Hello,
I´m trying to test the endogeneity in my model with two interpretation of the xtivreg2. I´m not sure about the interpretation of the results.
First model:
according to the Sanderson -Windmeijer F test and the prob > F (0.000), the instruments are valid. The results of the weak id is 18.32 which is under 10% of maximum size. Can I take this value valid and continue with it? I assume that not all model results will meet the hodnot above 19.93. The p-value of the Anderson-Rubin Wald test and the Stock-wright LM S statistic is above the 0.0005 significance level and thus the instruments are non-valid. The result of the endogeneity test shows a value of 0.8581, endogeneity was not resolved.
Second model:
according to the Sanderson -Windmeijer F test and the prob > F (0.0032), the instruments are valid. The results of the weak id is 5.99 which is under 25% of maximum size. Equation is weakly identified. The p-value of the Anderson-Rubin Wald test and the Stock-wright LM S statistic is above the 0.0005 significance level and thus the instruments are non-valid. The result of the endogeneity test shows a value of 0.3074, endogeneity was not resolved.
I would be very grateful for your help and any further solutions to my problem. This is the first time I have addressed the issue of endogeneity.
I´m trying to test the endogeneity in my model with two interpretation of the xtivreg2. I´m not sure about the interpretation of the results.
First model:
according to the Sanderson -Windmeijer F test and the prob > F (0.000), the instruments are valid. The results of the weak id is 18.32 which is under 10% of maximum size. Can I take this value valid and continue with it? I assume that not all model results will meet the hodnot above 19.93. The p-value of the Anderson-Rubin Wald test and the Stock-wright LM S statistic is above the 0.0005 significance level and thus the instruments are non-valid. The result of the endogeneity test shows a value of 0.8581, endogeneity was not resolved.
| . | ||||||||||
| . xtivreg2 g_GDP d_exchangerate inflation d_populationgrowth d_unemployment g_crudeoilproduction | g_crudeoilprice | g_oilconsumption | (l.g_GDP= | L2_g_GDP | L3_g_GDP | ), | fe | small | first | endog(l.g_GDP) |
| FIXED EFFECTS ESTIMATION | ||||||||||
| Number of groups = 5 Obs per group: min = 25 | ||||||||||
| avg = 29.4 | ||||||||||
| max = 31 | ||||||||||
| First-stage regressions | ||||||||||
| FIXED EFFECTS ESTIMATION | ||||||||||
| Number of groups = 5 Obs per group: min = 25 | ||||||||||
| avg = 29.4 | ||||||||||
| max = 31 | ||||||||||
| First-stage regression of L.g_GDP: | ||||||||||
| Statistics consistent for homoskedasticity only | ||||||||||
| Number of obs = 147 | ||||||||||
| L.g_GDP Coefficient Std. err. t P>t [95% conf. interval] | ||||||||||
| L2_g_GDP .2827826 .0646932 4.37 0.000 .1548219 .4107433 | ||||||||||
| L3_g_GDP .2764728 .068571 4.03 0.000 .140842 .4121036 | ||||||||||
| d_exchangerate -.0009135 .0007562 -1.21 0.229 -.0024093 .0005823 | ||||||||||
| inflation .0034516 .000444 7.77 0.000 .0025734 .0043297 | ||||||||||
| d_populationgrowth .0305203 .041981 0.73 0.469 -.0525165 .1135572 | ||||||||||
| d_unemployment -.0487385 .0254546 -1.91 0.058 -.0990867 .0016096 | ||||||||||
| g_crudeoilproduction -1.124446 .2144548 -5.24 0.000 -1.548629 -.7002622 | ||||||||||
| g_crudeoilprice .0679538 .0852186 0.80 0.427 -.1006052 .2365128 | ||||||||||
| g_oilconsumption -.9057594 .263227 -3.44 0.001 -1.426412 -.3851066 | ||||||||||
| F test of excluded instruments: | ||||||||||
| F( 2, 133) = 18.32 | ||||||||||
| Prob > F = 0.0000 | ||||||||||
| Sanderson-Windmeijer multivariate F test of excluded instruments: | ||||||||||
| F( 2, 133) = 18.32 | ||||||||||
| Prob > F = 0.0000 | ||||||||||
| Summary results for first-stage regressions | ||||||||||
| (Underid) (Weak id) | ||||||||||
| Variable F( 2, 133) P-val SW Chi-sq( 2) P-val SW F( 2, 133) | ||||||||||
| L.g_GDP 18.32 0.0000 39.13 0.0000 18.32 | ||||||||||
| Stock-Yogo weak ID F test critical values for single endogenous regressor: | ||||||||||
| 10% maximal IV size 19.93 | ||||||||||
| 15% maximal IV size 11.59 | ||||||||||
| 20% maximal IV size 8.75 | ||||||||||
