# The interactive effect of trade and education on growth

Celine Kauffmann

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The interactive effect of trade and education on growth

Celine KAUFFMANN

2000.22
# The interactive effect of trade and education on growth

Celine Kauermann

TEAM, Universite Paris I, CNRS

e-mail address: celk@univ-paris1.fr

January 17, 2000
**Abstract:** This empirical study consists of an econometric test of the complementary effect of trade and education on long run growth. The tests are perfomed using a mixed specification built on the Benhabib and Spiegel[7] model and include an estimator of trade openness. Regressions are run on a long term panel data base (100 years, 10 OECD countries) reconciling the two data sets of Maddison[26] and Banks[4]. The results strongly support the existence of an interaction between trade and education which appears to promote catch-up between countries. Moreover, using a structural change test, I also show that such an interaction is not constant but hinges on the level of GDP per capita already attained by the economy.

**Keywords:** growth regressions, long run economic growth, interaction between human capital and trade openness, panel data estimations

**Résumé:** Cette étude empirique s'attache à tester l'existence d'une interaction entre l'ouverture économique et le capital humain qui pourrait expliquer l'évolution de la croissance de long terme. Une telle hypothèse repose sur deux intuitions théoriques: d'une part, l'ouverture économique constitue un cadre économique qui permet une réallocation du capital humain vers les activités productives ; d'autre part, l'ouverture économique permet aux économies d'avoir accès aux nouvelles technologies produites à l'étranger, ce qui, par le processus d'imitation entraîne des gains de croissance. La complémentarité ouverture économique, capital humain est estimée par le biais d'une spécification empruntée à Benhabib et Spiegel (1994) et augmentée d'un estimateur d'ouverture commerciale. La base de données de référence est issue des recherches de Banks (1995) et Maddison (1995) et permet une étude sur un siècle (1880-1980) et dix pays de l'OCDE. Les résultats confirment l'existence d'une forte interaction entre éducation et commerce sur le long terme, cependant essentiellement pertinente pour expliquer le rat-trapage technologique entre pays. Ce travail est ensuite complété par une étude de la stabilité des coefficients qui nous amène ...nalement à diδérencier l'impact de l'interaction capital humain / ouverture économique en fonction du PIB par tête atteint par les pays.

**Mots clés:** croissance de long terme, complémentarité capital humain / ouverture économique, économétrie des données de panel

**JEL classi...cation:** C23, N10, O11, O40, O50
# 1 Introduction

According to the economic literature, human capital should be an important variable in explaining the differences in growth rates among countries. Lucas[25], Becker, Murphy and Tamura[6] and Azariadis and Drazen[2], among others, have provided persuasive theoretical models in which growth in GDP is driven by human capital accumulation. Yet, while cross-section analysis seems to con...rm this relation<fnref n="1" />, in studies using panel data, human capital appears either insigni...cantly, or even negatively related to growth<fnref n="2" />. These results suggest that if human capital plays the important role implied by theory, then its influence on growth may come through more indirect channels. This paper considers one such a mechanism by examining whether human capital affects growth through trade channel.

The relation between trade and growth has long been debated in the literature of economic growth<fnref n="3" />. The often cited bene...cial effects of trade openness include the international transmission of knowledge<fnref n="4" />, e[cient sectorial reallocation<fnref n="4" />, increasing returns to scale<fnref n="5" />, and incentives to reduce distortions<fnref n="6" />. However, while theory points to several bene...ts of trade openness, the empirical tests are not precise enough to discriminate between the sources of gains from trade. The cross-country studies—from Balassa[3] to Edwards[16], Sachs and Warner[35] and Vamvakidis[37]—generally yield evidence of a positive impact of openness on growth. However, few empirical studies have attempted to determine the relative importance of these channels. In one such study, Wacziarg[38] ...nds that trade openness mainly affects growth ...rst by raising the share of investment in GDP, and secondly by aiding technological transmissions.

This last result is most interesting in the context of this paper since it implies an active role for human capital, as underlined by Pissarides[31]. If, indeed, trade openness allows countries to gain access to technologies available abroad, it does not guarantee that they are capable to properly implement them for domestic use. Economies may need a certain stock of human capital in order to enhance their ability to use the technologies they acquire

<footnote n="1">¹See, for instance, Barro[5]</footnote>

<footnote n="2">²Knight, Loayza and Villanueva[22], Islam[20], Caselli, Esquivel and Lefort[12]</footnote>

<footnote n="3">³Sachs and Warner[35], Edwards[15]</footnote>

<footnote n="4">⁴Grossman and Helpman[19]</footnote>

<footnote n="5">⁵Romer[34]</footnote>

<footnote n="6">⁶Berthelemy, Pissarides and Varoudakis[9]</footnote>
through trade. In other words, imitation requires not only an object to imitate (provided through trade), but skills as well. Thus, human capital would affect growth through its interaction with trade openness. However, this channel is not the only one to justify a complementary effect between education and trade. As already underlined earlier, openness could affect growth by reducing distortions. Murphy, Shleifer and Vishny[28] and Berthelemy, Pissarides and Varoudakis[9] assume that policy distortions may induce the development of human capital intensive rent-seeking activities. Therefore, trade openness, by reducing these distortions, may generate a reallocation of human capital from rent-seeking activities towards growth enhancing sectors. Consequently, a high level of education combined with openness can lead to faster growth rates.

