Institutions, Foreign Direct Investment and Growth: A Hierarchical Bayesian Approach

Summary

We investigate empirically the existence of a heterogeneous relationship between foreign direct investment (FDI) and economic growth across developing countries. We argue that, across countries, differences in institutional quality are correlated with heterogeneous absorptive capacities and hence a heterogeneous FDI–growth relationship. Our empirical results show substantial heterogeneity in the FDI–growth relationship. We find that controlling for certain measures of institutional quality reduces the degree of heterogeneity. These findings question the orthodox assumption of a homogeneous return to FDI in the existing empirical literature and highlight the importance of specific aspects of institutional quality in the FDI–growth relationship.

Bayesian analysis, Economic growth, Foreign direct investment, Hierarchical model, Institutional quality, Parameter heterogeneity

1 Introduction

Heuristically, foreign direct investment (FDI) is the long-term investment by entities from one country in entities located in another country: the ‘host’ country. The literature documents that FDI is the main vehicle for transferring private capital, which results in capital flows and external productivity effects—economic outcomes in the host country that do not arise directly from the transactions between the foreign investor and host entity. In theory, these external productivity effects can contribute positively to economic growth through, for example, knowledge transfers from research and development and training for employees in host countries. This renders FDI particularly important to the developing host countries that are facing difficulties in achieving long-term economic growth by capitalizing on their ability to produce specific goods and services efficiently, in competition with other countries. In the existing empirical literature, however, there is no consensus on the effect of FDI on economic growth in developing host countries.

Some macroeconomic studies proffer the view that the abilities of host countries to take advantage of any positive external productivity effects from FDI to foster economic growth (absorptive capacities) depend on certain host country factors, including well-developed financial markets (see, for example, Alfaro et al. (2004)), a certain threshold of human capital (see, for example, Borensztein et al. (1998)) and trade policies that favour the development of manufacturing industries for export (see, for example, Balasubramayan et al. (1996)). Some international organizations have conducted broader studies that bolster this view and these foregoing empirical findings. The World Bank (2001), page 62, suggested that absorptive capacities of host countries depend on their levels of inflation, trade openness, human capital and infrastructure. Similarly, the Organisation for Economic Co-operation and Development (OECD) (2002), page 10, concluded that absorptive capacities of developing countries depend on their levels of infrastructural, educational, technological and financial development. Carkovic and Levine (2005), however, found no evidence that the additional increase in economic growth resulting from a 1-unit increase in FDI inflows (the marginal return to FDI) depends on educational attainment, economic development, financial development or trade openness. Furthermore, the microeconomic studies fail to resolve these conflicting findings as some studies imply no effect of FDI on growth (see, for example, Haddad and Harrison (1993) and Aitken and Harrison (1999)), whereas others find a positive effect of FDI on growth (see, for example, Blomström (1986)).

The present paper offers, and examines empirically, a plausible explanation for this lack of consensus in the empirical macroeconomics literature. We support the view that absorptive capacities play an important role in the FDI–growth nexus. Our point of departure is that differences in institutional quality—as measured by government interventions, public good provision, public sector efficiency and legal and enforcement mechanisms—are associated with differences in absorptive capacities, and hence a heterogeneous FDI–growth relationship. Thus, this paper incorporates the widely accepted view that low institutional quality is associated with economic distortions—various factors that obstruct the free flow of resources towards optimal output combinations—which affect the economic performance of a country (see, for example, North (1981), Shleifer and Vishny (1993), Mauro (1995), Hall and Jones (1999), La Porta et al. (1999) and Acemoglu et al. (2001, 2002, 2003, 2005)). These economic distortions may be associated with heterogeneity in, for example, the levels of infrastructural, educational and technological development, and the allocation of human capital across the productive sectors that innovate and promote growth and rent seeking sectors that permit the earning of income through the exploitation of barriers in the economy rather than through the participation in transactions that add value; thus, heterogeneity in these elements can give rise to heterogeneity in absorptive capacities across countries. In essence, our maintained hypothesis is that the quality of institution may be associated with a country’s ability to capitalize on any external productivity effects that may be generated from the presence of a foreign firm. To the best of our knowledge, the use of institutional quality to reconcile conflicting empirical evidence on the FDI–growth nexus has not been explored by the existing macroeconomics literature.

Numerous measures of institutions show the disparities in institutional quality across developing host countries, and examples of interactions between these different measures and the different components of absorptive capacities abound in theoretical and empirical works. Studies have shown that the level of corruption is negatively associated with government expenditure on education (see, for example, Mauro (1998), Gupta et al. (2002) and Tanzi et al. (2002)). Thus, highly corrupt host countries may have suboptimal levels of human capital attainment and consequently, in light of Borensztein et al. (1998), suboptimal levels of absorptive capacities.

In a country, institutional quality may also be correlated with human capital allocation between the productive and rent seeking sectors. Baumol (1990) and Murphy et al. (1991) argued that entrepreneurs allocate their talents between productive and rent seeking activities on the basis of the relative benefits to be generated from these activities. As such, any factor that reduces the private benefits that are associated with rent seeking activities may influence an individual’s choice of employer or professional career. For example, the supervision of foreign firms is usually characterized by more transparency and accountability than that of some domestic firms, hence providing workers of the latter with more latitude to accept or solicit bribes. Thus, host countries with low quality institutions, which usually have more rent seeking sectors with higher pay-offs relative to the productive sectors, may have fewer highly educated domestic labourers moving from foreign to domestic firms, and consequently a slower or zero rate of knowledge diffusion.

If heterogeneity in institutional quality is correlated with heterogeneity in absorptive capacities, then studies that do not allow the association between FDI and growth to depend on institutional quality might yield misleading results. Furthermore, if a heterogeneous relationship between FDI and economic growth exists across host countries then the orthodox assumption of a homogeneous marginal return to FDI is inappropriate for empirical works. The existence of an FDI–growth heterogeneous relationship implies that policy prescriptions that are directed at creating linkages between FDI and economic growth should not be homogeneous across countries. In essence, in the presence of a heterogeneous relationship between FDI and economic growth, the ‘average effect’ that is captured by a homogeneous coefficient in conventional modelling will not be robust to the different conditioning sets, sample sizes or functional forms that are evident across existing empirical studies. Indeed, this notion of relaxing the common assumption of parameter homogeneity in growth regressions is not new to the empirical growth literature (see, for example, Brock and Durlauf (2001), Durlauf (2001), Masanjala and Papageorgiou (2004), Minier (2007) and the references cited therein). The thrust in this strand of the empirical growth literature is that assuming homogeneous coefficients is tantamount to assuming that all countries produce goods and services by using identical technologies. Furthermore, Durlauf (2001) argued that coefficients in a growth equation should be functions of the ‘state of development’. Our modelling approach incorporates this view.

To investigate empirically the existence of a heterogeneous relationship between FDI and economic growth across developing host countries and the relationship between institutional quality and this heterogeneity, we use a panel data set on non-OECD countries. We allow for latent country-specific coefficients on FDI to account for the fact that other variables, which we do not explicitly model, may also be associated with this heterogeneity. To complete our econometric specification, we augment the model with plausible distributional assumptions to convert it to a Bayesian hierarchical model. We estimate the Bayesian model by using the Gibbs sampler. Our Bayesian hierarchical econometric approach is new to the FDI–growth literature and has several advantages over its classical counterpart. First, our dynamic, latent heterogeneous model is plagued by endogeneity, by construction, and existing classical approaches to estimating the parameters yield inconsistent estimators and consequently erroneous inferences. However, Hsiao et al. (1999) have shown that a Bayesian hierarchical approach mitigates these problems in finite samples. Second, unlike the classical approach to modelling latent coefficients, our Bayesian approach produces exact finite sample results and allows us to estimate the latent coefficients easily. Third, our Bayesian approach also mitigates the inherent bias that is present in the classical approach to estimating the variance of the latent coefficients (see, for example, Lindley and Smith (1972), Hsiao et al. (1999), Hsiao (2003) and Beck and Katz (2004)). Estimation of the variance of the latent coefficients is an important aspect of this paper given that our argument centres on heterogeneity in these coefficients. Fourth, the hierarchical nature of the model allows us to test different hypotheses within a unified framework.

