A Generalized Empirical Model of Corruption, Foreign Direct Investment, and Growth

Transcription

1 A Generalized Empirical Model of Corruption, Foreign Direct Investment, and Growth Michael S. Delgado Department of Economics Binghamton University Subal C. Kumbhakar Department of Economics Binghamton University Nadine McCloud Department of Economics University of the West Indies at Mona March 27, 2011 Abstract We propose a generalized empirical model for estimating the effect of foreign direct investment on GDP growth rates, as well as for determining the effect of corruption on the growth rate, and on the relationship between foreign direct investment and growth. Our model allows for parameter heterogeneity between all conditioning variables (including foreign direct investment) and growth, as well as in the effects of corruption on growth. We estimate the regression using a recently developed nonparametric method of moments estimator that allows us to concurrently use instrumental variables to mitigate any endogeneity bias that may be present in the relationship between foreign direct investment and growth, and model parameter heterogeneity. We find that there is substantial heterogeneity in the relationship between foreign direct investment and growth, and that foreign direct investment has a positive and significant effect on growth for many of the countries in our sample. Corruption is shown to significantly diminish the effectiveness of foreign direct investment at improving growth rates, but overall has an insignificant net effect on growth. Keywords: Foreign direct investment; corruption; parameter heterogeneity; economic growth; nonparametric method of moments; instrumental variables. Michael S. Delgado, Department of Economics, State University of New York at Binghamton, PO Box 6000, Binghamton, NY mdelgad1@binghamton.edu Corresponding author: Subal C. Kumbhakar, Department of Economics, State University of New York at Binghamton, PO Box 6000, Binghamton, NY Phone: Fax: kkar@binghamton.edu Nadine McCloud, Department of Economics, University of the West Indies at Mona, Kingston 7, Jamaica. nadine.mccloud02@uwimona.edu.jm 1

2 1 Introduction Foreign direct investment (FDI) is generally thought to be an important factor of growth and development in developing countries. It is through the investments of large multinational corporations that developing countries have access to advanced technologies, management practices, and research and development that are crucial for growth, but are otherwise unavailable in the developing world (e.g., Borensztein et al and Carkovic and Levine 2005). Unfortunately, while there has been a broad consensus as to the theoretical importance of FDI for growth and development in developing countries, there has yet to be a consensus among empirical researchers as to the significance of FDI at increasing growth rates. Blomstrom (1986), Borensztein et al. (1998) and Alfaro et al. (2004) all find evidence that FDI positively contributes to economic growth, whereas Haddad and Harrison (1993), Aitken and Harrison (1999), and Carkovic and Levine (2005) find no evidence in support of growth-enhancing effects of FDI. These conflicting empirical results among studies on the FDI-growth relationship may be due to the failure to appropriately incorporate parameter heterogeneities, which can lead to a misspecified model and inaccurate estimation of the relationships of interest. Durlauf (2001), for example, advocates modeling all the parameters in growth regressions as functions of developmental variables, rather than as constants. Constant parameter growth models may suffer from misspecification since they ignore crucial heterogeneities induced by the developmental variables that are fundamental to the growth process. Moreover, constant-parameter models will most likely be sensitive to different specifications of functional forms, or samples of observations. Growth models that allow for constant parameters provide a description of the average relation, at best. In the presence of substantial heterogeneity in the growth process, constant-parameter models are unlikely to accurately estimate the relationship between FDI and growth. One important developmental element that is likely correlated with the absorptive capabilities of host countries and ultimately influences the effectiveness of FDI at improving growth rates is institutional quality. While there are different measures of institutional quality that may result in heterogeneity in the effect of FDI on growth across developing countries, corruption may be of extra importance because of its effect on many avenues that all ultimately influence absorptive capabilities and growth rates. Mauro (1998), Gupta et al. (2002) and Tanzi et al. (2002) all document a negative relationship between corruption and human capital. Countries that are more corrupt tend to invest less in human capital, which ultimately decreases the ability of the country to absorb new technologies from developed nations (Borensztein et al. 1998). Bribery, for example, which is associated with higher levels of corruption, may lead to an imbalance in the relative payoffs between productive and unproductive sectors in the economy (Baumol 1990 and Murphy et al. 1991). Workers are less likely to move to domestic from foreign firms (i.e., the multinational corporations) where their payoffs are relatively higher; the result is less diffusion of technology from the domestic firms to foreign firms, and a weakening of the effect of FDI on growth. Building on previous studies that have identified heterogeneity within the relationship between FDI and GDP growth (e.g., Borensztein et al and Alfaro et al. 2004), as well as studies that have shown an important interaction between institutional factors (e.g., corruption) and the effectiveness of FDI at improving growth rates (e.g., McCloud and Kumbhakar 2

