A. External efficiency of education and FDI: a formalization

A model of a small open developing economy producing a composite good at each period, t is proposed. Constant returns to scale production technology is assumed and this could be captured by a Cobb-Douglas production function as follows:

L_t is the stock of labor, K_t is the stock of capital, 0 < α < 1 is the Cobb-Douglas parameter and A(q_t)= A₀q_t is the total factor productivity (TFP). The latter depends positively on the external efficiency of the education system denoted by q_t and a scale parameter = A₀ with 0 < q_t < 1. It is assumed that education enhances labor productivity (Schultz, 1961, Denison, 1962 and Lucas, 1998). In addition, there is a hypothetical perfect productivity level given by A₀ and deviations from this maximum productivity level is caused by some inefficiencies in the education system. A higher value of q_t implies a higher level of the efficiency with which education is translated into income in the labor market. The first order conditions with respect to production factors K_t and L_t lead to the rate of return (r_t) and the salary level (w_t ) respectively:

with k_t denoting the capital to labor ratio K_t/L_t.

The economy is open and capital is mobile internationally. However, international capital flows are such that the domestic interest rate is equal to the international interest rate augmented by a country-risk premium: $r_t=r_t^{*}+{\pi }_t\mathrm{.}{\pi }_t$. is related to internal factors such as, political instability, corruption, individual freedom, degree of trade liberalization, quality of governance, and so on. Equation 2 gives the capital-to-labor ratio equation:

Using equations (3) and (4) yields:

with the derivatives k_q > 0 and w_q > 0.²

The stock of capital in the economy at the equilibrium is given by:

The stock of capital could be shared between the domestic component $\overline{K_t}$ and the foreign component $K_t^{*}$ so that $K_t=\overline{K_t}+K_t^{*}$ with $K_t^{*}=K_{t-1}^{*}+FD{I}_t$ and $\overline{K_t}=\overline{K_{t-1}}+\overline{I_t}$, where $\overline{I_t}$ is the domestic investment. We have $K_t=\overline{K_{t-1}}+I_t+K_{t-1}^{*}+FD{I}_t$. Let’s denote this by λ_t, the proportion of the FDI in the stock of capital, so that $\frac{K_t}{FD{I}_t}=\frac{1}{{\lambda }_t}$.

The relationship between K_t and FDI_t is given by FDI_t = λ_tK_t leading to the following equation:

FDI_t is the net inflows of foreign direct investment at time t.

Equation (7) describes the relationship between the external efficiency of the education system and FDI. The first implication is that both, stock of the labor force and efficiency level of the education system have a positive impact on FDI. Perfect efficiency means that the workers are perfectly efficient in translating their education level into income in the economy. They could generate the highest level of production compared to their level of education with no possibility of doing better with the same level of education. This relationship is intuitive because a higher efficiency level is associated with higher productivity of the labor force and this could in turn attract foreign investors looking for countries with productive labor force. Second, the foreign interest rate, as well as factors related to country-risk has a negative impact on the FDI. An increase in the international interest rates may undermine the investment made by foreign investors. The model shows that the intensity of the capital in the production process captured by (1 — α) has a positive relationship with FDI inflows. The latter result means that countries with a higher demand for capital in the production process would better attract FDI, all things being equal.

B. Econometric strategy

From the formalization above, consider a set of M variables x_m with m = 1,…M; We could give the following functional form to the interest rate: $r_t=r_t^{*}+{\pi }_t=\exp ({\mathrm{\Sigma }}_m{\beta }_m{x}_m+u)$. β is a set of parameters, x is a matrix containing proxy variables for the country-risk and the international interest rate and u is a random variable capturing stochastic shocks on the interest rate. The idea underlying this functional form is that the cost associated to risks -the interest rate- is increasing more rapidly with respect to risk factors.³ Log-linearizing Equation 7 yields equation 8:

By assuming $fd{i}_{it}=Log\left(\frac{FD{I}_{it}}{L_{it}}\right),{\theta }_0=\frac{1}{\alpha }Log\left[(1-\alpha )A_0\right],{\theta }_1=\frac{1}{\alpha }$ and ${\theta }_{2m}=-\frac{1}{\alpha }{\beta }_m,v_{it}=-\frac{1}{\alpha }{u}_{it}+Log\left({\lambda }_{it}\right)$, the following econometric model can be derived and be estimated:

with q_it a proxy for the external efficiency of the education system for the country i at time t.

