We characterize the types of interactions between foreign direct investment (FDI) and economic growth, and analyze the effect of institutional quality on such interactions. To do this analysis, we develop a class of instrument-based semiparametric system of simultaneous equations estimators for panel data and prove that our estimators are consistent and asymptotically normal. Our new methodological tool suggests that across developed and developing economies, causal, heterogeneous symbiosis and commensalism are the most dominant types of interactions between FDI and economic growth. Higher institutional quality facilitates, impedes or has no effect on the interactions between FDI and economic growth.
Elizabeth Byrd and Shamar Stewart provided excellent research assistance. We thank participants at the 2013 China Meeting of the Econometric Society, the 2013 Asian Meeting of the Econometric Society, and the Department of Economics Research Seminar at the University of the West Indies at Mona for helpful comments. McCloud thanks the support of the Mona Research Fellowship from the Office of the Principal at University of the West Indies at Mona. This research was supported in part by computational resources provided by Information Technology at Purdue – Rosen Center for Advanced Computing, Purdue University, West Lafayette, Indiana. This paper has been presented under its previous title “Are There Feedbacks Between Foreign Direct Investment And Economic Growth? A Semiparametric System Of Simultaneous Equations Analysis With Instrumental Variables”.
In this appendix, we assume C ∈ (0, ∞) is an arbitrary bounded constant. Recall that n ≡ NT; we use these terms interchangeably. The integral symbol represents a multiple integral of varying dimensions depending on the context in which it is used. We provide the proofs for only Proposition 3.2, Proposition 3.3 and Proposition 3.9 and Theorem 3.4 because the proofs for Corollary 3.7 and Theorem 3.6 and Theorem 3.11 are less involved. Many of the ensuing proofs use convergence in mean square.
Proof of Proposition Proposition 3.2:.
(i) Note that
We now prove part (ib); the proof of part (ia) can be easily established using the approach below.
where the second equality is by virtue of Assumption A.1, the fourth equality follows from law of iterative expectations (LIE), the sixth equality uses a change of variable, and the remaining equalities are consequences of changes in the implied canonical differential form, Lebesgue Dominated Convergence Theorem, and Assumption A.2, Assumption A.3, and Assumption A.5.
We now show that as . We define
where W2, itr is the r-th element of W2, it and is the s-th element of . Then, by Assumption A.1, we obtain
Now, by Assumption A.1 and Assumption A.2, and for a fixed T, it is straightforward to show that . By similar arguments and using the Cauchy-Schwarz result that yield . Hence, we obtain as required. Therefore, we have
By invoking similar steps to those above, we deduce that
Thus, the proof of part (i) is complete.
(ii) Note that
The proofs for Bn,11 and Bn,22 follow directly from Cai and Li (2008) [Proof of Proposition (ii)], which yields and . To complete the proof, it remains to show that (iia) and (iib) .
Thus, . In addition, any (r, s)-entry of the Var(Bn,12) converges to zero.
Similarly, for (iib), we can show that , and any (r, s)-entry of the Var(Bn,21) converges to zero. Therefore, and , which respectively do not statistically dominate Bn, 11 and Bn,22. Hence, the proof of part (ii) is complete.
(iii) Note that
The proofs for Rn, 11 and Rn,22 follow directly from Cai and Li (2008) [Proof of Proposition (iii)], which yield that and . To complete the proof, we now show that (iiia) and (iiib) .
We prove part (iiib); by symmetry, the proof of part (iiia) easily follows.
where the last equality is a consequence of LIE. Applying a change of variables, the result that , Lebesgue Dominated Convergence Theorem, and Assumption A.1 to Assumption A.3, we obtain as required. By symmetry, it is straightforward to derive the result that . Furthermore, any (r, s)-entry of both the Var(Rn,21) and Var(Rn,12) converges to zero. In essence, the terms Rn,11 and Rn,22 stochastically dominate their counterparts. Therefore, we obtain the desired result. □
Proof of Proposition Proposition 3.3:.