3 2011), we present a generalized empirical growth model with which to re-analyze the relationship between corruption, FDI, and GDP growth (as well as the relationship between growth rates and other conditioning variables). Our generalization is based on a standard growth regression that assumes homogeneous parameters. We generalize the standard model to allow for a heterogeneous relationship between GDP growth and all conditioning variables, by making the coefficients unknown smooth-functions of an index of corruption, and country- and time-specific indicators. Thus, our model allows us to obtain estimates that are specific to each country in each year, and estimates that depend on the level of corruption in each country and in each year. While we present an alternative approach that complements previous studies that have allowed for heterogeneity within the corruption-fdi-growth relationship, our approach also allows us to analyze the effect of corruption on GDP growth rates through its effect on all conditioning variables (e.g., trade openness, or inflation), and not solely through its influence on the FDI-growth relationship. To estimate our generalized regression model, we use a recently developed nonparametric version of a standard method of moments estimator (Cai and Li 2008) that assumes the primary conditioning variables (e.g., FDI) enter linearly into the regression model, but allows the intercept and slope coefficients to vary nonparametrically (i.e., either linearly or nonlinearly) with respect to certain environmental factors (e.g., corruption). Hence, this model is a version of the varying coefficient models of Hastie and Tibshirani (1993), or more recently Li et al. (2002). One advantage of this nonparametric generalized methods of moments (NPGMM) estimator over other smooth coefficient models, e.g., Durlauf et al. (2001) and Li et al. (2002), is that it allows all of the conditioning variables to be endogenous. This, in part, addresses one concern raised by Durlauf (2001), who argues that in a growth specification, all conditioning variables can be taken to be endogenous; that is, all variables typically included in a growth specification are determined, in part, by omitted factors that also determine growth rates. In particular, Borensztein et al. (1998) provide a discussion of the potential endogeneity of FDI in a growth regression. Hence, it is important to consider an instrumental-variables approach to estimating the relationship between FDI (or any other conditioning variables of interest) and growth in order to obtain consistent estimates. 1 Although the generalized model differs from standard homogeneous models by incorporating parameter heterogeneity in the coefficients, the generalized model maintains the traditional functional form assumptions embedded in the standard models. The advantage of maintaining such assumptions (e.g., additive separability and linearity of the regressors), is that the standard model exists as a special case of the generalized model. We can econometrically test whether the data support the assumption of parameter homogeneity inherent in the standard model. Another advantage of maintaining such functional form assumptions is that we can avoid dimensionality issues that often arise in fully-specified nonparametric models. In the present context, dimensionality issues can only arise when estimating the coefficient functions in the smooth coefficient model; because the number of continuous environmental factors is likely to 1 In the empirical growth literature, Liu and Stengos (1999) and Durlauf et al. (2001) also use semiparametric models to examine parameter heterogeneity. Their works differ from that of the present paper in many ways including the use of cross-sectional and not panel data, exclusion of FDI from the set of independent variables, sample selection (inclusion of OECD and non-oecd countries), assumed sources(s) of parameter heterogeneity, and analysis of endogeneity. 3

4 be relatively small, or at least smaller than the entire conditioning set in a fully nonparametric regression, the curse of dimensionality can often be avoided. Our results confirm that there exists substantial heterogeneity in the relationship between FDI and growth, and we find strong evidence that FDI has a positive and significant influence on growth rates for about 80 percent of the developing countries in our sample. In addition to providing observation-specific estimates of the coefficients (e.g., the FDI coefficient), our model also provides estimates of the marginal effect of corruption on each of the coefficients. Our estimates show that corruption significantly reduces the effectiveness of FDI on growth, which supports previous studies that suggest that corruption influences the absorptive capabilities of developing countries. However, when considering the total effect of corruption on growth rates (i.e., the sum of the indirect effects of corruption on all of the coefficients in the model), we find that corruption does not significantly influence growth rates. Through our heterogeneous parameter estimates, we analyze separate groups of countries that have substantially different coefficients and isolate characteristics common within such groups. This type of analysis is useful for international investment policies: knowledge of whether there is a positive and significant relationship between FDI and growth rates for any particular country, or how this relationship varies with respect to corruption is crucial for designing policies aimed at improving growth rates. While we do not find evidence of regional or geographical groups, we find that with respect to heterogeneity within the FDI-growth relation, many countries with the highest returns to FDI also have the lowest returns to corruption. Conversely, countries with an insignificant or relatively low correlation between FDI and growth have the highest estimated returns to corruption. Hence, our results suggest that developing countries with relatively low correlations between FDI and growth may benefit substantially from a reduction in corruption. Our empirical results are robust to using different instruments for FDI, allowing for all conditioning variables to be endogenous, using different measures of corruption, controlling for other measures of institutional quality that may be correlated with the dependent and independent variables. Moreover, a specification test suggests our semiparametric model that allows for endogeneity is more consistent with the data than the standard-homogeneous model. The structure of the rest of the paper is as follows. Section 2 presents and discusses our generalized empirical growth model and its nonparametric method of moments estimator. Section 3 discusses the data. Section 4 provides the main empirical results and discusses their implied policy prescriptions. Section 5 investigates the robustness of our main results. Section 6 concludes. The excluded empirical results can be furnished on request. 2 Empirical Methodology 2.1 Growth Models We consider a standard growth model with the growth rate of real GDP per capita as the dependent variable and a set of control variables. Letting g it denote the real GDP per capita growth rate in country i at time t, we write the standard model as: 4

