Abstract
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.
Acknowledgement
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”.
Technical Appendix
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
The proofs for
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
where W2, itr is the r-th element of W2, it and
Now, by Assumption A.1 and Assumption A.2, and for a fixed T, it is straightforward to show that
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
For (iia),
Thus,
Similarly, for (iib), we can show that
(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
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
Proof of Proposition Proposition 3.3:.
Since
To prove that
we will show that the off-diagonal block terms for
(i) To compute
For the first term in (42), we have,
By Assumption A.1 and Assumption A.2, and invoking similar steps to Cai and Li (2008) [Proof of Proposition 2], we obtain
Hence, V11,2 = O(n−1) and therefore by virtue of Assumption A.2 we obtain
For the second term in (42), and using Assumption A.1 we have,
To see this observe the following. The third and fourth summands in
For a fixed T and by invoking Assumption A.2, Assumption A.3 and Assumption A.5, this first summand is O(N−1). Similarly, the second summand in
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,
For the first term in (45), and by Assumption A.1 and Assumption A.2,
Similarly, for the second term in (45),
For the third term in (45),
For the fourth term in (45),
(iii) To compute
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
In essence, the off-diagonal block terms for
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
By Assumption A.2 and Proposition 3.3, and for any i = 1, …, N and t = 1, …, T, we obtain
where
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:.
Note that
Then E[
and
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
The third and fourth terms in (52) are zero by Assumption A.1. For the first term in (52), we have
Hence, this completes the proof of Proposition 3.9. □
Proof of Theorem Theorem 3.11:.
This is straightforward given the above results in the proofs of Theorem 3.4 and Proposition 3.9, and the results in Cai and Li (2008). □
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