These two potential effects arising from the interaction of trade and education will have different impacts. The ...rst involves a process of imitation which implies the closing of the technological gap between countries. Technology will circulate through trade leading to a catch-up effect between less developed and more technologically advanced economies. The convergence involved here is different from the one derived from the Solow[36] model on which the Barro[5] regressions are based. Catch-up is not due to factor accumulation but to the circulation of technologies and can be durably hindered by the lack of trade openness or skills. The second effect does not refer to a convergence process since, in this case, the interaction under focus alters permanently the growth rates.

Several empirical studies have already taken into account a possible interaction between education and trade in the growth equation (see for instance Gould and Ručin[18], Berthelemy, Dessus and Varoudakis[8], Levin and Raut[24]). These studies provide robust evidence of a high degree of interaction between trade policies and education expenditures which stimulate economic growth. While the ...rst two papers focus on the increase in human capital productivity generated by openness using a Mankiw, Romer and Weil[27] specification, the last specification human capital as a total factor productivity determinant as in the Feder model[17]. Nevertheless, these papers only account for the direct effect on growth such an interaction between education and trade may generate. They do not consider that such effects could help lagging countries to catch-up with the more developed ones.

This paper tries to test for both effects through an augmented Benhabib and Spiegel specification[7]. Such a specification allows to model the catch-up process, which is not possible when human capital is only considered as an in-
put in the production function. The basic idea behind Benhabib and Spiegel [7] is to allow the technological term in the production function to depend on the gap in GDP per capita between countries which proxies the catch-up effect due to the diffusion of knowledge, as well as other variables which characterize each country individuality. The specification is then tested using a long term panel data base covering all the period from 1880 to 1980 for ten OECD countries. The length of the database is an additional contribution in this paper as previous studies on that subject are usually undertaken either on cross-section or over relatively short periods of time.

The results show strong evidence of an interaction between education and trade though mainly explaining the convergence effect among the countries. In addition, using a break in coefficient test -built to account both for the temporal and the cross-sectional dimensions of the dataset - I ...nd that such an effect is not constant but varies according to the level of GDP per capita.

The paper is organized as follows. The next section discusses the theoretical studies that justify the interaction between trade and human capital. Section 3 develops the empirical specification used to test the impact of education on growth when related to trade. The fourth section deals with the data and provides some descriptive statistics. The ...fth section presents the results, and the last one tests the possibility that the estimated coefficients may depend on the level of GDP. Finally, section 7 summarizes the main conclusions.

## 2 Theoretical background

There are at least two main types of models which support the joint importance of education and trade, in the growth process. The ...rst type consists of imitation models and emphasizes the joint necessity for a country to accumulate education and to adopt outward-oriented policies in order to experience a catch-up effect (section 2:1). The second one refers to rent-seeking models de...ning openness as the economic environment most likely to allow for optimal allocation of human capital (section 2:2).
## 2.1 Trade allows import and export of know-how

As underlined by Pissarides[31], in a world where countries from the South tend to imitate those from the North, trade appears as a route for transferring technology. Through trade, indeed, countries can access new technology coming from innovating economies. However, they are only able to apply this new technology, and hence experience higher growth rates, if their work force has the necessary skills. In other words, more open economies have a greater ability to copy more technologically advanced countries and, in this way, make advantage of their skilled labour force. Symmetrically, economies with a higher skilled labour force can more easily absorb foreign innovations. If we assume that growth rates are driven by technological accumulation, then simultaneously promoting education and strengthening trade openness should boost economic performance, at least among imitating countries. Since new technology tends to come from the more industrial economies to enhance the less advanced countries growth rates, this channel leads to a convergence effect which has been described by imitation models such as Grossman and Helpman[19]. However, this catch-up effect is a dynamic one, meaning that when some lagging countries imitate, others generate new technologies. Consequently, the potential growth gains generated by the technological catch-up are never really exhausted.

## 2.2 Trade reduces distortions

The starting point of the model in Berthelemy, Pissarides and Varoudakis [9] is that human capital is not always used in productive activity. In closed countries, for instance, where distortions seem to be particularly developed human capital tends to be mainly used to escape policy-induced constraints. Skilled people are diverted from the productive sector to devote their time to ...and ways of reducing taxes, avoiding restrictions (as lawyers, accountants or traders for example...). These activities are socially useful because they reduce the effects of the distortions on the productive sectors. They, nevertheless, constitute a diversion of human capital from the growth enhancing activities. Though difficult to identify which institutional environment allows for an optimal allocation of human capital, trade openness, being a sign that trade barriers are lowered and certainly inducing a reduction in every kind of distortion, appears to provide incentives to drive human capital towards the most productive activities. Thus, trade openness seems essential to boost
growth by allowing the human capital productivity to be higher. Such a reduction in misallocation of human capital, as underlined by Berthelemy, Pissarides and Varoudakis[9], can justify the existence of different growth patterns associated with different degrees of openness.