5 g it = β 0 + Y it β 1 + X itβ 2 + ǫ it, i = 1,...,n t = 1,...,T, (1) in which Y it is our measure of FDI, X it is a vector of control variables, β (β 0, β 1, β 2 ) is a vector of parameters to be estimated, and ǫ it is a zero-mean random error. The advantage of (1) is that, under certain regularity assumptions, it is easy to consistently estimate the effect of FDI on growth using a least squares criterion. One primary drawback of this model, however, is that it fails to incorporate parameter heterogeneity that more likely exists in a cross-country panel of observations. In particular, model (1) does not allow the effect of FDI on growth, β 1, to vary with respect to the index of corruption. Allowing the parameter estimates to vary with respect to corruption is a pragmatic way to identify the indirect effect of corruption on growth. An alternative way to incorporate the level of corruption into the growth regression would be to add the corruption index as another conditioning (i.e., X) variable, but this approach does not identify indirect channels through which corruption influences growth. Corrupt governments (or officials) are more likely to embezzle funds and redirect public expenditures towards personal and private ventures, rather than direct them towards more publicly beneficial avenues. The effect is that FDI and other correlates of economic growth may be directly influenced by the level of corruption. Through these channels, corruption may indirectly influence GDP growth rates. However, it is important to incorporate the direct effects of corruption in the regression model to obtain an accurate picture of the effect of corruption on growth rates and on the relationship between the conditioning variables (e.g., FDI) and growth, and results that are comparable to those of existing growth studies. Since our interest is on the estimation of the effect of FDI on growth, and how this effect varies with respect to the level of corruption, we generalize the model to incorporate the effect of corruption on the β-parameters. Specifically, we generalize (1) by allowing the β-parameters in the model to vary with respect to a particular set of environmental variables, Z it, which contains the index of corruption. Hence, we write our generalized model as: g it = β 0 (Z it ) + Y it β 1 (Z it ) + X itβ 2 (Z it ) + ǫ it, i = 1,...,n t = 1,...,T. (2) An advantage of using the generalized model in (2) is that it provides observation-specific estimates of the coefficients of the model thereby allowing us to analyze the heterogeneity in the effect of FDI (and other control variables) on growth rates. As previously argued, an accurate modeling of parameter heterogeneity is crucial for designing cross-country policies to increase growth rates in developing countries; if the effect of FDI on growth rates varies substantially across different countries (or different groups or types of countries), investment policies governing FDI should be tailored to each specific country (or group of countries). The policy prescriptions for boosting growth through FDI, which are implied by homogeneous parameter estimated, may be too passive or active for some developing countries. If we assume that corruption is orthogonal to the error term, then it is straightforward to extract the direct and indirect effects of corruption on growth. The direct effect of corruption on growth comes through the effect of corruption on the intercept function, β 0 ( ); we can obtain 5

6 an estimate of this direct effect through the partial derivative of the intercept function with respect to corruption at a particular point, z: β 0 / z. The indirect effects come through the effect of corruption on the other coefficient functions in the model, β j 0 ( ); we obtain these effects through the partial derivatives of each of the slope coefficient functions with respect to corruption, β j 0 / z. The total effect of corruption on GDP growth rates is the sum of the direct and indirect effects of corruption on growth. Hence, taking a partial derivative of the growth rate in (2) with respect to corruption at a particular point yields the total effect of corruption on growth: 2.2 Estimation g it z = β 0 z + Y β 1 it z + β 2 X it z. (3) To exploit the generality of our model in (2), we assume that the coefficient functions are unknown smooth functions of Z. For ease of exposition, we rewrite (2) more compactly as: g it = X itβ(z it ) + ǫ it, i = 1,...,n t = 1,...,T, (4) in which X it is a vector of dimension k with the first column containing a one and the remaining columns containing the (k 1) regressors (including FDI); β( ) is a vector of smooth coefficient functions of unknown form; Z it is a vector of dimension p containing environmental factors that are assumed to be the sources of parameter heterogeneity. If we assume also that all regressors in X are exogenous then (4) is a standard semiparametric smooth coefficient model that can be consistently estimated using the nonparametric kernel estimator proposed by Li et al. (2002). This exogeneity assumption seems strong in the present growth application, hence we allow the variables in X to be endogenous. This key endogeneity assumption distinguishes our model in (4) from other semiparametric smooth coefficient models. In the special case where all regressors in X are exogenous, our model is equivalent to a standard semiparametric smooth coefficient model. If any element in X is endogenous, then E[g it X it, Z it ] X it β(z it) and estimation using typical semiparametric estimators (e.g., Li et al. 2002) will provide inconsistent estimates of the unknown coefficient functions. Several nonparametric estimators have been proposed to deal with the problem of endogeneity in smooth coefficient models, for example, Das (2005), Cai et al. (2006), and Cai and Li (2008). Both the estimators in Das (2005) and Cai et al. (2006) are two-step estimators that require nonparametric estimation of the endogenous variables on the instruments and exogenous variables in the first step followed by semiparametric regression of the dependent variable on the first stage estimates of the endogenous variables. Cai and Li (2008), however, propose a one-step estimator of (4) when X is allowed to be endogenous. We apply this one-step Cai and Li (2008) estimator to reap the gains in efficiency that the one-step estimator likely has over the two-step estimators. We note that the Cai and Li (2008) framework allows for all X variables to be endogenous, and explicitly assumes that the environmental variables in Z are exogenous. To circumvent the endogeneity problem and obtain consistent estimates of the coefficient 6