Our empirical results support the existence of a heterogeneous relationship between FDI and economic growth across non-OECD countries and show that FDI and economic growth are positively related in only a few of these countries. These findings justify our latent coefficient hierarchical approach. We examine whether controlling for different proxies for institutional quality—including corruption, ethnolinguistic fractionalization (the probability that two people who are randomly selected from a country are not a member of the same ethnic and linguistic group), geographic latitude (the distance between a country and the equator), legal origin (the type of commercial legal traditions, either common law, French civil law, German civil law, Scandinavian law or socialist law), democracy, human capital, life expectancy and fertility rate—reduce the degree of heterogeneity in the FDI–growth relationship. These proxies do not constitute an exhaustive list for measures of institutional quality, but they are commonly used in the empirical literature on economic performance and institutions (see, for example, Mauro (1995), La Porta et al. (1999), Hall and Jones (1999) and Acemoglu et al. (2001, 2002, 2003, 2005)). The results suggest that the manner in and degree to which institutional quality is associated with economic growth appear to depend on how we measure institutional quality. We find that controlling for corruption engenders the largest reduction in the degree of heterogeneity in the FDI–growth relationship. In particular, corruption is negatively associated with the FDI–growth relationship. Our empirical results also suggest that our data are more in support of a heterogeneous FDI–growth relationship than the existence of heterogeneous relationships between the other covariates and economic growth.

The structure of the rest of the paper is as follows. Section 2 gives a brief description of the data. Section 3 presents and describes the Bayesian hierarchical model. Section 4 provides the main empirical results and discusses their implications. Section 5 concludes. We place all the mathematical details in  Appendix A. The excluded empirical results can be furnished on request.

The data that are analysed in the paper and the programs that were used to analyse them can be obtained from

  http://www.blackwellpublishing.com/rss

2 Data

We use a linear, hierarchical dynamic growth model to investigate heterogeneity in the FDI–growth relationship across countries. Identification of our heterogeneity parameters warrants the use of a longitudinal data set. The balanced longitudinal data set consists of 60 non-OECD countries over a time span of 19 years—from 1984 to 2002.  Appendix A contains additional details on this data set. The dependent variable is the rate of real per capita gross domestic product (GDP) growth, obtained from World Bank (2005). Our variable of interest is the percentage of FDI inflow relative to GDP, which we obtained from the United Nations Conference on Trade and Development on-line statistical database (http://www.unctadstat.unctad.org). The United Nations Conference on Trade and Development uses the definition of FDI that is outlined in Organisation for Economic Co-operation and Development (1996), which is a long-term business partnership between a foreign entity (the ‘direct investor’) and a local entity (which is in an economy outside that of the foreign entity: the host economy) whereby the foreign entity has at least 10% equity ownership and private capital transactions occur between both entities.

Our growth regression model uses two sets of covariates. The time varying, country-specific covariates in the growth equation are labelled as level 1 covariates. To explain heterogeneity in the FDI–growth nexus and country-specific intercepts, we allow the corresponding parameters to be functions of observed and unobserved time invariant, country-specific covariates. We label the observed, time invariant, country-specific covariates that are associated with the intercept and slope coefficients of FDI as level 2 covariates. Such specification renders the model hierarchical.

2.1 Covariates at level 1

Our goal for this paper is not to find the possible determinants of economic growth but to reanalyse empirically the relationship between FDI and economic growth. We therefore limit our level 1 covariates to variables that are commonly used as determinants of growth and have been found to be correlated with FDI. Our choice of conditioning set is somewhat ad hoc but it might mitigate any omitted variables bias that is associated with FDI. From World Bank (2005) and the Penn world table (version 6.2) of Heston et al. (2006) we obtain the following covariates:

• (a)

  the openness ratio—exports plus imports as a percentage of GDP,

• (b)

  the rate of inflation,

• (c)

  initial GDP per capita—the logarithm of real per capita GDP in the previous year,

• (d)

  the government consumption ratio—general government final consumption expenditure as a percentage of GDP—and

• (e)

  domestic investment as a percentage of GDP.

We also control for external conditions that could cause movements in the growth rate of GDP by using

• (f)

  the US treasury bill rate from the International Monetary Fund international financial statistics on-line database (http://www.imfstatistics.org/imf/).

In the context of our study this variable is strictly exogenous and therefore may reduce the error variances in the first level of our model by reducing any contemporaneous correlations across disturbance terms.

2.2 Covariates at level 2

The covariates at level 2 consist of an array of proxies for institutional quality that are used frequently in the existing literature on economic performance and institutions. These proxies, which include corruption, ethnolinguistic fractionalization, geographic latitude, legal origin and democracy, have been linked to different aspects of institutional quality. Shleifer and Vishny (1993) theorized that in corrupt economies government officials restrict the supply of government-produced or imported goods that are essential for private investment. Mauro (1995) found empirical evidence that corruption lowers economic growth by reducing private investment. La Porta et al. (1999) argued that higher ethnolinguistic fractionalization gives rise to different governments, each with different policies that are in favour of more private than social benefits, which results in poor government performance and inefficient institutions. Similarly, countries with French or socialist laws have more interventionist governments that engender more economic distortions. Countries with democratic governments have better institutional quality in that they are more efficient, engage in less interventionist policies and provide better public goods. Also, countries that are further from the equator have a more conducive environment for agricultural productivity which has allowed them to improve their economies and institutional quality. Hall and Jones (1999) documented that countries that are further from the equator have better institutions because most of these countries were those which were preferred for settlement, owing to their factor endowments such as climate and soil conditions, by western Europeans during the colonization period. These colonizers adopted similar institutional arrangements to those in their homelands and also invested more in the productive sectors of their economies, in particular human and physical capital.

We collect a subjective measure of corruption from Knack and Philip (1998), which is available for the period 1984–1996. This corruption index is a measure of corruption in government and ranges from 0 to 6. Lower scores indicate higher levels of corruption in that ‘high government officials are likely to demand special payments’ and ‘illegal payments are generally expected throughout lower levels of government’ in the form of ‘bribes connected with import and export licenses, exchange controls, tax assessment, police protection, or loans’. We transform this index to be within the range 0–10, but with higher values representing higher levels of corruption. An important assumption in this analysis is that our proxies for institutional quality are time invariant. Our rationale is based on the fact that the extent to which weak institutions are entrenched in many non-OECD countries makes it difficult for these countries to improve their institutional quality in the absence of proper legal recourse through institutional reform. Consequently, we use the average of Knack and Philip’s (1998) measure as the measure of corruption for the entire time span.

From La Porta et al. (1999) we obtain a measure of ethnolinguistic fractionalization and geographic latitude, and dummy variables for the legal origin of each country (our sample includes countries with French, English, socialist and German laws, the last being the reference group). We use the time average of an index of democracy from Marshall and Jaggers (2002) which ranges from −10 to 10 with 10 representing complete democracy and −10 complete autocracy. We include Barro and Lee’s (2001) average years of secondary schooling in the male population above 25 years in 1985 as a measure of human capital. We also include the time average of the fertility rate (total births per woman) and total life expectancy at birth (in years) which we obtain from World Bank (2005).

2.3 Descriptive statistics

As argued above, the importance of relaxing the parameter constancy assumption is to capture any heterogeneity in the association between FDI and economic growth that may exist across non-OECD countries, and to analyse the association between institutional quality and this heterogeneity. For illustration, we assume that corruption is our measure of institutional quality. Table 1 shows average FDI inflows by quartiles of the growth distribution for countries below and above the mean level of corruption (low and high corruption countries respectively). Panel (a) shows that, for low corruption countries, higher levels of FDI are positively associated with higher levels of economic growth up to the third quartile of the growth distribution. Panel (b) shows that, for high corruption countries, higher levels of FDI are positively associated with higher levels of economic growth up to the second quartile of the growth distribution. Thus, the association between economic growth and FDI appears to differ across low and high corruption countries.

Table 1

Conditional descriptive statistics^†

Statistics	1st quartile	2nd quartile	3rd quartile	4th quartile
(a) By quartiles of real GDP per capita growth rate, low corruption countries
Average growth rate	−0.125	1.634	3.607	8.611
Average FDI inflows	1.569	2.080	3.731	2.443
Observations	7	8	7	7
(b) By quartiles of real GDP per capita growth rate, high corruption countries
Average growth rate	0.012	1.131	2.172	4.632
Average FDI inflow	1.475	2.984	1.779	1.576
Observations	8	7	9	7

†

Low corruption and high corruption countries are respectively below and above the mean corruption level of 5.329. We compute the time average for real GDP per capita growth rate and FDI inflows for each country. For each set of low and high corruption countries we calculate the upper boundary values for the first, second, third and fourth quartiles of the distribution of the country-specific growth rates. Finally, within each quartile we compute the localized average for the FDI inflows.