C. External efficiency of the education system

It is assumed that there is a maximum level of income that a given skilled worker could expect given the number of years of schooling and the economic environment. The gap between the actual income and this optimal income approximates the efficiency with which education is translated into income in the labor market. The smaller this gap is, the more efficient is the hypothetical worker. In fact, perfect external efficiency implies that the skills acquired in the education system perfectly fit the demand for skilled workers. When this condition is met, the combination of years of schooling and income earned on the labor market is optimal and efficient.

The main assumption in the estimation of the external efficiency of the education system is related to the existence of a frontier representing the maximum income that the population of a given country could reach with the attained level of education. In other terms, we would like to build a frontier of best practices in terms of translating the years of schooling into income. Countries lying on the frontier are technically efficient while those below the frontier are considered technically inefficient. The distance to this frontier is used as proxy for the external efficiency of the education system.

In the literature on frontier analysis, two main approaches are commonly used in order to build production frontiers and estimate technical efficiency: non-parametric and parametric approaches. The non-parametric approaches do not allow the distinction between the efficiency measure and the ‘noises’, while some parametric models allow proper estimation of the technical efficiency. Stochastic Frontier Analysis (SFA) is among the most commonly used parametric approaches. It allows the estimation of efficiency terms, controlling not only for ‘noises’ but also for defined environmental factors that can influence the efficiency measure.

This study applied a Stochastic Frontier model in order to estimate a proxy for the external efficiency of the education system. It is assumed that the input (measured by the mean years of schooling) is used to generate the output (measured by the labor remuneration). Let us define the output variable by LABINC_it, that is, the labor remuneration in the country i at time t proxied by the GNI per unit of employment, and η as a set of parameters. Following Battese and Coelli (1995), and by assuming a Cobb Douglas function for the frontier, the SFA model that will be estimated is the following: ⁴

where MYS_it is the mean years of schooling in the country i at time t. ω is the technical inefficiency term that has a normal truncated distribution and μ is the error terms that are normally distributed. The Battese and Coelli (1995) model allows the inefficiency terms to vary over time. Another specificity of this model is that ω_it could be considered random time varying individual effects. Unobserved heterogeneity between countries is controlled for.

It is important to isolate the technical inefficiency terms from other variables that could be associated with them. Otherwise, the value of the efficiency measure could be imperfect. So, in the efficiency measurement, other economic variables that could affect the efficiency are controlled for. Two main explanatory factors are considered: factor associated with the labor market (the employment rate) and control variables for regions. The inefficiency model is given by Equation 11 as follows:

where the distribution of v_it is normal truncated. Z_it is a matrix of explanatory variables that could explain the inefficiency terms. After controlling for the inefficiency explanatory factors, the technical efficiency (the proxy for the external efficiency of the education system) is given by:

A. Estimate of external efficiency

Table 2 presents the results of the estimation of the external efficiency of the education system.⁶ Three different models are estimated for a robustness check purpose. Model 3 controls for the education and the labor market variables while Model 2 controls only for the labor market variables. Model 1 does not control for any of the two sets of variables. In all these three specifications, results show a positive relationship between the years of schooling and labor income. Countries with a higher primary school starting age and a larger proportion of adults involved in the labor market appear to have a higher inefficiency level.⁷ Countries with a higher share of vocational pupils in secondary education, as well as a higher enrollment rate in tertiary education appear to have a lower inefficiency level. Secondary vocational education and tertiary education could play a role in improving the external efficiency of the education system in the target countries. In the literature, both secondary vocational education and tertiary education are pointed out to be among the most important drivers for the external efficiency of education. For instance, McMahon and Boediono (1992) showed that imperfection in the financing of post primary education could explain the external inefficiency of the education system. Almeida, Behrman and Robalino (2012) highlighted that promoting secondary vocational training is one of the ways countries could provide the right skills for their labor market.

Table 2.

Stochastic Frontier Model: External Efficiency of the Education System

Note: *significant at 10 percent; ** significant at 5 percent; *** significant at 1 percent.

Table 2.

