduction to econometrics, for graduate students
with strong math and statistics backgrounds but little
econometrics training, or students with good, but not necessarily
rigorous, previous econometrics training. The course is taught
from a Bayesian perspective.
 Macroeconomic
Theory II (504) The second semester firstyear Princeton
graduate macro theory course.
 Previous (rather
different) Yale version.
 Advanced
Macroeconomics (521 or 2)
 Second year, second semester macro course. Rational inattention, models with price levels and inertias.
 Intermediate
Macro Theory, Honors Section (153a)
 An undergraduate course, taught using more math and a less
conventional approach than is usual at this level.
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