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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 Grants SES-0350686, SES-0719055, and . Any opinions, findings and conclusions or recomendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF)

Clickable Table of Contents

Contact 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.

Macroeconomics

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Microeconomics

Methodology

Finance

Econometrics

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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 monetary-fiscal 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 Information-Constrained 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 fiscal-monetary interactions and the crisis of 2008-9. 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 flex-price 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, expectational-Phillips-Curve "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 single-country 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 near-final 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 near-invertibility 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 identified-VAR 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 first-order 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 second-order 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 non-degenerate, continuous, distribution of net worth. A rare example of numerical solution of a competitive equilibrium with a non-trivial infinite-dimensional 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 non-monotone way.
Stickiness
Presented at Carnegie-Rochester Conference 11/21-22/97 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 non-neutralilty 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 non-smooth, 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 information-processing 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 equipped---or unequipped---to 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 re-estimate a time-varying-parameters Phillips Curve wtihout correctly modeling expectations shows that such policy makers may stay nearly all the time near the optimal policy attainable by policy-makers 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 unidirectional---they 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 foreign-currency or indexed debt.
Fiscal Consequences for Mexico of Adopting the Dollar
Fiat government debt --- debt that promises to pay only government-issued 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 dollar-denominated debt and committing to issue only dollar-denominated 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 linear-quadratic models of "Implications of Rational Inattention" are added a set of simple two-period savings models with non-LQ 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 fixed-parameter 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 mid-century 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, once-for-all 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 ill-determined. 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 non-model 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 post-sample 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 short-run 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 root-counting 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 policy-making, 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 model-based uncertainty with uncertain subjective judgment, and to bind data-based forecasting together with theory-based 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 Arbitrage-Free Asset Markets
(joint with S. Maheswaran) The result that asset prices in arbitrage-free 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 semi-martingales and therefore provide examples of what is excluded when analysis starts from the assumption that asset prices follow semi-martingale processes. This paper appeared in Models, Methods and Applications of Econometrics, Peter C. B. Phillips, ed., Basil Blackwell 1993
Martingale-Like 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 Arbitrage-Free 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".

Microeconomics

The Futility of Cost-Benefit Analysis for Data Dissemination
A near-final 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 cost-benefit 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 Function-based 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 cash-in-advance (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 in-sample 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 Non-Bayesians
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 "non-Bayesian". It also takes up the special problems of inference in high-dimensional 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 likelihood-based inference inevitably leads to bad estimators that are clearly worse than estimators that cannot be derived from a likelihood-based 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 non-Bayesian method that is proposed in the book. Work- ing through to this conclusion provides useful insights into the pitfalls of inference in high-dimensional 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 decision-theoretic 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. second-order 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 likelihood-based bands, rather than approximate confidence bands based on asymptotic theory, be standard in reporting results for this type of model.
Bayesian Hill-Climbing 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, quasi-newton 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 quasi-Newton 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 reduced-form and identified.
Inference For Multivariate Time Series Models With Trend
Flat-prior 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 well-known 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 Metropolis-Hastings, 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 cross-sections 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 well-functioning 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 first-year, first-semester 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 non-stationary, large model, small model, structural and non-structural. 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 sampling-theory 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 high-level 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 first-year 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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