Stochastic Frontier Model: External Efficiency of the Education System

Dependent Variable: Labor income		Model 1	Model 2	Model 3
Frontier model
	Intercept	9.866***	10.116***	10.785***
		(0.098)	(0.185)	(0.240)
	Mean years of schooling	1.272***	1.145***	0.804***
		(0.050)	(0.088)	(0.108)
Inefficiency model
	Employment to population ratio (15 +)		0.064***	0.024**
			(0.011)	(0.010)
	Primary school starting age			0.468***
	Secondary education vocational pupils (in percent of total pupils)			−0.041***
				(0.007)
	Gross tertiary enrolment rate			−0.040***
				(0.006)
Intercept		0.830**	−2.245***	−1.720
		(0.385)	(0.242)	(1.130)
Regions dummies		Yes	Yes	Yes
Observations		618	615	352
Countries		79	79	55

Note: *significant at 10 percent; ** significant at 5 percent; *** significant at 1 percent.

View Table

Table 2.

Stochastic Frontier Model: External Efficiency of the Education System

Dependent Variable: Labor income		Model 1	Model 2	Model 3
Frontier model
	Intercept	9.866***	10.116***	10.785***
		(0.098)	(0.185)	(0.240)
	Mean years of schooling	1.272***	1.145***	0.804***
		(0.050)	(0.088)	(0.108)
Inefficiency model
	Employment to population ratio (15 +)		0.064***	0.024**
			(0.011)	(0.010)
	Primary school starting age			0.468***
	Secondary education vocational pupils (in percent of total pupils)			−0.041***
				(0.007)
	Gross tertiary enrolment rate			−0.040***
				(0.006)
Intercept		0.830**	−2.245***	−1.720
		(0.385)	(0.242)	(1.130)
Regions dummies		Yes	Yes	Yes
Observations		618	615	352
Countries		79	79	55

Note: *significant at 10 percent; ** significant at 5 percent; *** significant at 1 percent.

The average technical efficiency is estimated to be about 44 percent.⁸ This means that countries could use, on average, 66 percent fewer inputs to achieve the same level of labor remuneration if the education system in all countries was perfectly efficient. Alternatively, with the actual education resources used, countries could achieve higher levels of income. These results show that the inefficiency level seems to be relatively high. Table 3 shows that the efficiency level varies across regions. While Latin America and the Caribbean, as well as Middle East and North Africa appear to register the highest average efficiency levels, Sub-Saharan Africa and South Asia have the lowest average efficiency.⁹

Table 3.

External Efficiency by Region

(in percent)

Table 3.

External Efficiency by Region

(in percent)

	Average	Minimum	Maximum
South Asia	18.0	24.0	34.0
Sub-Saharan Africa	2.0	36.0	80.0
East Asia and Pacific	8.0	37.0	79.0
Europe and Central Asia	1.0	38.0	91.0
Middle East and North Africa	20.0	48.0	95.0
Latin America	18.0	61.0	94.0

View Table

Table 3.

External Efficiency by Region

(in percent)

	Average	Minimum	Maximum
South Asia	18.0	24.0	34.0
Sub-Saharan Africa	2.0	36.0	80.0
East Asia and Pacific	8.0	37.0	79.0
Europe and Central Asia	1.0	38.0	91.0
Middle East and North Africa	20.0	48.0	95.0
Latin America	18.0	61.0	94.0

B. Impact of external efficiency on FDI

Equation 9 is estimated using the data described above and including a set of control variables as indicated by the matrix x. According to Assuncao et al. (2011), there are three main factors that could affect FDI flows in a given country: factors related to the localization, factors related to institutions and factors related to openness. We controlled for these factors by including appropriate variables in the matrix x. Econometric results are shown in Table 4. Equation 9 is first estimated by applying a pooled OLS model (Model 1) and a fixed effects model (Model 2). The pooled OLS estimations showed a positive relationship between the external efficiency of the education system and the FDI net inflows per unit of employment. To account for the panel structure of the data and control for individual heterogeneity, a fixed effects estimation is performed on the Equation 9. The fixed effects model suggested a positive relationship between the education efficiency and the FDI inflows¹⁰.

Table 4.

External Efficiency and FDI: Econometric Results

*significant at 10 percent; ** significant at 5 percent; *** significant at 1 percent

Table 4.

