Problems with Endogeneity

From the theoretical model, it has been established that both innovation and foreign direct investment are functions of IPRs in a given period. As a result some of the regressors in equation (4.16) are correlated with the error term. Estimating (4.16) using OLS would, therefore, lead to inconsistent and biased results. An instrumental variables approach is instead used to mitigate endogeneity among regressors.

The estimating equation in (4.16) contains two endogenous variables. Therefore, in order to utilize instrumental variable estimation, at least two variables must be identified that are correlated with FDI and/or innovation, but uncorrelated with the error term in the export equation. These excluded exogenous variables will serve as instruments in the empirical estimation of bilateral exports.

correlated with the two endogenous variables. In doing so, the estimating equation for innovation is first explored, followed by the estimating equation for FDI.

Estimating Innovation

Chen and Puttitanun (2005) model innovative output as a function of IPRs, per capita GDP, tertiary school enrollment rates, economic freedom, and population. Schneider (2005) estimated innovation as a function of IPRs, human capital stock, high technology imports, research and development, GDP, FDI, and infrastructure. The production function for innovation used in this paper is assumed to take a Cobb-Douglas form with inputs that closely resemble those used by Chen and Puttitanun.

Innovation is assumed to be a function of domestic IPRs, domestic GDP, tertiary school enrollment rates, business environment, population, and R&D expenditures. Each α coef- ficient in the estimating equation can be interpreted as the elasticity of that variable with respect to innovation. In most research where innovation is the dependent variable,6 each explanatory variable is assumed to have a constant elasticity such that a change in the explanatory variable will have the same change in innovation, regardless of the initial value of the variable. The constant elasticity of the explanatory variables is captured by the fact that each explanatory variable enters into log form in equation (4.17), below.

log(Innovation)it =α0+α1log(IPR)it+α2log(R&D)it+α3log(GDP)it (4.17) +α4log(tertiary school enrollment)it+α5log(business environment)it +α6log(population)it+εit+µi+ηt.

Innovation is expected to have a positive relationship with all of the above variables. A more sound business environment creates an economic environment capable of effectively utilizing innovation. Population is included as a regressor so to control for possible scale effects that may arise from the assumption that countries with larger populations will likely

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have a larger number of innovations (or patent counts) simply because they are more pop- ulous. Chen and Puttitanun (2005) provided theoretical support for the expected positive relationship between IPRs and innovation; in other words, they found theoretical support for the previously assumed notion that I0(β) > 0. This assumption arises from the belief that stronger IPRs support an environment conducive to innovation. Chen and Puttita- nun also provided theoretical support for the positive relationship between innovation and output concluding that innovation will be greater in more developed countries.

A discussion of the specific data used to estimate (4.17) will take place later in the paper. Before doing so, however, an estimation equation for the second endogenous variable, inward FDI, is discussed.

Estimating Inward FDI

There are many components that impact inward FDI in a country. It is assumed that:

Inward FDI =f(IPRs, business environment, GDP, population, K in the previous period) (4.18)

Each of the variables in (4.18) is expected to have a positive impact on FDI. Stronger IPRs in country i should attract more inward FDI into this country. In addition, a more sound business environment will also attract more FDI. The larger a country, as approximated by GDP, the greater the capacity for inward FDI. Similarly, the more populous a country, the greater the opportunity for domestic labor to support inward FDI. Lastly, capital stock in the previous period is related to how attractive foreign investors may find the market in the current period. In the context of developing countries, higher levels of capital stock in the previous period suggest that the domestic economy may be able to support further capital investments, therefore making the domestic market more attractive to inward FDI. This contrasts with the possible effect that higher levels of capital in the previous period signal a saturated market, which is better suited for developed countries.

As with the production function for innovation, the production function for FDI is as- sumed to be Cobb-Douglas in form. Such a Cobb-Douglas form lends itself to an estimation equation for FDI that is linear in logs. The specific estimating equation for inward FDI is as follows:

log(Inward FDI)it=θ0+θ1log(IPRs)it+θ2log(business environment)it (4.19) +θ3log(GDP)it+θ4log(population)it+θ5log(K)i,t−5+εit+µi+ηt

where t−5 represents the previous period for which there is complete data. (Data on the IPR Index is available every fifth year.)

Empirical estimation of the innovation and FDI equations support that the specified independent variables are in fact statistically significant in explaining innovation and inward FDI, respectively.

Identification

Given the explanatory variables for innovation and inward FDI listed in (4.17) and (4.19), respectively, the bilateral export equation is over-identified. The number of excluded exoge- nous variables in the innovation equation (R&D expenditures, tertiary school enrollment, business environment, population of the domestic economy, and capital in the previous pe- riod) exceeds the number of included endogenous variables in the bilateral export equation (innovation and inward FDI). Over or exact-identification is a necessary condition for two stage, instrumental variables estimation.

Empirical tests indicate that the above excluded exogenous variables are valid instru- ments in that they are not correlated with the error term in the export equation. To test this, tertiary school enrollment, business environment, and physical capital in the previous period are included in the estimation equation for bilateral exports, leaving R&D expenditures and population in the domestic economy to serve as instruments in the two-stage estimation.

A joint F-test supports that tertiary school enrollment, business environment, and capi- tal in the previous period are jointly insignificant in determining bilateral exports. Then, R&D expenditures and population in the domestic economy are included in the estimation equation for bilateral exports leaving tertiary school enrollment, business environment, and capital in the previous period to serve as instruments in the two-stage estimation. Again, a joint F-test supports that R&D expenditures and population in the domestic economy are jointly insignificant in determining bilateral exports.