International Trade and Economic Growth:Evidence from Singapore
Clarence Jun Khiang Tan
Submitted in partial fulfillment of therequirements for the degree of
Master of Artsin the Graduate School of Arts and Sciences
COLUMBIA UNIVERSITY
2012
Abstract
International Trade and Economic Growth:Evidence from Singapore
Clarence Jun Khiang Tan
One of the frequently cited, though hotly contested, determinants of eco-
nomic growth is exposure to international trade. This study focusses on
Singapore, a country with high per capita GDP growth rates and high trade
exposure to explore the relationship between these two variables. I use a
cross-country dataset to gain initial insight into the trade-growth relation,
then use Singapore time series data covering the period 1965 - 2009 to look
at how Singapore’s trade exposure has contributed to its economic growth.
I find some support that trade exposure has led to increased growth for
Singapore. Other important determinants of growth include educational ex-
penditure, inflation, and technological progress.
Contents
1 Introduction 1
2 Theoretical Framework 4
2.1 Defining trade openness . . . . . . . . . . . . . . . . . . . . . 4
2.2 Is trade openness the actual driving force behind growth? . . . 6
2.3 How does trade openness promote growth? . . . . . . . . . . . 11
3 Methodology 16
3.1 Cross-country data . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2 Singapore time series data . . . . . . . . . . . . . . . . . . . . 17
3.2.1 Unit root tests . . . . . . . . . . . . . . . . . . . . . . 19
3.2.2 A note about cointegration . . . . . . . . . . . . . . . . 21
3.2.3 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4 Data and Variables 27
4.1 Cross-country data . . . . . . . . . . . . . . . . . . . . . . . . 27
4.2 Singapore time series data . . . . . . . . . . . . . . . . . . . . 30
5 Results and Discussion 35
5.1 Cross-country data . . . . . . . . . . . . . . . . . . . . . . . . 35
5.2 Singapore time series data . . . . . . . . . . . . . . . . . . . . 40
5.2.1 Regression diagnostics . . . . . . . . . . . . . . . . . . 42
5.3 Limitations of the Study . . . . . . . . . . . . . . . . . . . . . 45
i
6 Conclusion 48
A List of countries ranked by γi 54
ii
List of Tables
1 Unit root tests . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2 Descriptive statistics for cross-country regression . . . . . . . 29
3 Bivariate correlations for cross-country regression . . . . . . . 29
4 Descriptive statistics for Singapore time series OLS regressions 33
5 Bivariate correlations for Singapore time series OLS regressions 34
6 OLS estimates using cross-country data . . . . . . . . . . . . 39
7 OLS estimates using Singapore time series data . . . . . . . . 43
8 List of countries included in cross-country regression, ranked
by γi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
iii
List of Figures
1 Partial Association between Mean Trade-to-GDP Ratio and
Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2 Leverage-vs-squared residual plot for cross-country regression . 38
iv
Acknowledgements
I thank Christopher Weiss, Gregory Eirich, Christy Baker-Smith, Vanessa
Ohta and my colleagues in the Quantitative Methods in the Social Sciences
program at Columbia University for insightful discussions and helpful com-
ments. All errors are mine.
I also thank Yi Han Chong, Chai Wun Goh, Yi Ning Lim and my family
for their unwavering support.
v
1
1 Introduction
Economic growth has always been a central concern for governments and
people all over the world. Real Gross Domestic Product (GDP) per capita,
that is, GDP per capita adjusted for inflation, is often used as a proxy for
the standard of living in different countries. Because the level of GDP per
capita only measures the average income of the typical individual at the
given point in time, a more salient indicator may be the growth rate of real
GDP per capita. Positive growth rates indicate cumulative increases in real
income, implying that two countries with similar levels of GDP but small
differences in growth rates can over time build up large differences in levels
of real GDP per capita. This phenomenon is illustrated by the following
example: In 1965, Uruguay and Peru had similar real GDP per capita levels
at $4,486.49 and $4,613.71, respectively. Average annualized growth rates
(γi) over the 44-year period from 1965 to 2009 were also seemingly close, at
2.053% for Uruguay and 1.037% for Peru. However, this 1.016% difference
increased GDP per capita in Uruguay to $11,069.23 in 2009 as opposed to
only $7,279.81 for Peru1
One factor frequently cited as a possible source of economic growth is
international trade. However, the ways in which a country’s exposure to1Real GDP per capita data was extracted from the Penn World Tables Version 7.0
compiled by Heston et al. (2011). The figures are expressed in 2005-chained dollars andadjusted for Purchasing Power Parity (PPP) so they can be compared across countriesand time periods. The average annualized growth rate, (γi), is used to measure growthrates over a given period. The rate for the period from 1965 to 2009 was calculated usingthe formula 1
44 ln(yi,2009
yi,1965), where i is a country index.
2
international trade, also referred to as its “trade openness”, promotes growth,
remains a contested subject in economic literature.
Singapore is an example of a country with a very open economy and high
levels of per capita GDP growth rates. Over the 44-year period from 1965 to
2009, the Singapore economy grew at an average annualized rate of 5.253%
per year, with real GDP per capita increasing from $4,694.44 in 1965 to
$47,357.27 in 2009, exceeding the real GDP per capita levels of the United
Kingdom, Australia, and even the United States (Heston et al., 2011). Such a
startling growth rate has led Singapore to be labeled an East Asian Miracle.
Significantly, international trade has long been a major part of the Sin-
gapore economy. Data from the Penn World Tables Version 7.0 (Heston
et al., 2011) show that even in 1965, Singapore already had an trade-to-
GDP ratio of 206.73%; by 2009, this number had almost doubled, increasing
to 408.51%. Indeed, Singaporean economists Abeysinghe and Choy (2007)
affirm that “Singapore began its economic history as an entrepôt for South-
East Asia, importing commodities from the regional hinterland and then
re-exporting them . . . and vice versa” (p.46). Furthermore, the Singapore
government makes intentional efforts to increase the country’s exposure to
international trade. This is achieved mainly through a statutory board un-
der the Ministry of Trade and Industry, International Enterprise (IE) Sin-
gapore. This agency has been assigned the mission of “driving Singapore’s
external economy”. IE Singapore seeks to “spearheads the overseas growth
3
of Singapore-based companies and promote[s] international trade” (Interna-
tional Enterprise Singapore, 2010), and also negotiates free trade agreements
(FTA) for Singapore.
Considering Singapore’s trade openness and consistently high real GDP
per capita growth rates, it seems logical to use Singapore to examine the link
between exposure to international trade and growth. This study will test
the hypothesis that Singapore’s exposure to international trade has been a
significant contributor to its economic growth.
4
2 Theoretical Framework
A general review of extant literature shows that the link between trade open-
ness and growth remains unclear.
2.1 Defining trade openness
The ambiguity begins with the definition of trade openness itself. Many
authors define trade openness as the ratio of the sum of imports and ex-
ports (trade) to GDP (see Chang et al., 2009; Lee et al., 2004). Others
use trade-to-GDP ratios as the basis for defining indicators of openness that
include other variables (see Frankel & Romer, 1999; Irwin & Terviö, 2002;
Noguer & Siscart, 2005). Unfortunately, the trade-to-GDP ratio is definitely
not a perfect measure, as trade openness is not a one-dimensional concept
measured solely by volume of trade. The number and effectiveness of trade
barriers and protection, and the presence of preferential trading agreements,
are examples of other factors that may affect a country’s trade openness.
Furthermore, these definitions of trade openness suffer from endogeneity be-
cause both the volume of exports and imports and the GDP level are directly
related to GDP growth rates. This has led critics to point out that while it
is tempting to conclude that greater trade openness leads to higher growth,
the causality may also be reversed; for example, countries with low growth
rates may choose to close their borders to trade in order to limit competition.
5
Hallak and Levinsohn (2004) note that such countries may also impose tariffs
as a means of increasing government revenue.
Several approaches have been proposed to help mitigate this endogeneity
problem. For example, Chang, Kaltani and Loayza (2009) introduce inter-
action terms between trade openness, and a series of factors such as educa-
tional investment, financial depth, and inflation stabilization. Lee, Ricci and
Rigobon (2004) point out the simultaneity bias in the trade-growth regression
since all the terms entering into the calculation of a country’s trade open-
ness are directly related to income level. They propose a technique called
identification through heteroskedasticity (IH), described as follows:
“In the standard simultaneous equations problem the instru-mental variables approach searches for a variable that shifts thedemand (for example) to estimate the supply. In other words,we need a variable that moves the mean of the demand curveto estimate the supply. [. . .W]e could also solve the problem ofidentification if instead of moving the mean we find a variablethat increases the variance of one of the equations to infinity.. . . This is known today as ‘near identification’. In 1929, Leontiefindicated that we did not have to move the variance to infinity,only knowing that it has changed implies that the distribution ofthe residuals rotate along the different schedules [. . . and] this isenough to achieve identification.” (p. 4)
The IH method can be employed to overcome endogeneity thanks to high
sample heteroskedasticity in country growth rates and trade openness levels.