While the ...rst channel refers to a convergence effect, the second allows the economies to experience different growth paths. The forces described above operate simultaneously. Therefore, testing them amounts to ...nding a model which includes the catch up effect and the endogenous growth one.

# 3 The econometric specification

The Benhabib and Spiegel model[7] can incorporate the two scenarios listed above. According to Benhabib and Spiegel[7], the accumulation of technology depends on several variables including a catch-up effect and the educational attainment of the labour force. To this structure, I add a variable which interacts trade with human capital that affects the technological term both directly and through the catch-up term.

## 3.1 Benhabib and Spiegel technological term

Assuming a Cobb-Douglas technology, the production function can be expressed as:

$$Y_{t,i} = A_{t,i} K_{t,i}^{\beta} L_{t,i}^{-\beta} \quad (1)$$

where $Y_{t,i}$ is the level of production, $K_{t,i}$ the physical capital, $L_{t,i}$ the labour and $A_{t,i}$ the total factor productivity.

Taking log differences in (1), the change in GDP can be specified as a linear function of the change in the production factors:

$$\phi \ln Y_{t,i} = \phi \ln A_{t,i} + \beta \phi \ln K_{t,i} + \gamma \ln L_{t,i} \quad (2)$$

Then, following Benhabib and Spiegel[7], the change in technology is assumed to depend on two factors:

$$\ln A_{t+1,i} - \ln A_{t,i} = c + dH_{t,i} + eH_{t,i} + \frac{\tilde{A}_{t,max} - A_{t,i}}{y_{t,i}} \quad (3)$$
where $y_{t,i}$ is the level of production per capita and $y_{t,max}$ the maximum level of production per capita attained within the set of countries of interest at year t.

The ...rst factor ($H_{t,i}$) is the level of human capital which proxies the domestic endogenous innovation process. The second one ($H_{t,i}$) is $\frac{y_{t,max} - \bar{y}_{t,i}}{y_{t,i}}$ is a term interacting the level of human capital with a variable representing the technological gap between the country i and the most developed country. This last term, ...rst proposed by Nelson and Phelps[30] to estimate the role of human capital in the adoption of new technologies, represents the catch-up effect due to the diffusion of technology.

One objection to this specification is that Benhabib and Spiegel did not model the channel through which technological catch-up can take place. They assumed perfect and unbounded diffusion of knowledge, uncorrelated with the degree of openness of the countries. As it is more likely that imitation requires at once commercial interaction between countries and skills within the imitating economies, in what follows an estimator of trade openness is incorporated in the Benhabib and Spiegel[7] specification.

## 3.2 The augmented Benhabib and Spiegel specification

To account for the two channels through which trade might interact with education, the Benhabib and Spiegel[7] specification is altered in two ways. First, an interactive variable involving education and trade is inserted directly as a factor of the technological term. This variable accounts for the direct effect I referred to earlier. Then, the catch-up effect is specified to depend not only on the level of human capital, but also on the degree of openness to the outside world. While the ...rst interactive variable represents the improvement in technological accumulation coming from a simultaneous increase in education and trade, the second variable proxies the convergence effect. Through the ...rst term I capture the Berthelemy, Pissarides and Varoudakis[9] productive reallocation of human capital effect which is due to trade. Through the second one, I capture the Grossman and Helpman[19] technological catch-up effect. Both effects are expected to enhance growth.

$$ \ln A_{t+1,i} - \ln A_{t,i} = c + dH_{t,i} + eH_{t,i} + \sum_{j} \tilde{A}_{ij} \frac{\sum_{k} \frac{y_{t,max} - \bar{y}_{t,k}}{y_{t,k}}}{y_{t,i}} + fH_{t,i} + \sum_{j} \tilde{A}_{ij} \frac{\sum_{k} \frac{y_{t,max} - \bar{y}_{t,k}}{y_{t,k}}}{y_{t,i}} \quad (4) $$
where ◦ is a linear function of trade (T r$_{t;i}$) which preserves the Benhabib and Spiegel term but also allows for the catch up effect due to the interaction between trade and education.

$$
\textcircled{2} (T r_{t,i}) = g + h T r_{t,i} \qquad (5)
$$

Going back to (2) and replacing the technological term with the equations
speci...ed above yields:

$$
\begin{equation}
\begin{split}
\phi \ln Y_{t,i} = {}& c + \phi \ln K_{t,i} + \bar{\phi} \ln L_{t,i} + dH_{t,i} + eH_{t,i} \quad \text{Tr}_{t,i} \\
& + fH_{t,i} \quad \frac{y_{t;\max} \mathbf{i} y_{t,i}}{y_{t,i}} (g + h \text{Tr}_{t,i}) + u_{i,t}
\end{split}
\tag{6}
\end{equation}
$$