The presence of heterogeneity accommodates the possibility that clusters of countries may have different relationships between FDI and growth. Thus, in the spirit of our main conjecture and to deduce any patterns in the raw data between the rate of growth and FDI, we partition the distribution of corruption into quartiles and make a bivariate plot of the association between FDI and growth in each quartile. Fig. 1 shows the differences in sign and magnitude of the relationship between real GDP per capita growth rate and FDI inflows, on average, across the quartiles of the corruption distribution. We do not interpret the relationship in each part as being statistically significant owing to the small effective sample size that is allocated to each quartile. We, however, see this as a discernible pattern that supports our main argument of explicitly modelling heterogeneity and controlling for institutional quality in the association between FDI and economic growth. In fact, Fig. 2 depicts the unconditional and homogeneous correlation between average FDI inflows and average real GDP per capita growth rate for the entire sample of non-OECD countries, which, in contrast with the conditional and heterogeneous correlation coefficients that are implied by Fig. 1, is positive but close to zero. Thus, Fig. 2 illustrates how examining the association between economic growth and FDI, without conditioning on corruption and without accounting for heterogeneity, can yield different conclusions.

Fig. 1

Segmented graph of average real GDP per capita growth rates against average FDI inflows: (a) corruption in the first quartile; (b) corruption in the second quartile; (c) corruption in the third quartile; (d) corruption in the fourth quartile

Fig. 2

Average real GDP per capita growth rates against average FDI inflows

3 The linear, dynamic hierarchical model

We discuss two econometric models that are motivated by our hypotheses and existing empirical evidence on characteristics of growth regressions. To ensure comparability with the classical FDI–growth literature, we begin with a linear dynamic growth model of the form

$$\text{Δ}{y}_{it}={\lambda }_i+{\theta }_1{y}_{it-1}+{\theta }_2^{\prime }{q}_{it}+w_{it}\beta +{\epsilon }_{it},\hspace{1em}i=1,\dots ,N,t=1,\dots ,T,-2<{\theta }_1<0,$$

(3.1)

which we compactly write for each country i as

$$Y_i={\iota }_T{\lambda }_i+X_i\alpha +W_i\beta +{\epsilon }_i,\hspace{1em}i=1,\dots ,N,$$

(3.2)

(model A) where Y_i=(Δy_i1,Δy_i2,…,Δy_iT)^′ is a T × 1 vector of real GDP per capita growth rates, Δy_it≡y_it−y_{it − 1}, ι_T is a T × 1 vector of 1s, $X_i=\left({y^{\prime }}_{i,-1},{q^{\prime }}_{i1},{q^{\prime }}_{i2},\dots ,{q^{\prime }}_{ip-1}\right)$ is a T×p design matrix with ${q^{\prime }}_{ik}={\left(q_{ik1},q_{ik2},\dots ,q_{ikT}\right)}^{\prime }$⁠, for each k ∈ {1, 2,…,p − 1}, and y_i,−1 is a T × 1 vector of the logarithm of lag real GDP per capita, and q_i,. are the other level 1 covariates excluding the variable of interest, W_i=(w_i1,w_i2,…,w_iT)^′ is a T × 1 design vector containing the variable of interest (the percentage of FDI inflow in the GDP), λ_i is the country-specific intercept, which accounts for country-specific factors such as productivity shocks, $\alpha ={\left({\theta }_1,{{\theta }^{\prime }}_2\right)}^{\prime }$ is a p × 1 common coefficient vector and ε_i is the level 1 disturbance term. The restriction on θ₁ is the implied stability condition for this dynamic model. Model A assumes a homogeneous association between FDI and economic growth across countries. Since this assumption is a major critique in the present paper, we put forward an alternative specification.

We relax the assumption of parameter constancy on the FDI variable in expression (3.2) to accommodate our hypothesis of a heterogeneous relationship between FDI and economic growth across countries:

$$\begin{array}{c}{Y}_i=X_i\alpha +{\tilde{W}}_i{\tilde{\beta }}_i+{\epsilon }_i,\\ {\tilde{\beta }}_i=Z_i\gamma +u_i,\hspace{1em}i=1,\dots ,N,\end{array}$$

(3.3)

(model B), where ${\tilde{W}}_i=\left({\iota }_T⋮W_i\right),{\tilde{\beta }}_i={\left({\lambda }_i,{\beta }_i\right)}^{\prime },u_i$ is the level 2 error term and all other variables are as previously defined. At level 2 in model B, we presume that ${\tilde{\beta }}_i$ is a latent, linear function of the 2×r matrix Z_i that is associated with institutional quality and other time invariant factors. This linearity assumption can be relaxed to allow for non-linear parameter heterogeneity. For our study, however, linearity may suffice to demonstrate the relationship between parameter heterogeneity and institutional quality. The latent country-specific intercepts ensure, among other things, that our analysis is not biased towards finding heterogeneity in the FDI–growth relationship. The error term u_i captures all other unobserved variables, which we do not explicitly model, that may be the source of the heterogeneity in the FDI–growth relationship. As emphasized above, our economic rationale for allowing ${\tilde{\beta }}_i$ to be a function of institutional quality is that variations in institutional quality may be associated with variations in absorptive capacities across countries, which in turn may be associated with a heterogeneous association between FDI and economic growth. Also, this specification of ${\tilde{\beta }}_i$ permits indirect, through FDI, and direct, through the country-specific intercepts, associations between institutional quality and economic growth. Furthermore, this latent approach at level 2 is more appropriate for modelling the relationship between institutions and macroeconomic outcomes relative to its deterministic counterpart, as in Minier (2007). Any aspect of institutional quality is either indirectly measured or measured with error; the latent approach serves as a remedy for shortcoming of proxies for institutional quality since it explicitly accounts for measurement error. Moreover, with appropriate assumptions the degree of heterogeneity can be modelled in this latent framework.

We assume that the error terms in expression (3.3) follow normal distributions so that

$${\epsilon }_{it}\stackrel{\text{ IID }}{\sim }N\left(0,{\sigma }_{{\epsilon }_i}^2\right), and E\left({\epsilon }_i{\epsilon }_j^{\prime }\right)=0,\hspace{1em} for i\ne j,u_i\stackrel{ \text{IID} }{\sim }N\left(0,{\text{Σ}}_b^2\right)\hspace{1em}\forall i,j,t.$$

(3.4)

Then using expressions (3.3) and (3.4) we obtain the following population distributions:

$$Y_i\mid {\lambda }_i,\alpha ,{\beta }_i,{\sigma }_{{\epsilon }_i}^2\stackrel{\text{ ind }}{\sim }{N}_T\left(X_i\alpha +{\tilde{W}}_i{\tilde{\beta }}_i,{\sigma }_{{\epsilon }_i}^2{I}_T\right),$$

(3.5)

$${\tilde{\beta }}_i\mid \gamma ,{\sigma }_b^2\stackrel{ \text{ind} }{\sim }N\left(Z_i\gamma ,{\text{Σ}}_b^2\right).$$

(3.6)

Our model is dynamic and therefore there is a mechanical correlation between the lagged right-hand side variable and error term regardless of the assumption on the other regressors. In addition, the use of yearly observations increases the prospect for serial correlation in the regressors, which can in turn induce correlation between these regressors and the error term. For our dynamic, latent heterogeneous panel, existing classical approaches to estimating the parameters yield inconsistent estimators and consequently erroneous inferences. Coupled with this, many existing methods for obtaining an estimate of ${\Sigma }_b^2—\text{a}$ parameter of central interest in our paper—are limited to a static, latent heterogeneous panel model that is fraught with problems. Swamy (1970) proposed a feasible two-step generalized least squares method to estimating such a model and offered two alternative estimators for ${\Sigma }_b^2$⁠. However, in finite samples one estimator may not be positive definite whereas the other is biased upwards (e.g. Hsiao (2003), chapter 6, and Beck and Katz (2004)). Maximum likelihood methods can also be used to estimate the model but difficulties may arise in these procedures (Beck and Katz (2004), page 13). Lindley and Smith (1972) derived a set of Bayes modal equations which can be solved by a sequence of iterations. However, this procedure does not yield standard errors of the estimators (Lindley and Smith (1972), page 12) and may only be useful if the sole interest is in the posterior modes. Furthermore, it is not clear how to extend these existing methods to our dynamic, latent heterogeneous panel model.

Bayesian analysis, in contrast, yields exact finite sample results and estimating ${\Sigma }_b^2$ is straightforward by using the Gibbs sampler. In fact, using a dynamic, latent heterogeneous panel model similar to that in this paper, Hsiao et al. (1999) documented the inconsistency of estimates of the model under the classical approach and the superiority of the Bayes estimators in finite samples. Thus, to mitigate endogeneity bias and to circumvent estimation problems and finite sample deficiencies that are associated with estimating the coefficients of interest, we do not use the classical approach to modelling heterogeneity. We adopt a Bayesian hierarchical approach, which has been used by Koop and Tobias (2004) to study the existence of heterogeneity in returns to schooling.