Recognizing the limitations of the trade-to-GDP ratio definition of open-
ness, other economists have proposed different indicators for measuring open-
6
ness. For example, Sachs and Warner (1995) measure openness by look-
ing at factors like the existence of nontariff barriers to trade, average tariff
rates, black market premiums, and existence of state monopolies on exports.
Frankel and Romer (1999) introduce geographical factors such as country
size, distance from other countries and access to maritime ports. They fo-
cus on geographical factors, as these factors are unlikely to be affected by
income, or government policies that affect income. Also, they note that the
main channel through which geographical factors may affect income, is trade.
2.2 Is trade openness the actual driving force behind
growth?
Notwithstanding the fact that openness is a difficult concept to define, the
economics profession remains divided about the influence of international
trade on growth. Some economists have concluded that the idea that open-
ness promotes growth is no more than an illusion. For example, Hallak and
Levinsohn (2004) criticize the research methodology used in the majority of
trade-growth studies conducted before their paper was written in January
2004. They are of the view that the positive relationship arises out of a
series of biases, and that “once [these] are properly addressed, the positive
relationship between openness and growth seems to vanish” (p. 9). They cite
endogeneity and omitted variable bias as the two major problems. Omitted
variable bias occurs if “variables omitted from the regression are those really
7
driving the relationship between openness and growth” (p. 6) . Essentially,
they maintain that this problem is often a result of the use of an inappropriate
dependent variable in the regression.
Hallak and Levinsohn also criticize the predominant use of country-level
macro data in the regressions. They explain that trade policy affects eco-
nomic growth through multiple channels, such as trade volume, market com-
petition, and growth of specific sectors of the economy. There are also many
different instruments affecting trade, for example, import tariffs, export sub-
sidies and subsidized credit. In view of this, many trade-growth regressions
consisting of linear or log-linear regressions of a single trade openness variable
fail to capture the complexity of trade policy described above. They advo-
cate the use of microeconomic data instead, reflecting the fact that firms and
consumers are the ones that trade with each other, and not the countries per
se. They contend that the use of country-level data results in an aggrega-
tion problem because it fails to accurately reflect the degree of sensitivity of
specific industries or consumers to changes in trade policy.
Perhaps one of the most cited papers questioning the positive relationship
between trade and growth is Rodriguez and Rodrik’s (2000) Trade Policy and
Economic Growth: A Skeptic’s Guide to the Cross-National Evidence. In this
work, Rodriguez and Rodrik eschew the simple question, “Does international
trade raise growth rates of income?”, in favor of a more specific one: “Do
countries with lower barriers to international trade grow faster, once other
8
relevant country characteristics are controlled for?” (p. 264) They justify the
use of this precise research question by saying that since trade restrictions
were put in place in response to “real or perceived market imperfections
or, at the other extreme, are mechanisms for rent extraction”, they should
be evaluated on different grounds than natural or geographical barriers to
trade. Also, they draw attention to the fact that in evaluating openness and
trade liberalization, the focus should be on the effect of trade policy and not
volume, thus also questioning the definition of the openness indicator using
trade volume.
Rodriguez and Rodrik also challenge the prevailing assumptions held by
intergovernmental organizations. One of the main activities of the World
Trade Organization (WTO) is “negotiating the reduction or elimination of
obstacles to trade (import tariffs, other barriers to trade) and agreeing on
rules governing the conduct of international trade (e.g. antidumping, subsi-
dies, product standards, etc.)” (World Trade Organization, n.d.a). Inherent
in this mission is the assumption that tariffs are necessarily bad for a coun-
try’s economy. Rodriguez and Rodrik (2000) challenge this assumption by
showing that the effect of a tariff is two-fold, using the example of a small2
open economy made up of manufacturing and agriculture, which in the manu-
facturing sector exhibits learning-by-doing behavior. The economy starts off
with a comparative disadvantage in manufacturing. Within this framework,2In literature relating to international trade, a country is considered “small” when it is
a price-taker on the world market. Changes in demand and supply in the country for agiven good do not affect the world price.
9
when a small tariff is imposed on manufacturing, it creates a distortion in
the allocation of resources on the production side, because the gap between
the manufacturing share of output at world prices is lower than the labor
share in manufacturing. This is known as the static efficiency loss. On the
other hand, the tariff also “[pulls] resources into the manufacturing sector,
[enlarging] the scope for dynamic scale benefits, thereby increasing growth”
(p. 271). Thus, depending on which two of these opposite effects dominate,
a small tariff may actually be beneficial to growth. This echoes Hallak and
Levinsohn’s (2004) view that there may be reason for some level of trade
protectionism in underemployed and underproductive economies. Rodriguez
and Rodrik (2000) eventually conclude that “the nature of the relationship
between trade policy and economic growth remains very much an open ques-
tion[, and] suspect that the relationship is a contingent one, dependent on a
host of country and external characteristics”.
Nobel Laureate Paul Krugman (1994) takes a strong stand as he flatly
denies that the high growth rates observed in East Asia were the result of any
growth miracle. Krugman argues that the sustained growth in real per capita
GDP observed in advanced economies was a result of technological progress
causing “continual increase[s] in total factor productivity”, thus improving the
efficiency of inputs used in the production process. For him, this rise in out-
put per unit of input is key. Specifically in reference to Singapore, Krugman
opines that the country’s spectacular growth rate is a result of “perspiration
rather than inspiration”, achieved through a more efficient mobilization of
10
resources, such as a doubling in the proportion of the population gainfully
employed, improved quality of the workforce through education, and a dra-
matic increase in the stock of physical capital, largely financed by domestic
saving. For Krugman, these are one-time increases that cannot be repeated,
and more importantly, the efficiency of the economy did not increase signifi-
cantly.
Of course, in exploring the link between economic growth and trade,
one must not lose sight of the fact that there are many other determinants
of economic growth besides international trade and openness. One of the
leading growth economists today, Robert Barro, elicited these determinants
in his 1996 paper, Determinants of Economic Growth: A Cross-Country
Empirical Study. Using panel data for 100 countries spanning 1960 to 1990,
Barro (1996) finds that “for a given starting level of real per capita GDP, the
growth rate is enhanced by higher initial schooling and life expectancy, lower
fertility, lower government consumption, better maintenance of the rule of
law, lower inflation, and improvements in the terms of trade" (p. 2).
Two of the factors cited by Barro were higher initial schooling and bet-
ter maintenance of the rule of law. With regards to higher initial schooling,
Barro finds that “an extra year of male upper–level schooling3 is . . . estimated
to raise the growth rate by a substantial 1.2 percentage points per year”. This
seems to support Krugman’s (1994) point that Singapore’s growth can be at-
tributed in part to the improved quality of the workforce through education.3At secondary levels and above.
11
Specifically, Krugman (1994) found that “while in 1966 more than half the
workers had no formal education at all, by 1990 two-thirds had completed
secondary education” (p. 10).
The other factor of interest is better maintenance of the rule of law, and
in the present case, this refers to the successful enforcement of contracts
and intellectual property rights by an impartial judiciary as a support for
greater innovation in the economy. Barro (1996) explains that the efficient
enforcement of the rule of law creates a favorable environment for potential
investors. Using an index created by the International Country Risk Guide,
he finds that “greater maintenance of the rule of law is favorable to growth”,
and that “an improvement by one rank in the underlying index . . . is estimated
to raise the growth rate on impact by 0.5 percentage points” (p. 20).
2.3 How does trade openness promote growth?
Economists who support the view that trade openness is beneficial to growth
have identified different channels through which trade openness may result
in growth.
Andersen and Babula (2008) study the openness-growth link by looking
at the channels through which international trade affects economic growth.
They identify capital accumulation and productivity growth as two sources of
growth in GDP per capita. They cite studies showing that the main source of
growth is not capital accumulation, and conclude that the effects of trade on
12
growth mainly operate through productivity growth. In a framework where
growth is driven by innovation, they attribute the influence of international
trade on growth to three factors. First, trade provides access to foreign
intermediate inputs and technologies. This can take the form of importing
foreign inputs not produced in the home country that are used directly in
production, or as inputs for research and development. Second, trade also
increases market size for new product varieties, incentivizing research and
development to continually produce new products. Finally, trade allows for
diffusion of general knowledge across geographical boundaries. The non-rival
nature of knowledge allows trading partners to share information, leading to
knowledge spillovers that further facilitate the R&D process and subsequent
innovation.