Since , we write . Now
To prove that
we will show that the off-diagonal block terms for in A.4 are of smaller order than its (1, 1) and (2, 2) main-diagonal block terms, which are of orders and respectively.
(i) To compute , note that
For the first term in (42), we have,
Hence, V11,2 = O(n−1) and therefore by virtue of Assumption A.2 we obtain
To see this observe the following. The third and fourth summands in are zero by Assumption A.1. For the first summand in , note that
For the fourth term in (42),
Then, for a fixed T, V12,1 = O(N−1) = o(1). In a similar manner, we obtain V12,2 = o(1).
(ii) Note that by symmetry, . To compute , we use the decomposition
Similarly, for the second term in (45),
For the third term in (45),
For the fourth term in (45),
(iii) To compute , note that
For the first term in (46), we proceed as follows,
Using the steps in (44), we can show that
Hence, for a fixed T, V21,1 = O(N−1). Similarly, we obtain V21,2 = o(1).
For the second term in (46),
For the fourth term in (46),
Similar to the above proof of , we can easily show that
In essence, the off-diagonal block terms for in A.4 are of smaller order than its (1, 1) and (2, 2) main-diagonal block terms, which are of orders and respectively. Therefore, this completes the proof of Proposition 3.3. □
Proof of Theorem Theorem 3.4:.
We apply the Cramér-Wold device to assist in establishing asymptotic normality, given the multivariate nature of our semiparametric system estimator. We introduce some additional notations for ease of exposition. We define
For any such that , we set , where Qit = block diag (Q1,it, Q2,it) and for i = 1, …, N and t = 1, …, T. Thus, we have
where . Thus, .
Continuing in this way, it remains to show that the Lyapounov condition holds. This is easily achieved by invoking the stipulated assumptions, Minkowski’s inequality and similar steps to Proof of Theorem 2 in Cai and Li (2008). □
Proof of Proposition Proposition 3.9:.
and , , and . Using the results in Cai and Li (2008), it is easy to show that
Thus, it suffices to show that the off-diagonal block terms in (51) are also of the order of magnitude n−1h−d. We only consider the (1,2) block-entry in (51), as the result for the (2,1) block-entry will follow by virtue of symmetry. To begin, we express as
Hence, this completes the proof of Proposition 3.9. □
Alfaro, L., and M. Johnson. 2013. “Foreign Direct Investment and Growth, Chap. 20.” In The Evidence and Impact of Financial Globalization, edited by Gerard Caprio, 299–307. Elsevier.10.1016/B978-0-12-397874-5.00016-6Search in Google Scholar
Alfaro, L., A. Chanda, S. Kalemli-Ozcan, and S. Sayek. 2004. “FDI and Economic Growth: The Role of Local Financial Markets.” Journal of International Economics 64: 89–112.10.1016/S0022-1996(03)00081-3Search in Google Scholar
Borensztein, E., J. De Gregorio, and J. W. Lee. 1998. “How Does Foreign Direct Investment Affect Economic Growth?” Journal of International Economics 45: 115–135.10.1016/S0022-1996(97)00033-0Search in Google Scholar
Carkovic, M., and R. Levine. 2005. “Does foreign direct investment accelerate economic growth?” In Does Foreign Direct Investment Promote Development?, edited by H. Moran, E. M. Graham. Washington, D.C.: Institute for International Economics.Search in Google Scholar
Das, M. 2005. “Instrumental Variables Estimators for Nonparametric Models with Discrete Endogenous Variables.” Journal of Econometrics 124: 335–361.10.1016/j.jeconom.2004.02.001Search in Google Scholar
Delgado, M. S., N. McCloud, and S. C. Kumbhakar. 2014. “A Generalized Empirical Model of Corruption Foreign Direct Investment and Growth.” Journal of Macroeconomics 42: 298–316.10.1016/j.jmacro.2014.09.007Search in Google Scholar