To formulate the Bayesian hierarchical structure we impose the following distributional specifications and independence assumption on the priors for α, ${\sigma }_{{\epsilon }_i}^2$⁠, ${\Sigma }_b^2$ and γ:

$$p\left(\alpha ,{\sigma }_{\epsilon }^2,{\text{Σ}}_b^2,\gamma \right)=p(\alpha )p\left({\sigma }_{\epsilon }^2\right)p\left({\text{Σ}}_b^2\right)p(\gamma ),$$

where

• (a)

  α∼N_p(α₀,Σ₀),

• (b)

  ${\sigma }_{{\epsilon }_i}^{-2}\sim G\left({\nu }_{0_i},{\delta }_{0_i}\right), for i=1,\dots ,N,$

• (c)

  ${\text{Σ}}_b^{-2}\sim W\left({\mu }_0,R_0^{-1}\right)$ and

• (d)

  γ∼N_r(γ₀, Γ₀).

G denotes the gamma distribution, W is the Wishart distribution, N_p and N_r are multivariate normal distributions and the hyperparameters α₀,Σ₀, ν_0i,δ_0iμ₀,R₀, γ₀ and Γ₀ are prespecified constants. We note that this independence assumption on the prior specifications does not imply independence of the posterior specifications, since the data govern the degree of independence in the latter case.  Appendix A contains the derivations for the posterior specifications and the values that we assume for all hyperparameters.

4 Empirical results

This section contains the empirical results from the Bayesian hierarchical models A and B, which were introduced in the preceding section. In model A, we allow for latent, country-specific intercepts. In model B, our empirical strategy is to fix the set of level 1 covariates but to vary the set of level 2 covariates to yield different specifications. To compare the fit of these specifications to the data, we use the deviance information criterion (DIC) that was introduced by Spiegelhalter et al. (2002)and analyse the posterior means and standard deviations of the parameters. For brevity, in Table 2 we display only the posterior means and standard deviations of the α-, γ- and ${\Sigma }_b^2$-parameters that are from model A (see column A) and model B (see columns B1–B12). The general patterns in the α-parameters across specifications are that the posterior means of the coefficients that are associated with domestic investment, trade openness, inflation and US treasury bill rate are more than 1 standard deviation away from 0. The posterior means of the contribution of government consumption to economic growth are all less than 1 standard deviation from 0. The posterior means of lagged real GDP per capita are less than 1 standard deviation in some specifications. In most specifications, all the coefficients have their expected signs and the magnitudes of the θ₁-parameter indicate that these dynamic panel models are stable. In column A, the posterior mean and standard deviation for θ₁ respectively are 0.141 and 0.294, suggesting a possible model misspecification. The posterior mean and standard deviation of the homogeneous FDI coefficient respectively are 0.051 and 0.054, suggesting that on average there is no correlation between FDI and economic growth within developing host countries.

Table 2

Bayesian results^†

Variable	A	B1	B2	B3	B4	B5	B6	B7	B8	B9	B10	B11	B12
Level 1 parameters
Initial GDP	0.141	−0.240	−0.636	−0.229	−0.256	−0.312	−0.171	−1.684	−0.374	−1.738	−0.200	−0.258	−0.500
	(0.294)	(0.322)	(0.346)	(0.324)	(0.326)	(0.306)	(0.329)	(0.443)	(0.335)	(0.439)	(0.301)	(0.336)	(0.322)
Openness	−0.009	−0.013	−0.016	−0.015	−0.014	−0.015	−0.015	−0.017	−0.015	−0.018	−0.011	−0.011	−0.013
	(0.006)	(0.006)	(0.005)	(0.005)	(0.005)	(0.006)	(0.005)	(0.005)	(0.006)	(0.005)	(0.006)	(0.006)	(0.006)
Government consumption	−0.034	−0.004	0.002	−0.007	−0.004	−0.008	−0.003	−0.023	−0.011	−0.023	0.016	0.015	0.021
	(0.029)	(0.024)	(0.025)	(0.025)	(0.025)	(0.021)	(0.025)	(0.024)	(0.026)	(0.023)	(0.025)	(0.026)	(0.025)
Domestic investment	0.204	0.206	0.222	0.218	0.211	0.212	0.211	0.207	0.228	0.204	0.211	0.205	0.213
	(0.031)	(0.028)	(0.029)	(0.029)	(0.028)	(0.031)	(0.028)	(0.027)	(0.031)	(0.027)	(0.033)	(0.033)	(0.033)
US treasury bill rate	0.195	0.218	0.195	0.214	0.220	0.209	0.215	0.158	0.205	0.154	0.196	0.193	0.176
	(0.063)	(0.061)	(0.057)	(0.057)	(0.057)	(0.060)	(0.058)	(0.059)	(0.058)	(0.059)	(0.061)	(0.070)	(0.065)
Inflation	−1.003	−1.091	−1.112	−1.099	−1.085	−1.110	−1.093	−1.217	−1.107	−1.214	−1.030	−1.037	−1.080
	(0.163)	(0.149)	(0.144)	(0.145)	(0.144)	(0.140)	(0.144)	(0.148)	(0.146)	(0.148)	(0.171)	(0.164)	(0.157)
Level 2 parameters associated with FDI
Constant		0.144	0.741	0.047	0.079	0.059	0.182	0.249	0.283	0.577	0.105	0.133	0.721
		(0.076)	(0.263)	(0.119)	(0.118)	(0.455)	(0.089)	(0.953)	(0.223)	(0.251)	(0.084)	(0.216)	(0.371)
Corruption			−0.114							−0.085			−0.109
			(0.048)							(0.046)			(0.056)
Ethnolinguistic				0.320
Fractionalization				(0.261)
Geographic latitude					0.341
					(0.419)
English						0.210
						(0.459)
Socialist						0.329
						(0.477)
French						−0.048
						(0.452)
Democracy							−0.010
							(0.014)
Log-life-expectancy								−0.025
								(0.229)
Log-fertility-rate									−0.114
									(0.175)
Human capital												−0.025	−0.053
												(0.184)	(0.182)
Observations	1080	1080	1080	1080	1080	1080	1080	1080	1080	1080	846	846	846
${\Sigma }_b^2$(1, 1)	6.297	1.418	1.409	1.374	1.363	1.380	1.308	1.072	1.555	1.041	0.916	0.869	0.909
	(1.730)	(0.518)	(0.529)	(0.510)	(0.521)	(0.589)	(0.511)	(0.425)	(0.562)	(0.414)	(0.485)	(0.458)	(0.485)
${\Sigma }_b^2$(2, 2)		0.086	0.073	0.093	0.092	0.088	0.093	0.095	0.094	0.069	0.114	0.117	0.116
		(0.027)	(0.022)	(0.030)	(0.030)	(0.028)	(0.031)	(0.031)	(0.031)	(0.021)	(0.042)	(0.046)	(0.044)
DIC	3306.71	3314.44	3310.86	3313.82	3314.42	3312.52	3314.98	3304.73	3315.18	3302.84	2513.75	2514.69	2512.28

†

The dependent variable in each regression is the real per capita GDP growth rate. For each regression the first number is the posterior mean; the posterior standard deviation is in parentheses. Column A assumes a homogeneous FDI–growth relationship; the posterior mean and standard deviation of the FDI parameter are respectively 0.051 and 0.054. Columns B1 and B10 assume a heterogeneous FDI–growth relationship with ${\tilde{\beta }}_i=\gamma +u_i$⁠. Columns B2–B9, B11 and B12 also assume a heterogeneous FDI–growth relationship but the specification of the random coefficient is ${\tilde{\beta }}_i=Z_{i\gamma }+u_i$⁠, where Z_i is the 2×r matrix of a constant and level 2 covariates.

We now focus on the estimates of γ and ${\Sigma }_b^2$⁠, with and without controlling for different proxies of institutional quality. Thus, we analyse changes, if any, in the estimate of γ and the 2–2 and 1–1 entries of ${\Sigma }_b^2$—${\Sigma }_b^2$(2, 2) and ${\Sigma }_b^2$(1, 1)—which respectively capture the degree of heterogeneity in the FDI–growth relationship and the country-specific intercepts.

4.1 Hypothesis 1: there is heterogeneity in the foreign direct investment–growth relationship

For hypothesis 1 it suffices to show that in the absence of level 2 covariates, i.e. when ${\tilde{\beta }}_i=\gamma +u_i$⁠, our posterior mean of ${\Sigma }_b^2$(2, 2) is concentrated away from 0. Indeed, column B1 in Table 2 shows that the posterior mean and standard deviation for ${\Sigma }_b^2$(2, 2) are 0.086 and 0.027 respectively, which provide empirical support for the hypothesis of a heterogeneous FDI–growth relationship. The posterior mean and standard deviation for ${\Sigma }_b^2$(1, 1), 1.418 and 0.518 respectively, indicate unobserved heterogeneity in the country-specific intercepts. We note that the posterior mean of ${\Sigma }_b^2$(1, 1) is much lower that its homogeneous counterpart from model A, 6.297, suggesting that, for our data, model A suffers from neglected parameter heterogeneity. Therefore, although the DIC value for model A (3304.71) is lower than that of the model B in column B1 (3314.44), we cannot reject our hypothesis of a heterogeneous FDI–growth relationship.