7 functions, Cai and Li (2008) propose the following conditional moment restriction: E[Q(Ω it )ǫ it Ω it ] = E[Q(Ω it ){g it X itβ(z it )} Ω it ] = 0, (5) in which Ω it = (W it, Z it ), W it is a vector of instrumental variables such that E[ǫ it W it ] = 0, and Q(Ω it ) is some vector function such that the conditional moment restriction in equation (5) is satisfied. While in principle any vector for Q(Ω it ) that satisfies the conditional moment restriction in (5) can be used, Cai and Li (2008) suggest using Q(Ω it ) = ( W it W it (Z it z)/h), where h is a smoothing parameter, and is the Kronecker product operator, to make use of the instrumental variables in W it. Cai and Li (2008) suggest estimating the coefficients, β(z it ), with nonparametric kernel methods which, combined with the conditional moment restriction in (5), yields a nonparametric equivalent of a GMM estimator (or NPGMM). We assume the coefficients, β(z it ), are twice continuously differentiable, so that we can apply local-linear least-squares to estimate the unknown functions. A first order Taylor expansion around a given point z yields an approximation to the function β j (Z it ) given by β j (z)+δ j (Z it z), in which δ j is a gradient vector of the partial effects β j (z)/ z. Thus the local-linear procedure provides a vector of estimated coefficient functions, ˆβ j (Z it ), along with their first order gradient vectors, ˆβ j (z)/ z. Letting U it = ( Xit X it (Z it z)) and α = (βj (z), δ j ) be the vector of coefficients and their first order partial derivatives, the conditional moment restriction in equation (5) gives rise to the following locally weighted orthogonality condition: n i=1 t=1 T Q(Ω it )(g it U itα)k h (Z it z) = 0 (6) in which K h (Z it z) is a generalized product kernel of dimension p that admits a mix of continuous and discrete environmental factors contained in Z (see Racine and Li 2004), and h denotes a vector of smoothing parameters. Cai and Li (2008) show that a consistent estimate of α can be obtained from: in which and S n = 1 n T n = 1 n ˆα = (S ns n ) 1 (S nt n ), (7) n i=1 t=1 n i=1 t=1 T Q(Ω it )U itk h (Z it z) (8) T Q(Ω it )K h (Z it z)g it. (9) To avoid any pitfalls associated with an ad hoc choice of smoothing parameters, we use least-squares cross-validation to select the parameters in h. The least-squares cross-validation criterion function is given by min h nt i=1 (g i ĝ i ) 2 (10) in which ĝ i is the leave-one-out estimate of the conditional mean, X ˆβ(Z). All standard errors 7

8 are estimated using a wild-bootstrap. 3 Data 3.1 Overview The data set comes from McCloud and Kumbhakar (2011). It consists of a balanced panel of 60 non-oecd countries spanning the period giving a total of 1080 observations. Our primary interest is in estimation of the effect of FDI on GDP growth and how this effect varies with respect to the level of corruption in each country in each year. Our secondary interest is in identifying the overall effect of corruption on GDP growth, both directly through its influence on the intercept term and indirectly through its role in the effects of other control variables on growth. Our measure of GDP growth is the per capita GDP growth rate that comes from the Penn World Table (version 6.2). 3.2 FDI Our measure of FDI is the percentage of FDI inflow relative to GDP in constant 2002 dollars, which comes from the United Nations Conference on Trade and Development online statistical database. It is generally believed that FDI may be correlated with any factors that influence growth rates but are omitted from the regression model; that is, FDI may be endogenous in a growth specification such as (1). The empirical FDI literature has been unable to identify an ideal instrumental variable to completely control for any endogeneity bias. Several studies have proposed several different instrumental variables that have been shown to mitigate, at least part of, the endogeneity of FDI. Borensztein et al. (1998), for example, suggest using lagged values of FDI or measures of institutional quality. Carkovic and Levine (2005) suggest using lagged FDI as well as lagged differences of FDI as instrumental variables. We find that in our data set, lagged values of FDI work reasonably well and appear to mitigate, at least part of, the endogeneity of FDI; see section 4.1. Measures of institutional quality (i.e., ethnolinguistic fractionalization and latitude from La Porta et al. (2009), and the log of the life expectancy and log of the fertility rate from the 2005 World Development Indicators) and lagged differences of FDI appear irrelevant based on their low explanatory power in the first-stage parametric regressions. Moreover, semiparametric regressions using these latter instrumental variables did not yield meaningful estimates or appear to mitigate any endogeneity bias. In addition to the above instrumental variables proposed in previous studies, we propose using total world FDI flows and total FDI flows to developing countries as alternative instrumental variables. Currently, we are unaware of other studies that use these total FDI flows as instrumental variables for individual country FDI flows. Our rationale for using these variables is that measures of total FDI flows will cause fluctuations in individual country FDI flows, but are uncorrelated with growth rates of individual countries. Parametric first-stage regressions suggest that total world FDI flows and total FDI flows to developing nations may be reasonable alternative instrumental variables for FDI. The sample correlations between FDI (the endogenous variable of interest) and each of the instrumental variables are 0.74, 0.32, and 0.13, for lagged FDI, world FDI flows, and developing world FDI flows, respectively. We use lagged FDI 8

