FABIO MILANI - Research

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Recent Working Papers

 "Learning About the Interdependence Between the Macroeconomy and the Stock Market",
    University of California, Irvine, May 2008. (abstract)

 "The Impact of Foreign Stock Markets on Macroeconomic Dynamics in Open Economies: a Structural Estimation",
     (coming soon), July, 2008. (abstract)

 "Expectations, Learning, and the Changing Oil Price/Macroeconomy Relationship",
     (to be posted), July, 2008. (abstract)

 "Political Business Cycles in the New Keynesian Model",
    University of California, Irvine, October 2007. (abstract)

 "Learning and Time-Varying Macroeconomic Volatility",
    University of California, Irvine, May 2007. (abstract)

 "Adaptive Learning and Macroeconomic Inertia in the Euro Area",
    University of California, Irvine, December 2006. (abstract)

 "The Evolution of the Fed's Inflation Target in an Estimated Model under RE and Learning",
    University of California, Irvine, August 2006. (abstract)

 "Adaptive Learning and Inflation Persistence",
    Princeton University, June 2004. This version: February 2005. (abstract)

  "Parameter Instability, Model Uncertainty and the Choice of Monetary Policy",
    (with Carlo A. Favero), CEPR Discussion Paper No. 4909, February 2005. First version: June 2001. (abstract)


Publications

 "Learning, Monetary Policy Rules, and Macroeconomic Stability",
    Journal of Economic Dynamics and Control, forthcoming. (abstract)

 "Monetary Policy with a Wider Information Set: a Bayesian Model Averaging Approach",
    Scottish Journal of Political Economy, Vol. 55, No. 1, February, 2008. (abstract)

 "Expectations, Learning and Macroeconomic Persistence",  
    Journal of Monetary Economics, Volume 54, Issue 7, Pages 2065-2082, October 2007. (abstract)

 "Econometric Issues in DSGE Models", (with Dale Poirier)
   Comment on "Bayesian Analysis of DSGE Models" by An and Schorfheide ,  
    Econometric Reviews, Volume 26, Issue 2 - 4, March 2007, pages 201 - 204.

 "A Bayesian DSGE Model with Infinite-Horizon Learning: Do "Mechanical" Sources of Persistence Become Superfluous?",  
    International Journal of Central Banking, Iss. 6, September 2006. (abstract)

 "Structural Factor-Augmented VARs (SFAVARs) and the Effects of Monetary Policy",
    (with Francesco Belviso), Topics in Macroeconomics, Vol. 6, Iss. 3, 2006. (abstract)

  "Parameter Instability, Model Uncertainty and the Choice of Monetary Policy",
    (with Carlo A. Favero), Topics in Macroeconomics, Vol. 5, Iss. 1, 2005.


Work in progress

  "Estimating and Comparing NK Models with Adaptive Learning", in progress.

Comments & Discussions

  Discussion on "Evaluating An Estimated New Keynesian Small Open Economy Model",
    by M. Adolfson, S. Laséen, J. Lindé, and M. Villani, August 2006.

  Discussion on "The Lucas Critique and the Stability of Empirical Models",
    by Thomas Lubik and Paolo Surico, October 2006.

  Discussion on "Monetary Policy with Model Uncertainty: Distribution Forecast Targeting",
    by Lars Svensson and Noah Williams, January 2007.

  Discussion on "Revealing the Secrets of the Temple: the Value of Publishing Central Bank's Forecasts",
    by Glenn Rudebusch and John Williams, June 2007.





ABSTRACTS


"LEARNING ABOUT THE INDETRDEPENDENCE BETWEEN THE MACROECONOMY AND THE STOCK MARKET"  
  Fabio Milani, May, 2008.