4.2 Hypothesis 2: controlling for institutional quality reduces the heterogeneity in the foreign direct investment–growth relationship

We examine whether controlling for corruption, ethnolinguistic fractionalization, geographic latitude, legal origin, democracy, life expectancy, fertility rate and human capital reduce the heterogeneity in the FDI–growth relationship. To see the role of corruption in the heterogeneous FDI–growth relationship and country-specific intercepts, in column B2 in Table 2 we control for corruption at level 2. The posterior means of the coefficients of FDI and its interaction with corruption are more than 2 standard deviations from 0, which imply that there is some correlation between the FDI–growth relationship and corruption. Furthermore, we see that, without controlling for corruption, an increase of 10% in the percentage of FDI inflow to GDP is associated with an increase of 1.44% (see column B1) in the country’s rate of growth. However, (in column B2) an increase of 1 standard deviation in corruption is associated with a decrease of 0.16% (1.366×0.114) in the partial correlation between FDI and growth; the number 1.366 is the standard deviation of the corruption index and 0.114 is the absolute value of the posterior mean of the interaction between FDI and corruption in column B2. The DIC value for the specification in column B2, 3310.86, is less than its counterpart in column B1, 3314.44, which suggests that including corruption at level 2 improves the fit of the model to the data.

We now examine the effect of corruption on the posterior mean of ${\Sigma }_b^2$(2, 2). Intuitively, if controlling for corruption reduces part of the unobserved heterogeneity in the FDI–growth relationship then the inclusion of corruption in the model should reduce the posterior mean of ${\Sigma }_b^2$(2, 2). We find that the inclusion of corruption reduces the posterior mean of ${\Sigma }_b^2$(2, 2) by approximately 15%, from 0.086 (column B1) to 0.073 (column B2). The inclusion of corruption at level 2, however, reduces ${\Sigma }_b^2$(1, 1) by only 0.6%, which suggests that corruption matters more for heterogeneity in the FDI–growth relationship than for heterogeneity in the random effects.

From the results in columns B3–B8 we observe that none of the other institutional measures, ethnolinguistic fractionalization, geographic latitude, legal origin, democracy, life expectancy or fertility rate, induces a reduction in the posterior mean of ${\Sigma }_b^2$(2, 2) that exceeds its counterpart in column B2. These results suggest that the level of corruption matters more in the FDI–growth relationship. In addition, the estimates of γ that are associated with FDI confirm that these other proxies for institutional quality are not correlated with the FDI–growth relationship. In column B7 where we control for life expectancy, however, the DIC value is 3304.74. This is the lowest of the DIC values in columns B1–B8. This reduction in the DIC value is driven by the 24% reduction in the posterior mean of ${\Sigma }_b^2$(1, 1), from 1.418 to 1.072, and it suggests that the life expectancy rate has a significant role in the heterogeneity in the country-specific effects across non-OECD countries. We note that columns B2 and B7 are the only two columns for which the absolute value of initial GDP per capita increases substantially and is concentrated away from 0. This suggests that the rate at which non-OECD countries converge to their mean steady state is associated with their level of corruption and life expectancy rate. Furthermore, this significance of initial GDP accords with existing classical studies. In column B9 we therefore combine the model specifications in columns B2 and B7 by allowing the country-specific intercepts to be a function of life expectancy and the country-specific FDI coefficients to be a function of corruption. We observe reductions in ${\Sigma }_b^2$(1, 1) and ${\Sigma }_b^2$(2, 2) that are similar to their counterparts in columns B2 and B7, and a DIC value of 3302.84 that is less than the DIC values in columns B1–B8. These results so far suggest that the model specification in column B9 provides an adequate fit to the data. To examine whether our results so far are driven by omitted variable bias, we control simultaneously for all the level 2 covariates. We observe results, which are not reported here, that are consistent with those in the previous columns. All the α-coefficient estimates, except initial GDP per capita, remain invariant to the simultaneous inclusion of all the level 2 covariates. The γ-coefficient estimates that are insignificant in columns B2–B8 remain insignificant. Furthermore, the DIC value is 3309.35, which exceeds the DIC value in column B9.

In columns B10–B12 we investigate the role of human capital in the heterogeneous FDI–growth relationship. Incorporating the Barro and Lee (2001) measure of human capital in our analysis reduces the number of non-OECD countries from 60 to 47. We first check whether there is heterogeneity in the country-specific intercepts and FDI–growth relationship for this smaller sample. Column B10 shows that heterogeneity still exists in that the posterior mean and standard deviation of ${\Sigma }_b^2$(1, 1) and ${\Sigma }_b^2$(2, 2) are respectively 0.916 (0.485) and 0.114 (0.042). Although the DIC value is 2513.75, which is much smaller than those values in the previous columns, we do not view the model in column B10 as the best model given the change in sample size. We only compare model specifications with the same sample size. In column B11, we control for only human capital at level 2. We observe no meaningful reductions in either ${\Sigma }_b^2$(1, 1), ${\Sigma }_b^2$(2, 2) or the DIC. The γ-coefficient estimates show no association between human capital and heterogeneity in the country-specific intercepts and FDI–growth relationship. In column B12, we control for human capital and corruption at level 2 to see whether omitted variable bias plays any role. Again, we find no association between human capital and the heterogeneity in the country-specific intercepts and FDI–growth relationship. It is possible that this small sample size is inadequate for investigating the relationship between human capital and the heterogeneity in the FDI–growth relationship. However, we leave any further analysis of this result for future research.

4.3 Robust diagnostics

Our foregoing results hinge on some restrictive modelling assumptions that may be at odds with our data. Although extensive and econometrically involved analyses are ideally warranted for assessing the validity of our assumptions, in particular their quantitative and qualitative effects on our results, we are unaware of existing Bayesian methods that can help us in this regard. Indeed, it is the absence of such formal Bayesian methods that precludes us from making causal assertions on the relationship between institutional quality, FDI and economic growth in this paper. Nevertheless, we undertake minimalist approaches in assessing the extent to which two of these assumptions—exogeneity and homogeneous marginal returns of the X-regressors—affect, at minimum, the qualitative implications of our results (all the results for this subsection can be furnished on request). These two assumptions are not mutually exclusive, since, for example, neglecting parameter heterogeneity can induce endogeneity; we, however, analyse them separately.

In the first approach, we examine the incidence of endogenous regressors in three ways. First, we re-estimate model B by using predetermined covariates, lagged one and two periods, which can lessen but does not necessarily eliminate endogeneity problems. Second, we re-estimate model B by using aggregated panel data to minimize the incidence of serial correlation in the regressors, which can induce correlation between the regressors and the error term. The use of aggregated panel data may be advantageous in other ways. Across countries, the year-to-year variations in some covariates may not be sufficiently large to produce a meaningful relationship between the real per capita rate of growth and these regressors, including FDI. Also, it is well known that macroeconomic distortions are prevalent in most non-OECD countries and these distortions usually manifest themselves in the form of outliers, which can, among other things, weaken any significant relationship in any regression. The time period in our study is one of economic and financial liberalization in which many countries experienced, among other things, currency crises. These crises had significant macroeconomic effects, in particular on the rate of inflation, since, unlike OECD countries, many non-OECD countries lack the resources to offset the distortionary effects of currency crises. We generate two aggregated panel data sets by partitioning the entire time span into

• (a)

  six 3-year panels and

• (b)

  five 4-year panels in which the last panel contains only 2 years.

We then average all variables, except initial GDP, over the various time periods. We take initial GDP to be GDP per capita at the beginning of each time period to mitigate the mechanical correlation between this lagged right-hand-side variable and the error term. Third, we re-estimate the specifications in the first and second cases by using social indicators, namely life expectancy and fertility rate, as level 1 covariates in an effort to control for omitted variable bias. We note that our sample size has been reduced to 1020, 960, 360 and 300 for the models with one-period lagged regressors, two-period lagged regressors, six 3-year panels and five 4-year panels respectively. We estimate all these specifications, with and without controlling for corruption at level 2, and compare the results with those in columns B1 and B9 of Table 2 (in which the X-regressors and corruption simultaneously enter the model). In all these cases into which we have delved, the qualitative implications of our central results remain unchanged. Specifically, the third and most general case suggests

• (a)

  the existence of heterogeneity in the relationship between FDI and economic growth and the country-specific intercepts,

• (b)

  controlling for corruption engenders a reduction of at most 11% in the FDI heterogeneity parameter and lower DIC values and

• (c)

  the posterior means of the interaction term between FDI and corruption are negative and concentrated away from 0.

