Revisiting the FDI impact on GDP growth in errors-in-variables models: a panel data GMM analysis allowing for error memory

Abstract

GMM estimation of autoregressive equations in error-ridden variables with error memory is considered in exploring the impact of foreign direct investment (FDI) on GDP from country panel data, contrasting, inter alia, the manufacturing and the service sector. To evaluate finite-sample properties of the methods selected, results from Monte Carlo simulations are reported. Contrary to the previous findings, no negative spillover effects from the service FDI on manufacturing GDP growth are obtained; the estimates indicate a positive effect, while (surprisingly) the effect of service FDI on the service GDP growth comes out as insignificant. Overall conclusions are: (1) Aggregate FDI has a positive, but insignificant effect on aggregate GDP based on the full country panel; (2) for the developing Asian countries, FDI significantly improves GDP growth; and (3) manufacturing FDI impacts both manufacturing and service GDP growth positively.

Appendices

Appendix 1: Design of simulations

This appendix describes the Monte Carlo simulation framework for the general model (1) The processes generating $(\varvec{\eta }_{it},\nu _{it},u_{it},\varvec{\xi }_{it})$ are, respectively:

$$\begin{aligned} \varvec{\eta }_{it}= & {} \textstyle \sum _{s=0}^{N_\eta }\varvec{\epsilon }_{i,t-s}\varvec{B}_s, \qquad \varvec{\epsilon }_{it}\sim \mathsf{{IIN}}_K(\varvec{0},\varvec{\Sigma }_{\varvec{\epsilon }}),\\ \nu _{it}= & {} \textstyle \sum _{s=0}^{N_{\nu }}\delta _{i,t-s}d_s, \qquad \delta _{it}\sim \mathsf{{IIN}}_1(0,\sigma _\delta ^2),\\ u_{it}= & {} \textstyle \sum _{s=0}^{N_u}v_{i,t-s}c_s, \qquad v_{it}\sim \mathsf{{IIN}}_1(0,\sigma _v^2), \\ \varvec{\xi }_{it}= & {} \varvec{\chi }_i+\textstyle \sum _{s=0}^{N_\xi }\varvec{\psi }_{i,t-s}\varvec{A}_s, \qquad \varvec{\psi }_{it}\sim \mathsf{{IIN}}_K(\varvec{0},\varvec{\Sigma }_{\varvec{\psi }}),\ \ \ \varvec{\chi }_i\sim \mathsf{{IIN}}_K(\bar{\varvec{\chi }},\varvec{\Sigma }_{\varvec{\chi }}),\\ i= & {} 1,\ldots ,N;\,t=1,\ldots ,T, \end{aligned}$$

$\mathsf{{IIN}}$ denotes ‘identically independently normal’ and subscript K indicates the distribution’s dimension. Heterogeneity is generated by $\alpha _i\sim \mathsf{{IIN}}_1(0,\sigma _\alpha ^2)$. These assumptions in combination with (1) and (2) imply

$$\begin{aligned} \varvec{q}_{it}&=\varvec{\chi }_i+\textstyle \sum _{s=0}^{N_\xi }\varvec{\psi }_{i,t-s}\varvec{A}_s+\textstyle \sum _{s=0}^{N_\eta }\varvec{\epsilon }_{i,t-s}\varvec{B}_s,\\ (1-\lambda \mathsf{{L}})(y_{it}-\nu _{it})\mu _{it}&=\alpha _i+\left( \varvec{\chi }_i+\textstyle \sum _{s=0}^{N_\xi }\varvec{\psi }_{i,t-s}\varvec{A}_s\right) \varvec{\beta }+\textstyle \sum _{s=0}^{N_u}v_{i,t-s}c_s,\\ w_{it}&=\textstyle \sum _{s=0}^{N_u}v_{i,t-s}c_s+\textstyle \sum _{s=0}^{N_{\nu }}(1-\lambda \mathsf{{L}})\delta _{i,t-s}d_s-\textstyle \left( \sum _{s=0}^{N_\eta }\varvec{\epsilon }_{i,t-s}\varvec{B}_s\right) \varvec{\beta }. \end{aligned}$$

Since $\varvec{\chi }_i$ and $\alpha _i$ enter the model asymmetrically and the variables in levels and in differences fill opposite roles in the estimators $\widetilde{\varvec{\gamma }}_L$ and $\widetilde{\varvec{\gamma }}_D$, given by (9) and (10), changes in heterogeneity, measured by $\sigma _\chi ^2$ and $\sigma _\alpha ^2$, affect the estimators’ distribution in quite different ways. For example, changes in $\bar{\varvec{\chi }}$ or in $\sigma _\chi ^2$ affect $\varvec{q}_{it}$ and $y_{it}$, but not $\Delta \varvec{q}_{it}$ or $\Delta y_{it}$, since differencing eliminates any time-invariant variable, while a change in $\sigma _\alpha ^2$ affects only the distribution of the level $y_{it}$. The $\mu _{it}$ process is initialized by using as start values the ‘long-run expectation’ $\mu _{i0}=\mathsf{{E}}[\mu _{it}/(1-\lambda \mathsf{{L}})]=\bar{\varvec{\chi }}\varvec{\beta }/(1-\lambda )$. $R=500$ replications are performed. The baseline parameter set is:

Coefficients::

$(\beta _1,\beta _2,\lambda )= (0.6,0.3,0.8)$.