Chang, et al. (2009) consider the effect of complementary policies that
accompany a country’s decision to liberalize trade, and show that these poli-
cies are important in bringing about subsequent growth. They note that
although opening up to trade often has a positive effect in the initial stages,
“the aftermath of trade liberalization varies considerably across countries and
depends on a variety of conditions related to the structure of the economy
and its institutions” (p. 6). Examples of these complementary conditions
include the level of human capital investment, the amount of public infras-
tructure, the quality of governance and labor market flexibility. Chang et al.
(2009) find that per capita GDP only increases with more free trade when
there are minimal labor market distortions. Thus, there might be a case for
13
protectionism if the country is in a state of underemployment or underpro-
duction. This lends support to the idea that trade liberalization is not a
“one size fits all" prescription for economic growth, and that country-specific
factors should enter the decision whether or not to liberalize trade.
Chang, et al. then go on to discuss the complementary policies that
should accompany trade liberalization. Two examples of these include in-
vestment in human capital, and the protection of intellectual property rights.
In their opinion, the need to adopt new technologies and be able to employ
capital and labor efficiently is crucial to the success of the trade liberalization
process as they help a country face foreign competition. Taylor (1998) and
Wacziarg (2001) also support the view that sound investment policies are
crucial in order for countries to reap the full benefits of trade.
In spite of the earlier noted concern that trade liberalization is not “one
size fits all”, Chang et al. (2009) find that in general, trade does improve
growth. Without considering the interaction terms, the general finding is
that trade liberalization leads to faster growth on average. With the interac-
tion terms included, the relation still holds, except in countries where there
are strong distortions in complementary areas, as described earlier. Also,
continued policy reforms after liberalization help a country to reap the full
benefits of its decision to liberalize.
Dollar and Kraay (2004) explore the relation between trade and growth by
looking at the “top one-third of developing countries in terms of increases in
14
trade-to-GDP over the past 20 years” (p. F23), labeling this the “globalizing
group” of developing countries. In the 20-year period, Dollar and Kraay find
that the ratio of trade-to-GDP doubled in this group, and that the group also
significantly reduced tariff levels. By comparison, the remaining two thirds of
developing countries actually saw a reduction in trade openness in the same
period, and the degree to which they cut tariffs was also significantly smaller
than the globalizing group. They find that growth rates increased for these
“recent globalisers”, from 2.9% per year in the 1970s to 3.5% in the 1980s, and
5.0% in the 1990s, while rich country growth rates slowed over this period.
In the other group of non-globalizing developing countries, they observed a
“decline in the average growth rate from 3.3% per year in the 1970s to 0.8%
in the 1980s and recovering to only 1.4% in the 1990s” (p. F24).
In order to test the generalizability of their results, Dollar and Kraay
look at “decade-over-decade changes in the volume of trade as an imperfect
proxy for changes in trade policy”. (p. F24) This eliminates the possibility
that the results they obtained were driven by geography or some unobserved
characteristic affecting both growth and trade, thus addressing some of the
criticism leveled at trade-growth studies by Rodriguez and Rodrik (2000). In
their study of 100 countries, Dollar and Kraay (2004) found that changes in
growth rates showed a strong correlation with increases in trade volume.
Frankel and Romer (1999), as well as further studies building on the
same methodology using geographical variables to measure openness, such
15
as Irwin and Terviö (2002) and Noguer and Siscart (2005), all yield encour-
aging results. They all find that trade raises income, even after controlling
for endogeneity. Frankel and Romer (1999) attribute this to the increasing
accumulation of physical and human capital, as well as increasing levels of
income at each level of capital. Irwin and Terviö (2002) find that this re-
sult is consistent across time. Noguer and Siscart (2005) arrive at the same
conclusion that trade increases income using a better dataset than the previ-
ous two studies with less missing data, and sensitivity analyses confirm the
robustness of their results across geographical and institutional controls.
16
3 Methodology
This section details the methods that will be used to study the trade-growth
relationship, and specifies the models that will be tested. Cross-country
data is used for an initial examination of how trade and population size
affect growth in 112 different countries. Focussing on the Singapore case,
time series data is used to estimate models incorporating various covariates.
Hereafter in this study, Y refers to real GDP, while y is used for real GDP
per capita.
3.1 Cross-country data
First, I use cross-country data to estimate Equation (1) using Ordinary Least
Squares (OLS):
(1)γi = β0 + β1openi6509 + β2 ln(popi6509) + εi
where γi is the average annualized growth rate in real GDP per capita (yi,t)
for country i over the period from 1965 to 2009 that satisfies the equation
(2)yi,2009 = yi,1965 · e[2009−1965]γi
openi6509 is is the mean level of trade-to-GDP ratio for the period 1965-
2009 for country i, calculated at 2005-chained prices, and ln(popi6509) is the
natural logarithm of the mean population level (expressed in millions) for
the period 1965-2009 for country i.
Looking at Equation (2), I see that γi shows the average rate at which
real GDP per capita had to grow every year between 1965 and 2009, in order
17
to reach the level in 2009. Using the average annualized growth rate, γi,
instead of year-on-year (y-o-y) changes in real GDP per capita is helpful
as it removes the short-term fluctuations in γi This reflects that economic
growth occurs over a long period of time and that increases in income level
are a result of small, repeated additions over time. Short-term reductions in
y-o-y growth rates in response to business cycle fluctuations are expected of
every economy, and are unlikely to be indicative of any long run or structural
problems. Thus, γi is expected to be positive for most countries, even with
short-run fluctuations. However, troubled economies with persistently low or
negative y-o-y growth rates will also have low, or even negative, values of γi
, if log per capita GDP in 2009 is lower than in 1965.
ln(popi6509) is included to control for the size of the country’s domestic
market. Noguer and Siscart (2005) note that lower trade-to-GDP ratios in
larger countries are possibly reflective of greater intra-country trade and a
larger domestic market, rather than reduced trade openness as determined
by policy.
3.2 Singapore time series data
The decision to focus on one country, Singapore, implies that I can no longer
consider average growth rates over the period of study, but instead have to
use time series data and look at y-o-y growth rates instead. From this point
18
forward, ∆ is used to denote the difference operator, such that for a variable
gt,∆gt = gt − gt−1.
When working with time series data, it is important to ensure that the
data is stationary, and weakly dependent. In a highly influential 1974 paper,
Spurious Regression in Econometrics, Granger and Newbold show that OLS
regressions using the levels of non-stationary time series data often produce
spurious results, with significant t-statistics and high degree-of-fit (as mea-
sured by R2 or R̄2), coupled with low Durbin Watson statistics, indicating
high serial correlation in the error terms. It is clear that such regressions
do not in any way represent the true relationship between the variables, re-
gardless of the value of the t-statistics or R2. Granger and Newbold run 100
OLS regressions on two independent random walks and show that “[u]sing
the traditional t test at the 5% level, the null hypothesis of no relationship
between the two series would be rejected (wrongly) on approximately three-
quarters of all occasions” (p. 5).
Ensuring stationarity of time series data becomes especially crucial when
I consider that “[with] economic time series, one typically finds a very high se-
rial correlation between adjacent values,. . . with changes being small in mag-
nitude compared to the current level” (Granger & Newbold, 1974, p. 2).
This implies that many economic time series are not stationary in the levels
and often contain unit roots.
19
3.2.1 Unit root tests
A time series Yt is covariance stationary if it has a constant mean µ < ∞,
a constant variance σ2 < ∞, and the covariance between any two terms Yt
and Yt+h depends only on h and not t, for all t and h ≥ 1 (Woolridge, 2010).
Given the following general AR(1) model of Yt:
(3)Yt = ρYt−1 + ut
Yt is stationary if and only if |ρ| < 1. If |ρ| = 1, Yt contains a unit root
and is non-stationary. If |ρ| > 1, Yt is also non-stationary, and contains an
explosive root.
To test for the presence of unit roots in the various time series, I use
the Augmented Dickey-Fuller (ADF) test in Said and Dickey (1984), which
expands on the original Dickey-Fuller (DF) test proposed by Dickey and
Fuller (1979) to allow for the inclusion of trends, and lags to correct for
serial correlation in the error terms. Lag selection is particularly important
in the ADF test. When lag length k is too small, the errors may still be
autocorrelated, biasing the test statistic, while an overly large value of k
reduces the power of the test. In order to avoid arbitrary lag selection, I rely
on the Akaike Information Criterion (AIC), selecting k to minimize the AIC.
I include a trend term when a visual inspection of the time series plot reveals
an upward or downward trend. The ADF tests the null hypothesis that the
series contains a unit root (i.e. H0 : |ρ| = 1) against the alternative that the
20
series is stationary (H1 : |ρ| < 1). If a unit root is detected in the levels, I
difference the series and run the ADF test again.