External Efficiency and FDI: Econometric Results

Dependent Variable: FDI inflows		Model 1	Model 2	Model 3	Model 4	Model 5
		Pooled OLS	Fixed Effects	GMM	GMM	GMM
Key variables
	Log FDI per worker (t-1)			0.585***	0.633***	0.537)***
				(0.090)	(0.111)	(0.151)
	External efficiency of education	0.317***	1.497**	0.393**
		(0.074)	(0.682)	(0.152)
	External efficiency of education × Mean years of schooling					0.420**
						(0.207)
	Mean years of schooling				−0.338
					(0.426)
Infrastructure
	Telephone lines	0.057***	0.070***	0.018**	0.025	0.014
		(0.005)	(0.025)	(0.008)	(0.016)	(0.011)
Institutions
	Regulation quality	1.327***	1.259	0.480 **	0.557**	0.393*
		(0.133)	(0.759)	(0.197)	(0.223)	(0.216)
	Voice and accountability	−0.518***	−0.418		−0.081	−0.167
		(0.104)	(0.509)		(0.144)	(0.149)
Openness and international interest rate
	Exports (percent of GDP)	0.013***	0.01	0.015*	0.021**	0.019**
		(0.004)	(0.009)	(0.008)	(0.008)	(0.009)
	Official interest on new external debt commitments	0.128***	0.03	−0.001	0.031	0.039
		(0.033)	(0.036)	(0.027)	(0.029)	(0.030)
	Private interest on new external debt commitments	−0.058***	−0.024	0.001	−0.037	−0.098**
		(0.020)	(0.023)	(0.019)	(0.051)	(0.047)
Other control variables
	Inflation (GDP deflator)	0.035)***	0.022*	0.029*	0.018	0.012
		(0.008)	(0.012)	(0.016)	(0.013)	(0.017)
	GDP growth	0.008	0.022	0.048**	0.066***	0.054**
		(0.017)	(0.019)	(0.021)	(0.024)	(0.023)
Intercept		3.426***	4.967***	1.189**	0.964	0.907
		(0.227)	(1.067)	(0.555)	(0.971)	(0.748)
Time dummies		Yes	Yes	Yes	Yes	Yes
F-stat		p=0.000	p=0.000	p=0.000	p=0.000	p=0.000
R2		0.611	…	…	…	…
Observations		368	368	368	368	368
Sargan test of overidentication restrictions		…	…	p=0.630	p=0.389	p=0.602
Arellano-Bond test for AR(1)		…	…	p=0.001	p=0.001	p=0.001
Arellano-Bond AR(2)		…	…	p=0.162	p=0.160	p=0.147
Countries		59	59	59	59	59

*significant at 10 percent; ** significant at 5 percent; *** significant at 1 percent

View Table

Table 4.

External Efficiency and FDI: Econometric Results

Dependent Variable: FDI inflows		Model 1	Model 2	Model 3	Model 4	Model 5
		Pooled OLS	Fixed Effects	GMM	GMM	GMM
Key variables
	Log FDI per worker (t-1)			0.585***	0.633***	0.537)***
				(0.090)	(0.111)	(0.151)
	External efficiency of education	0.317***	1.497**	0.393**
		(0.074)	(0.682)	(0.152)
	External efficiency of education × Mean years of schooling					0.420**
						(0.207)
	Mean years of schooling				−0.338
					(0.426)
Infrastructure
	Telephone lines	0.057***	0.070***	0.018**	0.025	0.014
		(0.005)	(0.025)	(0.008)	(0.016)	(0.011)
Institutions
	Regulation quality	1.327***	1.259	0.480 **	0.557**	0.393*
		(0.133)	(0.759)	(0.197)	(0.223)	(0.216)
	Voice and accountability	−0.518***	−0.418		−0.081	−0.167
		(0.104)	(0.509)		(0.144)	(0.149)
Openness and international interest rate
	Exports (percent of GDP)	0.013***	0.01	0.015*	0.021**	0.019**
		(0.004)	(0.009)	(0.008)	(0.008)	(0.009)
	Official interest on new external debt commitments	0.128***	0.03	−0.001	0.031	0.039
		(0.033)	(0.036)	(0.027)	(0.029)	(0.030)
	Private interest on new external debt commitments	−0.058***	−0.024	0.001	−0.037	−0.098**
		(0.020)	(0.023)	(0.019)	(0.051)	(0.047)
Other control variables
	Inflation (GDP deflator)	0.035)***	0.022*	0.029*	0.018	0.012
		(0.008)	(0.012)	(0.016)	(0.013)	(0.017)
	GDP growth	0.008	0.022	0.048**	0.066***	0.054**
		(0.017)	(0.019)	(0.021)	(0.024)	(0.023)
Intercept		3.426***	4.967***	1.189**	0.964	0.907
		(0.227)	(1.067)	(0.555)	(0.971)	(0.748)
Time dummies		Yes	Yes	Yes	Yes	Yes
F-stat		p=0.000	p=0.000	p=0.000	p=0.000	p=0.000
R2		0.611	…	…	…	…
Observations		368	368	368	368	368
Sargan test of overidentication restrictions		…	…	p=0.630	p=0.389	p=0.602
Arellano-Bond test for AR(1)		…	…	p=0.001	p=0.001	p=0.001
Arellano-Bond AR(2)		…	…	p=0.162	p=0.160	p=0.147
Countries		59	59	59	59	59