 Abstract
How strong is the interdependence between the macroeconomy and the stock market?
This paper estimates a New Keynesian general equilibrium model, which includes a wealth effect from asset price fluctuations to consumption, to assess the quantitative importance of interactions among the stock market, macroeconomic variables, and monetary policy.
The paper relaxes the assumption of rational expectations and assumes that economic agents learn over time and form near-rational expectations from their perceived model of the economy. The stock market, therefore, affects the economy through two channels: through a traditional ``wealth effect" and through its impact on agents' expectations. Monetary policy decisions also affect and are potentially affected by the stock market.
The empirical results show that the direct wealth effect is modest, but asset price fluctuations have had important effects on output expectations. Shocks in the stock market can account for a large portion of output fluctuations. The effect on expectations, however, has declined over time.

Keywords: Stock Market, Wealth Channel, Monetary Policy, Constant-Gain Learning, Bayesian Estimation, Expectations.
JEL classification: E32, E44, E52, E58.


"POLITICAL BUSINESS CYCLES IN THE NEW KEYNESIAN MODEL"  
  Fabio Milani, October, 2007.

 Abstract
This paper tests various Political Business Cycle theories in a New Keynesian model with a monetary and fiscal policy mix. All the policy coefficients, the target levels of inflation and the budget deficit, the firms' frequency of price setting, and the standard deviations of the structural shocks are allowed to depend on `political' regimes: a pre-election vs. post-election regime, a regime that depends on whether the President (or the Fed Chairman) is a Democrat or a Republican, and a regime under which the President and the Fed Chairman share party affiliation in pre-election quarters or not.
The model is estimated using full-information Bayesian methods. The assumption of rational expectations is relaxed: economic agents can learn about the effect of political variables over time.
The results provide evidence that several coefficients depend on political variables. The best-fitting specification is one that allows coefficients to depend on a pre-election vs. non-election regime. Monetary policy becomes considerably more inertial before elections and fiscal policy deviations from a simple rule are more common. The results overall support the view of an independent Fed that avoids taking policy decisions right before elections. There is some evidence, however, that policies become more expansionary before elections, but this evidence seems to disappear in the post-1985 sample. The estimates also indicate that firms similarly delay their price-setting decisions until after the upcoming Presidential election.

Keywords: Political Business Cycles, Opportunistic Cycles, Partisan Cycles, Monetary and Fiscal Policy, Adaptive Learning, Bayesian Estimation.
JEL classification: C11, D72, E32, E52, E58, E63.


"LEARNING AND TIME-VARYING MACROECONOMIC VOLATILITY"  
  Fabio Milani, May, 2007.

 Abstract
This paper presents a DSGE model in which agents' learning about the economy can endogenously generate time-varying macroeconomic volatility. Economic agents use simple models to form expectations and need to learn the relevant parameters. Their gain coefficient is endogenous and is adjusted according to past forecast errors.
The model is estimated using likelihood-based Bayesian methods. The endogenous gain is jointly estimated with the structural parameters of the system.
The estimation results show that private agents appear to have often switched to constant-gain learning, with a high constant gain, during most of the 1970s and until the early 1980s, while reverting to a decreasing gain later on. As a result, the model can generate a pattern of volatility, which is increasing in the 1970s and falling in the second half of the sample, with a decline that can roughly match the magnitude of the "Great Moderation". The paper also documents how a failure to incorporate learning into the estimation may lead econometricians to spuriously find time-varying volatility in the exogenous shocks, even when these have constant variance by construction. 

Keywords: adaptive learning, constant gain, monetary policy, macroeconomic volatility, inflation dynamics.
JEL classification: C11, D84, E30, E50, E52, E58, E66.


"THE EVOLUTION OF THE FED'S INFLATION TARGET IN AN ESTIMATED MODEL UNDER RE AND LEARNING"  
  Fabio Milani, August, 2006.

 Abstract
This paper aims to infer the evolving Fed's inflation target by estimating a monetary model under the assumptions of RE and learning. The results emphasize how different assumptions about expectations may have important effects on the inferred target movements.

Keywords: time-varying inflation target, constant-gain learning, expectations, Bayesian estimation.
JEL classification: C11, E50, E52, E58.


"LEARNING, MONETARY POLICY RULES, AND MACROECONOMIC STABILITY"  
  Fabio Milani, April, 2005.