| 25% maximal IV size 7.25 | ||||||||||
| Source: Stock-Yogo (2005). Reproduced by permission. | ||||||||||
| NB: Critical values are for Sanderson-Windmeijer F statistic. | ||||||||||
| Underidentification test | ||||||||||
| Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) | ||||||||||
| Ha: matrix has rank=K1 (identified) | ||||||||||
| Anderson canon. corr. LM statistic Chi-sq(2)=30.68 P-val=0.0000 | ||||||||||
| Weak identification test | ||||||||||
| Ho: equation is weakly identified | ||||||||||
| Cragg-Donald Wald F statistic 18.32 | ||||||||||
| Stock-Yogo weak ID test critical values for K1=1 and L1=2: | ||||||||||
| 10% maximal IV size 19.93 | ||||||||||
| 15% maximal IV size 11.59 | ||||||||||
| 20% maximal IV size 8.75 | ||||||||||
| 25% maximal IV size 7.25 | ||||||||||
| Source: Stock-Yogo (2005). Reproduced by permission. | ||||||||||
| Weak-instrument-robust inference | ||||||||||
| Tests of joint significance of endogenous regressors B1 in main equation | ||||||||||
| Ho: B1=0 and orthogonality conditions are valid | ||||||||||
| Anderson-Rubin Wald test F(2,133)= 0.43 P-val=0.6545 | ||||||||||
| Anderson-Rubin Wald test Chi-sq(2)= 0.91 P-val=0.6351 | ||||||||||
| Stock-Wright LM S statistic Chi-sq(2)= 0.90 P-val=0.6369 | ||||||||||
| Number of observations N = 147 | ||||||||||
| Number of regressors K = 8 | ||||||||||
| Number of endogenous regressors K1 = 1 | ||||||||||
| Number of instruments L = 9 | ||||||||||
| Number of excluded instruments L1 = 2 | ||||||||||
| IV (2SLS) estimation | ||||||||||
| Estimates efficient for homoskedasticity only | ||||||||||
| Statistics consistent for homoskedasticity only | ||||||||||
| Number of obs = 147 | ||||||||||
| F( 8, 134) = 70.72 | ||||||||||
| Prob > F = 0.0000 | ||||||||||
| Total (centered) SS = 14.01333734 Centered R2 = 0.8086 | ||||||||||
| Total (uncentered) SS = 14.01333734 Uncentered R2 = 0.8086 | ||||||||||
| Residual SS = 2.681906481 Root MSE = .1415 | ||||||||||
| g_GDP Coefficient Std. err. t P>t [95% conf. interval] | ||||||||||
| g_GDP | ||||||||||
| L1. .0528711 .0919669 0.57 0.566 -.1290234 .2347656 | ||||||||||
| d_exchangerate -.0011154 .0004366 -2.55 0.012 -.001979 -.0002519 | ||||||||||
| inflation .0050868 .0003702 13.74 0.000 .0043546 .005819 | ||||||||||
| d_populationgrowth -.0135984 .0231272 -0.59 0.558 -.0593399 .0321432 | ||||||||||
| d_unemployment .0001545 .0144282 0.01 0.991 -.028382 .028691 | ||||||||||
| g_crudeoilproduction .4785238 .1156545 4.14 0.000 .2497793 .7072682 | ||||||||||
| g_crudeoilprice .3644186 .0476564 7.65 0.000 .2701626 .4586745 | ||||||||||
| g_oilconsumption -.186071 .1641646 -1.13 0.259 -.5107599 .1386179 | ||||||||||
| Underidentification test (Anderson canon. corr. LM statistic): 30.676 | ||||||||||
| Chi-sq(2) P-val = 0.0000 | ||||||||||
| Weak identification test (Cragg-Donald Wald F statistic): 18.325 | ||||||||||
| Stock-Yogo weak ID test critical values: 10% maximal IV size 19.93 | ||||||||||
| 15% maximal IV size 11.59 | ||||||||||
| 20% maximal IV size 8.75 | ||||||||||
| 25% maximal IV size 7.25 | ||||||||||
| Source: Stock-Yogo (2005). Reproduced by permission. | ||||||||||
| Sargan statistic (overidentification test of all instruments): 0.557 | ||||||||||
| Chi-sq(1) P-val = 0.4555 | ||||||||||
| -endog- option: | ||||||||||
| Endogeneity test of endogenous regressors: 0.032 | ||||||||||
| Chi-sq(1) P-val = 0.8581 | ||||||||||
| Regressors tested: L.g_GDP | ||||||||||
| Instrumented: L.g_GDP | ||||||||||
| Included instruments: d_exchangerate inflation d_populationgrowth | ||||||||||
| d_unemployment g_crudeoilproduction g_crudeoilprice | ||||||||||
| g_oilconsumption | ||||||||||
| Excluded instruments: L2_g_GDP L3_g_GDP | ||||||||||
Second model:
according to the Sanderson -Windmeijer F test and the prob > F (0.0032), the instruments are valid. The results of the weak id is 5.99 which is under 25% of maximum size. Equation is weakly identified. The p-value of the Anderson-Rubin Wald test and the Stock-wright LM S statistic is above the 0.0005 significance level and thus the instruments are non-valid. The result of the endogeneity test shows a value of 0.3074, endogeneity was not resolved.