9 as our preferred instrumental variable since it provides the strongest first-stage correlations with FDI (as well as strongest sample correlation), but we consider both measures of total FDI flows as alternative instrumental variables in our sensitivity analysis. 3.3 Corruption We combine two indices of corruption that are widely used in the existing empirical literature. One index of corruption is from Knack and Philip (1998), which is for the period 1984 to This index ranges from 0 to 6 and lower scores indicate lower 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. The other corruption index is from Transparency International (TI) for the period 1997 to The TI s corruption index measures the overall extent of corruption and therefore does not distinguish between administrative and political corruption, nor between petty and grand corruption. It ranges from 0 to 10 with higher values indicating lower levels of corruption. For ease of exposition, we rescale the TI index so that lower values represent lower levels of corruption. An important assumption in this analysis is that our proxies for corruption are time invariant. Our rationale is based on the fact that the extent to which corruption is entrenched in many non-oecd countries makes it difficult for these countries to lower their corruption levels in the absence of proper legal recourse through institutional reform. Consequently, we transform the Knack and Philip index to be within the range of 0 to 10 and then construct an aggregated corruption index by using the time average of the Knack and Philip and TI indices as the measure of corruption for the entire time span. We note that the Spearman s rank correlation coefficient for the average PRS and TI indices is with a p-value of 0 for the null hypothesis of independence. Hence, combining the different measures of corruption from these two sources should not bias the qualitative implications about the effect of corruption on FDI-growth relation. 3.4 Additional Control Variables We use the following list of covariates to control primarily for any omitted variables bias between GDP growth and FDI, but also to serve as possible channels through which corruption may effect growth. The variables include initial GDP per capita defined as GDP per capita in the previous year; openness, defined as the ratio of exports plus imports as a percentage of GDP; government consumption, defined as the ratio of general government consumption as a percentage of GDP; domestic investment as a percentage of GDP; the US treasury bill rate; and the inflation rate. All variables come from the Penn World Table (version 6.2) except for the US treasury bill rate which comes from the IMF International Financial Statistics Database. We include the US treasury bill rate to control for changes in the growth rate that are caused by macroeconomic conditions that are exogenous to each individual country. 2 The TI index was first launched in 1995 with only a small number of countries. Using earlier years of this index would have reduced our effective sample size. 9

10 In addition to corruption, the vector of environmental variables, Z, also contains an unordered categorical country indicator and an ordered categorical indicator for year to control for country and year fixed effects, respectively. Alternative specifications include the fertility rate (total births per woman) and an index of democracy as additional environmental variables. Our index of democracy comes from the Polity IV database and ranges from -10 to +10 with +10 representing complete democracy and -10 complete autocracy. With the exception of the variables already measured in percentage terms or growth rates, all continuous variables are measured in logs. 4 Results 4.1 Ordinary Least Squares We first estimate the standard homogeneous model in (1) using ordinary least squares. Since the coefficients do not vary in this model, we include corruption and country and time dummy variables as standard conditioning (i.e., X) variables. The purpose of estimating the homogeneous model is to provide estimates that are directly comparable to other studies that do not use semiparametric estimators, and to anchor our semiparametric results to the standard case. Table 1 contains the results from the different model specifications. The first three columns in Table 1 show estimates from three standard models: the first column reports the results from a parsimonious model in which the only regressors are FDI and fixed effect dummy variables; the second column adds corruption; and the third column adds the rest of the conditioning set. We find that FDI has a positive and significant effect on growth rates in columns 1 and 2; that is, including corruption in the regression does not erode the effect of FDI on growth. In particular, an increase of 10 percent in the FDI inflows to GDP is associated with an increase of 3 percent in economic growth rate. Interestingly, the coefficient on corruption is positive and significant. A positive coefficient on corruption implies that holding everything else constant, increasing the level of corruption in a country will increase its rate of real GDP per capita growth. We find this result to be counter-intuitive; our prior expectation is that corruption has a negative (or perhaps insignificant) effect on GDP growth rates. Moreover, the R 2 does not improve substantially after including corruption into the regression, which suggests that corruption may not contain much predictive power. Including the rest of the conditioning set (column 3) does not change the effect of corruption on growth, but it does erode the effect of FDI on growth by approximately 67 percent. This large reduction in the estimated FDI coefficient suggests that the FDI-growth effects in the columns 1 and 2 may be driven by omitted variables bias. Indeed, there may be other factors that are subsumed in the errors and are correlated with both FDI and economic growth. To explore this possibility, we use instrumental variables methods. Columns 4 through 6 report estimates from two-stage least squares regressions that use the one-period lagged value of FDI to control for any possible endogeneity of FDI in the standard models. Specifically, we include all exogenous variables including corruption in the first stage regression, as well as country and time dummy variables to control for country and time fixed effects. We find that for each first-stage specification, the FDI instrument is positive and sta- 10

