Chris Papageorgiou

English

Research Papers in Economics

Trade as a Threshold Variable for Multiple Regimes
Chris Papageorgiou¤
Department of Economics
Louisiana State University
Baton Rouge, LA 70803
cpapa@lsu.edu
February, 2001
Abstract. This paper employs the data-sorting method developed by Hansen (2000)
which allows the data to endogenously select regimes using di®erent variables. It is shown
that openness, as measured by the trade share to GDP, is a threshold variable that can cluster
middle-income countries into two distinct regimes that obey di®erent statistical models. Our
result suggests that openness may not be as crucial in the growth process of low and high-income
countries but it is instrumental in identifying middle-income countries into high and low-growth
groups.
Keywords: Endogenous splitting; Threshold variables; Openness; Growth
JEL classi¯cation: C13; C21; O47
¤I thank Bruce E. Hansen for making his programs available to me and for his valuable comments.Trade as a Threshold Variable for Multiple Regimes 1
\... wecan use measures of foreign trade and opennessto help explain theclustering
of middle-income economies into high-growth and low-growth groups."
Costas Azariadis (1996)
1. Introduction
Therelationship between openness and growth is at the center of lively discussions amongst econo-
mist. On the onehand, recent work by Sachs and Warner (1995), Edwards (1998) and Frankel and
Romer (1999), just to name a few, assigns an important role of trade and openness to economic
growth. On the other hand, there exists a fair amount of scepticism about this relationship, both
on theoretical and empirical grounds, as summarized in Rodr¶ ³guez and Rodrik (2000).
Some evidence in favor of a positive openness-growth relationship is obtained by plotting the
cross-country average annual growth rate of trade volume against the average annual growth rate
of per capita GDP from 1960 to 1993. The relationship that emerges is clearly positive indicating
that a component of thegrowth performance of many economies maybe associated with an increase
in trade intensity. However, for the same time period, the trade intensity in many rapidly growing
countries, like Japan, has been declining. Moreover, the majority of sub-Sahara African countries
have exhibited trade intensity increases while having virtually no growth. This evidence suggests
that the relationship between openness and growth is far from simple.
This paper examines an alternative way by which openness maybe in°uencing economic perfor-
mance. Following Durlauf and Johnson (1995) (DJ) and more recently Hansen (2000) we employ a
data-sorting method which allows thedata to endogenously select regimes using di®erent variables.
We show that openness, as measured by the ratio of trade volume to GDP, is a threshold variable
that can cluster middle-income countries into two regimes that obey di®erent statistical models.
This ¯nding is in favor of theoretical models in which trade and openness is a plausible source
of multiple equilibria such as Trejos (1992), Azariadis (1996, pp.464-465) and Trejos and Ferreira
(2000).
2. Estimation
In this section we follow Hansen (2000) to search for multiple regimes in the data by using, in
addition to initial per capita output (y1960) and initial literacy rate (LIT), trade share (TS) as
a possible threshold variable. The advantage of Hansen's methodology over the regression-tree
methodology used in DJ is that it is based on an asymptotic distribution theory. Unlike theTrade as a Threshold Variable for Multiple Regimes 2
regression-tree approach, Hansen's method can test the statistical signi¯cance of regimes selected
by the data.1
In line with most empirical growth literature, we consider the following regression equation:
logyi;1985 ¡logyi;1960 =a0 +a1logyi;1960 +a2 logsik +a3 logsih +a4 log(ni +g +±) +"i; (1)
where yi is per capita GDP for country i; sk is physical capital investment (investment share to
GDP), sh is human capital investment (secondary-school enrollment of working-age population),
n is population growth, g +± = 0:05 as in Mankiw, Romer, Weil (1992), and " is a random error
term.
The country-sample (96 countries) and data (real GDP, working-age population, average share
of real investment, secondary-school enrolment rates and adult literacy rates) are from DJ.2 Data
on trade share de¯ned as theratio of imports plus exports to real GDP in 1985, arefrom PWT-5.6
(series, OPEN).3
Since Hansen's theory allows for one threshold for each threshold variable, we proceed by se-
lecting among the three threshold variables (y1960, LIT, TS) by employing the heteroskedasticity-
consistent Lagrange Multiplier test for a threshold obtained in Hansen (1996). Our ¯rst round of
threshold model selection obtains the following p-values: 0:270 for trade share, 0:168 for literacy
rate and 0:080 for initial per capita output. These results indicate that there maybe a samplesplit
based on initial per capita output. As shown in Hansen (2000), the threshold value occurs at $863
and the asymptotic 95% con¯dence set is [$594; $1794]. This threshold value divides our entire
sample of 96 countries into a low-income group with 18 countries and a high-income group with 78
countries.
Our second round of threshold model selection involves the78 countries with per capital output
