Moreover, standard _JN_ -statistics can be used for hypothesis and specification tests. The statistic _JN_ has an asymptotic _χ_ 2 distribution with degrees of freedom equal to the number of moments minus the number of parameters.

Table 7: Model Moments and Sample Analogs

||Moment|Model<br>_Ml_(_Xi_, _ψ_)|Sample<br>_ml_|
|---|---|---|---|
|1.<br>2.|Prob. formal<br>Prob. formal,_x < xm_<sup>_∗_</sup>|1<br>_nj_ <sup>∑</sup><br>_nj_<br>_i_=1 <sup>Pr[</sup><sup>_Fij_ = 1</sup><sup>_|·_]</sup><br>∑<br>_nj_<br>_i_=1 <sup>Pr[</sup><sup>_Fij_ = 1</sup><sup>_|·_]</sup><sup>**1**[</sup><sup>_zij < zm_]</sup><br>∑<br>_nj_<br>_i_=1 <sup>**1**[</sup><sup>_zij < zm_]</sup>|1<br>_nj_ <sup>∑</sup><br>_nj_<br>_i_=1 <sup>_Fij_</sup><br>∑<br>_nj_<br>_i_=1 <sup>_Fij_</sup><sup>**1**[</sup><sup>_zij < zm_]</sup><br>∑<br>_nj_<br>_i_=1 <sup>**1**[</sup><sup>_zij < zm_]</sup>|
|3.|Prob. informal|1<br>_nj_ <sup>∑</sup><br>_nj_<br>_i_=1 <sup>Pr[</sup><sup>_Iij_ = 1</sup><sup>_|·_]</sup><br>|1<br>_nj_ <sup>∑</sup><br>_nj_<br>_i_=1 <sup>_Iij_</sup><br>|
||Pbifl|∑<br>_nj_<br>_i_=1 <sup>Pr[</sup><sup>_Iij_ = 1</sup><sup>_|·_]</sup><sup>**1**[</sup><sup>_xij < xm_]</sup>|∑<br>_nj_<br>_i_=1 <sup>_Iij_</sup><sup>**1**[</sup><sup>_xij < xm_]</sup>|
|4.|ro. norma,_x < xm_|∑<br>_nj_<br>_i_=1 <sup>**1**[</sup><sup>_xij < xm_]</sup>|∑<br>_nj_<br>_i_=1 <sup>**1**[</sup><sup>_xij < xm_]</sup>|
|5.|Income formal|∑<br>_nj_<br>_i_=1 <sup>**E**[</sup><sup>_yij|Fij_ = 1] Pr[</sup><sup>_Fij_ = 1</sup><sup>_|·_]</sup><br>∑<br>_nj_<br>_i_=1 <sup>Pr[</sup><sup>_Fij_ = 1</sup><sup>_|·_]</sup>|∑<br>_nj_<br>_i_=1 <sup>_yijFij_</sup><br>∑<br>_nj_<br>_i_=1 <sup>_Fij_</sup>|
|6|I fl_<_|∑<br>_nj_<br>_i_=1 <sup>**E**[</sup><sup>_yi|Fij_ = 1] Pr[</sup><sup>_Fij_ = 1</sup><sup>_|·_]</sup><sup>**1**[</sup><sup>_xij < xm_]</sup>|∑<br>_nj_<br>_i_=1 <sup>_yijFij_</sup><sup>**1**[</sup><sup>_xij < xm_]</sup>|
|.|ncome orma,_x xm_|∑<br>_nj_<br>_i_=1 <sup>Pr[</sup><sup>_Fij_ = 1</sup><sup>_|·_]</sup><sup>**1**[</sup><sup>_xij < xm_]</sup>|∑<br>_nj_<br>_i_=1 <sup>_Fij_</sup><sup>**1**[</sup><sup>_xij < xm_]</sup>|
|7.|Income informal|∑<br>_nj_<br>_i_=1 <sup>**E**[</sup><sup>_yij|Iij_ = 1] Pr[</sup><sup>_Iij_ = 1</sup><sup>_|·_]</sup><br>∑<sup>_n_</sup><br>_i_=1 <sup>Pr[</sup><sup>_Iij_ = 1</sup><sup>_|·_]</sup>|∑<br>_nj_<br>_i_=1 <sup>_yijIij_</sup><br>∑<br>_nj_<br>_i_=1 <sup>_Iij_</sup>|
|8|I ifl|∑<br>_nj_<br>_i_=1 <sup>**E**[</sup><sup>_yij|Iij_ = 1] Pr[</sup><sup>_Iij_ = 1</sup><sup>_|·_]</sup><sup>**1**[</sup><sup>_xij < xm_]</sup>|∑<br>_nj_<br>_i_=1 <sup>_yijIij_</sup><sup>**1**[</sup><sup>_xij < xm_]</sup>|
|.|ncome norma,_x < xm_|∑<br>_nj_<br>_i_=1 <sup>Pr[</sup><sup>_Iij_ = 1</sup><sup>_|·_]</sup><sup>**1**[</sup><sup>_xij < xm_]</sup>|∑<br>_nj_<br>_i_=1 <sup>_Iij_</sup><sup>**1**[</sup><sup>_xij < xm_]</sup>|
|9.|Income non-entrep|∑<br>_nj_<br>_i_=1 <sup>**E**[</sup><sup>_yij|Wij_ = 1] Pr[</sup><sup>_Wij_ = 1</sup><sup>_|·_]</sup><br>∑<br>_nj_<br>_i_=1 <sup>Pr[</sup><sup>_Wij_ = 1</sup><sup>_|·_]</sup>|∑<br>_nj_<br>_i_=1 <sup>_yijWij_</sup><br>∑<br>_nj_<br>_i_=1 <sup>_Wij_</sup>|

_Notes._ The table reports averages of the described quantities. The derivation of the predicted model moments are given in Nguimkeu (2015) _∗ xm_ is the median years of schooling.

# **4.2 Estimation results**

The results of the gmm parameter estimates are reported in Tables 8 and 9. Table 8 presents the structural estimates according to sectors. These estimates are obtained for Agriculture, Manufacturing, Commerce and Services. Pairwise residual correlations among these industries are not reported in the Table but are available from the authors. The results show that average expected monthly wages are not significantly different across sector and are roughly the same as the national average of 104, 000 fcfa. The estimates of _δ_ 1 show that education has a differential effect on productivity, depending on the sector of activity in which one operates. At the national level, a 29