| . xtivreg2 g_GDP d_exchangerate inflation d_populationgrowth d_unemployment g_crudeoilproduction | g_crudeoilprice | g_oilconsumption | (l.g_GDP= | L2_g_GDP | L3_g_GDP | ), | fd | small | first | endog(l.g_GDP) |
| Warning: time variable Year has 1 gap(s) in relevant range | ||||||||||
| FIRST DIFFERENCES ESTIMATION | ||||||||||
| Number of groups = 5 Obs per group: min = 24 | ||||||||||
| avg = 28.2 | ||||||||||
| max = 30 | ||||||||||
| First-stage regressions | ||||||||||
| First-stage regression of LD.g_GDP: | ||||||||||
| Statistics consistent for homoskedasticity only | ||||||||||
| Number of obs = 141 | ||||||||||
| LD.g_GDP Coefficient Std. err. t P>t [95% conf. interval] | ||||||||||
| L2_g_GDP | ||||||||||
| D1. -.2483486 .0860376 -2.89 0.005 -.4185515 -.0781457 | ||||||||||
| L3_g_GDP | ||||||||||
| D1. -.0398718 .0820008 -0.49 0.628 -.2020888 .1223453 | ||||||||||
| d_exchangerate | ||||||||||
| D1. -.0003968 .0007128 -0.56 0.579 -.0018068 .0010132 | ||||||||||
| inflation | ||||||||||
| D1. -.0001237 .0007667 -0.16 0.872 -.0016404 .001393 | ||||||||||
| d_populationgrowth | ||||||||||
| D1. .0143116 .0423403 0.34 0.736 -.0694475 .0980707 | ||||||||||
| d_unemployment | ||||||||||
| D1. -.0378066 .0245356 -1.54 0.126 -.0863439 .0107307 | ||||||||||
| g_crudeoilproduction | ||||||||||
| D1. -1.304692 .2289236 -5.70 0.000 -1.757558 -.8518269 | ||||||||||
| g_crudeoilprice | ||||||||||
| D1. -.1405434 .0794812 -1.77 0.079 -.2977762 .0166893 | ||||||||||
| g_oilconsumption | ||||||||||
| D1. -.1092462 .2591715 -0.42 0.674 -.6219492 .4034568 | ||||||||||
| _cons -.005742 .0254806 -0.23 0.822 -.0561486 .0446646 | ||||||||||
| F test of excluded instruments: | ||||||||||
| F( 2, 131) = 5.99 | ||||||||||
| Prob > F = 0.0032 | ||||||||||
| Sanderson-Windmeijer multivariate F test of excluded instruments: | ||||||||||
| F( 2, 131) = 5.99 | ||||||||||
| Prob > F = 0.0032 | ||||||||||
| Summary results for first-stage regressions | ||||||||||
| (Underid) (Weak id) | ||||||||||
| Variable F( 2, 131) P-val SW Chi-sq( 2) P-val SW F( 2, 131) | ||||||||||
| LD.g_GDP 5.99 0.0032 12.90 0.0016 5.99 | ||||||||||
| Stock-Yogo weak ID F test critical values for single endogenous regressor: | ||||||||||
| 10% maximal IV size 19.93 | ||||||||||
| 15% maximal IV size 11.59 | ||||||||||
| 20% maximal IV size 8.75 | ||||||||||
| 25% maximal IV size 7.25 | ||||||||||
| Source: Stock-Yogo (2005). Reproduced by permission. | ||||||||||
| NB: Critical values are for Sanderson-Windmeijer F statistic. | ||||||||||
| Underidentification test | ||||||||||
| Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) | ||||||||||
| Ha: matrix has rank=K1 (identified) | ||||||||||
| Anderson canon. corr. LM statistic Chi-sq(2)=11.82 P-val=0.0027 | ||||||||||
| Weak identification test | ||||||||||
| Ho: equation is weakly identified | ||||||||||
| Cragg-Donald Wald F statistic 5.99 | ||||||||||
| Stock-Yogo weak ID test critical values for K1=1 and L1=2: | ||||||||||
| 10% maximal IV size 19.93 | ||||||||||
| 15% maximal IV size 11.59 | ||||||||||
| 20% maximal IV size 8.75 | ||||||||||
| 25% maximal IV size 7.25 | ||||||||||
| Source: Stock-Yogo (2005). Reproduced by permission. | ||||||||||