above $863 and obtains the following p-values for our three threshold variables: 0:552 for trade
share, 0:055 for literacy rate and 0:146 for per capita output. These results indicate a possible
sample split based on literacy rate. The threshold value occurs at 45% and the asymptotic 95%
con¯dence set is [19%; 57%]. The literacy-rate threshold variable splits the high-income subsample
1For a detailed discussion on the statistical theory for threshold estimation in the regression context, see Hansen
(2000).
2With the exception of the adult literacy rates that are from the World Bank's World Report, all of the data used
in DJ are from the Real National Accounts constructed by Summers and Heston (1988).
3Trade share in our country sample varies dramatically from 13:16% in Burma to 318:07% in Singapore. The data
and programs used in this paper are available by the author upon request.Trade as a Threshold Variable for Multiple Regimes 3
Figure 1: Threshold Variable Con¯dence Interval
of 78 countries into two further groups; the low-literacy group with 30 countries and the high-
literacy group with 48 countries.
In the third round, we obtain our key ¯nding. In this round we try spliting the high-income-
low-literacy subsample with 30 countries (income above $863 and literacy rate below 45%). The
p-values obtained from the three alternative threshold models are, 0:033 for trade share, 0:121 for
literacy rate and 0:105 for initial per capita output, indicating that there may be a sample split
based on trade share. Figure 1 presents the normalized likelihood ratio sequence LR¤
n(°) statistic
as a function of the trade share. The least-squares estimate ° is the value that minimizes the
function LR¤
n(°) which occurs at ^ ° = 30:27%. The asymptotic 95% critical value (7:35) is shown
by the dotted line and where it crosses LR¤
n(°) displays the con¯dence set [28:53%;37:23%]. This
threshold divides our subsample of 30 countries into a high-income-low-literacy-low-trade group
with 8 countries and a high-income-low-literacy-high-trade group with 22 countries. Notice that
our third splitting is the most signi¯cant (at the 3:3% level) indicating strong evidence in favor of
trade share as a threshold variable among middle-income countries.
We have tried to further split the high-income-high-literacy rate group of 48 countries but noneTrade as a Threshold Variable for Multiple Regimes 4
Table 1: Four Regimes Obtained by Hansen's Threshold Regression Estimation
Regime 1: yi;1960 ·$863 (18 countries)
Regime 2: yi;1960 >$863; LITi;1960 ·45%; TSi;1985 ·30:27 (8 countries)
Regime 3: yi;1960 >$863; LITi;1960 ·45%; TSi;1985 >30:27 (22 countries)
Regime 4: yi;1960 >$863; LITi;1960 >45% (48 countries)
Notes: LIT denotes literacy rate and TS denotes trade share.
of the bootstrap test statistics were signi¯cant and therefore no further splitting was possible with
theexisting threshold variables. Wehavealso checked therobustness of thesethree variables (y1960,
LIT, TS) by examining a list of other possible threshold variables suggested in the theoretical
literature of multiple equilibria and growth; these include corruption (data from Mauro 1995),
in°ation, and political instability (data from Sachs and Warner 1995). None of the bootstrap test
statistics for these variables were statistically signi¯cant at any round of the selection process.
Table 1 illustrates the four regimes whereas Table 2 presents the countries in each regime
determined by our threshold estimation. The countries in each regime compare well with those
identi¯ed by the regression-tree approach in DJ (1995 p.374). Like DJ we obtain four regimes,
however these regimes are identi¯ed with di®erent threshold variables. Our main di®erence is
twofold: ¯rst their regimes 3 and 4 are clustered into our Regime 4; that is we do not obtain a
statistically signi¯cant threshold for splitting the high-income-high-literacy ratecountries using per
capita output. Second, their Regime 2 is, in our work, divided into two regimes (Regime 2 and
Regime 3) based on the countries' trade share.
Next, we turn our attention to the estimation of equation (1) for the four regimes. Table 3
presents estimates for each regime in the unrestricted and restricted models.4 The heterogeneity
of the coe±cient estimates across regimes is evident. Starting with the unrestricted model, point
estimates on initial income level (logy1960) vary from ¡0:657 and signi¯cant at the 1% level for
Regime1, to 0:652 and signi¯cant at the5% level for Regime2. The coe±cient estimateon physical
capital investment (logsk) is 0:099 but insigni¯cant for Regime 3, and 0:834 and highly signi¯cant
for Regime 4. Finally, estimated coe±cients on human capital investment (logsh) rangefrom 0:018
but insigni¯cant for Regime 1 to 0:589 and highly signi¯cant for Regime 3.
4The restricted model imposes the constraint that the coe±cient on log(ni + g + ±) is equal in magnitude and
opposite in sign to the sum of the coe±cients on logsik and logsih.Trade as a Threshold Variable for Multiple Regimes 5
Table 2: Country Classi¯cation in Four Regimes
Regime 1 Regime 2 Regime 3 Regime 4
1 B. Faso Bolivia Algeria Argentina Mexico
2 Bangladesh Ghana Angola Australia N. Zealand
3 Burma Guatemala Benin Austria Netherlands
4 Burundi India Cameroon Belgium Nicaragua
5 C. Afri. Rep. Mozambique Chad Brazil Norway
6 Ethiopia Nigeria Congo Canada Panama
7 Liberia Somalia Egypt Chile Paraguay