Therefore, although there may be endogeneity biases, the Bayesian framework seems to mitigate the size of these biases to levels that do not alter qualitative implications of our finding.

In the second approach, we examine whether there are heterogeneous relationships in our data between the other covariates and economic growth. As Hsiao et al. (1999) emphasized, neglecting coefficient heterogeneity in dynamic models induces correlation between the regressors and disturbance term and also results in serially correlated disturbances. We investigate neglected heterogeneities by using two strategies. First, we examine whether the simultaneous inclusion of interaction terms between each level 1 covariate, including life expectancy and fertility rate, and corruption in the design set at level 1 renders the posterior means of all the interactions terms concentrated away from 0. This deterministic approach of assessing institution-induced parameter heterogeneity in growth regressions has been employed by Minier (2007). Although we favour our latent heterogeneity approach, Minier’s (2007) approach allows us to investigate parameter heterogeneity without sacrificing degrees of freedom. We estimate the contemporaneous model and the six 3-year and five 4-year panel models with the interaction terms. For the contemporaneous model, we observe that none of the posterior means of the interaction terms is concentrated away from 0. For the six 3-year and five 4-year panel models, we observe that only the interaction terms that are associated with initial GDP, government consumption and US treasury bill rate have a posterior mean in excess of 2 standard deviations. However, it is not clear whether these results are an indication of heterogeneity or a consequence of the reduction in sample size, given the conflicting results between the two aggregated panels. Second, we examine the economic and statistical (in the frequentist sense) significance of the posterior means of the level 1 and 2 parameters and the DIC values that are obtained when we estimate model B sequentially using each of the other covariates as the variable of interest (i.e. in lieu of FDI but while controlling for FDI) but without controlling for corruption at level 2. In this case we estimate the six 3-year panel model and the contemporaneous model, without controlling for the social indicators at levels 1 and 2. We observe that these different models do not consistently outperform their respective benchmark models. In essence, these additional empirical results suggest that our data are more in support of a heterogeneous FDI–growth relationship than the existence of heterogeneous relationships between the other covariates and economic growth. Interestingly, Minier (2007) found little evidence that institutional quality has an indirect effect on economic growth by introducing heterogeneity in the traditional growth parameters, e.g. those that are associated with initial GDP per capita, investment and schooling. Minier’s (2007) empirical evidence shows, however, that institutional quality has an indirect effect on economic growth by engendering parameter heterogeneity in the trade policy parameters. Our work therefore complements Minier (2007) given that we show institutional quality, or at least some aspects of it, to be associated with parameter heterogeneity in the FDI–growth relationship. We note that Minier (2007)did not include FDI as one of the trade policy variables.

In the third approach, we extend our list of institutional quality variables to include the historical and current measures in Acemoglu et al. (2002, 2005). The historical measures are the logarithm of the population density in the year 1500, urbanization in 1500 and democracy in 1900; these historical data restrict our effective number of countries to 32, 32 and 48 respectively. The current measures of institutional quality are urbanization (from World Bank (2005)), risk of expropriation (from Knack and Philip (1998)) and constraint on the executive (from Marshall and Jaggers (2002)); we use these in time-average form and at the beginning of our time period, 1984. Using the measures of these current institutional quality variables of Acemoglu et al. (2002, 2005) would have yielded much smaller sample sizes in some cases. Acemoglu et al. (2002, 2005) have provided excellent descriptions of these variables and their roles as measures of institutional quality. We estimate model B by using sequentially each of these variables, the first principal component of urbanization in 1500 and logarithm of the population density in 1500, and all historical measures as a level 2 covariate. We observe that, in our data, urbanization in 1500 and the population density in 1500 reduce the degree of heterogeneity in the FDI–growth nexus, but by only 4%, whereas the population density in 1500 yields a slightly lower DIC value than urbanization in 1500. All the level 2 parameters that are associated with FDI are concentrated around 0. We also observe that the population density in 1500 and the current measures of urbanization respectively engender reductions—approximately 32% and 15%—in the heterogeneity in the country-specific intercepts. More importantly, controlling for these historical measures, which can be viewed as the most exogenous of our set of institutional quality variables, does not eliminate the heterogeneity in either the FDI–growth relationship or the country-specific intercepts. These results suggest

• (a)

  some direct and indirect associations between historical measures of institutional quality and economic growth and

• (b)

  that the existence of heterogeneities is not a manifestation of omitted time invariant institutional quality variables at levels 1 or 2.

Some caution should be exercised in drawing policy implications from the above-mentioned models, however, as they do not satisfy the stability condition. The instability of these models is not attributable to controlling for the historical factors.

4.4 Discussion

Overall, the preceding results suggest that the manner in and degree to which institutional quality is associated with economic growth appear to depend on how we measure institutional quality. On the basis of the reductions in the DIC values, posterior estimates of ${\Sigma }_b^2$(2, 2), ${\Sigma }_b^2$(1, 1) and the stability parameter, the results in column B9 of Table 2 appear most favourable and lend support to different roles for life expectancy and corruption in the growth model. The institutional quality measure that appears to be most directly associated with differences in mean country-specific growth rates across non-OECD countries is life expectancy. Specifically, the results that we have excluded from column B9 in Table 2 suggest that an increase of 10% in life expectancy at birth is directly associated with an increase of 0.22% in economic growth. This result seems economically meaningful and may be a manifestation of the direct association between life expectancy and productivity; for example, higher life expectancy may be associated with a more productive labour force. Acemoglu and Johnson (2007) found no evidence that an increase in life expectancy leads to an increase in economic growth, since the increase in life expectancy beginning in the 1940s had a disproportionately larger increase in population than in GDP. They highlighted, however, that, on the basis of the time span that was used, their ‘results may not be directly applicable to today’s world’ (Acemoglu and Johnson (2007), page 975). Our time period of study, from 1984 to 2002, among other things, differs from that of Acemoglu and Johnson (2007). Thus, their work does not necessarily render our result meaningless.

The institutional quality measure that appears to be most indirectly associated, through FDI, with economic growth is corruption. From column B9 in Table 2 only a few of the 60 non-OECD countries show positive and significant partial correlation between FDI and growth. In particular, 15 non-OECD countries have positive partial correlation that is at least 1 standard deviation away from 0, whereas eight of the 15 countries have a 95% highest posterior density interval that excludes zero. Table 3 contains the list of these eight countries, along with their posterior mean, standard deviation and 95% highest posterior density interval of the random coefficients that are associated with FDI and growth. The disparities in the posterior means in Table 3 highlight how misspecification of the FDI–growth relationship can yield misleading results. In particular, Table 3 implies that for some non-OECD countries an increase of 10% in FDI inflows relative to GDP is associated with an increase of at least 3% in economic growth. Also, in some non-OECD countries, lower corruption levels are associated with more positive association between FDI and growth. We emphasize that these results could not be extracted from a model, such as model A above, that assumes a homogeneous relationship between FDI and economic growth.

Table 3

Countries with positive partial FDI–growth correlation^†

Country	Mean	Standard deviation	95% highest posterior density interval
Botswana	0.445	0.252	[0.019, 0.848]
Bulgaria	0.499	0.262	[0.085, 0.935]
China	0.488	0.187	[0.192, 0.824]
Costa Rica	0.515	0.208	[0.134, 0.839]
Hungary	0.303	0.131	[0.085, 0.513]
Malaysia	0.484	0.152	[0.191, 0.729]
Poland	0.300	0.181	[0.013, 0.592]
South Africa	0.534	0.209	[0.161, 0.898]

†

The table shows the posterior mean, standard deviation and 95% highest posterior density interval of the random coefficients from column B9 in Table 2.

Our analysis therefore suggests important policy prescriptions that may not accord with those which are implied by the existing literature. In using a homogeneous modelling approach, existing studies have consistently made general assertions about the FDI–growth relationship, and how host countries can reap the positive benefits of FDI, if any. The results of the present paper, however, suggest a need for using policies that are implied by a heterogeneous analysis of the FDI–growth relationship, rather than using policy prescriptions for fostering growth that are implied by homogeneous growth models for non-OECD countries. A heterogeneous analysis can certainly militate against misallocating scarce resources to policies that are purported to complement growth-enhancing effects of FDI in other countries. By curbing corruption, some host developing countries may benefit more from FDI. In other words, reducing corruption may not stimulate growth promoting effects of FDI in all developing host countries in the exact same way. Thus, in some developing host countries, other aspects of institutions, which were not analysed in this study, may be more important in the FDI–growth nexus.