 Abstract
This paper estimates a DSGE model with learning to reexamine the evidence on time variation in post-war U.S. monetary policy. Several papers document a regime switch, by showing that policy went from `passive' and destabilizing in the pre-1979 period to `active' and stabilizing in the following decades. These papers typically work with DSGE models with rational expectations.
This paper relaxes the assumption of rational expectations and it allows for learning instead. Economic agents form expectations from simple models and update the parameters through constant-gain learning.
I estimate the model by Bayesian methods. The constant gain coefficient is jointly estimated with the structural and policy parameters of the system.
I find that the feedback coefficient to inflation was well above 1 also in the 1960s and 1970s and therefore policy was not leading to macroeconomic instability. The results reconcile the evidence from DSGE models with what obtained by time-varying VAR studies, which typically find only modest changes in policy coefficients over the post-war sample.

Keywords: monetary policy, new Keynesian DSGE model, constant-gain learning, expectations, Bayesian estimation, macroeconomic instability.
JEL classification: C11, D84, E30, E50, E52, E58.



"A BAYESIAN DSGE MODEL WITH INFINITE_HORIZON LEARNING:
DO "MECHANICAL" SOURCES OF PERSISTENCE BECOME SUPERFLUOUS?"  
  Fabio Milani,
  International Journal of Central Banking, Iss. 6, September 2006.

 Abstract
This paper estimates a monetary DSGE model with learning introduced from the primitive assumptions. The model nests infinite-horizon learning and features, such as habit formation in consumption and inflation indexation, that are essential for the model fit under rational expectations.
I estimate the DSGE model by Bayesian methods, obtaining estimates of the main learning parameter, the constant gain, jointly with the deep parameters of the economy.
The results show that relaxing the assumption of rational expectations in favor of learning may render mechanical sources of persistence superfluous. In particular, learning appears a crucial determinant of inflation inertia.

Keywords: Infinite-Horizon Learning, DSGE model, Bayesian Estimation, Non-Rational Expectations, Inflation Persistence, Habit Formation.
JEL classification: C11, D84, E30, E50, E52.



"EXPECTATIONS, LEARNING AND MACROECONOMIC PERSISTENCE"  
, click here for  (shorter version)
  Fabio Milani, November 2004.

 Abstract
This paper presents an estimated model with learning and provides evidence that learning can improve the fit of popular monetary DSGE models and endogenously generate realistic levels of persistence. The standard rational expectations specification is nested in the model as a limiting case.
The paper starts with an agnostic view, developing a model that nests learning and some of the structural sources of persistence, such as habit formation in consumption and inflation indexation, that are typically needed in monetary models with rational expectations to match the persistence of macroeconomic variables. I estimate the model by likelihood-based Bayesian methods, which allow the estimation of agents' beliefs and constant-gain coefficient jointly with the 'deep' parameters of the economy. The empirical results show that when learning replaces fully rational expectations, the estimated degrees of habits and indexation drop to zero. This finding suggests that persistence arises in the model economy mainly from expectations and learning. The posterior model probabilities show that the specification with learning fits significantly better than does the specification with rational expectations.
Finally, if learning rather than mechanical sources of persistence provides a more appropriate representation of the economy, the implied optimal policy will be different. The policymaker will also incur substantial costs from misspecifying private expectations formation.

Keywords: persistence, constant-gain learning, expectations, habit formation in consumption, inflation inertia, Phillips curve, Bayesian econometrics, New-Keynesian model, gain estimation.
JEL classification: C11, D84, E30, E50, E52.



"ADAPTIVE LEARNING AND INFLATION PERSISTENCE"  
 Fabio Milani, March, 2004.
This draft: February 25, 2005.