Expanding (6) results in the following testable speci...cation:

$$
\begin{equation}
\begin{split}
\phi \ln Y_{t,i} = {}& c + \phi \ln K_{t,i} + \bar{\phi} \ln L_{t,i} + (d \mathbf{i} f g) H_{t,i} + (e \mathbf{i} f h) H_{t,i} \quad \text{Tr}_{t,i} \\
& + f g H_{t,i} \quad \frac{y_{t;\max}}{y_{t,i}} + f h H_{t,i} \quad \text{Tr}_{t,i} \quad \frac{y_{t;\max}}{y_{t,i}} + u_{i,t}
\end{split}
\tag{7}
\end{equation}
$$

The sign of the coefficient on both human capital and the pure interactive
effect between trade and education is ambiguous: depending on whether the
catch-up phenomenon dominates the direct effect on technological accumu-
lation the overall impact can be positive or negative.

4 The long term evidences

4.1 The data

The interactive effect between trade and education is analysed by using a data
set derived from three different databases provided by Banks[4], Maddison[26]
and Jones and Obstfeld[21] and including exports, GDP, population growth,
enrollment rates and investment share in GDP. The resulting data base is a
long term annual panel from 1880 to 1980, including 10 OECD countries<fnref n="7" />.
For the purpose of the article, the war period observations are excluded from
the dataset.

<footnote n="7"><sup>7</sup>Canada, Denmark, Germany, France, Italy, Japan, Norway, Sweden, UK, USA</footnote>
## 4.2 The estimators

The investment variable is proxied by the share of capital formation in GDP, the variation in labour by the population growth, human capital by the enrollment rates and the indicator of trade by the share of exports in GDP corrected for the size of countries. Since trade and education are the variables of interest, the following two sections are devoted to discussing the relevance of the indicators used.

### 4.2.1 The estimator of human capital

When selecting a measure of human capital, one must choose between building a stock estimator and using an education rate. The latter option seems problematic since, as underlined by Pritchett[32], the enrollment rates simply represent *how* investment rates. They, then, do not account appropriately for human capital accumulation. However, testing for the correlation between the education rates and the corresponding human capital stocks on the recent period casts a serious doubt over the *how* nature of the enrollment rates. It appears, indeed, that education rates are highly correlated to the existing human capital stocks<fnref n="8" /> for most of the countries under consideration, suggesting that their changes over time could appropriately proxy the evolution of the stock variables. In this case trading the stock estimators for the education rates would not be a too rough approximation.

Another reason is driving such a choice: stock estimators are not available for the length of the dataset used. Consequently, building stock estimators from education rates would require either to extrapolate values from a already existing stock (but available data do not correspond exactly to the definition of the education rates such as those listed in the Banks[4] and Maddison[26]

<footnote n="8">⁸Comparing the Nehru, Swanson and Dubey[29] average number of years in secondary school* and the Banks[4] education rates (in primary and secondary school) on 1960-1979 yields the following correlation coefficients:</footnote>

<footnote>Canada .327 Denm. .964 France .934 Germ. .704 Italy .987 Japan .396 Norway .946 UK .832 US -.742 Sweden .958</footnote>

<footnote>According to this table 7 countries over 10, essentially the european countries, are characterised by a high correlation between the stock variable and the education rate.</footnote>

<footnote>* Such a choice makes sense since on 1960-1979 the changes in the overall education rate (primary + secondary) are certainly driven by the variance in the secondary education rate. Indeed, for the countries of interest, the primary education rate had, at this time, already reached a ceiling.</footnote>
database) or to sacrifice 40 years to determine the starting values, possibility
that would compromise the aim of the paper, i.e. studying long run growth.

Nevertheless, the education rate is used in the regressions as a lagged
variable. There is no reason, indeed, to think that current education has
a direct influence on economic performance. The process takes time, for
instance, the time for a student to exit school and ...nd a job. Therefore, the
regressions are performed using the education variable lagged by ten years.

4.2.2 A proxy of trade

The measure of trade used is the share of exports in GDP. Several economists have pointed out the limits of such an indicator, stressing in particular the endogeneity between GDP and exports as a severe drawback (among them Bradford and Chakwin[11], Rodrik[33] and Cyrus, Frankel and Romer[13]). Nevertheless, the share of exports in GDP is a convenient estimator for essentially two reasons. First, as underlined by Alesina and Wacziarg[1], such a variable appears to be a good measure of the fraction of the economy which actually interacts with the rest of the world. Secondly, it has the advantage of measuring the openness both in cross-country and time series data (Vamvakidis[37]). Imports would certainly do a better proxy to account for the imitation process since the products entering the country incorporate the technologies used abroad. Yet, since data on imports are not available on a long period for the range of countries of interest, and providing that for the available values of imports both series are highly correlated<sup>9</sup>, the regressions are performed using the share of exports in GDP.