Table 1: Unit root tests
Variable Zta Conclusionb
ln( ytyt−1
) level -4.737∗∗∗ I(0)
opentlevel -2.945
I(1)1st diff. -3.238∗
ln(edexpt)level -2.459
I(1)1st diff. -5.369∗∗∗
inft level -3.377∗ I(0)
∆mfptc 1st diff. -3.518∗∗ I(1)
usrect level -6.027∗∗∗ I(0)
ttit level -3.837∗ I(0)
reert level -2.955∗∗ I(0)
ftatlevel -0.942
I(1)1st diff. -5.895∗∗∗
pctlevel -1.329
I(1)1st diff. -5.224∗∗∗
mktcaptlevel -2.195
I(1)1st diff. -5.127∗
a∗∗∗ p<0.001, ∗∗ p<0.01, ∗p<0.05bA series is integrated of order n if it must be differenced n times before it becomes
stationary. I(1) series are difference-stationary; stationary series are trivially, I(0).cData collected for multi-factor productivity measure was “Change in Multi-factor Pro-
ductivity”, and is thus reflected here in first differences. Data for levels is not available
21
Table 1 shows the series that are I(1) in the levels become stationary
when differenced, at the 5% level. The series of first differences can now be
used in regressions without the risk of spurious results.
3.2.2 A note about cointegration
It is important to note that not all regressions between non-stationary time
series are spurious. For example, consider the case of two time series Yt and Xt
that are integrated of order 1, denoted I(1). In general a linear combination
of I(1) variables Yt−βXt is also expected to be I(1). However, if there exists
a value of β such that Yt−βXt is I(0), Yt and Xt are said to be cointegrated.
This implies that that while the two series vary when considered individually,
when taken together, the path that the two series take over time are closely
related, and this is usually indicative of some long-term relationship between
the two variables. In this case, since the dependent variable ∆ ln(yt−1) is
I(0), cointegration analysis would not be appropriate.
3.2.3 Models
In the ADF tests for unit roots reported in Table 1, I confirm that the
series that are I(1) in the levels become stationary when differenced. With
stationary data, OLS can be used without the risk of spurious results detailed
in Granger and Newbold (1974). In addition, OLS is also the Best Linear
Unbiased Estimator (BLUE) if the error terms are homoskedastic and are
not serially correlated. I will test for heteroskedasticity and serial correlation
22
following the estimations4. To mitigate the endogeneity problem posed by
the trade-to-GDP ratio definition of trade openness, I include interaction
terms between ∆opent and the appropriate explanatory variables.
I start off by using OLS to estimate Equation (4), that does not include
any interaction terms. This will serve as the benchmark for comparison with
subsequent models:
(4)∆ ln(yt) = β0 + β1∆ ln(yt−1) + β2∆opent + β3∆ ln(edexpt)+ β4inft + β5∆mfpt + β6year + εt
where ∆ ln(yt) is the y-o-y growth rate of real GDP per capita (yt) at time
t5, ∆opent is the change in trade-to-GDP ratio at time t, ∆ ln(edexpt) is the
change in the natural logarithm of total education expenditure at time t,
inft is inflation at time t as measured using the Consumer Price Index (CPI,
2005 = 100), ∆mfpt is the change in multi-factor productivity at time t and
year incorporates a linear time trend.
The lagged dependent variable ∆ ln(yt−1) is included to account for de-
pendence in the ∆ ln(yt) series, making Equation (4) a Lagged Dependent
Variable model. ∆ ln(edexpt) is included to study the effect of human capital
investment on economic growth, and proxies for the quality of the workforce.
A better-educated workforce is expected to be able to assimilate, and react
to, the “knowledge spillovers”6 resulting from trade more effectively, leading4See Section 5.2.1 Regression diagnostics on page 42.5To see why this is so, consider that ∆ ln(yt) = ln(yt)− ln(yt−1) = ln( yt
yt−1)
6See Andersen and Babula (2008)
23
to greater innovation. Thus, I expect the coefficients on ∆ ln(edexpt) and
the associated interaction term to be positive.
inft shows how changes in the price level (i.e. inflation) affect economic
growth. The effect of inflation on growth is another hotly contested topic
in economics. On one hand, inflation can be good for growth when the
excess of aggregate demand over aggregate supply is driven by factors such
as high export levels or strong investment. On the other hand, inflation can
be detrimental if it is the result of the money supply increasing faster than
the economic growth.
As for multi-factor productivity (MFP), within a standard neoclassical
growth model framework, MFP is represented by the At term, and is often
used as a measure of technological progress. Assuming that production at
time t, Yt, is defined by the following Cobb-Douglas function with constant
returns to scale,(5)Yt = Kα
t (AtLt)1−α 0 < α < 1
At is labor-augmenting, and can be interpreted as the contribution of tech-
nological progress to improving the “effectiveness of labor” (Romer, 2005, p.
9). I expect the coefficient on mfpt to be positive.
It goes without saying that trade openness, human capital investment, in-
flation, and technological progress are not the only factors affecting economic
growth. Many other factors such as political stability, good governance and
maintenance of the rule of law can also be related to growth. However, in
24
view of the limited number of available observations7, for various reasons,
it would be impractical to include all possible covariates in one model. For
example, the dataset used for this time series analysis was assembled from
different sources, and the date range covered differs from one data source
to the next. Thus, including all covariates in one model may significantly
decrease the number of observations entering the regression. Furthermore, if
I include every explanatory variable and the associated interaction terms, I
would be estimating a model with 21 regressors. With only 28 observations,
this would do little more than increase the R̄2 without revealing much about
the relationship between the variable.
To mitigate this problem, I include additional explanatory variables one
at a time, along with the appropriate interaction term and compare the
resulting estimates and R̄2 with those obtained using the benchmark model.
For example, in Model (5) of Table 7, I look at how a recession in the US
affects Singapore’s economic growth and trade openness level. Thus, I add
the terms usrect and ∆opent × usrect into the model.
The additional variables I include in the regressions are a US recession
dummy variable(usrect), indices for the terms of trade (ttit) and real effective
exchange rate (REER), the number of countries with at least one FTA with
Singapore (ftat), total claims on the private sector held by deposit money
banks (pct), and stock-market capitalization (mktcapt).7The benchmark Equation (4) only has 28 observations.
25
The US recession dummy variable studies the effect of a recession in the
United States on Singapore. As a small open economy with a high level
of trade exposure, I expect that Singapore would be particularly sensitive
to changes in the world economy. When a large country like the US goes
into a recession, general global demand can be expected to drop, associated
with decreased economic growth, and also a decrease in demand for exports.
Data from the IMF’s (n.d.a) Direction of Trade Statistics (DOTS) database
shows that in 2010, Singapore’s total trade with the US (in nominal terms)
was US$58.6 billion, making the US Singapore’s third-largest trading partner
after Malaysia and Mainland China. Thus, I expect the coefficient on this
variable to be negative.
reert is an index of the REER, itself a measure of the value of the Singa-
pore dollar against a weighted basket of foreign currencies (Nominal Effective
Exchange Rate, NEER), adjusted for inflation using the CPI.
The terms of trade is defined as a ratio of the price of exports to the price
of exports, and the terms of trade are said to improve if this ratio rises (i.e.
if the price index of exports rises or the price index of imports falls). This is
termed an improvement because intuitively, exports are “sold” by a country
to a trading partner, and a rise in export prices results in an increase in the
revenues from trade, if the quantity of exports remains unchanged. However,
an increase in export prices also decreases the price competitiveness of a
country’s exports vis-à-vis those of its competitors, possibly reducing the final
26
quantity exported as a result. The overall effect of this change in the terms
of trade will depend on which one of these two opposing forces dominates.
Free trade agreements encourage trade by reducing or eliminating the
import tariffs (a barrier to trade) incurred. This reduction in tariffs increases
the price competitiveness of the products sold by the country with an FTA
as compared to competitor countries without FTAs. The indicator chosen
here is the number of countries with at least one FTA with Singapore, and
not the number of FTAs of which Singapore is a signatory. This is because
Singapore has multiple FTAs with certain countries. If the premise that freer
trade leads to greater growth is true, the correlation between growth and the
number of countries covered by at least one FTA should be positive. Also,
while a more informative indicator may be the volume of goods that were
imported using an FTA, unfortunately that data is not publicly available.
The financial variables pct and mktcapt are included to see how the fi-
nancial system impacts growth. mktcapt is the stock market capitalization
as a percentage of GDP, and measures the size and importance of the stock
market in relation to the entire economy, while pct shows the claims on the
private sector held by deposit money banks at time t, indicating the efficiency
of deposit money banks in credit allocation (Beck et al., 2009).
