Robust Inference on Average Economic Growth*
| Author | Philip Hans Franses,H. Peter Boswijk |
| Date | 01 June 2006 |
| Published date | 01 June 2006 |
| DOI | http://doi.org/10.1111/j.1468-0084.2006.00165.x |
Robust Inference on Average Economic
Growth*
H. Peter Boswijk* and Philip Hans Franses
*Department of Quantitative Economics, University of Amsterdam, Amsterdam,
The Netherlands (e-mail: h.p.boswijk@uva.nl)
Econometric Institute, Erasmus University Rotterdam, Rotterdam,
The Netherlands (e-mail: franses@few.eur.nl)
Abstract
We discuss a method to estimate the confidence bounds for average economic
growth, which is robust to misspecification of the unit root property of a given
time series. We derive asymptotic theory for the consequences of such
misspecification. Our empirical method amounts to an implementation of the
subsampling procedure advocated in Romano and Wolf (Econometrica, 2001,
Vol. 69, p. 1283). Simulation evidence supports the theory and it also indicates
the practical relevance of the subsampling method. We use quarterly postwar
US industrial production for illustration and we show that non-robust
approaches rather lead to different conclusions on average economic growth
than our robust approach.
I. Introduction
The question of the size of average economic growth, and its associated
confidence bounds, seems like a rather trivial one. Yet, time-series econo-
metricians know that the answer is far from straightforward. Indeed, the answer
for the point estimate of average growth already hinges upon the time series
model employed. Usually, one tends to choose between a trend-stationary (TS)
*Helpful comments from the co-editor and two anonymous referees are gratefully acknowledged.
The computer programs used for all calculations in this paper can be obtained from the corresponding
author.
JEL Classification numbers: C15, C22, O47.
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 68, 3 (2006) 0305-9049
345
Blackwell Publishing Ltd, 2006. Published by Blackwell Publishing Ltd, 9600 Garsington Road, Oxford OX4 2DQ, UK
and 350 Main Street, Malden, MA 02148, USA.
model and a difference-stationary (DS) model, and often the numerical value
of the average growth estimate differs across the two models. Additionally, the
associated confidence intervals also depend on the chosen model. Those of the
TS model are usually rather narrow, while those of the DS model are rather
wide. In this paper, we will examine to what extent these outcomes might be
caused by model misspecification.
As the estimate of average economic growth depends on the model, one
would be inclined to make a selection between the models first, and based on
the outcome, to estimate average growth. Such a selection typically depends
on the outcome of a test for a unit root. Unfortunately, these tests have
notoriously low power, and hence it is quite likely that one ends up with the
DS model, while a TS model with a close-to-unity root would have been a
better option. Furthermore, the pretesting aspect of such a procedure tends to
complicate the distribution of estimators and associated t-statistics. Therefore,
it seems relevant to have a method that is robust to model misspecification.
In this paper, we put forward such a method, where the focus is on the
confidence bounds of average economic growth.
The analysis is closely related to the work of Canjels and Watson (1997),
who consider various point estimators and confidence interval methods for the
trend slope in a model with a near-unit root. A main difference with their
analysis is that we avoid the use of asymptotic critical values, by using the
subsampling method recently put forward by Romano and Wolf (2001). Unlike
more conventional bootstrap procedures, this subsampling method is asymp-
totically valid in the presence of a near-unit root, and therefore suitable to
obtain robust estimates and confidence intervals for the average economic
growth, where the robustness is with respect to the deviation from the unit root.
This paper is organized as follows. In section II, we discuss the TS and DS
models and we consider three associated methods for point and interval
estimation of the average growth rate. We use quarterly seasonally adjusted
post-world war-II (WW-II) US total industrial production as the running
example throughout this paper. In section III, we provide the asymptotic
distribution theory for the effects of model misspecification on the confidence
bounds. We illustrate its implications for the running empirical example, and
we document that the impact of misspecification is quite substantial. In
section IV, we discuss a subsampling method for computing confidence
bounds, adapting the elegant approach put forward in Romano and Wolf
(2001), together with its application to the industrial production data.
section V reports on a simulation experiment which is used to investigate how
robust the subsampling method really is, and how reliable it is in smaller
samples. We also compare our approach to the procedure for obtaining
confidence intervals proposed by Canjels and Watson (1997). In section VI
we conclude and we mention a few future research topics.
346 Bulletin
Blackwell Publishing Ltd 2006
To continue reading
Request your trial