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References

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Appendix I. OLS and 2SLS Growth Regression

This appendix compares standard OLS and 2SLS growth regression results with export diversification (see Table A3).

OLS Results

The OLS results provide a baseline for direct comparison with previous growth determinant studies. Column 1 in Appendix Table A3 reports OLS results without export diversification, producing roughly comparable results to the OLS regressions in Barro (2003). As expected, InitialGDP, Investment and PopulationGrowth are significant as suggested by the neoclassical model. Institutional factors suggested by new growth theories are also significant (GovExpenditures, and ExecutiveConstraints). In addition, one individual religious measure (Jewish) is significant while the only trade measure, FilteredOpenness (the filtered ratio of imports plus exports over GDP), is significant at the 10 percent level. Both Barro (2003) and DKT (2008) found that the weak OLS trade effect disappeared once they controlled for endogeneity. Inflation, Fertility and LandNearCostPct are also found to have a significant effect on growth.

The linear export diversification term (Diversification) in column 2 is not significant in the global OLS panel. This result is not surprising given that the slope of the partial correlation between growth and export diversification is close to zero in Figure 2. Column 3 allows for nonlinearities in the relationship between export diversification in growth by introducing income dummies and their respective interaction terms with diversification. The income dummies are derived from the World Bank’s definition of high-, upper-middle-, lower-middle-, and low-income levels. However, in the OLS specification, export diversification still has no significant effect for any income group.5 The absence of any effect in the OLS specification, however, does not surprise given the ample evidence for feedback effects between growth and trade.

Controlling for Endogeneity

Column 4 in Appendix Table 3 acknowledges not only trade endogeneity, but also the potential endogeneity of 18 other growth determinants in the dataset.6 Given the large number of endogenous regressors, the Angrist-Pischke test statistics are reported. These test statistics indicate whether a particular endogenous regressor alone is identified. The Angrist-Pischke first-stage chi-squared and F statistics are tests of under-identification and weak identification.7 Under-identification and weak identification are rejected at the 1 percent level for all endogenous variables. The Sargan-Hansen J statistic rejects, however, instrument validity in the 2SLS regression, indicating that a more parsimonious 2SLS specification is likely to be preferred.

In terms of significance, the 2SLS results in column 4 coincide by and large with the OLS growth determinants in column 3. Now, after controlling for endogeneity, export diversification becomes significant for LICs. The economic effect of diversification on LICs is sizable, implying that a one standard deviation increase in export diversification raises average annual growth in LICs by about 0.9 percentage points.8 Investment and the marginally significant variables ExecutiveConstraint and Fertility all lose significance in the 2SLS approach. The loss of significance for Investment is worrisome, but not surprising. While Investment is seen as a universal growth determinant in theory, previous panel studies (e.g.,, DKT, 2008, and Barro, 2003) also find that the significance of Investment decreases substantially after controlling for endogeneity. Note that investment becomes insignificant only after controlling for endogeneity but before addressing model uncertainty.

Appendix II. IVBMA Methodology

IVBMA (Instrumental Variable Bayesian Model Averaging) functions as a Bayesian Model Averaging (BMA) procedure at the first and second stages where the final model weight takes into account the model uncertainty in both stages. The sketch of the mechanics below follows Eicher et al., (2009). Traditionally, endogeneity is addressed by applying 2SLS and certifying over-identification and instrument restrictions (e.g.,, Wooldridge, 2002). The canonical setup is characterized by
y=β(wx)+η,(1)
w=θzz+θxx+ε,(2)
where y is the dependent variable, x is a set of covariates, w is the set of endogenous variables, and z is the set of instruments. The x and θx are of dimension px, and z and θz have dimension pz. To simplify the exposition, it is assumed that w is univariate. Assuming that
(ηε)~N((00),(ση2σηε2σηε2σε2)),(3)

the classical endogenous variable situation arises when σηε20, causing w to violate the regression assumption of independence of the error term, η. The determination of w then leads to inconsistent estimates of the entire coefficient vector, β. 2SLS solves the consistency problem, but relies on the existence of a set of instrumental variables (IV), z, which are independent of y, given w and the vector of covariates, x. The IV-based estimates, βIV=(w¯w¯)1w¯y, obtained using the fitted values from the first stage, w¯, are consistent if the conditional independence assumptions are valid.