27
4 Data and Variables
This next section provides descriptions of the datasets and variables that will
be used to conduct my analysis. I will also cover the coding of variables and
provide descriptive statistics and bivariate correlations for them. Descriptive
statistics give a first view of the dataset: the mean is a measure of central
tendency, while the variance and range measure the dispersion of the data.
Bivariate correlations, on the other hand, show how strongly the two vari-
ables under consideration are related to each other: the greater the absolute
value, the stronger the relationship, while the associated p-value shows the
likelihood the correlation occurred by chance.
4.1 Cross-country data
The cross-country data used to estimate Equation (1) was drawn from the
Penn World Tables Version 7.0 (PWT 7.0) compiled by Heston, Summers
and Aten (2011) at the University of Pennsylvania. The PWT 7.0 data has
been adjusted for inflation and Purchasing Power Parity (PPP) in order to
make it comparable across countries and time periods. The original dataset
comprised data for 189 countries, and reported two versions of data for China.
The first version was based on official data provided in the 2005 edition of
the United Nations International Comparisons Project (ICP). The second
version adjusts the official growth-rate and price data to account for the
28
sheer size of China’s population, and differences in price levels between cities
(Heston, 2011). Data for China Version 1 were included in this regression.
Countries for which real GDP per capita was missing in either 1965 or
2009 were dropped, and γi was calculated using Equation (2). The final
regression included 112 countries. γi and openi6509 were expressed as a
percentages, and popi6509 was expressed in millions.
Table 2 reports descriptive statistics for this set of data. popi6509 has
a very large standard deviation and range, with a maximum of 1074.9 mil-
lion (for China). This suggests a right-skewed distribution, and thus, a log
transformation was used to help normalize the data. Table 3 provides bi-
variate correlation between the variables. I note that the correlation be-
tween gammai and openi6509 is positive, and has a low p-value, indicating
that I should reject the null hypothesis that the correlation between the two
variables occurred by chance. On the other hand, the correlation between
gammai and ln(popi6509), while positive, has a high p-value, and thus, I fail
to reject the null hypothesis that this correlation occurred by chance. This
indicates that using this dataset, the relationship between openi6509 and γi
is probably worthy of attention.
29
Table 2: Descriptive statistics for cross-country regression
Variable Mean Std. Dev. Min. Max.
γi 0.019 0.017 -0.033 0.082openi6509 67.058 42.951 14.025 321.947popi6509 38.597 128.832 0.069 1074.943ln(popi6509) 2.156 1.677 -2.679 6.98N 112
Table 3: Bivariate correlations for cross-country regression
Variable γi openi6509 ln(popi6509)
γi 1.000
openi6509 0.279 1.000(0.003)
ln(popi6509) 0.013 -0.465 1.000(0.895) (0.000)
p-values in parentheses
30
4.2 Singapore time series data
No single dataset contained all the variables required for this study; thus ,the
data was assembled from various sources.
∆ ln(yt) is y-o-y growth rate in PPP-adjusted GDP per capita, calculated
using the rgdpch8 series in Heston et al. (2011), expressed in 2005 interna-
tional dollars per person:
(6)∆ ln(yt) = ln(yt)− ln(yt−1)= ln(rgdpcht)− ln(rgdpcht−1)
∆opent is the first difference of the openk 9 series in the same dataset, which
gives the ratio of the sum of imports and exports expressed as a percentage
of real GDP. Both ∆ ln(yt) and ∆opent have 44 annual observations for each
year between 1966 and 2009.
∆ ln(edexpt) is the growth rate of total educational expenditure, ex-
pressed as a percentage. The original data series,“Government Expenditure
on Education - Total”, expressed in thousands of Singapore dollars, was pro-
vided by the Singapore Ministry of Education (2010), and contained 28 an-
nual observations from 1981 to 2009.
∆mfpt is the y-o-y percentage change in multi-factor productivity pro-
vided by the Singapore Department of Statistics. The series includes data
from 1976 to 2009.8PPP Converted GDP Per Capita (Chain Series), at 2005 Constant Prices9Openness at 2005 Constant Prices (%)
31
usrect is a dummy variable that takes on the value 1 during a recessionary
year in the United States, and 0 otherwise. Monthly data was collected from
Federal Reserve Bank of St. Louis (2011), and for any given year t, usrect
was coded 1 if for more than 6 months during the year the US economy
was in recession, and 0 otherwise. All 45 years between 1965 and 2009 were
included.
Two time series were extracted from the IMF’s (n.d.b) International Fi-
nancial Statistics (IFS) database : reert and ttit. reert is an index of the
real effective exchange rate, while ttit is a terms of trade index, calculated
as the ratio of the export price index to the import price index at time t.
All three indices take the value 100 in 2005. Data for reert ran from 1976 to
2009, while that for ttit covered 1979 to 2009.
ftat tracks the number of countries that have at least one FTA with
Singapore at time t. It is constructed using the Regional Trade Agreements
Database from the World Trade Organization (n.d.b). If a country has more
than one FTA with Singapore, that country is included as of the year of the
earliest FTA, as determined using the date of entry into force as opposed to
the date of signing.
The two financial variables pct andmktcapt were taken from Beck, Demirgüç-
Kunt and Levine (2009). pct shows the claims on the private sector held by
deposit money banks at time t, andmktcapt is the stock market capitalization
at time t. Both variables are expressed as percentages of GDP, and include
32
data from 1965 - 2009, and 1989 - 2009 respectively. Tables 4 and 5 provide
descriptive statistics and bivariate correlations for this dataset respectively.
Focussing on the first column of Table 5, I note that the signs for most
of the correlations obtained between ∆ ln(yt) and the various independent
variables are consistent with the extant literature. Of particular note are
the correlations between ∆ ln(yt) and ∆ftat and ∆pct. As explained in the
previous section, the correlation between growth and the number of countries
covered by at least one FTA should be positive. The negative correlation
observed here may indicate that the ∆ftat variable (number of FTAs) does
not effectively capture the influence of FTAs on trade openness and growth.
As for ∆pct, the negative correlation is expected, as recessions are associated
with reduced liquidity as banks and other financial institutions are more
cautious about taking risks, and choose to cut back on loans and financing,
thus also reducing the efficiency of credit allocation.
33
Table 4: Descriptive statistics for Singapore time series OLS regressions
Variable Mean Std. Dev Min. Max. N
∆ ln(yt) 5.253 4.62 -7.388 11.867 44∆opent 4.586 24.557 -57.7 64.836 44∆ ln(edexpt) 0.063 0.098 -0.103 0.327 28inft 1.765 2.142 -1.062 9.710 44∆mfpt 0.811 3.441 -7.600 6.2 36usrect 0.156 0.367 0 1 45ttit 123.751 17.599 95.238 152.124 31reert 109.271 8.124 92.815 125.53 34∆ftat 0.545 1.606 0 9 44∆pct 1.135 5.055 -12.263 15.765 44∆mktcapt 2.458 32.439 -34.432 58.542 20
34
Table 5: Bivariate correlations for Singapore time series OLS regressions
Variable ∆ ln(yt) ∆opent ∆ ln(edexpt) inft ∆mfpt usrect ttit reert ∆ftat ∆pct ∆mktcapt
∆ ln(yt) 1.000
∆opent 0.115 1.000(0.458)
∆ ln(edexpt) 0.253 -0.549 1.000(0.194) (0.003)
inft 0.210 0.202 0.317 1.000(0.171) (0.188) (0.100)
∆mfpt 0.675 0.278 -0.171 -0.153 1.000(0.000) (0.101) (0.384) (0.373)
usrect -0.241 -0.009 0.212 0.404 -0.548 1.000(0.115) (0.952) (0.279) (0.007) (0.001)
ttit 0.159 -0.207 0.272 0.150 0.064 -0.092 1.000(0.394) (0.265) (0.161) (0.419) (0.732) (0.624)
reert -0.121 -0.329 0.415 0.002 -0.514 0.036 0.307 1.000(0.497) (0.057) (0.028) (0.991) (0.002) (0.839) (0.093)
∆ftat -0.258 0.011 -0.230 -0.044 -0.047 0.150 -0.943 -0.242 1.000(0.091) (0.944) (0.238) (0.775) (0.785) (0.324) (0.000) (0.168)
∆pct -0.495 -0.065 -0.252 -0.165 0.013 -0.001 -0.572 -0.155 0.604 1.000(0.001) (0.674) (0.195) (0.284) (0.939) (0.993) (0.001) (0.381) (0.000)
∆mktcapt 0.351 0.384 -0.267 -0.104 0.591 -0.383 0.194 -0.212 -0.150 -0.003 1.000(0.129) (0.094) (0.255) (0.663) (0.006) (0.096) (0.412) (0.371) (0.528) (0.990)
p - values in parentheses
35
5 Results and Discussion
5.1 Cross-country data
The OLS estimation of Equation (1) yielded a positive and highly statistically
significant coefficient on mean trade openness (openi6509) of 0.0142. A 1%
increase in mean trade-to-GDP ratio was associated with a 1.42% increase
in average annualized growth rate, ceteris paribus. This is consistent with
the findings in Noguer and Siscart (2005), who estimate a similar model
using log per capita GDP levels, and including an additional control for
land area. They, too, find a positive and statistically significant relation
between trade openness and real GDP per capita. A Breusch-Pagan test for
heteroskedasticity in the error term produced a χ2 statistic of 0.52 (p-value
= 0.469); thus, I fail to reject the null hypothesis that the error term has the
same variance given any value of openi6509 and ln(popi6509), and conclude
that the error is homoskedastic.
