RECENT
RESEARCH AND ONGOING WORK 2000:
OVERVIEW |
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| (i) Econometric Model
Determination |
This research seeks to provide a general asymptotic theory for model
determination techniques that are suited to with time series data that may be
stochastically nonstationary. The primary result is the isolation of an asymptotically
valid form of the conditional data density, or marginal likelihood, that can be used for
model determination, inference and forecast evaluation. This has been shown to be an
interesting exponential density that is easily used in practical work. The level of
generality in the asymptotic theory allows for integrated and cointegrated processes, so
that a wide range of potential applications come within the compass of the asymptotics.
The asymptotic form of the conditional data density is equivalent to the prequential form
of the likelihood, relating this approach to earlier work by Dawid (in JRSS, 1984), and
this provides an alternative conceptual justification for the model selection methods. A
special advantage of the methods in nonstationary data models is that they avoid the
awkwardness of the nonstandard, model-specific (and sometimes nuisance-parameter
dependent) asymptotic theory of conventional estimators and tests. The methods can also be
used to select cointegrating rank in a general cointegrated VAR, or even jointly select
cointegrating rank and lag order in a VAR. In this context, the methods give consistent
order estimates, and this has been shown in joint work with John Chao in Journal of
Econometrics, 1999, "Bayesian Model Selection in Partially Nonstationary Vector
Autoregressive Processes with Reduced Rank Structure". Part of the theory involved
the use of embedding techniques that permit the embedding of a discrete time density in a
continuous time density process in a manner that is analogous to the Skorohod embedding of
a discrete scalar martingale in a Brownian motion. The theory then justifies the use of
the conditional Bayes densities as proper probability densities and gives the form of the
model to which these densities correspond. So the procedures have an asymptotic Bayesian
justification. The main ideas and asymptotic analysis is contained in "Econometric
Model Determination'' in Econometrica, 1996. and an earlier paper in Econometrica,
1996 with Werner Ploberger on asymptotic theory for time series. Research also involved
the implementation of these methods to produce multivariate forecasting models in the
Bayesian VAR (BVAR) class. This allows for reduced rank regressions(RRR's) and error
correction models (ECM's), as well as conventional Bayesian VAR's with unit root priors. A
by-product of the model selection work is an optimized version of the BVAR in which the
hyperparameters are data-determined. This means that in practice these models can be used
in a nearly automated way for forecasting purposes, and leads naturally to practical
applications.
(Supported by NSF Grant No. SBR 94-22922) |
| (ii) Practical Ex Ante
Forecasting Work |
The goal of this research is the practical implementation of automated
econometric forecasting and policy analysis techniques based on ideas in my paper
"Econometric Model Determination'' in Econometrica, 1996. The methods are data-driven
and almost completely automatic, requiring only minimal input from the investigator in the
selection of model classes and maximal lags. I have been applying these methods to provide
quarterly forecasts of macroeconomic activity for a group of Asia- Pacific countries
(including the USA, Japan, Korea, Australia and New Zealand) for the last three years
Ongoing results of this research are published as a regular feature in the Asia
Pacific Economic Review. Forecasts from the automated time series models are compared
with the quarterly forecasts obtained from the Fair structural econometric model. So far,
the results indicate that data-based ECM models have an ex ante forecasting performance
that is almost as good as that of the Fair model for inflation and real GDP. It is also
apparent from the results so far that, for the USA at least, ECM methods generally provide
better forecasts 1-8 periods ahead than Bayesian VAR methods.
(Supported by NSF Grant No. SBR 94-22922) |
| (iii) Economic News and
Economic Activity |
This research is joint with Deborah Blood and studies empirical links
between mass media communication, consumer sentiment and economic activity. Cointegration
tests, causality tests and some recursive analyses were run in VAR's with economic
headline news, consumer sentiment, presidential popularity and leading economic
indicators. The empirical results show strong evidence of the agenda setting effects of
the media, especially on consumer sentiment, allowing for actual economic conditions. The
evidence also indicates a disruption in the normal pattern of the relationship between the
news, economic activity and presidential popularity during the period 1990--1991, a period
of foreign and economic upheaval for the Bush administration wherein the presidency
enjoyed high approval ratings over the Gulf crisis but faced increasing criticism from the
press over economic policy. Empirical results are reported in "Recession Headline
News, Consumer Sentiment, the State of the Economy and Presidential Popularity: A Time
Series Analysis 1989-1993" (with D. J. Blood), International Journal of Public
Opinion Research, 1995.
(Supported by NSF Grant No. SBR 94-22922) |
| (iv) Nonstationary
Economic Time Series |
Recent and ongoing work cover a variety of topics: inter alia, efficient
quasi-differencing (QD) and trend estimation procedures; robust methods of estimation and
inference for nonstationary time series; simultaneous equations cointegrating estimation;
foreign exchange market unbiasedness tests; FM-regression methods and extensions;
nonlinear I(1) analysis; kernel regression asymptotics, asymptotic policy analysis for
cointegrated VAR's.
(Supported by NSF Grant Nos. SBR 97-30295 and SES 00-92509) |
| (v) Nonstationary Panel
Data |
A general asymptotic theory for panel data applications with
nonstationary data has been obtained in joint work in Econometrica, 1999, with
Hyungsik Moon, "Linear Regression Limit Theory for Nonstationary Panel Data".
This paper considers the general problem of multidimensional asymptotics, where more than
one index may pass to infinity. Both sequential and joint limits are obtained. In a
related work, we have shown how consistent estimation of local to unity parameters is
possible using panel data. Research on several aspects of this general topic is
continuing. Some of these papers may be downloaded from this website.
(Supported by NSF Grant Nos. SBR 97-30295 and SES 00-92509) |
| (vi) Developments of
Hannan Regression |
Second order asymptotics for Hannan and periodogram regression methods
have been developed in joint work with Zhijie Xiao. We have also developed expansions for
Wald tests in cointegrated regression models. Asymptotics for time detrended spectral
regressions have been obtained and shown to have unexpected biases, even asymptotically,
in joint work in Econometrica, 2001, with Dean Corbae and Sam Ouliaris "Band
Spectral Regression with Trending Data".
(Supported by NSF Grant No. SBR 97-30295 and SES 00-92509) |
| (vii) Descriptive
Statistics for Nonstationary Data |
While there are many techniques of descriptive statistics for stationary
time series, few techniques have been developed for doing descriptive statistics for
nonstationary time series. In ongoing research, new methods for describing the features of
time series that behave in a nonstationary way have been developed by the author. Some of
these methods are discussed and illustrated in an empirical application to interest rate
data on measuring the Fisher effect that the author presented at the Yale/Cowles
Foundation Irving Fisher Conference in May 1998 (downloadable from this website). Ongoing
empirical work on this problem is being conducted with Yixiao Sun.
(Supported by NSF Grant No. SBR 97-30295 and SES 00-92509)Watch this site for regular updates. |
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