Auxiliary matrices::

$\varvec{I}_2=\left[ \begin{array}{cc} 1 &{} 0\\ 0 &{} 1\end{array}\right] \varvec{J}_2=\left[ \begin{array}{cc} 1 &{} \frac{1}{2}\\ \frac{1}{2} &{} 1 \end{array}\right]$

$\varvec{\xi }_{it}\, \mathrm{process}:$ :

$(\bar{\chi }_1,\bar{\chi }_2)=(5,10);$

$\sigma _\chi ^2=0.1; \varvec{\Sigma }_\chi =\textstyle \sigma _\chi ^2\varvec{J}_2;$

$\sigma _\psi ^2=1; \varvec{\Sigma }_\psi =\sigma _\psi ^2\varvec{I}_2;$

$N_\xi =4: \quad \varvec{A}_s=(1-\frac{s}{5})\varvec{I}_2,s=0,1,\ldots ,4.$

$\Longrightarrow \ {\mathrm {diag}}[\mathsf{{V}}(\varvec{\xi }_{it})]: \quad \sigma _{\xi 1}^2=\sigma _{\xi 2}^2= \sigma _\chi ^2+\sigma _\psi ^2\times 2.200.$

$\varvec{\eta }_{it} \,\mathrm{process}:$ :

$\sigma _\epsilon ^2=0.1;\ \ \ \varvec{\Sigma }_\epsilon =\sigma _\epsilon ^2\varvec{I}_2;$

$N_\eta =0: \ \ \varvec{B}_0=\varvec{I}_2;$

$N_\eta =1: \ \ \varvec{B}_0=\varvec{I}_2,\ \ \varvec{B}_1=\frac{1}{2}\varvec{I}_2;$

$N_\eta =2: \ \ \varvec{B}_0=\varvec{I}_2,\ \ \varvec{B}_1=\frac{2}{3}\varvec{I}_2, \ \ \varvec{B}_2=\frac{1}{3}\varvec{I}_2;$

$\Longrightarrow \ {\mathrm {diag}}[\mathsf{{V}}(\varvec{\eta }_{it})]:\ \ \sigma _{\eta 1}^2=\sigma _{\eta 2}^2=\left\{ \begin{array}{ll} \sigma _\epsilon ^2\times 1.000, &{} N_\eta =0.\\ \sigma _\epsilon ^2\times 1.250, &{} N_\eta =1.\\ \sigma _\epsilon ^2\times 1.556, &{} N_\eta =2.\end{array}\right.$

$\alpha _i\,\mathrm{process}:$ :

$\sigma _{\alpha }^{2}=0.1$.

$u_{it}\,\mathrm{process}:$ :

$\sigma _v^2=\sigma _u^2=0.1$;

$N_u=0,\,c_0=1$.

$\nu _{it}\, \mathrm{process}:$ :

$\sigma _\delta ^2=0.1$;

Table 10 Persistence and error memory: impact on mean coefficients $(N,T)=(100,10)$

Table 11 Persistence and error memory: impact on long-run effects $(N,T)=(100,10)$

Appendix 2: Persistence and long-run responses

Tables 10 and 11 give simulation results to illustrate contrasts between short-run and long-run responses and between the precision with which they are estimated. They specifically exemplify the impact on the mean estimates of $(\beta _1,\beta _2,\lambda )$ and their long-run counterparts $[\beta _1/(1-\lambda ), \beta _2/(1-\lambda )]$ when persistence, represented by $\lambda$, varies. The entries in bold are the input values used in the simulations. We find that the $(\beta _1,\beta _2)$ estimates are negatively biased in all examples, including the static as well as the static and the weak and strong autoregression cases ($\lambda =0, 0.2, 0.8$, respectively), with one exception: $\beta _2$ is approximately unbiased (mean estimate 0.3004) for $\sigma _\psi ^2=1$ and $(N_\xi ,N_\eta ,N_\nu )=(4,0,0)$. For $\lambda$, the sign of the bias differs between the level and difference versions of the equation. For the level version, there is a positive bias, which is increased when an error memory is introduced or the signal variance is reduced. For example, with $(\beta _1,\beta _2,\lambda )=(0.3,0.6,0.0)$, the mean $\lambda =0.0178$ for ($N_\xi ,N_\eta ,N_\nu )=(4,0,0)$ under large signal spread increases to 0.0381 under small signal spread or increases to 0.0661 under large signal spread for $(N_\xi ,N_\eta ,N_\nu )=(4,1,0)$. For the difference version, there is a negative bias, with a magnitude similar to that of the level version.

The results for the long-run coefficients depart in several respects from those for the short-run coefficients. First, the conclusion that biases are smaller when the signal spread is large $(\sigma _\psi ^2=1)$ than when it is small $(\sigma _\psi ^2=0.5)$ does not hold invariably for the long-run coefficients. An example is provided for the equation in levels for $(\beta _1,\beta _2,\lambda )=(0.3,0.6,0.0)$ and $(N_\xi ,N_\eta ,N_\nu )=(4,2,0)$. Secondly, the systematic negative bias of $(\beta _1,\beta _2)$ does no longer hold. For example, for the equation in levels, $(\beta _1,\beta _2,\lambda )=(0.3,0.6,0.0)$ and $\sigma _\psi ^2=1$ give $\beta _1/(1-\lambda )=0.3010$ (i.e., a small positive bias) when ($N_\xi ,N_\eta ,N_\nu$)$=$(4,1,0) and $\beta _1/(1-\lambda )=0.2990$ (i.e., a small negative bias) when $(N_\xi ,N_\eta ,N_\nu )=(4,2,0)$. Finally, for the equation in differences, the long-run coefficients are still negatively biased. The biases increase when an error memory is introduced or the signal variance is reduced. A comparison of Tables 10 and 11 shows that when long-run effects of exogenous variables are our main concern, the attraction of keeping equations in levels and using IVs in differences is strengthened.