The trade estimator is also corrected for the size of the countries. As
underlined by Alesina and Wacziarg[1], small countries, because they cannot
bene...t from access to a large market, tend to be more open to trade whereas
bigger countries have "naturally" less incentive to trade with the rest of
the world. This hypothesis points toward a negative relationship between
country size and the degree of trade openness that should be controlled for.
I choose not to proxy the size of countries by their population, as usually
done in the literature, to avoid the endogeneity problem between this last
variable and the growth rate. Rather, I turn to the Lee[23] measure<sup>10</sup> of free

<footnote n="9">⁹According to the NBER macrohistory database the correlation coefficient between exports and imports is 0.93 for France (data from 1878 to 1938), 0.97 for US (data from 1867 to 1969), 0.89 for UK (data from 1856 to 1950).</footnote>

<footnote n="10">¹⁰Regressing the import share on natural resource endowments (proxied by the land size</footnote>
trade openness<fnref n="11" />.

The trade variable eventually derived has the following specification:

$$Tr_{t,i} = \frac{\frac{X_{t,i}}{GDP_{t,i}}}{LeeV ar_i}$$

Where $\frac{X}{GDP}$ represents the share of exports in GDP and LeeV ar the measure calculated by Lee[23]. It proxies the degree to which a country interacts with the rest of the world through trade, controlling for the fact that bigger countries naturally need to trade less.

## 4.3 Some empirical evidence

This section is devoted to a short historical review of the evolution of GDP per capita (section 4.3.1), export share in GDP (section 4.3.2) and enrollment rate (section 4.3.3) over the twentieth century. The graphs are inserted at the end of the paper. For the sake of clarity, the number of countries which behaviour is analysed is reduced to four. Therefore, the selected examples belong to different geographical areas so as to make them representative of the sample.

### 4.3.1 Income, growth and convergence

Figure 1 presents evidence of the catch-up effect towards US. This phenomenon seems to be mainly relevant after the second world war though.

### 4.3.2 The trade estimator

Figure 2 shows the measure of trade openness of four countries: France, Japan, UK and US, from 1870 to 1994. These indexes can not be read

<footnote>of each country) and on trade distortion (among them distance to major world exporters as a proxy for transportation costs), and replacing the coefficients on trade distortions with zeros, Lee[23] defines an alternative measure of free trade openness for each country. Such a measure should be relevant to correct the trade variable even on a long term setting since it is calculated from variables which are unlikely to change over time.</footnote>

<footnote n="11">¹¹However, the estimations are robust to these corrections. Correcting the trade estimator either by the population of countries, or by the Lee variable or even not correcting for it yield the same results. This robustness check Vamvakidis[37] result according to which correction for the size of countries was mainly relevant for cross-country analysis.</footnote>
directly as the share of exports in GDP since they are corrected for the
"size" of the countries. Nevertheless, they give a good idea of the ranking of
countries and of the evolution of those countries trade orientation over the
20th century. At the end of the 19th century, the degree of openness is quite
heterogenous: while UK is rather outward oriented, Japan is totally closed.
Then, the two World Wars appear to create big breaks in the French, British
and Japanese openness trends: before World War I, the di¤erent trends are
quite stable and slightly increasing, after that, the picture gets blurred. The
countries tend to close and converge towards a low level of openness. This
tendency, however, reverses after World War II when every country clearly
tends to interact more and more with the rest of the world. This e¤ect has a
catch-up connotation as, by the end of the period, every country's openness
level lies in the interval 0.77 -0.85.

4.3.3 The education rate

In ...gure 3,the cumulative enrollment rate in primary and secondary school<fnref n="12" />
is presented. While Japan has increased its education rate all through the
period, France and UK appear to have su¤ered from the ...rst and second
World Wars. The US experience the highest education rates throughout the
20th century, but lose the supremacy by the end of the period. By contrast
with the previous graph, catch-up here is mainly relevant before the ...rst
world war. After that, the picture gets less clear: while France and the UK
experience a collapse in their trends, from a 60% enrolment rate to less than
40% of 5-19 year olds in primary and secondary schools, the US jump to
a higher path and Japan continues to increase its education rate smoothly.
After the second world war, all countries seem to reach a ceiling between
80% and 90%.

5 The results of the augmented Benhabib and Spiegel speci...cation

Results are reported in table 1. A Fisher test on the regressions shows that
the ...xed e¤ects estimators perform better. The time dummies are included
in the regressions though not reported. The robustness of the speci...cation

<footnote n="12"><sup>12</sup>The data for the war periods are not available</footnote>
is also checked by adding the share of export in GDP and the initial GDP per capita to the initial speci...cation.