 Abstract
What generates persistence in inflation? Is inflation persistence structural?
This paper investigates learning as a potential source of persistence in inflation. The paper focuses on the price-setting problem of firms and presents a model that nests structural sources of persistence (indexation) and learning. Indexation is typically necessary under rational expectations to match the inertia in the data and to improve the fit of estimated New Keynesian Phillips curves.
The empirical results show that when learning replaces the assumption of fully rational expectations, structural sources of persistence in inflation, such as indexation, become unsupported by the data. The results suggest learning behavior as the main source of persistence in inflation. This finding has implications for the optimal monetary policy.
The paper finally shows how one's results can heavily depend on the assumed gain coefficient. It illustrates how the estimated persistence and the model fit vary across the whole range of constant gain values. The paper derives the best-fitting constant gains in the sample and shows that the learning speed has substantially changed over time.

Keywords: adaptive learning, inflation persistence, sticky prices, best-fitting constant gain, learning speed, expectations.
JEL classification: D84, E30, E50.



"STRUCTURAL FACTOR-AUGMENTED VAR (SFAVAR) AND THE EFFECTS OF MONETARY POLICY"  
 Francesco Belviso and Fabio Milani, First version: January, 2003.
Published in:Topics in Macroeconomics, Vol. 6, Iss. 3, 2006.

 Abstract
Factor-augmented VARs (FAVARs) have combined standard VARs with factor analysis to exploit large data sets in the study of monetary policy. FAVARs enjoy a number of advantages over VARs: they allow a better identification of the monetary policy shock; they can avoid the use of a single variable to proxy theoretical constructs, such as the output gap; they allow researchers to compute impulse responses for hundreds of variables. Their shortcoming, however, is that the factors are not identified and, therefore, lack any economic interpretation.
This paper seeks to provide an interpretation to the factors. We propose a novel Structural Factor-Augmented VAR (SFAVAR) model, where the factors have a clear meaning: "Real Activity" factor, "Price Pressures" factor, "Financial Market" factor, "Credit Conditions" factor, "Expectations" factor, etc. The paper employs a Bayesian approach to extract the factors and jointly estimate the model. This framework is then suited to study the effects on a wide range of macroeconomic variables of monetary policy and non-policy shocks.

Keywords: VAR, Dynamic Factors, Monetary Policy, Structural FAVAR.
JEL classification: C32, C43, E50, E52, E58.


"MONETARY POLICY WITH A WIDER INFORMATION SET: A BAYESIAN MODEL AVERAGING APPROACH"  
 Fabio Milani, August 2002 (Revised December 2003).

 Abstract
Monetary policy has been usually analyzed in the context of small macroeconomic models, where central banks are allowed to exploit a limited amount of information. Under these frameworks, researchers typically derive the optimality of aggressive monetary rules, contrasting with the observed policy conservatism and interest rate smoothing. This paper allows the central bank to exploit a wider information set, while taking into account the associated model uncertainty, by employing Bayesian Model Averaging with Markov Chain Model Composition (MC³). In this enriched environment, we derive the optimality of smoother and more cautious policy rates, together with clear gains in macroeconomic efficiency.

Keywords: Bayesian model averaging, leading indicators, model uncertainty, optimal monetary policy, interest rate smoothing..
JEL classification: C11, C15, C52, E52, E58.



"PARAMETER INSTABILITY, MODEL UNCERTAINTY AND THE CHOICE OF MONETARY POLICY"  
 Carlo Favero and Fabio Milani,
IGIER Working Paper n.196, May 2001, and CEPR Discussion Paper No. 4909, February 2005.
Published in:Topics in Macroeconomics, Vol. 5, Iss. 1, 2005.
Final version: February 2005.

 Abstract
This paper starts from the observation that parameter instability and model uncertainty are relevant problems for the analysis of monetary policy in small macroeconomic models. We propose to deal with these two problems by implementing a novel "thick recursive modelling" approach. At each point in time we estimate all models generated by the combinations of a base-set of k observable regressors for aggregate demand and supply. We compute optimal monetary policies for all possible models and consider alternative ways of summarizing their distribution. Our main results show that thick recursive modelling delivers optimal policy rates that track the observed policy rates better than the optimal policy rates obtained under a constant parameter specification with no role for model uncertainty.

Keywords: model uncertainty, parameter instability, optimal monetary policy.
JEL classification: E44, E52, F41.

Comments are welcome.




to be continued...