Dear all,
I have the following model:
gdp=alpha+beta1*pc+beta2*pc^2+beta*controls+error
pc is assumed to be endogenous and, hence, also its squared values is. I have an instrument, say lnrain for pc. Therefore, I squared it to be used as an instrument for pc^2. Moreover, I supplement additional instruments by using ivreg2h. I got the following result:
I have two questions:
1) Suppose that the theory predicts that lnrain has a positive impact on pc. Now, obviously in the equation for pc I have both lnrain and lnrain2 (the squared of lnrain). This makes me difficult to provide an interpretation. In this case the squared values is not significant, but in some other estimations it is. Which interpretation should I provide for that instrument and its squared values? Clearly, the same difficulty arises when I look at the equation for pc2, where both the linear and the quadratic term are significant;
2) Which interpretation should I provide for the additional instruments that ivreg2h generates (by the way, is there a way to understand to which of the exogenous variable each of those instruments refers?)
Thanks in advance for your help.
Dario
I have the following model:
gdp=alpha+beta1*pc+beta2*pc^2+beta*controls+error
pc is assumed to be endogenous and, hence, also its squared values is. I have an instrument, say lnrain for pc. Therefore, I squared it to be used as an instrument for pc^2. Moreover, I supplement additional instruments by using ivreg2h. I got the following result:
Code:
First-stage regression of pc:
Statistics robust to heteroskedasticity
Number of obs = 103
------------------------------------------------------------------------------
| Robust
pc | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
distcap_a | -.8690289 2.608417 -0.33 0.740 -6.051898 4.31384
distcap2_a | -.2637774 1.518992 -0.17 0.863 -3.281982 2.754428
lnrain | 5.456346 3.071147 1.78 0.079 -.6459571 11.55865
lnrain2 | -.3542422 .2269273 -1.56 0.122 -.8051419 .0966574
__00000I | -.8333196 .2995012 -2.78 0.007 -1.428422 -.2382171
__00000J | -3.034087 1.542979 -1.97 0.052 -6.099953 .03178
__00000K | 3.948176 2.788783 1.42 0.160 -1.593076 9.489428
__00000M | .0694718 .0309836 2.24 0.027 .0079079 .1310356
__00000N | .3397004 .1392292 2.44 0.017 .063055 .6163458
__00000O | -.321525 .1891878 -1.70 0.093 -.697437 .054387
y75 | .3166252 .2388304 1.33 0.188 -.1579258 .7911762
lnwi | 2.079096 .8233567 2.53 0.013 .4431036 3.715088
lnnda | -5.388118 1.376801 -3.91 0.000 -8.123792 -2.652444
_cons | -10.8495 12.59887 -0.86 0.391 -35.88318 14.18418
------------------------------------------------------------------------------
First-stage regression of pc2:
Statistics robust to heteroskedasticity
Number of obs = 103
------------------------------------------------------------------------------
| Robust
pc2 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
distcap_a | -20.69817 26.05677 -0.79 0.429 -72.47241 31.07607
distcap2_a | 2.320504 15.36639 0.15 0.880 -28.21218 32.85319
lnrain | 64.82141 34.28991 1.89 0.062 -3.311907 132.9547
lnrain2 | -4.411558 2.597482 -1.70 0.093 -9.5727 .7495845
__00000I | -8.413202 3.152297 -2.67 0.009 -14.67675 -2.149655
__00000J | -45.33625 17.37461 -2.61 0.011 -79.85923 -10.81326
__00000K | 35.29904 28.10461 1.26 0.212 -20.54423 91.14231
__00000M | .7177471 .3269092 2.20 0.031 .0681856 1.367309
__00000N | 5.177699 1.568982 3.30 0.001 2.060166 8.295232
__00000O | -3.441723 1.948233 -1.77 0.081 -7.312821 .4293759
y75 | 4.775427 2.450612 1.95 0.054 -.0938861 9.64474
lnwi | 26.11898 9.252734 2.82 0.006 7.733993 44.50396
lnnda | -73.228 15.34604 -4.77 0.000 -103.7203 -42.73574
_cons | -135.822 127.899 -1.06 0.291 -389.9546 118.3106
------------------------------------------------------------------------------
IV (2SLS) estimation
--------------------
Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity
Number of obs = 103
F( 5, 97) = 811.02
Prob > F = 0.0000
Total (centered) SS = 201.1464811 Centered R2 = 0.9519
Total (uncentered) SS = 7996.542283 Uncentered R2 = 0.9988
Residual SS = 9.685026275 Root MSE = .3066
------------------------------------------------------------------------------
| Robust
wlnyw | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
pc | -.334632 .1004371 -3.33 0.001 -.531485 -.137779
pc2 | .0302291 .0090812 3.33 0.001 .0124303 .0480279
y75 | .8019289 .0450266 17.81 0.000 .7136784 .8901795
lnwi | .5945961 .1610648 3.69 0.000 .278915 .9102772
lnnda | -.328347 .2901876 -1.13 0.258 -.8971044 .2404103
_cons | 1.448079 .8995337 1.61 0.107 -.3149743 3.211133
------------------------------------------------------------------------------
1) Suppose that the theory predicts that lnrain has a positive impact on pc. Now, obviously in the equation for pc I have both lnrain and lnrain2 (the squared of lnrain). This makes me difficult to provide an interpretation. In this case the squared values is not significant, but in some other estimations it is. Which interpretation should I provide for that instrument and its squared values? Clearly, the same difficulty arises when I look at the equation for pc2, where both the linear and the quadratic term are significant;
2) Which interpretation should I provide for the additional instruments that ivreg2h generates (by the way, is there a way to understand to which of the exogenous variable each of those instruments refers?)
Thanks in advance for your help.
Dario