*significant at 10 percent; ** significant at 5 percent; *** significant at 1 percent

In the literature on the determinant of FDI, some studies suggested that past FDI flows could affect present FDI flows (Egger, 2001; Carstensen and Toubal, 2004; Naude and Krugell, 2007). For this reason, dynamic equations were sometimes estimated to investigate the determinants of FDI. Authors of literature found that FDI flows in a given country could have an impact on a country’s educational achievements (Blomstrom and Kokko, 2003; Zhuang, 2008; Mughal and Vechiu, 2010). This may induce a reverse causality between the external efficiency of education and the FDI inflows raising an endogeneity issue. To properly control for this endogeneity problem and include FDI lags in the matrix x, we implemented the dynamic panel GMM estimation technique introduced by Arellano and Bond (1991) and Arellano and Bover (1995). This method controls for endogeneity by using lags of the endogenous variables as instruments in the econometric equation and controls for autocorrelation issues that could appear after introducing lags of the dependent variable as regressors. We assume that FDI inflows could affect economic growth and openness.¹¹ Thus, we control for the endogeneity associated with these two variables using the lags of these endogenous regressors as instruments.¹²

As shown in Table 4, results from Arellano and Bover (1995) dynamic panel GMM estimation showed that after controlling for the endogeneity of the external efficiency of the education system variable and including lag of the FDI on the right side of Equation 9, education efficiency remained a significant determinant for FDI flows. All these results are robust after controlling for any category of the FDI determinants, as described above; and the education efficiency remains a significant determinant of FDI net inflows.¹³ After controlling for localization, institutions and openness, results (for Model 3) suggested an increase of about 0.4 percent in the FDI net inflow per unit of employment after a 1 percent improvement in the efficiency level. Equivalently, one standard deviation increase in the efficiency level is associated with 24 percent increase in the FDI net inflow per unit of employment. These results suggest that improving the efficiency of the education system, by giving the appropriate abilities to workers according to the requirements of the economy, could be a way for improving the attractiveness of countries with regard to foreign investments. Other variables such as, economic growth, infrastructure, openness and the quality of the institutions appear to have statistically significant effects on the FDI.

Another regression is performed applying dynamic panel model to investigate the relationship between FDI and the years of schooling (Model 4). The results showed no significant effect of the years of schooling on the FDI net inflows. This finding supports the evidence that the number of years of schooling does not necessarily have an effect on FDI. However, the efficiency with which the education level is used in the labor market matters for attracting FDI. We investigate the joint effect of the mean years of schooling and the education efficiency variable and find that these two variables together have a significant effect on FDI inflows (Model 5). The joint effect of the years of schooling and the efficiency of the education system on the FDI is stronger compared to the effect of the external efficiency of the education system only. Improving both the years of schooling and the efficiency of the education system could play an important role in attracting FDI.