11 tistically significant, and the F-statistic for the null hypothesis of no regression exceeds 10, suggesting strength of the instrumental variable (Staiger and Stock, 1997). We find that in the second-stage regressions, including the fully specified model in column 6, the instrumented FDI variable has a positive and significant effect on growth rates. In addition, the magnitude of the FDI coefficient is substantially larger than in the simple ordinary least squares models. This suggests that there is a downward bias in the ordinary least squares estimates of FDI, most likely caused by endogeneity; the lagged FDI instrument is able to correct for (at least part of) the downward bias on the FDI coefficient. Corruption remains positive and significant, and many other conditioning variables maintain their sign and significance observed in their ordinary least squares counterparts. The explanatory power in the two-stage least squares models is comparable to that from the ordinary least squares models. The aforementioned ordinary least squares and two-stage least squares homogeneous estimates yield three important observations: One, on average, FDI has a positive and significant effect on GDP growth rates in non-oecd countries, but the effect is subject to a downward endogeneity bias that will potentially mask the significance of FDI. Two, the use of lagged FDI as an instrument for FDI is able to mitigate this downward bias and provides more precise estimates of the effect of FDI on growth. This positive mean effect of FDI on growth, as implied by the homogeneous models, should not be taken to imply that in all countries, FDI has a positive and significant effect on growth rates. Three, corruption appear to have strongly positive and significant, albeit counter-intuitive, effect on growth rates. This latter counterintutive result may be a manifestation of model misspecification, at least with regards to the way in which corruption is included in the model. A maintained hypothesis is this paper is that corruption itself is an environmental variable and thus it should be included as such in the regression, and not included as a typical conditioning (i.e., X) regressor. In light of these observations, we move on to the results from our generalized semiparametric specifications that concurrently allow for (a) corruption to enter into the model indirectly through its influence on the relationship between the conditioning variables and GDP growth rates, (b) parameter heterogeneity and (c) endogenous regressors. 4.2 Semiparametric Smooth Coefficient Models Columns 7 through 10 in Table 1 report the mean coefficients and standard errors for four semiparametric smooth coefficient specifications. The first two specifications (columns 7 and 8) do not control for endogeneity of FDI; hence, these models are standard semiparametric smooth coefficient models (SPSCM). Columns 9 and 10 control for endogeneity of FDI using lagged FDI and the Cai and Li (2008) NPGMM estimator. Columns 7 and 9 include only FDI as a conditioning variable, whereas columns 8 and 10 include all other conditioning variables. Each of the four models include corruption and indicators for country and year as environmental variables Mean Parameter Estimates We find that the mean coefficient on FDI is positive and statistically significant in all semiparametric specifications. In the semiparametric models that do not allow for instrumental variables 11

12 (columns 7 and 8), we observe FDI coefficients that are similar in magnitude to their ordinary least squares estimates in columns 1 and 2. After controlling for endogeneity, we observe that the mean FDI coefficients in the semiparametric models (columns 9 and 10) are close in magnitude to their counterparts from the two-stage least squares models. In essence, the FDI coefficients are substantially larger in magnitude in the semiparametric models that control for endogeneity, suggesting that the endogeneity of FDI biased its coefficients downward bias. Thus, we again find evidence that supports the validity of using lagged FDI values to correct for any endogeneity bias associated with FDI. Turning to the additional conditioning variables in the fully-specified models (columns 8 and 10), we find that regardless of whether we instrument for FDI, the mean estimates of initial income, openness and the inflation rate are negative and highly statistically significant, whereas those associated with domestic investment are positive and highly statistically significant. The mean estimates of all other conditioning variables are insignificant. Turning to the total effect of corruption on growth, g/ Z, we find in each of the four semiparametric models that corruption has an insignificant effect on GDP growth rates. This result is more in line with our prior expectations, and is in contrast to the results from the ordinary least squares and two-stage least squares estimates that found corruption to have a positive and significant effect on growth rates. Table 2 shows the means and standard errors of the direct effect of corruption on the coefficients in the semiparametric models. At the mean, we find that corruption has a negative and significant effect on the coefficient on FDI (columns 2 to 4). Thus, coupling this result with the positive and significant FDI coefficients in Table 1 (columns 8 to 10) implies that an increase in corruption will decrease the effectiveness of FDI on growth, and through this channel, holding everything else constant, decrease GDP growth. From Table 2, we also find that corruption has a positive and significant effect on the coefficient on openness (column 2) and on inflation (column 4). Since both the openness and inflation coefficients are negative and significant (see columns 8 and 10 of Table 1), these positive partial derivatives imply that the effect of openness and inflation on growth is dampened by an increase in corruption. In addition, we find that in each of the four semiparametric models, the R 2 is substantially higher than in the corresponding homogeneous regressions. These higher R 2 values suggest that there are sizeable parameter heterogeneities across countries and modeling these parameter heterogeneities substantially improves the fit of the model to the data. We now turn to the distribution of the coefficients and their partial effects with respect to corruption to further assess the degree of parameter heterogeneity that exists in the estimates, and to understand the policy implications of heterogeneity in the relationship between FDI and growth Heterogeneous Parameter Estimates To present the distribution of coefficients in a concise manner, we use 45-degree gradient plots to simultaneously show the magnitude, sign, standard errors, statistical significance and density of the coefficients. To construct these plots, we first plot the observation-specific coefficients on the 45 degree line. The location of any particular coefficient to the horizontal axis determines the sign and magnitude of the coefficient, whereas the density can be seen by the proximity 12