Our Bayesian hierarchical model is not a complete solution to modelling the FDI–growth relationship, but it does provide a new avenue of modelling this relationship both at the macroeconomic and the microeconomic levels. Given the dynamic nature of our Bayesian model, however, our relaxation of the commonly used homogeneity assumption introduces difficulty in testing formally for the presence of endogeneity, at both levels of the hierarchy, and the extent to which such misspecification affects the qualitative and quantitative implications of our results. This difficulty stems from the dual requirement for a Bayesian method that can directly address endogeneity of and preserve heterogeneity in the covariates. The design of such a specialized Bayesian method is certainly an important avenue for future research. Our use of less sophisticated, minimalist, specification tests, which are sometimes employed by the classical growth literature, provides, nevertheless, empirical support for our main hypotheses of interest. By and large, our empirical results do not appear to reflect severe endogeneity biases at levels 1 and 2, or neglected parameter heterogeneities that are associated with our other covariates at level 1. If our model suffers from these specification biases that are attributable to differences in institutional quality across developing countries then, across all specifications and sample sizes, the qualitative implications of the homogeneous coefficients should vary considerably. The results show no indication that this is so.

It is quite plausible and possible that parameter heterogeneities that are associated with traditional growth determinants are more prevalent and substantial in samples that pool developed and developing, or OECD and non-OECD countries. This is because of the significant differential in growth mechanism between developed and developing countries as argued by Durlauf (2001) and others. Thus, pooling developed and developing countries can substantially bias estimation results in favour of finding parameter heterogeneity. Indeed, many of the existing studies, if not all, on parameter heterogeneity in growth regressions use a pooled sample of countries. Our data consist only of non-OECD countries, and hence our posterior estimate of the heterogeneity parameter may be viewed as a lower bound. If parameter heterogeneity for all other regressors exists, we cannot model it in the way that we do FDI because of identification problems. A possible approach in this case is to impose a parametric function with more structure, such as cross-variable restrictions. Although the Solow framework provides such restrictions, it seems more applicable to traditional growth models such as those in, for example, Masanjala and Papageorgiou (2004). This issue seems to be a non-trivial and meaningful extension of our paper, which we hope to explore in the future.

Many of our proxies for institutional quality could be perceived as proximate and not fundamental causes of economic growth. However, both proximate and fundamental factors could also be viewed as deep hard-to-change characteristics of an economy. It is this feature of institutions that assists in our choice of covariates at level 2. Therefore, given the lack of a formal causal analysis and thus an absence of a causal interpretation of the results in this paper, our qualitative implications do not warrant a distinction between proximate and fundamental factors.

5 Conclusion

Empirically, there seems to be no consensus on the relationship between inflows of FDI and economic growth in host countries. There is a consensus, however, that poor institutions are associated with economic distortions. In this paper we hypothesize that the distortionary effects of poor institutions are associated with heterogeneous absorptive capacities, which are associated with a heterogeneous relationship between FDI and economic growth across countries. We use a Bayesian hierarchical model to analyse the relationship between FDI and economic growth within a set of non-OECD countries. We first test for the presence of heterogeneity in the FDI–growth relationship. We subsequently examine the change in the magnitude of this heterogeneity after controlling for various proxies for institutional quality. Our empirical results support the existence of a heterogeneous FDI–growth relationship in non-OECD countries. We find evidence that controlling for corruption reduces the magnitude of unobserved heterogeneity in the FDI–growth relationship. This result suggests that certain aspects of institutional quality may matter more in the FDI–growth relationship within some countries.

We emphasize that, instead of contributing to the existing debate on the importance of FDI in fostering economic growth, this paper identifies a source of the conflicting results in the FDI literature. Since some countries do not benefit economically from FDI, using a constant parameter in a panel regression to capture the marginal return to FDI for all countries yields ambiguous empirical results and policy implications. Moreover, omitting measures of institutional quality from the FDI–growth nexus has a considerable effect on the analysis. Our results also suggest that other variables, macroeconomic or possibly microeconomic in nature, may be helpful in explaining why only a few countries consistently enjoy a positive marginal return to FDI.

Acknowledgements

We are sincerely grateful to the Joint Editor, an Associate Editor and two referees for their invaluable and detailed critiques that helped to craft the exposition of this paper. Also, we thank Mark Figueroa, Christopher Hanes, Daniel Henderson and participants of the second New York Camp Econometrics conference for their helpful suggestions and comments. McCloud thanks the Department of Economics at the State University of New York at Binghamton and the Faculty of Social Sciences at the University of the West Indies at Mona for financial support. The usual disclaimer applies.

Appendix A

A.1 List of countries

The countries that were studied in this analysis are Albania, Angola, Argentina, Bangladesh, Bolivia, Botswana, Brazil, Bulgaria, Burkina Faso, Cameroon, Chile, China, Colombia, Costa Rica, Dominican Republic, Ecuador, Egypt (Arab Republic), El Salvador, Ethiopia, Ghana, Guatemala, Haiti, Honduras, Hungary, India, Indonesia, Jamaica, Jordan, Kenya, Korea, Madagascar, Malawi, Malaysia, Mexico, Mongolia, Morocco, Mozambique, Nicaragua, Nigeria, Pakistan, Panama, Paraguay, Peru, the Philippines, Poland, Romania, Senegal, Singapore, South Africa, Sri Lanka, Tanzania, Thailand, Trinidad and Tobago, Tunisia, Uganda, Uruguay, Venezuela, Vietnam, Zambia and Zimbabwe.

Our list of countries includes Mexico, Poland and Korea since their dates of membership in the OECD respectively are 1994, 1996 and 1996.

A.2 Data

The data set consists of 60 non-OECD countries over the time span 1984–2002. The numeraire year is 2000. The total number of observations is 1080. The values for initial real GDP per capita, life expectancy and fertility rate are their logarithmic transform. The original values of inflation are shifted by the first decile of the distribution so that a logarithmic transformation is possible.

A.3 Two-level hierarchical model

At the first stage of the hierarchy we have

$$Y_i={\iota }_T{\lambda }_i+X_i\alpha +W_i{\beta }_i+{\epsilon }_i,\hspace{1em}i=1,\dots ,N.$$

(A.1)

For ease of exposition, let ${\tilde{\beta }}_i={\left({\lambda }_i,{\beta }_i\right)}^{\prime }$ be the 2×1 vector of the country-specific intercept and slope. Now define ${\tilde{W}}_i=\left({\iota }_T⋮W_i\right)$⁠. We can rewrite expression (A.1) as

$$Y_i=X_i\alpha +{\tilde{W}}_i{\tilde{\beta }}_i+{\epsilon }_i,\hspace{1em}i=1,\dots ,N.$$

(A.2)

At the second stage we have

$${\tilde{\beta }}_i=Z_i\gamma +u_i\hspace{1em} for i=1,\dots ,N,$$

(A.3)

where u_i is the level 2 error term and Z_i is a 2×r design block matrix at level 2, i.e.

$$Z_i=\left(\begin{array}{cc}{Z}_{1i}& 0\\ 0& Z_{2i}\end{array}\right).$$

We impose the following distributional assumptions:

$${\epsilon }_{it}\stackrel{\text{IID}}{\sim }N\left(0,{\sigma }_{{\epsilon }_i}^2\right)\hspace{1em} \text{and} \hspace{1em}E\left({\epsilon }_i{\epsilon }_j^{\prime }\right)=0,\hspace{1em} \text{for }i\ne j,\hspace{1em}{u}_i\stackrel{\text{IID}}{\sim }N\left(0,{\text{Σ}}_b^2\right)\hspace{1em}\forall i,j,t.$$

(A.4)

Then using expressions (A.2)–(A.4) the likelihood and population distribution respectively are

$$\begin{array}{c}{Y}_i\mid \alpha ,{\tilde{\beta }}_i,{\sigma }_{{\epsilon }_i}^2\stackrel{ \text{ind} }{\sim }{N}_T\left(X_i\alpha +{\tilde{W}}_i{\tilde{\beta }}_i,{\sigma }_{{\epsilon }_l}^2{I}_T\right),\\ {\tilde{\beta }}_i\mid \gamma ,{\text{Σ}}_b^2\stackrel{ \text{ind} }{\sim }{N}_2\left(Z_i\gamma ,{\text{Σ}}_b^2\right).\end{array}$$

(A.5)

We append the following priors to complete the Bayesian hierarchical model:

$$\alpha \sim N_p\left({\alpha }_0,{\text{Σ}}_0\right),$$

(A.6)

$${\text{Σ}}_b^{-2}\sim W\left({\mu }_0,R_0^{-1}\right),$$

(A.7)

$$\gamma \sim N_r\left({\gamma }_0,{\text{Γ}}_0\right),$$

(A.8)

$${\sigma }_{{\epsilon }_i}^{-2}\sim G\left({\nu }_{0i},{\delta }_{0i}\right),$$

(A.9)

where W is the Wishart distribution. To obtain the full conditional posterior distributions for $\tilde{\beta }$ we make use of the following well-known decompositions of quadratic forms.