<table><caption>Table 1: Estimation of a Benhabib and Spiegel augmented speci...cation</caption><thead><tr><th></th><th>Speci...cation (7)</th><th>robustness<br>to Tr</th><th>robustness<br>to Lny<sub>t</sub></th></tr></thead><tbody><tr><td>I/Y</td><td>0.095<br>(2.56)</td><td>0.095<br>(2.56)</td><td>0.091<br>(2.39)</td></tr><tr><td>n</td><td>.375<br>(1.93)</td><td>.375<br>(1.92)</td><td>.366<br>(1.87)</td></tr><tr><td>H</td><td>0.070<br>(2.22)</td><td>0.069<br>(2.05)</td><td>0.079<br>(4.98)</td></tr><tr><td>Inter<br>(H<sub>t;i</sub> Tr<sub>t;i</sub>)</td><td>0.145<br>(2.73)</td><td>0.146<br>(2.00)</td><td>0.149<br>(2.76)</td></tr><tr><td>Catchupbs<br>(H<sub>t;i</sub> Y<sub>t;max</sub> Y<sub>t;i</sub>)</td><td>0.018<br>(1.38)</td><td>0.018<br>(1.30)</td><td>0.022<br>(1.29)</td></tr><tr><td>Complbs<br>(H<sub>t;i</sub> Tr<sub>t;i</sub> Y<sub>t;max</sub> Y<sub>t;i</sub>)</td><td>0.150<br>(4.11)</td><td>0.150<br>(3.72)</td><td>0.150<br>(4.12)</td></tr><tr><td>Lny<sub>t</sub></td><td></td><td></td><td>.0007<br>(.39)</td></tr><tr><td>Tr</td><td></td><td>.0003<br>(.006)</td><td></td></tr><tr><td>Tests</td><td></td><td></td><td></td></tr><tr><td>Obs</td><td>710</td><td>710</td><td>710</td></tr><tr><td>R<sup>2</sup></td><td>0.29</td><td>0.29</td><td>0.30</td></tr><tr><td>Fixed effects test (p-value)</td><td>.000</td><td>.000</td><td>.000</td></tr><tr><td>Hausman test (p-value)</td><td>.010</td><td>.040</td><td>.030</td></tr></tbody></table>

Dependant variable: ln Y<sub>t+1;i</sub> ln Y<sub>t;i</sub>. T-stat are in parentheses.
The Benhabib and Spiegel interactive term appears to be positive, but only weakly significant. By contrast, the interactive term amplified by the level of openness is positive and strongly significant. Education is negative and significant, suggesting, as found by Benhabib and Spiegel, that catch-up is certainly a more important channel through which human capital affects growth than the endogenous country-specific technological progress. The size of the coefficient even indicates that once the convergence effect taken into account (fg in equation 7), H remains negatively correlated to growth suggesting that education is a cost for society. The pure interactive variable — share of export in GDP times education rate — is significant and negative, which indicates that trade interacts with education but mainly in the catch-up process. A Student test provides some evidence of equality (in absolute value) between the coefficient of Inter and Complbs implying, if we go back to the initial specification, that the only channel through which the interactive variable affects growth is technological catch-up<fnref n="13" />.

The results are robust to the inclusion of new variables. Adding the share of exports in GDP and the initial GDP per capita does not change the significance or the magnitude of the coefficients. It suggests that Catchupbs and Complbs are not driven by a traditional convergence effect.

Finally, from the regression presented above, the Benhabib and Spiegel term seems to have little influence on growth, and the catch-up effect appears to be better captured when weighted by trade and education. In other words, improving only the level of human capital as argued by Benhabib and Spiegel[7] is not enough to experience a catch-up effect. In order to catch up faster a country should simultaneously develop both its education and its trade.

There is also weak evidence that the interaction between trade and education affects growth directly. While a complementary effect between education and trade could justify an increase in the speed of convergence, it is not a relevant variable in explaining permanent differences in growth rates. However, the Benhabib and Spiegel[7] specification may not be the most appropriate way to test the effect of openness on human capital reallocation between sectors. As underlined by Berthélémy, Dessus and Varoudakis[8], such a re-allocative effect and its consequences on human capital productivity should be better captured by a variable coefficients model which would allow the

<footnote n="13">¹³ If eᵢ and fᵢ are as in equation (7), then e = 0.</footnote>
structural coefficient on education to vary according to other factors<fnref n="14" />.

# 6 A structural change test

The next issue the paper analyses is whether the interaction between trade and education always affects the convergence in the same way, or if it varies according to the stage of development attained by the countries. The idea behind this is that the complementary effect could hinge on the level of income already accumulated by the country. Benhabib and Spiegel[7] have shown that the efficiency of technology adoption may change with the relative position of the country on the GDP per capita scale. By separating their sample into three equal sub-samples on the basis of initial per capita income, they ...and that the catch-up effect is mainly relevant for the poorest countries whereas the innovation term is positive and significant for the richest ones. This paper proposes to test this conjecture in a more systematic way by reviewing every sub-sample that can be generated from the initial sample instead of assuming a priori the critical level of GDP per capita.

