Palgrave Handbook of Econometrics: Applied Econometrics

Sergio J. Rey and Julie Le Gallo 1265

data analysis (EDA) to examine growth datasets. EDA has its roots in the work of
John Tukey (Tukey, 1977), who defined the field as a set of statistical methods
designed to detect and describe patterns, trends, and relationships in data. EDA
methods often rely on interactive statistical graphics to support different types of
interrogation of the data.
In this section we provide an overview of the main branches of EDA methods that
have appeared in the convergence literature. These follow from some of the partic-
ular challenges posed by the study of growth and convergence in a spatial context.
On the one hand, traditional EDA techniques often rest on the same restrictive
assumptions regarding random sampling that we encountered in early economet-
ric work on regional convergence. There has been much recent work developing
spatially explicit methods of EDA designed to take the spatial characteristics of the
data into account. These methods fall under the heading ofexploratory spatial data
analysis(ESDA) (Anselin, 1996).
At the same time, the dynamic characteristics of growth datasets pose inter-
esting challenges for the use of ESDA methods, since the latter have primarily
been designed for cross-sectional datasets. The second branch of the exploratory
literature we review consists of efforts designed to extend ESDA methods to the
dynamic context. We refer to this branch of the literature asexploratory space-time
data analysis(ESTDA).
The use of ESDA and ESTDA methods for convergence and growth analysis relies
on a number of computational tools as well as interactive statistical graphics and
maps for data exploration. In what follows, we draw on examples using the sta-
tistical package STARS: Space-Time Analysis of Regional Systems (Rey and Janikas,
2006), which has implemented a number of these methods for spatial convergence
analysis.^5

27.3.1 Exploratory spatial data analysis

27.3.1.1 Spatialσ-convergence

The point of departure in the EDA branch of the convergence literature has been
the entire distribution of regional incomes itself, with a focus on a number of char-
acteristics of this distribution. The earliest studies examined the level of dispersion
in the distribution and its evolution over time. Labeled asσ-convergence, the typ-
ical approach is to consider the cross-sectional variance (or standard deviation) of
the incomes:

σˆt^2 =

1

(n− 1 )

∑n

i= 1

(yi,t− ̄yt)^2 , (27.14)

whereyi,tis the per capita income or product of economyiin time periodtandy ̄t=
1
n

∑n
i= 1 yi,t. Implicit in the application of this measure is its theoretical relationship
toβ-convergence:

σt^2 =( 1 −β)^2 σt^2 − 1 +σ 

2 , (27.15)