| Weak-instrument-robust inference | ||||||||||
| Tests of joint significance of endogenous regressors B1 in main equation | ||||||||||
| Ho: B1=0 and orthogonality conditions are valid | ||||||||||
| Anderson-Rubin Wald test F(2,131)= 2.46 P-val=0.0893 | ||||||||||
| Anderson-Rubin Wald test Chi-sq(2)= 5.30 P-val=0.0708 | ||||||||||
| Stock-Wright LM S statistic Chi-sq(2)= 5.10 P-val=0.0779 | ||||||||||
| Number of observations N = 141 | ||||||||||
| Number of regressors K = 9 | ||||||||||
| Number of endogenous regressors K1 = 1 | ||||||||||
| Number of instruments L = 10 | ||||||||||
| Number of excluded instruments L1 = 2 | ||||||||||
| IV (2SLS) estimation | ||||||||||
| Estimates efficient for homoskedasticity only | ||||||||||
| Statistics consistent for homoskedasticity only | ||||||||||
| Number of obs = 141 | ||||||||||
| F( 8, 132) = 50.56 | ||||||||||
| Prob > F = 0.0000 | ||||||||||
| Total (centered) SS = 16.77342482 Centered R2 = 0.7551 | ||||||||||
| Total (uncentered) SS = 16.77363452 Uncentered R2 = 0.7551 | ||||||||||
| Residual SS = 4.108316349 Root MSE = .1764 | ||||||||||
| D.g_GDP Coefficient Std. err. t P>t [95% conf. interval] | ||||||||||
| g_GDP | ||||||||||
| LD. -.3539798 .1691303 -2.09 0.038 -.6885361 -.0194234 | ||||||||||
| d_exchangerate | ||||||||||
| D1. -.0015997 .0004279 -3.74 0.000 -.0024462 -.0007532 | ||||||||||
| inflation | ||||||||||
| D1. .0065046 .0003884 16.75 0.000 .0057363 .0072729 | ||||||||||
| d_populationgrowth | ||||||||||
| D1. .0227521 .0250216 0.91 0.365 -.026743 .0722472 | ||||||||||
| d_unemployment | ||||||||||
| D1. .0028073 .0158635 0.18 0.860 -.0285724 .0341869 | ||||||||||
| g_crudeoilproduction | ||||||||||
| D1. .149792 .2791891 0.54 0.592 -.4024717 .7020557 | ||||||||||
| g_crudeoilprice | ||||||||||
| D1. .3132407 .0517672 6.05 0.000 .2108401 .4156414 | ||||||||||
| g_oilconsumption | ||||||||||
| D1. .0501327 .1462935 0.34 0.732 -.2392503 .3395158 | ||||||||||
| _cons .0027581 .0149239 0.18 0.854 -.0267628 .0322789 | ||||||||||
| Underidentification test (Anderson canon. corr. LM statistic): 11.816 | ||||||||||
| Chi-sq(2) P-val = 0.0027 | ||||||||||
| Weak identification test (Cragg-Donald Wald F statistic): 5.991 | ||||||||||
| Stock-Yogo weak ID test critical values: 10% maximal IV size 19.93 | ||||||||||
| 15% maximal IV size 11.59 | ||||||||||
| 20% maximal IV size 8.75 | ||||||||||
| 25% maximal IV size 7.25 | ||||||||||
| Source: Stock-Yogo (2005). Reproduced by permission. | ||||||||||
| Sargan statistic (overidentification test of all instruments): 0.691 | ||||||||||
| Chi-sq(1) P-val = 0.4060 | ||||||||||
| -endog- option: | ||||||||||
| Endogeneity test of endogenous regressors: 1.042 | ||||||||||
| Chi-sq(1) P-val = 0.3074 | ||||||||||
| Regressors tested: LD.g_GDP | ||||||||||
| Instrumented: LD.g_GDP | ||||||||||
| Included instruments: D.d_exchangerate D.inflation D.d_populationgrowth | ||||||||||
| D.d_unemployment D.g_crudeoilproduction D.g_crudeoilprice | ||||||||||
| D.g_oilconsumption | ||||||||||
| Excluded instruments: D.L2_g_GDP D.L3_g_GDP | ||||||||||
I would be very grateful for your help and any further solutions to my problem. This is the first time I have addressed the issue of endogeneity.