13 of surrounding observations to any particular observation. Areas with a high concentration of coefficients are areas of higher density. We then calculate observation-specific confidence bounds by adding (and subtracting) twice the observation-specific standard error from each coefficient. We then overlay the confidence bounds above (and below) the scatterplot of coefficients. This allows us to assess whether each observation is statistically significant; if the horizontal line at zero runs between the coefficient and its upper or lower confidence bound, the observation has a statistically insignificant coefficient. If the horizontal line at zero does not intersect the confidence bound for a particular observation, that observation is statistically significant. Figure 1 displays the 45-degree gradient plots for the distribution of observation-specific FDI coefficients and standard errors for each of the four semiparametric models that are described in Table 1. In each model, many of the observations are positive. Specifically, for the standard semiparametric models that do not use instrumental variables (SPSCM models), 56 percent and 65 percent of the FDI coefficients are positive and significant, respectively SPSCM1 and SP- SCM2. In the semiparametric models that use lagged FDI as an instrumental variable (NPGMM models), the FDI coefficients are positive and significant for 59 percent and 76 percent of the observations, respectively NPGMM1 and NPGMM2. While the plots show a substantial amount of heterogeneity in the parameter estimates, it is clear that, on average, FDI has a positive and significant effect on GDP growth rates. Moreover, after instrumenting for any endogeneity bias on the coefficients, we find that the fraction of coefficients that are positive and significant increases. These results provide evidence that the lagged value of FDI is also able to mitigate (at least part of) the downward bias on the FDI coefficients in the semiparametric models. In reference to the additional conditioning variables in the fully-specified models that have statistically significant mean estimates, we find that 59 percent of the initial income coefficients are negative and significant in the model that does not instrument for FDI, whereas 72 percent of the coefficients are negative and significant in the instrumental variables model. We find that 46 percent of the coefficients on openness are negative and significant in the non-instrumental variables model, and 75 percent of the coefficients are negative and significant in the instrumental variables model. In the non-instrumental variables model we find that 94 percent of the coefficients on domestic investment are positive and significant, and 94 percent of the coefficients on inflation are negative and significant. In the instrumental variables model, we find that 95 percent of the coefficients on domestic investment are positive and significant, and 91 percent of the coefficients on inflation are negative and significant. These results suggest that endogeneity of FDI induces biases in the estimates associated with the other regression coefficients, and the size and direction of these biases appear to differ across countries and regressors. Figure 2 contains 45 degree plots for the partial effects of the FDI coefficients with respect to corruption. For the standard semiparametric models, 42 percent and 74 percent of the FDI coefficients show a significantly negative partial effect with respect to corruption, respectively SPSCM1 and SPSCM2. In the semiparametric instrumental variables models, 45 percent and 84 percent of the FDI coefficients show a negative and significant partial effect with respect to corruption, respectively NPGMM1 and NPGMM2. These results, especially in the fully specified models, lend additional support to the view that corruption decreases the effectiveness of FDI on GDP growth. 13