IVBMA combines the IV and BMA methodologies. It processes the data much like a two stage least square estimator while also addressing model uncertainty in both stages. The first stage is a straight BMA application to identify effective instruments, where the properties of BMA in stage 1 are as follows. Let Δ be a quantity of interest and let the set of potential models in the first stage, M˜, be comprised of M˜iM˜ individual models. The posterior distribution of Δ given the data, D, is given by the weighted average of the predictive distribution under each model, using as weight the models’ corresponding posterior probabilities:
pr(Δ|D)=M˜iM˜pr(Δ|M˜i,D)pr(M˜i|D)(4)
where pr(Δ|M˜i,D) is the predictive distribution and pr(M˜i|D) is the posterior model probability of model M˜i. The posterior model probability, π˜i, for each model in the first stage is given by π˜i=pr(M˜i|D)pr(D|M˜i)pr(M˜i) where pr(D|M˜i)=pr(D|θi,M˜i)pr(θi|M˜i)dθi is the integrated likelihood of model M˜i with model parameters θi. The prior densities for parameters and models are given by pr(θi|M˜i) and pr(M˜i), respectively. The posterior mean in stage 1 is θ^BMA=ΣM˜iM˜θ^iπ˜i, which is given by the sum of the posterior means of all models, weighted by their respective posterior model probabilities. Similarly, the posterior variance can be calculated as
σ^BMA[θ]=M˜iM˜π˜iσ^i+M˜iM˜π˜i(θ^iθ^BMA)2.(5)

The variance has a clear interpretation that highlights how model uncertainty is accounted for by standard errors of the BMA methodology. The first term in (5) is the weighted variance for each model, σ^i=Var(θ^i|M˜i,D), summed over all relevant models, and the second term indicates how stable the estimates are across models. The more the estimates differ across models, the greater is the posterior variance.

The posterior distribution for a parameter is a mixture of a regular posterior distribution and a point mass at zero, which represents the probability that the parameter equals zero. The sum of the posterior probabilities of the models that contain the variable is called the inclusion probability and can then be taken as a measure of the importance of a variable
μBMA[θ]=pr(θ^0|D)=M˜iM˜Aπi.(6)

where M˜A is the set of models in the first stage in which parameter θ is not constrained to zero.

IVBMA is then a nested approach that first determines the posterior model probabilities in the first stage according to the BMA methodology, and then uses the predicted values from each model, w¯i, to derive second stage model posterior model probabilities, πj[w¯i], and estimates, β^j[w¯i]. The set of models in the second stage is denoted by M, which consists of all second stage models MjM. The posterior means for the second stage can then be derived to be β^IVBMA=ΣM˜iM˜ΣMjMπ˜iπj[w¯i]β^j[w¯i]=ΣM˜iM˜π˜iβ^˜i,BMA, which implies that the IVBMA estimate is the sum of the averaged posterior IV means obtained using the fitted values from each first stage model, M˜i, weighted by the respective quality of each individual first stage specification.

The posterior variance reflects how stable the estimates are across models, and how estimates differ across models in both the first and second stage, just as in the canonical BMA setup in (5) (captured in the σ^BMA[β] term). However, IVBMA also takes into account the model weights derived in the first stage so that the posterior variance is again weighted by the quality of its incrementing models: σ^˜IVBMA[β]=ΣM˜iM˜π˜iσ^˜i,BMA[β]. Therefore, results generated by underperforming instrument models are deemphasized, while those based on strong instrument models receive relatively high posterior weights. A similar interpretation holds for the IVBMA inclusion probabilities: μIVBMA[β]=pr(β^0|D)=ΣM˜iM˜,MMAπ˜iμi,BMA[β], where MA indicates the subset of second stage models for which the coefficient β is not constrained to zero.

Appendix Table A1.

Export Diversification

article image
♠ Composite coefficient reported, based on the joint posterior distribution of Diversification and Diversification*CountryIncome interaction.Since the PIP is not defined for the composite, we report the percentage of the joint posterior distribution of Diversification*CountryIncome interaction that is non-zero.
Appendix Table A2.

Output Diversification

article image
♠ Composite coefficient reported, based on the joint posterior distribution of Diversification and Diversification*CountryIncome interaction. Since the PIP is not defined for the composite, only the percentage of the joint posterior distribution of Diversification*Country Income interaction that is non-zero is reported.
Appendix Table A3.

OLS and 2SLS Estimation

article image
♠ Composite coefficient comprised of Diversification and Diversification*CountryIncome interaction, calculated using Delta Method.