Figure 1 shows the partial association between mean trade-to-GDP ratio
and growth. It is much like a “scatter plot” of gammai against openi6509,
showing the visual distribution of points around the “regression line”10. Look-
ing at Figure 1, one might be tempted to conclude that the statistically sig-10The terms “scatter plot” and “regression line” are in quotation marks because they are
only valid when used in association with a simple linear regression with one dependentvariable and one independent variable. However, the Frisch-Waugh-Lovell theorem (Lovell,2008) provides a means to focus on one explanatory variable, in this case, opent, by“removing” the effects of other variable(s), in this case, ln(popi6509). This is the theoreticalbasis for the partial association plot.
36
nificant coefficient on mean trade openness was driven by a few potentially
influential data points like Singapore (SGP) or Equatorial Guinea (GNQ).
However, a plot of leverage against the squared residuals provided in Figure
2 shows that none of the data points are highly influential11. Furthermore,
a robust regression of Equation (1) (reported as Model (2) in Table 6) pro-
duces largely similar results, and included all 112 countries. The coefficient
on mean trade openness increased from 0.0142 to 0.0163, and the associated
t-statistic rose from 3.55 to 5.25.
However, as explained earlier, one should be careful when considering
the statistical significance of these coefficients, as the trade-to-GDP ratio
definition of trade openness suffers from endogeneity. Furthermore, Equation
(1), including only two dependent variables, is most probably underspecified,
and suffers from omitted variable bias, as there are many other variables that
may be related to economic growth, such as education, political stability and
inflation. Regardless, it still provides some initial insight into the relationship
between trade openness and growth.
This cross-country dataset also lends support to the view that real GDP
per capita is at best an imperfect proxy of welfare and standard of living.
A ranking of all countries by average annualized growth rate γi (provided at
Appendix A) sees Equatorial Guinea (GNQ) at the top of the list, with an11Leverage measures deviation from the mean. An observation with high leverage is far
from the mean value of the sample. An outlier is an observation with a large residual, or alarge difference between the observed and predicted value. A highly influential observationhas both high leverage and a large residual. Thus it would be found in the upper-right-hand or “north-east” corner of the graph. Figure 2 shows no such points.
37
annualized growth rate of 8.21%. This reflects the rise in real GDP per capita
from $593.16 in 1965 to $22,016.84 in 2009 (Heston et al., 2011). However,
in its 2011 edition of the Human Development Report (HDR), the United
Nations Development Program (UNDP) ranked Equatorial Guinea 136th out
of 187 countries based on the Human Development Index12. Even though
the Gross National Income (GNI) per capita13 for Equatorial Guinea, at
$17,608, is well above the average for Sub-Saharan Africa of $1,966, its life
expectancy at birth of 51.1 years trails the average of 54.4 years, as does the
number of expected years of schooling. While an in-depth treatment of the
Equatoguinean case is beyond the scope of this paper, it is a good example
of how welfare is not an unidimensional concept measured by income alone.
12The Human Development Index is a summary measure of human development incorpo-rating indicators for life expectancy, education, and income. (United Nations DevelopmentProgramme, 2011)
13GNI per capita is the income measure used in the HDR. The OECD provides a cleardefinition of GNI and its relation to GDP: “Gross national income (GNI) is GDP less nettaxes on production and imports, less compensation of employees and property incomepayable to the rest of the world plus the corresponding items receivable from the rest ofthe world” (Organization for Economic Cooperation and Development (OECD), 2001).
38
Figure 1: Partial Association between Mean Trade-to-GDP Ratio andGrowth
COM
ISL
BDI
HTI
URY
ZMBCAF
NZL
CPV
SYC
GMB
SLECMR
AUSGRC
SLV
NIC
ARGUGA
GNQ
ROM
FIN
PERNPL
COL
BENTCD
TUR
PRT
BFAMWI
CRI
BOL
BRAJPNESP
ZWE
ECU
RWA
TZA
CHL
TGO
DNKMLIMOZ
NER
GIN
CYP
MEX
NOR
BGD
ISR
KOR
FRAUSA
ETHCHESWEGTM
MAR
VEN
DOM
GBRITAAUT
NAM
PAKCAN
KEN
ZAF
SEN
BWA
PRYPNGSYR
JAM
FJI
IRL
GAB
GNB
IND
NGACIV
LKA
MRT
NLDBRB
TWN
IDN
MDG
JOR
CHN
IRNDZA
TTOTUNMUS
ZAR
EGY
PHLCOG
THA
BELLSO
HND
GHA
PRI
MYS
PANLUX
HKG
SGP
−5
05
10
Avera
ge a
nnualis
ed g
row
th in r
eal G
DP
per
capita (
PP
P)
−100 0 100 200 300Mean Trade/GDP,1965 − 2009
coef = .01418734, se = .00400158, t = 3.55
Figure 2: Leverage-vs-squared residual plot for cross-country regression
GNQ
CHN
BWAKORTWN
SGP
SYC
THAMYS
HKG
IDN
LKA
CPV
LUX
CYPROM
IND
DOMTTOMUS
IRLEGY
PRT
PAN
JPN
NORTUNGRCCHL
PRIESPAUTFINCOLMARTURAUSBELISR
ISL
BRA
NLD
LSOITACOG
BRB
URYFRAPAK
PNGCANGBRMLI
USA
DNKGHAFJI
SWETZAECUMEXGNBSYRCRIMOZGTM
PHLPRYNPL
IRNDZACHE
BGD
BFANZLARGZAFSLVETHPERUGA
HNDMRT
GMB
TCDGAB
MWINGA
RWABENBDICMRJAMJORBOL
NAMCIVVENKENSEN
SLE MDG
COM
ZMBGIN
HTITGO
CAFNICNERZWEZAR
0.1
.2.3
.4Levera
ge
0 .05 .1 .15Normalized residual squared
39
Table 6: OLS estimates using cross-country data
Variable γi γi
Model (1) (2)
openi6509 0.0142∗∗∗ 0.0163∗∗∗
(0.00400) (0.00311)
ln(popi6509) 0.182 0.316∗∗∗
(0.103) (0.0796)
constant 0.527 -0.0319(0.446) (0.346)
N 112 112R̄2 0.087 0.205
∗∗∗ p<0.001, ∗∗ p<0.01, ∗p<0.05Standard errors in parentheses
40
5.2 Singapore time series data
I begin by looking at the benchmark equation (4) without interaction terms,
reported as Model (1) in Table 7. All else held constant, a 1 unit increase in
the change of trade-to-GDP ratio is associated with a 0.089% increase in the
current y-o-y growth rate of real GDP per capita. This result is significant
at the 5% level. A 10% increase in total education expenditure is associated
with a 1.7% increase in the growth rate 14, all else held constant. This is
also significant at the 5% level. A 1 unit increase in inflation leads to a
1.59% increase in the growth rate, ceteris paribus. All else held constant, a 1
unit increase in the change of multi-factor producitivity is associated with a
1.076% increase in the growth rate. The coefficient on the lagged dependent
variable ∆ ln(yt−1) is positive, and statistically significant at the 5% level,
suggesting that there is indeed some dependence in the ∆ ln(yt) series, and
that effects from the previous time period t−1 persist into the current period
t.
Surprisingly, only two out of the nine interaction terms included were
statistically significant, ∆opent × ttit and ∆opent × ∆ftat. In Model (6),
both the coefficient on ttit and the interaction term are negative. The latter
is also statistically significant at the 5% level. This shows that all else held
constant, an increase in the ratio of export prices to import prices has a
negative effect on the growth rate of GDP per capita, lending support to the14Calculated using (1.100.17736)− 1 = 0.0170.
41
view that a rise in export prices hurts the price competitiveness of Singapore’s
exports, thus reducing growth.
In Model (8), the coefficients on ∆ftat and ∆opent × ∆ftat are both
positive, and the interaction term is statistically significant at the 10% level.