14 The effect of corruption on the additional coefficients in the fully-specified models is insignificant, except for the coefficients associated with openness and inflation. In the non-instrumental variables model, we find that corruption significantly reduces the effectiveness of openness on growth rates for 58 percent of the observations. In the instrumental variables model, the effect of corruption on openness ceases to be statistically significant; however, we find that 56 percent of the observations have a positive and significant partial effect of the inflation coefficient with respect to corruption. In general, these results suggest that corruption strongly affects the FDI coefficient, and has a neutral effect on the coefficients of (many of) the other conditioning variables in the model. For the fully-specified models, 45-degree gradient plots for the additional conditioning variables are available upon request from the authors. Figure 3 shows the 45 degree plots for the total effect of corruption on growth rates. In the first two semiparametric models (that do not instrument for endogeneity), we find 64 percent and 70 percent of the partial effects to be insignificant, respectively SPSCM1 and SPSCM2. In the semiparametric instrumental variables models, we find 66 percent and 72 percent of the partial effects to be insignificant, respectively NPGMM1 and NPGMM2. Hence, we find strong evidence that although corruption decreases the effectiveness of FDI on growth rates, corruption has an overall insignificant effect on growth. With regards to the estimated bandwidths, we find in each of our four semiparametric models that the bandwidth on corruption exceeds several standard deviations of the data. In the local-linear least-squares context, a relatively large bandwidth on corruption implies that corruption enters linearly into the parameters, β j ( ). Local-linear least-squares is nothing more than weighted least-squares through the kernel function providing a local weight for each observation; a large bandwidth means that the local neighborhood includes all observations, and hence a globally linear estimate with respect to corruption. 3 We leave further analysis of any potential linearity between corruption, FDI, and GDP growth for future research. Our empirical results so far are in favor of parameter heterogeneity. To formally test whether the semiparametric models yielding heterogeneous parameter estimates are indeed preferred to the homogeneous parameter models, we use the model specification test of Cai et al. (2000). The Cai et al. (2000) test allows us to determine whether the data support the null hypothesis of the simple two-stage least-squares model. We test the null hypothesis against two alternative hypotheses: the two primary semiparametric smooth coefficient models that include the entire conditioning set of regressors (one using instrumental variables and the other without). We are able to reject the null hypothesis of correct specification for the constant parameter model in both tests with a p-value of Hence, the data support our generalized semiparametric specification that admits parameter heterogeneity as a function of corruption over the homogeneous parameter specification. 3 This does not imply any particular parametric functional form for the coefficients, β j( ), since a large bandwidth on corruption does not necessarily point towards any specifications regarding interactions between corruption and other environmental variables, or towards correct parametric specification for other environmental variables. 14

15 4.2.3 Policy Implications One of the advantages of incorporating parameter heterogeneity into the regression model is that it allows us to identify the country specific returns to both FDI and a marginal change in corruption. We can analyze the placement of countries in the distribution of FDI coefficients to ascertain which countries have the highest returns to FDI. In addition, we can identify which group of countries may benefit the most from a reduction in corruption; countries that have the highest partial effect of the FDI coefficient with respect to corruption may benefit substantially from FDI if their level of corruption were to decrease. Moreover, the present analysis may help directly with international FDI policies. One stipulation in an international FDI agreement may be a mandatory reduction in the level of corruption in the developing host country. At the very least, this analysis can assist policymakers in determining in which countries FDI will most effectively improve growth rates, and in which countries FDI may have a neutral effect. Focusing now on the fully-specified semiparametric instrumental variables model (NPGMM), we analyze which countries appear to have the highest and lowest returns to FDI. Table 3 shows the lists of countries divided based on their relative returns to FDI. For those observations with positive and significant FDI coefficients, we divide the countries into separate lists for each of the four quantiles based on the magnitude of the coefficient. That is, the countries with FDI coefficients that are in the highest 75 percentile are grouped together in the 4 th quantile group; we do the same for each quantile. 4 Since all of the countries in these quantile lists realize positive returns to FDI, we also include a list of countries that have insignificant FDI coefficients. 5 Because we have a panel data set, some countries have FDI coefficients that appear in each category for at least one year. To provide a bit more clarity as to which countries receive high or low returns, we group the countries based on their modal classification: if a country appears most frequently in the column for insignificant returns to FDI, we classify it as insignificant. It is important to highlight which countries have consistently insignificant returns to FDI; policymakers may want to reconsider investment policies or investment stipulations aimed at these particular countries. 6 We can see in Table 3 that there does not appear to be any geographical similarities between the groupings of countries. Each group of countries contains countries from each continent or geographical region. This result implies that there exists heterogeneity in FDI returns even within geographical regions. Hence, geographical-oriented investment policies may be inappropriate for enhancing growth-effects of FDI, the best FDI policies may most likely be country-specific. With this in mind, the country lists in Table 3 provide preliminary estimates of the potential returns each country may realize from further FDI. Table 4 shows a similar breakdown of countries based on the partial derivative of the FDI coefficient with respect to corruption. 7 Here, we classify the modal observation into quantiles of 4 The smallest positive and significant coefficient is 0.004, and the largest positive and significant coefficient is The quartile values are 0.37, 0.61, and 0.78, respectively, for the 25 th, 50 th, and 75 th percentiles. All estimated values are in percentage terms. 5 Only 2 percent of the coefficients were negative and significant; none of the negative and significant coefficients represented the modal classification, so we do not include a category for negative returns. 6 It is important to acknowledge that although these classifications are based on the modal observations, many of the countries appear in the same category for many of the years in the panel. Hence the modal classification provides an accurate depiction of the distribution of the countries across the classification groups. 7 Specifically, the largest negative and significant partial effect is -4.16, and the smallest negative and significant 15