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