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Underpinned by rising hydrocarbon revenues, the stock markets of the six GCC (Gulf Cooperation Council) countries have demonstrated significant integration over the past decade. This paper studies the dependence patterns of the bivariate distribution of returns across seven GCC stock markets over the period 2004-2013 using copula models. The results of the marginal models indicate strong volatility persistence in all the seven equity markets. The results from the copula models indicate that the conditional dependence across all 21 pairs of equity markets' returns is not strictly symmetric in that the lower tail dependence is significantly greater that the upper tail dependence. The stock markets of Abu Dhabi and Dubai appear as the primary source of asymmetric dependence across the different equity market pairs.

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This paper proposes new estimation techniques for gravity models with zero trade values and heteroscedasticity. We revisit the standard PPML estimator and we propose an improved version. We also propose various Heckman estimators with different distributions of the residuals, nonlinear forms of both selection and measure equations, and various process of the variance. We add to the existent literature alternative estimation methods taking into account the non-linearity of both the variance and the selection equation. Moreover, because of the unavailability of pre-set package in the econometrics software (Stata, Eviews, Matlab, etc.) to perform the estimation of the above-mentioned Heckman versions, we had to code it in Matlab using a combination of fminsearch and fminunc functions. Using numerical gradient matrix G, we report standard errors based on the BHHH technique. The proposed new Heckman version could be used in other applications. Our results suggest that previous empirical studies might be overestimating the contribution of the GDP of both import and export countries in determining the bilateral trade.

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