sector with the biggest total factor productivity in 2011 which is consistent with our priors, while under setup 2, is the second lowest TFP holder. Besides, in table 14 our results show that with the exception of services, all the Korean sectors present a labor augmenting productivity with upward trend, being agriculture the one with the biggest change during the period 1990-2011 under setup 1. However, the LAP coefficients behave different for manufacturing, mining and services under setup 2. LAP for mining and manufacturing present downward sloping trends whereas services an upward path.

# Model selection and parameter assessment

In a context of ambiguous results we would like to differentiate the model setups, and the CGE-SAM-CE procedure automatically fits this task. First, for data validation, we make use of equations (17) and (18) to estimate the adjusted and the AIC statistics under models 1, 2 and 3. The Korean aggregated adjusted and the AIC of table 16 indicate that between 1990 and 2011, case 1 works better to explain and validate RR<sup>2</sup> the SAMs’ information, while in table 17, the SSA regional results imply that model 2 explain and validate RR<sup>2</sup> better the CGE model and data for the period 2004-2011.

For the specific case of Korea, the Kullback-Leibler (KL) statistic in (19) shows that among setups 1 and 2, there is a bigger reduction of data noise in results of model 1 during the period 1990-2011. Nonetheless, model 1 has bigger Kullback-Leibler statistic in 1995 for the prediction side than model 2; this implies that the standard CGE fits better in 1995 under the assumptions of dynamic delta-shares and fixed elasticities.

On the other side, the parameter evaluation in the CGE-SAM-CE setup is elaborated through the cross-entropy statistic as in (16). In this regard, where correspondent, in tables of appendix 3 we show that generally under models 1 and 2 our prior parameter error Gaussian assumptions deviates from the total RR<sup>�2</sup> degree of ignorance assumption<sup>17</sup> in systematic way, i.e., cross-entropy values of at least 0.30. There are also cases where the method identifies recovered parameters with more data noise and/or with bigger gain RR<sup>�2</sup> of information, for instance, in table 12, 13, 14 and table 15 we have examples that TFP growth rates and labor augmenting productivity coefficients have bigger cross-entropy values ≥0.30�, i.e., bigger difference between the ignorance (uniform) distribution and the posterior-recovered one. RR<sup>�2</sup> �RR<sup>�2</sup> As previously commented, the method is subject to the amount of parameters we want to estimate simultaneously: the more parameters the more flexible estimation and the less likelihood to recover a posterior distribution far from the prior. In model 3 for the Korean analysis we specify a setup that is an imperfect mirror of model 1, where the difference relies on fixed elasticities during the period 1990-2011 of the Armington and CET functions instead of the dynamic behavior with linear trend of the elasticity, i.e., model 3 means less parameters to estimate than model 1. Given model 3 rigidness, we observe in table 4 that the posterior mean of the CES Armington elasticity moves from a prior of 2.80 to an inelastic value of 0.10.

> 17 See the description of the uninformative prior from appendix 2.

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