r brackets —decrease as the sample size increases. Notice that in some cases— as evidenced by non-positive values of ASE—the mis-specified model outperforms the true model in terms of the size of the expected squared-bias. This happens at all sample sizes and for all attributes when the true DGP is MNL-Asc and the specification is MXL-e (Table 13.4). Under this DGP the specification MXL-e seems to perform at least as well as the NL one, except at small sample sizes, and limited to r0.05 and to individual I( ) values.
In terms of expected squared bias, when the DGP is NL the MXL-e (Table 13.5) performs either as well (AF), or better than the correct specification at small sample sizes, but not at medium to high. Interestingly, at this sample size the MNL-Asc specification outperforms the true one for one attribute (OF). However, for this attribute the mis-specification MXL-e gives more accurate estimates than the true specification 16% of the times, versus a 4 and 11% for the MNL and MNL-Asc, respectively. In terms of cases within the 5% interval around the true values, MXL-e performs very similarly to the true specification at all sample sizes.
Notice, though, that the results in Table 13.6 show that when the true DGP is MXL-e the mis-specifications never outperform the true specification in all the criteria, across all sample sizes. When, instead, MXL-e was not the true DGP the mis-specifications never substantially outperform it. This is suggestive that, in the absence of a strong a-priori information on the true specification, the MXL-e is preferable across the board.
In figure 13.1 we present a kernel plot of the distributions of the RAE for the WTP for Area Flooding when the true model is a nested logit, with N=2,900. From this figure it is evident how the real choice is between MNL, and the group MNL-Asc, NL and MXL-e. Similar patterns emerge when the DGP is MNL-Asc, suggesting that these three models are effectively interchangeable. A stronger difference across specifications accounting for SQ emerges when the DGP is MXL-e, as shown in figure 13.2. Here the true specification (dot-dashed line) shows a distribution of RAE values that outperforms the other two (dotted and continuous line) in that it is much more tightly concentrated on zero, while the MNL (dashed line) remains strongly biased.
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