Durham, J. B. 2004. “Absorptive Capacity and the Effects of Foreign Direct Investment and Equity Foreign Portfolio Investment on Economic Growth.” European Economic Review 48: 285–306.10.1016/S0014-2921(02)00264-7Search in Google Scholar
Fan, J., and I. Gijbels. 1996. Local Polynomial Modeling and its Applications. New York: Chapman and Hall.Search in Google Scholar
Henderson, D. J., S. C. Kumbhakar, and C. F. Parmeter. 2012a. “A Simple Method to Visualize Results in Nonlinear Regression Models.” Economics Letters 117: 578–581.10.1016/j.econlet.2012.07.040Search in Google Scholar
Henderson, D. J., S. C. Kumbhakar, Q. Li, and C. F. Parmeter. 2015. “Smooth Coefficient Estimation of a Seemingly Unrelated Regression.” Journal of Econometrics 189: 148–162.10.1016/j.jeconom.2015.07.002Search in Google Scholar
Heston, A., R. Summers, and B. Aten. 2012. Penn World Table Version 7.1. Center for International Comparisons of Production, Income and Prices at the University of Pennsylvania.Search in Google Scholar
Huynh, K. P., and D. T. Jacho-Chávez. 2009b. “A Nonparametric Quantile Analysis of Growth and Governance.” Advances in Econometrics 25: 193–221.10.1108/S0731-9053(2009)0000025009Search in Google Scholar
Kottaridi, C., and T. Stengos. 2010. “Foreign Direct Investment, Human Capital and Nonlinearities in Economic Growth.” Journal of Macroeconomics 32: 858–871.10.1016/j.jmacro.2010.01.004Search in Google Scholar
Li, X., and X. Liu. 2005. “Foreign Direct Investment and Economic Growth: An Increasingly Endogenous Relationship.” World Development 33: 393–407.10.1016/j.worlddev.2004.11.001Search in Google Scholar
Li, Q., and J. S. Racine. 2007. Nonparametric Econometrics: Theory and Practice. Princeton, NJ: Princeton University Press.Search in Google Scholar
Li, Q., and J. S. Racine. 2010. “Smooth Varying Coefficient Estimation and Inference for Qualitative and Quantitative Data.” Econometric Theory 26: 1607–1637.10.1017/S0266466609990739Search in Google Scholar
Li, Q., E. Maasoumi, and J. S. Racine. 2009. “A Nonparametric Tests for Equality of Distributions with Mixed Categorical and Continuous Data.” Journal of Econometrics 148: 186–200.10.1016/j.jeconom.2008.10.007Search in Google Scholar
McCloud, N., and S. C. Kumbhakar. 2012. “Institutions, Foreign Direct Investment, and Growth: A Hierarchical Bayesian Approach.” Journal of the Royal Statistical Society: Series A 175: 83–105.10.1111/j.1467-985X.2011.00710.xSearch in Google Scholar
Papaioannou, E. 2009. “What Drives International Financial Flows? Politics, Institutions and Other Determinants.” Journal of Development Economics 88: 269–281.10.1016/j.jdeveco.2008.04.001Search in Google Scholar
Racine, J. S., and Q. Li. 2004. “Nonparametric Estimation of Regression Functions with Both Categorical and Continuous Data.” Journal of Econometrics 119: 99–130.10.1016/S0304-4076(03)00157-XSearch in Google Scholar
Racine, J. S., and C. F. Parmeter. 2013. “Data-Driven Model Evaluation: A Test for Revealed Performance.” In Handbook of Applied Nonparametric and Semiparametric Econometrics and Statistics, edited by Jeffrey S. Racine, Liangjun Su and Aman Ullah, 308–345. Oxford University Press.10.1093/oxfordhb/9780199857944.013.010Search in Google Scholar
Tran, K. C., and E. G. Tsionas. 2009. “Local GMM Estimation of Semiparametric Panel Data with Smooth Coefficient Models.” Econometric Reviews 29: 39–61.10.1080/07474930903327856Search in Google Scholar
World Bank. 2012. World Development Indicators [CD-ROM] Washington, DC.Search in Google Scholar
©2018 Walter de Gruyter GmbH, Berlin/Boston