## 6.1 The test

In order to test whether $H_{t;i} \alpha Tr_{t;i} \alpha \frac{y_{t;max}}{y_{t;i}}$ always affects growth by the same amount whatever the level of GDP per capita, the test should allow the coefficient of $H_{t;i} \alpha Tr_{t;i} \alpha \frac{y_{t;max}}{y_{t;i}}$ to depend on GDP per capita. The Chow test is not appropriate since it studies the variation in coefficient according to time and not to the level of another variable. The Durlauf and Johnson[14] test and its extensions<fnref n="15" /> are only applicable to cross-sections. Therefore, they are not suitable for the purpose of this paper. The test presented below is an attempt to reconcile both bunches of methods by taking into account the panel aspect of the dataset as well as the cross-sectional one.

Recalling the initial specification:

<footnote n="14">¹⁴Testing a Mankiw, Romer and Weil[27] specification over a panel of 83 countries on 1960-1990, Berthélémy, Dessus and Varoudakis[8] control the impact of trade openness on human capital productivity. However a similar regression performed on the Banks[4] and Maddison[26] database does not provide conclusive results.</footnote>

<footnote n="15">¹⁵Berthelemy and Varoudakis[10]</footnote>
$$
\begin{equation}
\begin{aligned}
\c{c} \ln Y_{t,i} = & c + \c{c} \ln K_{t,i} + \bar{\c{c}} \ln L_{t,i} + b_1 H_{t,i} + \bar{b}_2 H_{t,i} \quad \begin{array}{@{}c@{}} \c{a} \\ \c{a} \end{array} \mathrm{Tr}_{t,i} \\
& + b_3 H_{t,i} \quad \begin{array}{@{}c@{}} \c{a} \\ \c{a} \end{array} \frac{y_{t;\max}}{y_{t,i}} + b_4 H_{t,i} \quad \begin{array}{@{}c@{}} \c{a} \\ \c{a} \end{array} \mathrm{Tr}_{t,i} \quad \begin{array}{@{}c@{}} \c{a} \\ \c{a} \end{array} \frac{y_{t;\max}}{y_{t,i}} + u_{i,t}
\end{aligned}
\tag{7}
\end{equation}
$$

$b_4$ is assumed to be no longer a constant, but to depend on the level of
$y_{t,i}$ (GDP per capita) so that:

$$
b_4 = b_4^0 \quad 8 \quad y_{t,i} - y \blacksquare
$$

$$
b_4 = b_4^{00} \quad 8 \quad y_{t,i} > y \blacksquare
$$

Thus above and below a certain level of income, the coeçient of the
interactive variable weighted by trade is di√erent. To test the change in the
coefficient two truncated variables are derived from H$_{t;i}$ ¤ Tr$_{t;i}$ ¤ y$_{t;}$max y$_{t;i}$ , the
variable which is assumed to be the one affected by the level of development:

$$
\text{Complbs}_{\text{inf } t,i} = H_{t;i} \blacksquare \mathrm{Tr}_{t;i} \blacksquare \frac{\tilde{A}}{y_{t;i}} \text{ !} \quad 8 \quad y_{t;i} - y \blacksquare; \ 0 \ \text{otherwise}
$$

$$
\text{Complbs}_{\text{sup } t,i} = H_{t;i} \blacksquare \mathrm{Tr}_{t;i} \blacksquare \frac{y_{t;\max}}{y_{t;i}} \quad 8 \quad y_{t;i} > y \blacksquare; \ 0 \ \text{otherwise}
$$

A Student T-test is then performed to determine whether one of the
truncated variables presented above significantly affects growth even though
the initial variable $H_{t;i} \blacksquare \mathrm{Tr}_{t;i} \blacksquare \frac{y_{t;\max}}{y_{t;i}}$ is included in the regression, in which
case the existence of a threshold is inferred. Formally, the test is the following:

$$
\begin{equation}
\begin{split}
\c{c} \ln Y_{t,i} = & c + \c{c} \ln K_{t,i} + \bar{\c{c}} \ln L_{t,i} + b_1 H_{t,i} + b_2 H_{t,i} \blacksquare \mathrm{Tr}_{t,i} + b_3 H_{t,i} \blacksquare \frac{\tilde{A}}{y_{t,i}} \quad \begin{array}{@{}c@{}} \blacksquare \\ \blacksquare \end{array} \\
& + b_4 H_{t,i} \blacksquare \mathrm{Tr}_{t,i} \blacksquare \frac{y_{t;\max}}{y_{t,i}} + (b_4 \blacksquare b_4) \mathrm{Complbs}_{\text{inf } t,i} + u_{t,i}
\end{split}
\tag{8}
\end{equation}
$$

$$
H_0: b_4^0 = b_4^{00} = b_4 = \blacksquare \quad b_4^0 \blacksquare b_4 = 0
$$

