Hello,

I am trying to see whether financial development (measured as liquid liabilities divided to GDP) has an effect on the convergence between countries. For that purpose, I have generated an interaction term

I am using Cross-country IV Regressions to address the problem of endogeneity that comes from the initial value of growth of real GDP per capita. The results below come with two tests: Hasen J test and Underidentification test. I know that my Hansen test shows that the instruments used are not correlated with residuals. Nonetheless, I am not entirely sure about the interpretation of Underidentification test and whether it shows that I can accept my results. Can somebody help me with the interpretation?

Too few excluded instruments: standard IV model not estimable

IV with Generated Instruments only

Instruments created from Z:

linitial log_infl log_trade log_govsize log_school

2-Step GMM estimation

Estimates efficient for arbitrary heteroskedasticity

Statistics robust to heteroskedasticity

Number of obs = 37

F( 8, 28) = 25.52

Prob > F = 0.0000

Total (centered) SS = 44.63952131 Centered R2 = 0.6601

Total (uncentered) SS = 161.3884031 Uncentered R2 = 0.9060

Residual SS = 15.17405041 Root MSE = .6404

Robust

gr Coef. Std. Err. z P>z [95% Conf. Interval]

linitial_LL .2557908 .0572746 4.47 0.000 .1435346 .368047

Lliab -3.93395 .8873929 -4.43 0.000 -5.673208 -2.194692

Lliab2 .4522403 .1071857 4.22 0.000 .2421603 .6623204

linitial -1.084343 .2176225 -4.98 0.000 -1.510875 -.6578104

log_infl -.2873005 .056014 -5.13 0.000 -.3970859 -.1775151

log_trade .6776841 .0998588 6.79 0.000 .4819644 .8734038

log_govsize -1.101553 .3356589 -3.28 0.001 -1.759432 -.4436736

log_school 2.787074 .3847577 7.24 0.000 2.032963 3.541185

_cons 10.33173 2.546661 4.06 0.000 5.340368 15.3231

Underidentification test (Kleibergen-Paap rk LM statistic): 14.632

Chi-sq(13) P-val = 0.3309

Weak identification test (Cragg-Donald Wald F statistic): 3.029

(Kleibergen-Paap rk Wald F statistic): 10.108

Stock-Yogo weak ID test critical values: 5% maximal IV relative bias 18.73

10% maximal IV relative bias 10.33

20% maximal IV relative bias 5.94

30% maximal IV relative bias 4.37

Source: Stock-Yogo (2005). Reproduced by permission.

NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.

Hansen J statistic (overidentification test of all instruments): 8.213

Chi-sq(12) P-val = 0.7683

Instrumented: linitial_LL Lliab Lliab2

Included instruments: linitial log_infl log_trade log_govsize log_school

Excluded instruments: linitial_LL_linitial_g linitial_LL_log_infl_g

linitial_LL_log_trade_g linitial_LL_log_govsize_g

linitial_LL_log_school_g Lliab_linitial_g Lliab_log_infl_g

Lliab_log_trade_g Lliab_log_govsize_g Lliab_log_school_g

Lliab2_linitial_g Lliab2_log_infl_g Lliab2_log_trade_g

Lliab2_log_govsize_g Lliab2_log_school_g

I am trying to see whether financial development (measured as liquid liabilities divided to GDP) has an effect on the convergence between countries. For that purpose, I have generated an interaction term

*"linitial_LL***".**I am using Cross-country IV Regressions to address the problem of endogeneity that comes from the initial value of growth of real GDP per capita. The results below come with two tests: Hasen J test and Underidentification test. I know that my Hansen test shows that the instruments used are not correlated with residuals. Nonetheless, I am not entirely sure about the interpretation of Underidentification test and whether it shows that I can accept my results. Can somebody help me with the interpretation?

**ivreg2h gr linitial log_infl log_trade log_govsize log_school (linitial_LL Lliab Lliab2=) , gmm2s robust**Too few excluded instruments: standard IV model not estimable

IV with Generated Instruments only

Instruments created from Z:

linitial log_infl log_trade log_govsize log_school

2-Step GMM estimation

Estimates efficient for arbitrary heteroskedasticity

Statistics robust to heteroskedasticity

Number of obs = 37

F( 8, 28) = 25.52

Prob > F = 0.0000

Total (centered) SS = 44.63952131 Centered R2 = 0.6601

Total (uncentered) SS = 161.3884031 Uncentered R2 = 0.9060

Residual SS = 15.17405041 Root MSE = .6404

Robust

gr Coef. Std. Err. z P>z [95% Conf. Interval]

linitial_LL .2557908 .0572746 4.47 0.000 .1435346 .368047

Lliab -3.93395 .8873929 -4.43 0.000 -5.673208 -2.194692

Lliab2 .4522403 .1071857 4.22 0.000 .2421603 .6623204

linitial -1.084343 .2176225 -4.98 0.000 -1.510875 -.6578104

log_infl -.2873005 .056014 -5.13 0.000 -.3970859 -.1775151

log_trade .6776841 .0998588 6.79 0.000 .4819644 .8734038

log_govsize -1.101553 .3356589 -3.28 0.001 -1.759432 -.4436736

log_school 2.787074 .3847577 7.24 0.000 2.032963 3.541185

_cons 10.33173 2.546661 4.06 0.000 5.340368 15.3231

Underidentification test (Kleibergen-Paap rk LM statistic): 14.632

Chi-sq(13) P-val = 0.3309

Weak identification test (Cragg-Donald Wald F statistic): 3.029

(Kleibergen-Paap rk Wald F statistic): 10.108

Stock-Yogo weak ID test critical values: 5% maximal IV relative bias 18.73

10% maximal IV relative bias 10.33

20% maximal IV relative bias 5.94

30% maximal IV relative bias 4.37

Source: Stock-Yogo (2005). Reproduced by permission.

NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.

Hansen J statistic (overidentification test of all instruments): 8.213

Chi-sq(12) P-val = 0.7683

Instrumented: linitial_LL Lliab Lliab2

Included instruments: linitial log_infl log_trade log_govsize log_school

Excluded instruments: linitial_LL_linitial_g linitial_LL_log_infl_g

linitial_LL_log_trade_g linitial_LL_log_govsize_g

linitial_LL_log_school_g Lliab_linitial_g Lliab_log_infl_g

Lliab_log_trade_g Lliab_log_govsize_g Lliab_log_school_g

Lliab2_linitial_g Lliab2_log_infl_g Lliab2_log_trade_g

Lliab2_log_govsize_g Lliab2_log_school_g