Lemma 1. Let a,b,c_i and d be random vectors and A,B,C and D_i be matrices of conformable dimensions. Suppose that a is the vector of interest. Then conditioning on b,c_i and d we have

• (a)

  (b−Ca)^′(b−Ca)∝(a−a^*)^′(C^′C)(a−a^*), where a^*≡(C^′C)⁻¹C^′b.

• (b)

  ${\text{Σ}}_{i=1}^M{\left(a-c_i\right)}^{\prime }\left(D_i^{\prime }{D}_i\right)\left(a-c_i\right)\propto {\left(a-c_i^{\ast }\right)}^{\prime }\left({\text{Σ}}_{i=1}^M{D}_i^{\prime }{D}_i\right)\left(a-c_i^{\ast }\right),$ where $c_i^{\ast }\equiv {\left({\text{Σ}}_{i=1}^M{D}_i^{\prime }{D}_i\right)}^{-1}{\text{Σ}}_{i=1}^M{D}_i^{\prime }{c}_i$⁠.

• (c)

  (a−b)^′A(a−b)+(a−d)^′B(a−d)∝(a−a^*)^′(A + B)(a−a^*), where a^*≡(A + B)⁻¹(Ab + Bd).

Using expressions (A.5)–(A.9) and lemma 1 where necessary, we derive the full posterior conditionals for the parameters of the model. It is straightforward to show that the full conditional posterior distribution for β_i for each i ∈ {1, 2,…,N} is

$$\left[{\tilde{\beta }}_i\mid Y_i,{\text{Σ}}_b^{-2},\alpha ,\gamma \right]\sim N\left({\text{Ψ}}_i{\psi }_i,{\text{Ψ}}_i\right),$$

(A.10)

where ${\text{Ψ}}_i={\left\{{\text{Σ}}_b^{-2}+{\sigma }_{{\epsilon }_i}^{-2}\left({\tilde{W}}_i^{\prime }{\tilde{W}}_i\right)\right\}}^{-1}$ and ${\psi }_i={\text{Σ}}_b^{-2}{Z}_i^{\prime }\gamma +{\sigma }_{{\epsilon }_i}^{-2}{\tilde{W}}_i^{\prime }\left(Y_i-X_i\alpha \right)$⁠. Also,

$$\left[\alpha \mid Y_i,{\text{Σ}}_b^{-2},\tilde{\beta },\gamma \right]\sim N(Vc,V),$$

(A.11)

where $V={\left({\text{Σ}}_0^{-1}+{\displaystyle {\sum }_0^{-1}{\sigma }_{{\epsilon }_i}^{-2}{X}_i^{\prime }{X}_i}\right)}^{-1}$ and $c={\text{Σ}}_0^{-1}{\alpha }_0+{\displaystyle {\sum }_{-1}^N{\sigma }_{{\epsilon }_i}^{-2}{X}_i^{\prime }}\left(Y_i-{\tilde{W}}_i{\tilde{\beta }}_i\right)$ We also derive

$${\sigma }_{{\epsilon }_i}^{-2}\sim G\left({\nu }_{1j},{\delta }_{1j}\right),$$

(A.12)

where ν_1i = ν_0i + T and ${\delta }_{1i}={\delta }_{0i}+{\left(Y_i-X_i\alpha -{\tilde{W}}_i{\tilde{\beta }}_i\right)}^{\prime }\left(Y_i-X_i\alpha -{\tilde{W}}_i{\tilde{\beta }}_i\right)$⁠. The full conditional posterior for ${\Sigma }_b^{-2}$ is

$$\left[{\text{Σ}}_b^{-2}\mid Y,\tilde{\beta },\gamma ,\alpha ,{\sigma }_{\epsilon }^2\right]\sim W\left({\mu }_1,R_1^{-1}\right)$$

(A.13)

where μ₁ = μ₀ + n and $R_1=R_0+{\text{Σ}}_{i=1}^N\left({\tilde{\beta }}_i-Z_i\gamma \right){\left({\tilde{\beta }}_i-Z_i\gamma \right)}^{\prime }$⁠. Finally, the full conditional posterior for γ is

$$\left[\gamma \mid Y,\tilde{\beta },\alpha ,{\sigma }_{\epsilon }^2,{\text{Σ}}_b^2\right]\sim N(\text{Ω}\tau ,\text{Ω})$$

(A.14)

where $\text{Ω}={\left({\text{Γ}}_0^{-1}+{\text{Σ}}_{i=1}^N{Z}_i^{\prime }{\text{Σ}}_b^{-2}{Z}_i\right)}^{-1}$ and ${\text{Γ}}_0^{-1}{\gamma }_0+{\text{Σ}}_{i=1}^N{Z}_i^{\prime }{\text{Σ}}_b^{-2}{\tilde{\beta }}_i$⁠.

A.4 Prior elicitation: values for selected hyperparameters

For estimation we assign values to the parameters of the prior distributions. Our knowledge of economic theory provides us with specific restrictions on some of these hyperparameters. Also, the extensive empirical work on the determinants of long-term economic growth offers various sets of potential determinants in this regard. We use the classical empirical study of Barro and Sala-i-Martin (2003), chapter 12, Table 12.3, column 2, and the Bayesian study of Sala-i-Martin et al. (2004), Table 2, to guide us in eliciting values for some of the hyperparameters. Sala-i-Martin et al. (2004) introduced a type of Bayesian model averaging that identifies a set of variables that are robustly correlated with long-term growth. These studies exclude FDI whereas Sala-i-Martin et al. (2004) also excluded corruption owing to limited data. We take into account the transformations of the variables in Barro and Sala-i-Martin (2003) and Sala-i-Martin et al. (2004) and make the necessary adjustments to the coefficients.

By imposing independence on α^* we set

• (a)

  λ∼N_N(0,10²I_Nτ_a) for the country-specific intercept,

• (b)

  α₁∼N(−1.5,2.5×10⁻¹τ_a) for the logarithm of lagged GDP per capita,

• (c)

  α₂∼N(0.0272,1.6×10⁻⁴τ_a) for openness,

• (d)

  α₃∼N(−0.13,4.0×10⁻⁴τ_a) for the government consumption ratio,

• (e)

  α₄∼N(0.083,1.4×10⁻⁴τ_a) for domestic investment,

• (f)

  α₅∼N(−1.9,2.5×10⁻²τ_a) for the logarithm of inflation and

• (g)

  α₆∼N(0,1×10²τ_a) for US treasury bill rate;

here τ_a = 1, 5,10,10² is an arbitrary tuning constant, ${\sigma }_{{\epsilon }_i}^{-2}\sim G\left({10}^{-4},{10}^{-4}\right)$ and ${\text{Σ}}_b^{-2}\sim W\left({\mu }_0,R_0^{-1}\right)$⁠, with μ₀ = 3 and R₀ = I₂, the 2×2 identity matrix.

We choose the prior mean of the coefficient on GDP per capita to reflect stability of the panel model although our period of study overlaps with the period of economic and financial liberalization for most of these countries. We choose Barro and Sala-i-Martin’s (2003) estimate of the coefficient on domestic investment as our prior mean for the marginal return to domestic investment. Domestic investment has been labelled as a robust determinant of growth in the empirical literature and we find that changes in this prior mean have no qualitative effect on our analysis. We choose the prior mean that is associated with the US treasury bill rate to be 0 but the prior variance to be large to reflect our ignorance about the effect of the variable on economic growth in non-OECD countries.

Given that the focal point of this paper is on heterogeneity in the FDI–growth nexus and the relationship between this heterogeneity and institutional quality, and we have no prior knowledge of the magnitude and sign of these relationships, we set γ₀ = 0 and Γ₀ = τ_s×I_r, where τ_s = 1, 10²,10⁴ is an arbitrary tuning constant for the prior variance of γ and I_r is the identity matrix in ${ℝ}^{r\times r}$⁠. This prior is proper but highly diffuse. In our sensitivity analysis, the tuning constants have no qualitative effect on the empirical findings.

A.5 Estimation

To obtain parameter estimates of the hierarchical model we utilize the Gibbs sampler. We simulate the model by using 30000 iterations and for each iteration generate random draws from the set of posterior conditionals: expressions (A.10)–(A.14). In the ‘burning-in phase’ we discard the first 5000 iterates to reduce the dependence of the values of the final estimate on the starting values of the chain. The Gelman–Rubin statistics for ${\Sigma }_b^2$(1, 1) and ${\Sigma }_b^2$(2, 2) are approximately 1.03 and 1.01, which suggest that convergence is attained for these key parameters. In the ‘thinning phase’ we then skip every 100 observations, reducing the auto-correlations close to 0. Using the remaining iterates we approximate the posterior mean and standard deviation for each parameter by using Monte Carlo estimates. We adjust each standard deviation for the small degree of auto-correlation that remains after thinning.