8 Malawi Sudan Haiti Colombia Peru
9 Mali Honduras Costa Rica Philippines
10 Mauritania I. Coast Denmark Portugal
11 Nepal Indonesia Dom. Rep. S. Africa
12 Niger Jordan Ecuador S. Korea
13 Rwanda Kenya El Salvador Singapore
14 Sierra Leone Morocco Finland Spain
15 Tanzania Pakistan France Sri Lanka
16 Togo Papua N. G Greece Sweden
17 Uganda Senegal Hong Kong Switzerland
18 Zaire Syria Ireland Thailand
19 Tunisia Israel Tri & Tobago
20 Turkey Italy U.K.
21 Zambia Jamaica U.S.A.
22 Zimbabwe Japan Uruguay
23 Madagascar Venezuela
24 Malaysia W. Germany
Disparity in coe±cient estimates across regimes in the restricted model is as large as in the
unrestricted model. The estimated share of physical capital ®, varies from 0:06 but insigni¯cant
for Regime 3 to 0:413 and highly signi¯cant for Regime 1. Human capital shares are substantially
di®erent across regimes too, ranging from 0:014 but insigni¯cant for Regime 1 to 0:349 and highly
signi¯cant for Regime 3.5
Heterogeneity of coe±cient estimates is particularly striking between Regime 2 and Regime 3
(both in the unrestricted and restricted regressions) which are clustered according to the trade
threshold variable. This reinforces our ¯nding that more open middle-income economies obey a
5Computing the shares of labor input across regimes obtains: 0:802 for Regime 1, 0:617 for Regime 2, 0:591
for Regime 3, and 0:553 for Regime 4. This results is consistent (even though not as strong in magnitude) with
DJ's observation that labor shares decline with economic development. In a recent paper, Du®y and Papageorgiou
(2000) have used panel data techniques to estimate a two-factor Constant Elasticity of Substitution (CES) aggregate
production function speci¯cation for a cross-section of 82 countries over a period of 28 years. They ¯nd that the
elasticity of substitution and therefore the capital share is increasing with economic development, which is consistent
with the declining labor shares across regimes obtained here.Trade as a Threshold Variable for Multiple Regimes 6
Table 3: Cross-Country Regressions for the Four Regimes
Speci¯cation Regime 1 Regime 2 Regime 3 Regime 4
Unrestricted
Constant 4:312¤¤
(1:627)
¡8:584
(5:736)
3:979¤¤
(1:874)
4:310¤¤¤
(0:965)
logy1960 ¡0:657¤¤¤
(0:218)
0:652¤¤
(0:204)
¡0:395¤¤
(0:147)
¡0:395¤¤¤
(0:061)
logsk 0:228¤¤¤
(0:072)
0:603
(0:280)
0:099
(0:190)
0:834¤¤¤
(0:139)
logsh 0:018
(0:097)
0:027
(0:143)
0:589¤¤¤
(0:101)
0:095
(0:135)
log(n+g +±) ¡0:295
(0:337)
¡2:063
(1:775)
¡0:598
(0:462)
¡0:418
(0:270)
s.e.e. 0:368 0:230 0:254 0:289
Adj. R2 0:36 0:32 0:69 0:54
Restricted
Constant 4:434¤¤¤
(1:558)
¡4:094¤¤
(1:195)
3:719¤¤¤
(1:065)
3:221¤¤¤
(0:562)
Implied ® 0:184¤¤¤
(0:053)
0:324¤¤¤
(0:113)
0:060
(0:108)
0:413¤¤¤
(0:061)
Implied ¯ 0:014
(0:077)
0:059
(0:059)
0:349¤¤¤
(0:072)
0:034
(0:076)
s.e.e. 0:220 0:204 0:247 0:291
Adj. R2 0:41 0:46 0:71 0:53
Obs. 18 8 22 48
Notes: ® and ¯ are the shares of physical and human capital respectively. Standard errors are given in parentheses.
The standard errors for ® and ¯ were recovered using standard approximation methods for testing nonlinear functions
of parameters. White's heteroskedasticity correction was used. *** Signi¯cantly di®erent from 0 at the 1% level. **
Signi¯cantly di®erent from 0 at the 5% level. * Signi¯cantly di®erent from 0 at the 10% level.
model that is signi¯cantly di®erent from that in more closed middle-income economies.
It iswell-known in theliteraturethat cross-country level regressions, such asours, maybesubject
to a list of econometric problems; two potentially serious problems are the omitted-variables error
and the endogeneity error. DJ(pp.371-372, Table III) examined thepossibility of omitted-variables
error showing that evidence of multiple regimes is robust to the addition of a set of 13 control
variables. Since our threshold estimation includes tradeshares, thereare legitimate concerns about
potential endogeneity problems between trade and growth. Put di®erently, it maybe that income
a®ects thelevel of openness and not the reverse. Frankel and Romer (1999) show that correcting for
endogeneity problems by using instruments obtained from geographical components of countries,Trade as a Threshold Variable for Multiple Regimes 7
yields a stronger positive e®ect of trade on economic growth.
3. Conclusion
Thispaper proposesan alternativeway by which opennessmaybea®ecting growth. It isshown that
openness, as measured by the trade share to GDP, is a threshold variable that can cluster middle-
incomecountries into two distinct regimesthat obey di®erent statistical models. Ourresult suggests
that openness may not be as crucial in the growth process of high and low-income countries but it
is instrumental in clustering middle-incomecountries into high and low-growth groups. Our¯nding
is consistent with, and provides evidence in favor of a small but growing class of theoretical papers
that view openness as a potential source of multiple equilibria. In a more general sense, our ¯nding
is in agreement with Durlauf and Johnson (1995), Liu and Stengos (1999) and Durlauf (2001) in
that theconstant coe±cient linear model assumptionsmade in standard growth regressionsare not
supported by the data.Trade as a Threshold Variable for Multiple Regimes 8
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A Contribution to the Empirics of Economic Growth,&quot;