C. Extensions: sample heterogeneity

Table 5 shows that the effect of the external efficiency of the education system on FDI inflows varies across groups of countries depending on their geographical characteristic (e.g. landlocked), Human Development Index (HDI), income level, endowment in natural resources, external efficiency score, and FDI inflows.¹⁴ The results show that the external efficiency of the education system matters in non-landlocked countries, in non-resource rich countries, in countries with low development levels (HDI and income levels), and in countries with low efficiency score and low FDI inflows. The external efficiency of the education system does not necessarily attract FDI in landlocked countries but it could do so in non-landlocked countries. The external efficiency of the education system does not have any effect on FDI in the group of countries with high and very high human development levels. However, one standard deviation increase in the efficiency score is associated with 14 percent in the FDI per unit of employment in countries belonging to the group of low and medium human development levels. In a similar vein, the external efficiency of the education system has an effect on FDI inflows in countries with low GDP per capita. There is a significant relationship between FDI and the external efficiency of education in non-resource rich countries while this relationship is not statistically significant in resource rich countries. One standard deviation increase in the efficiency score is associated with 24 percent increase in the FDI inflows in non-resource rich countries. In fact, some studies show that resource rich countries have a higher potential to attract FDI (Cleeve, et al 2015 and Van der Ploeg and Poelhekke, 2016) compared to non-resource rich countries. The current results support the evidence that non-resource rich countries can fill the gap in terms of FDI attractiveness by improving the external efficiency of their education systems. Efficiency and FDI inflows levels also count. FDI attractiveness is stronger when efficiency and FDI inflows are low.

Table 5.

External Efficiency and FDI

(additional results) Dependent variable: FDI inflows

Note: Countries are considered resource rich when the total resource rents as a percentage of the GDP is above the median and non-resource rich when the total resource rents as a percentage of the GDP is below the median. Countries are also grouped according to the 2010 Human Development Report which classifies countries into four categories (low, medium, high and very high human development levels) based on the Human Development Index. All controls variables (infrastructure institutions, openness, interest rate) are included. Standard deviation in parenthesis. *significant at 10 percent; ** significant at 5 percent; *** significant at 1 percent.

Table 5.

External Efficiency and FDI

(additional results) Dependent variable: FDI inflows

Model 4 (GMM)
Characteristics		External efficiency of education		Observations
Landlocked	Yes	0.187	(0.108)	67
	No	0.431*	(0.218)	301
Resource rich	Yes	0.221	(0.157)	178
	No	0.389**	(0.142)	190
Human Development Index	Low	0.225*	(0.113)	192
	High	0.084	(0.249)	176
GDP per capita	Below median	0.329**	(0.123)	203
	Above median	0.200	(0.244)	165
Efficiency score	Below median	0.527***	(0.123)	207
	Above median	0.070	(0.497)	161
FDI inflows	Below median	0.269*	(0.134)	172
	Above median	−0.037	(0.165)	196

Note: Countries are considered resource rich when the total resource rents as a percentage of the GDP is above the median and non-resource rich when the total resource rents as a percentage of the GDP is below the median. Countries are also grouped according to the 2010 Human Development Report which classifies countries into four categories (low, medium, high and very high human development levels) based on the Human Development Index. All controls variables (infrastructure institutions, openness, interest rate) are included. Standard deviation in parenthesis. *significant at 10 percent; ** significant at 5 percent; *** significant at 1 percent.

View Table

Table 5.

External Efficiency and FDI

(additional results) Dependent variable: FDI inflows

Model 4 (GMM)
Characteristics		External efficiency of education		Observations
Landlocked	Yes	0.187	(0.108)	67
	No	0.431*	(0.218)	301
Resource rich	Yes	0.221	(0.157)	178
	No	0.389**	(0.142)	190
Human Development Index	Low	0.225*	(0.113)	192
	High	0.084	(0.249)	176
GDP per capita	Below median	0.329**	(0.123)	203
	Above median	0.200	(0.244)	165
Efficiency score	Below median	0.527***	(0.123)	207
	Above median	0.070	(0.497)	161
FDI inflows	Below median	0.269*	(0.134)	172
	Above median	−0.037	(0.165)	196

Note: Countries are considered resource rich when the total resource rents as a percentage of the GDP is above the median and non-resource rich when the total resource rents as a percentage of the GDP is below the median. Countries are also grouped according to the 2010 Human Development Report which classifies countries into four categories (low, medium, high and very high human development levels) based on the Human Development Index. All controls variables (infrastructure institutions, openness, interest rate) are included. Standard deviation in parenthesis. *significant at 10 percent; ** significant at 5 percent; *** significant at 1 percent.