This indicates that an increase in the number of countries covered by an
FTA with Singapore has helped helped increase encourage economic growth
through an increase in Singapore’s trade openness.
In addition, the coefficient on the usrect variable is also statistically sig-
nificant, at the 10% level. However, the interaction term is not statistically
significant, suggesting that recessions in large economies such as the US neg-
atively affect growth in Singapore, but trade openness may not be the main
channel through which this negative effect influences the economy.
Overall, in the ten models estimated, several variables were consistently
statistically significant. These are educational expenditure, inflation, and
multi-factor productivity, indicating that these are important determinants
of Singapore’s growth for the period of study from 1981 - 2009. Specifically,
the positive coefficients on inft indicate that inflation was beneficial for Sin-
gapore’s growth, and this occurs when aggregate demand exceeds aggregate
supply, driven by factors such as high export levels or strong investment.
Data from Heston et al. (2011) supports this claim, showing that Singa-
pore’s mean trade openness for the period was 347% of GDP, and the mean
investment share of GDP was 40.3%. The trade openness variable was statis-
42
tically significant in five of the ten models estimated, showing some support
for the positive relation between trade openness and Singapore’s economic
growth.
5.2.1 Regression diagnostics
To ensure that OLS is the BLUE, I test the residuals in the OLS regres-
sions for serial correlation and heteroskedasticity. Since a lagged dependent
variable is included as one of the regressors, the Durbin-Watson test for first-
order autocorrelation is no longer valid. Instead, I use Durbin’s h statistic,
and the Breusch-Godfrey Lagrange multiplier (LM) test for higher order se-
rial correlation. For each of the 10 models estimated, the h and χ2 statistics
from the Durbin’s h and LM test were low and not statistically significant,
indicating that I cannot reject the null hypothesis that there is no serial
correlation in the error terms.
The Breusch-Pagan test for heteroskedasticity in the error terms produced
low χ2 statistics in each of the 10 models estimated. The highest χ2 value
recorded was 0.78 in Model (4), corresponding to a p-value of 0.377. As
such, I fail to reject the null hypothesis that the error terms have constant
variance given any value of the independent variables, and conclude that the
error terms are homoskedastic.
The homoskedastic and serially uncorrelated error terms prove that OLS
is the BLUE, making it an appropriate estimation method.
43
Table 7: OLS estimates using Singapore time series data
Variable (1) (2) (3) (4) (5)
∆ ln(yt−1) 0.571∗∗ 0.648∗∗∗ 0.558∗∗ 0.458∗ 0.379(0.208) (0.222) (0.217) (0.261) (0.231)
∆opent 0.089∗∗ 0.102∗∗ 0.077 0.103∗∗ 0.066(0.035) (0.038) (0.054) (0.04) (0.039)
∆ ln(edexpt) 17.736∗∗ 14.059 19.093∗∗ 21.893∗∗ 14.172∗
(7.885) (8.713) (9.158) (9.791) (8.186)
inft 1.590∗∗∗ 1.542 ∗∗∗ 1.574∗∗∗ 1.609∗∗∗ 2.101∗∗∗
(0.505) (0.508) (0.519) (0.512) (0.571)
∆mfpt 1.076∗∗∗ 1.142∗∗∗ 1.071∗∗∗ 1.023∗∗∗ 0.801∗∗∗
(0.209) (0.22) (0.215) (0.224) (0.253)
year -.099 -.066 -.109 -.117 -.045(0.081) (0.088) (0.089) (0.085) (0.084)
usrect -5.970∗
(3.314)
∆opent ×∆ ln(edexpt) -.294(0.296)
∆opent × inft 0.013(0.042)
∆opent ×∆mfpt -.010(0.014)
∆opent × usrect -.095(0.099)
constant 196.422 128.963 216.855 233.063 90.086(161.035) (174.824) (177.153) (170.373) (166.829)
N 28 28 28 28 28R̄2 0.597 0.597 0.579 0.588 0.622Durbin’s h 0.06 -.086 0.117 0.183 -.073LM test χ2 0.227 0.018 0.502 0.924 0.803Breusch-Pagan test χ2 0.42 0.29 0.57 0.78 0.26∗∗∗p < 0.01,∗∗ p < 0.05,∗ p < 0.1
(Continued. . . )Standard errors in parentheses
44
Variable (6) (7) (8) (9) (10)
∆ ln(yt−1) 0.539∗∗ 0.576∗∗∗ 0.585∗∗∗ 0.415∗ 0.856∗∗∗
(0.221) (0.21) (0.198) (0.226) (0.27)
∆opent 0.489∗∗∗ 0.21 0.047 -.100 0.145∗∗∗
(0.184) (0.39) (0.047) (0.274) (0.044)
∆ ln(edexpt) 16.777∗∗ 19.111∗∗ 16.865∗∗ 18.832∗∗ 14.774∗
(8.386) (8.214) (8.222) (7.827) (8.697)
inft 1.378∗∗∗ 1.552∗∗∗ 1.381∗∗∗ 0.963 1.510∗∗∗
(0.485) (0.514) (0.49) (0.593) (0.474)
∆mfpt 1.056∗∗∗ 1.044∗∗∗ 1.094∗∗∗ 0.899∗∗∗ 1.233∗∗∗
(0.206) (0.214) (0.198) (0.224) (0.279)
year -.726 -.098 -.290 0.006 0.052(0.747) (0.089) (0.248) (0.099) (0.143)
ttit -.337(0.376)
reert -.102(0.092)
∆ftat 0.223(0.246)
∆pct -.166∗
(0.09)
∆mktcapt 0.036(0.034)
∆opent × ttit -.003∗∗
(0.001)
∆opent × reert -.001(0.004)
∆opent ×∆ftat 0.006∗
(0.003)
∆opent ×∆pct 0.002(0.003)
∆opent ×∆mktcapt -.002(0.002)
constant 1487.134 204.797 574.856 3.408 -106.760(1536.232) (180.001) (492.953) (191.919) (286.651)
N 28 28 28 28 20R̄2 0.66 0.587 0.648 0.624 0.717Durbin’s h 0.09 0.076 -.013 -.122 -.218LM test χ2 0.183 0.143 0.028 0.233 0.545Breusch-Pagan test χ2 0.02 0.36 0.17 0.12 0.06∗∗∗p < 0.01,∗∗ p < 0.05,∗ p < 0.1 Standard errors in parentheses
45
5.3 Limitations of the Study
One of the greatest challenges associated with this study is the limited avail-
ability of time series data. While data for real GDP per capita and trade-to-
GDP ratio were available for all 44 years between 1965 and 2009, other se-
ries such as educational expenditure and multi-factor productivity were only
available starting from 1981. For some datasets, such as Barro-Lee (2010),
observations are not available for every year in a date range15. As such, even
though educational attainment and, by extension, the quality of human capi-
tal, may be more closely related to growth than educational expenditure, the
latter is chosen only because of data availability. Also, while interpolation
may be able to fill in missing values in a time series, the interpolated values
are not “true” data, and introduce (or increase) serial correlation into the
data by virtue of the interpolation process.
In addition, the small sample size limits the ability to draw generalizations
from the results of this study. The dataset used included selected years
between 1965 and 2009. Even if data were available for every year in this
period, the total number of observations would total only 45. Conclusions
drawn from such a small sample may not always be generalizable. Of course,
one way to increase the number of observations is to increase the frequency
of the data, for example, using quarterly instead of annual data16. However,15There are a variety of possible reasons for this, for example, that the data is not
collected on a yearly basis. An obvious example of this would be the decennial census.16This approach was explored initially, but found to be unfeasible.
46
this introduces greater seasonality into the data, which has to be controlled
for in turn. This may also exacerbate the data availability problem.
The two issues cited above are probably rooted in the decision to focus on
one country. Including more countries in the dataset would easily overcome
the small sample problem, as well as mitigate the issue of data availability.
With more countries included, the time period under study could be short-
ened, while maintaining a sizable sample, thus easing the data collection
process. Furthermore, working with cross-country data, one can use means
and average changes over a given period instead of looking to y-o-y changes,
which are often prone to short-run fluctuations. As mentioned before, us-
ing average changes reflects that economic growth occurs over a long period
of time, and that increases in income level are a result of small, repeated
additions over time. Unfortunately, with a small sample size, averaging ob-
servations is a luxury I cannot afford.
Focussing on the Singapore case also limits the types of explanatory vari-
ables that can be included in the growth regressions. For example, following
independence in 1965, the People’s Action Party has been the incumbent
party in government. This has naturally led to political stability for the
country, and while political stability is likely to be positively correlated with
growth, the Singapore time series data can neither prove nor disprove this
claim, simply because a dataset including data only from Singapore pro-
47
vides no basis for comparison with another country that has had changes in
political leadership during the period of study.