If $b_4^0 \blacksquare b_4$ is significant, then $H_0$ is rejected and the two coefficients are significant different. Otherwise, $H_0$ is not rejected and $y$ does not generate a threshold effect in $H_{t;i} \blacksquare \mathrm{Tr}_{t;i} \blacksquare \frac{y_{t;\max}}{y_{t;i}}$.
The next step of the test is to endogenise the threshold. Since, I do not wish to impose a certain level of GDP per capita as a threshold, I choose to estimate each possible threshold in the database by performing the regressions for every available value of y. Each value of y used as a potential threshold (y*) provides a certain t-statistic associated with the coefficient of Complbs<sub>inf</sub>;i that I then plot. In what follows, the existence of a cuto* point in the growth path will be inferred whenever the graph shows a t-statistic signi...cant at the 5% level.

## 6.2 Evidence of thresholds

When H<sub>t;i</sub> Tr<sub>t;i</sub> (yt;max/y<sub>t;i</sub>) depends on the level of GDP per capita, the distribution of T<sub>t</sub> stat has the shape presented in ...gure 4. This graph suggests there should be a threshold in the database at Iny = 7.97. From the graphs, such a level of log GDP per capita was reached by Canada and the European countries around the ...rst World War and Japan after the second World War. The US is the only country which has always been above the threshold.

I then estimate the coefficients which result from a model with the threshold at 7.97 and report them in table 2. In this specification, countries with log of GDP per capita lower than 7.97 are represented by Complbs<sub>inf</sub> and the others by Complbs<sub>sup</sub>.

The new specification restores the significance of the Benhabib and Spiegel catch-up term. One can explain this result by a better specification. However, even if significance, the Benhabib and Spiegel catch-up term is weak whereas the catch-up term amplified by trade and education is stronger. Such a result implies that education enhances the speed of adoption of technology from abroad, but this effect is much bigger when education and trade interact.

Another significant outcome from this regression is that the interactive variable has a stronger impact for a country lying above the threshold point of GDP per capita = 7.97. This result suggests that at a relatively low level of income countries experience a relatively "weak" catch-up effect while at a higher one this effect becomes stronger. Consequently, and contrary to Benhabib and Spiegel[7], the catch-up effect does not decrease when income increases. It works more like a learning by doing process: the more the country develops, the more it is able to take advantages of the new technologies it absorbs from outside. Symmetrically, opening up and simultaneously de-
veloping the level of education allows economies to experience higher growth rates.

<table><caption>Table 2: Model with threshold</caption><thead><tr><th></th><th>Dep. Var.: ln Y<sub>t+1;i</sub> i ln Y<sub>t;i</sub></th></tr></thead><tbody><tr><td>I=Y</td><td>.079<br>(2.14)</td></tr><tr><td>n</td><td>.358<br>(1.86)</td></tr><tr><td>H</td><td>-.060<br>(-4.93)</td></tr><tr><td>H<sub>t;i</sub> Tr<sub>t;i</sub></td><td>0.205<br>(-3.70)</td></tr><tr><td>H<sub>t;i</sub> <sup>3</sup>&frasl;<sub>3 y<sub>t;i</sub></sub></td><td>0.026<br>(2.02)</td></tr><tr><td>Complbs<sub>inf</sub></td><td>0.135<br>(3.72)</td></tr><tr><td>Complbs<sub>sup</sub></td><td>0.179<br>(4.84)</td></tr><tr><td>tests</td><td></td></tr><tr><td>Obs</td><td>710</td></tr><tr><td>R<sup>2</sup></td><td>0.31</td></tr><tr><td>Fixed effects test (p-value)</td><td>.000</td></tr><tr><td>Hausman test (p-value)</td><td>.000</td></tr></tbody></table>
# 7 Conclusion

This paper uses panel data to empirically evaluate whether education and trade affect growth when interacting together. The regressions provide robust evidence that such a complementary effect has accelerated technological catch-up between OECD countries all through the twentieth century.

Going back to the initial purpose of this article, this result also means that education can affect growth positively. While education, taken as a production factor, appears unrelated to growth, it becomes important when interacting with trade. Consequently, this paper underlines the importance for a country of coordinating economic policies concerning trade and education.

However, as shown in the paper, simultaneously promoting investment in human capital as well as in education does not affect growth constantly with equal intensity. Since the interactive effect is mainly relevant in explaining catch-up, such a policy should essentially benefit lagging countries. And, moreover, since the catch-up effect itself also exhibits nonlinearity as it increases with GDP per capita, the more countries develop, the easier it should get for them to catch-up.
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<figure><img src="image_2.png" /><figcaption>Figure 2: Corrected share of exports in GDP: France, Japan, UK, US</figcaption></figure>

<figure><img src="image_3.png" /></figure>
<figure><img src="image_4.png" /><figcaption>Figure 4: T-test, increasing values of y</figcaption></figure>

<figure><img src="image_5.png" /></figure>