A Cross-Country Empirical Investigation oftheAggregate Production Function Speci¯cation,&quot;

A New Set of International Comparisons of Real Product and Price Levels: Estimates for 130 Countries, 1950-1985,&quot; Review of Income and

Corruption and Growth,&quot;

Does Trade Cause Growth?&quot;

EconomicReform and the Processof Global Integration,&quot;

Inference When a Nuisance Parameter is not Identi¯ed Under the Null Hypothesis,&quot;

Manifesto for a Growth Econometrics,&quot;

Multiple Regimes and Cross-Country Growth Behavior,&quot;

Non-Linearities in Cross-Country Growth Regressions: A Semiparametric Approach,&quot;

On the Growth E®ects of Barriers to Entry,&quot; working paper,

On theShort-Run DynamicsE®ect of ComparativeAdvantageTrade,&quot; working paper,

Openness, Productivity and Growth: What Do We Really Know?&quot;

Sample Splitting and Threshold Estimation,&quot;

The Economics of Poverty Traps Part One: Complete Markets,&quot;

Trade Policy and Economic Growth: A Skeptic's Guide to the Cross-National Evidence,&quot; working paper,

Twin Peaks: Growth and Convergence in Models of Distributional Dynamics,&quot;

Trade as a Threshold Variable for Multiple Regimes

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Trade as a Threshold Variable for Multiple Regimes

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