48
6 Conclusion
This study looked at the channels through which international trade af-
fects economic growth. I used a panel dataset of 112 countries and find
a strong cross-country relationship between trade openness and economic
growth. Even though the regression equation was probably underspecified
and suffers from endogeneity, the panel dataset provided initial insight into
the trade-growth relation. I then examined time series data from Singapore,
a country with high per capita GDP growth rates and trade openness levels,
to see if the country’s economic growth is indeed driven by its level of trade
exposure.
In sum, I find some support for the hypothesis that exposure to inter-
national trade has been beneficial to Singapore’s growth. Other important
determinants of Singapore’s growth over the period of study include educa-
tional expenditure, inflation and technological progress.
However, as noted in Section 5.3, limited availability of time series data
was the main reason for a small sample size of 28. Thus, for greater general-
izability of results, and to allow for comparison between countries, the study
can be repeated with a cross-country dataset so that the sample is enlarged,
and other covariates can be added.
49
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Appendix
A List of countries ranked by γi
Table 8: List of countries included in cross-country regression,ranked by γi
Rank Country CodeReal GDP per capita(US$)
γi1965 2009
1 Equatorial Guinea GNQ 593.16 22,016.84 8.21
2 China CHN 356.71 7,011.57 6.77
3 Botswana BWA 628.11 8,868.16 6.02
4 Republic of Korea KOR 2,052.92 25,029.01 5.68
5 Taiwan TWN 2,465.12 28,693.00 5.58
6 Singapore SGP 4,694.44 47,357.27 5.25
7 Seychelles SYC 3,504.13 23,801.85 4.35
8 Thailand THA 1,174.62 7,793.65 4.3
9 Malaysia MYS 1,770.17 11,295.08 4.21
10 Hong Kong HKG 5,905.33 36,286.26 4.13
11 Indonesia IDN 675.03 4,075.05 4.09
12 Sri Lanka LKA 869.22 4,034.42 3.49
13 Cape Verde CPV 835.67 3,779.20 3.43
14 Luxembourg LUX 19,554.27 84,510.57 3.33
15 Cyprus CYP 4,445.69 18,981.09 3.3
16 Romania ROM 2,290.51 9,736.75 3.29
17 India IND 775.07 3,237.98 3.25
18 Dominican Republic DOM 2,412.52 9,912.04 3.21
19 Trinidad & Tobago TTO 7,648.11 30,990.67 3.18
20 Mauritius MUS 2,358.23 9,483.60 3.16
(Continued. . . )
55
Table 8 – Continued
Rank Country CodeReal GDP per capita(US$)
γi1965 2009
21 Ireland IRL 8,376.27 33,347.45 3.14
22 Egypt EGY 1,247.60 4,955.85 3.13
23 Portugal PRT 5,373.30 19,889.91 2.97
24 Panama PAN 2,771.27 10,196.15 2.96
25 Japan JPN 9,043.20 31,957.85 2.87
26 Norway NOR 15,017.26 49,939.94 2.73
27 Tunisia TUN 1,936.56 6,300.35 2.68
28 Greece GRC 8,948.34 27,285.50 2.53
29 Chile CHL 3,950.78 11,998.79 2.52
30 Puerto Rico PRI 7,813.63 23,661.09 2.52
31 Spain ESP 9,335.66 27,631.96 2.47
32 Austria AUT 12,651.62 37,399.77 2.46
33 Finland FIN 11,247.38 32,160.07 2.39
34 Colombia COL 2,636.93 7,528.69 2.38
35 Morocco MAR 1,210.02 3,293.97 2.28
36 Turkey TUR 3,649.44 9,910.42 2.27
37 Australia AUS 15,234.40 41,298.05 2.27
38 Belgium BEL 12,810.17 34,620.50 2.26
39 Israel ISR 9,453.90 25,548.96 2.26
40 Iceland ISL 13,742.65 37,112.36 2.26
41 Brazil BRA 3,564.26 9,352.81 2.19
42 Netherlands NLD 15,608.19 40,565.93 2.17
43 Lesotho LSO 514.29 1,311.47 2.13
44 Italy ITA 11,029.18 27,691.75 2.09
45 Republic of Congo COG 894.31 2,219.80 2.07
46 Barbados BRB 9,272.30 22,913.57 2.06
47 Uruguay URY 4,486.49 11,069.23 2.05
(Continued. . . )
56
Table 8 – Continued
Rank Country CodeReal GDP per capita(US$)
γi1965 2009
48 France FRA 12,554.56 30,821.49 2.04
49 Pakistan PAK 971.80 2,353.25 2.01
50 Papua New Guinea PNG 1,173.85 2,746.31 1.93
51 Canada CAN 15,554.18 36,208.07 1.92
52 United Kingdom GBR 14,357.56 33,385.98 1.92
53 Mali MLI 438.74 999.38 1.87
54 United States USA 18,350.65 41,101.86 1.83
55 Denmark DNK 15,146.67 33,906.11 1.83
56 Ghana GHA 565.22 1,239.19 1.78
57 Fiji FJI 1,960.40 4,284.47 1.78
58 Sweden SWE 16,404.59 35,224.10 1.74
59 Tanzania TZA 557.50 1,188.89 1.72
60 Ecuador ECU 2,909.68 6,170.96 1.71
61 Mexico MEX 5,486.60 11,629.61 1.71
62 Guinea-Bissau GNB 390.10 818.38 1.68
63 Syria SYR 1,996.98 4,001.89 1.58
64 Costa Rica CRI 5,605.43 11,216.67 1.58
65 Mozambique MOZ 383.54 759.48 1.55
66 Guatemala GTM 3,279.88 6,284.95 1.48
67 Philippines PHL 1,484.29 2,838.63 1.47
68 Paraguay PRY 1,943.76 3,704.76 1.47
69 Nepal NPL 655.55 1,211.48 1.4
70 Iran IRN 5,790.50 10,621.92 1.38
71 Algeria DZA 3,375.73 6,067.59 1.33
72 Switzerland CHE 22,069.02 39,619.45 1.33
73 Bangladesh BGD 780.98 1,397.05 1.32
74 Burkina Faso BFA 513.83 902.44 1.28
(Continued. . . )
57
Table 8 – Continued
Rank Country CodeReal GDP per capita(US$)
γi1965 2009
75 New Zealand NZL 15,920.82 27,864.80 1.27
76 Argentina ARG 6,871.52 11,961.30 1.26
77 South Africa ZAF 4,625.95 7,588.43 1.12
78 El Salvador SLV 3,931.99 6,339.00 1.09
79 Ethiopia ETH 430.68 683.66 1.05
80 Peru PER 4,613.71 7,279.81 1.04
81 Uganda UGA 731.50 1,151.75 1.03
82 Honduras HND 2,301.59 3,605.01 1.02
83 Mauritania MRT 1,014.32 1,573.77 1
84 The Gambia GMB 947.57 1,464.76 .99
85 Chad TCD 829.22 1,276.40 .98
86 Gabon GAB 6,832.00 10,280.37 .93
87 Malawi MWI 440.35 653.04 .9
88 Nigeria NGA 1,410.75 2,034.15 .83
89 Rwanda RWA 731.97 1,031.09 .78
90 Benin BEN 800.50 1,115.71 .75
91 Burundi BDI 264.40 368.06 .75
92 Cameroon CMR 1,327.28 1,811.00 .71
93 Jamaica JAM 6,510.51 8,794.49 .68
94 Jordan JOR 3,576.84 4,643.94 .59
95 Bolivia BOL 3,066.43 3,793.85 .48
96 Namibia NAM 3,873.57 4,732.94 .46
97 Côte d’Ivoire CIV 1,166.68 1,343.22 .32
98 Venezuela VEN 8,014.00 9,115.23 .29
99 Kenya KEN 1,063.28 1,206.17 .29
100 Senegal SEN 1,349.66 1,492.04 .23
101 Sierra Leone SLE 854.41 872.68 .05
(Continued. . . )
58
Table 8 – Continued
Rank Country CodeReal GDP per capita(US$)
γi1965 2009
102 Madagascar MDG 815.33 753.22 -.18
103 Comoros COM 1,036.00 915.71 -.28
104 Zambia ZMB 2,044.41 1,764.72 -.33
105 Guinea GIN 970.70 826.33 -.37
106 Haiti HTI 1,774.81 1,444.55 -.47
107 Togo TGO 1,056.28 734.20 -.83
108 Central African Republic CAF 992.61 647.71 -.97
109 Nicaragua NIC 3,574.97 2,191.36 -1.11
110 Niger NER 884.20 534.34 -1.14
111 Zimbabwe ZWE 267.92 142.56 -1.43
112 Dem. Rep of the Congo ZAR 1,004.29 231.28 -3.34
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