Calculating the same unknown using two coefficient regression results

[KiuYuetTiffany Lee]

Hi all,

I'm currently doing two separate multi-variable regression model, the regression models that I would like to estimate are:

model 1: y=constant+(a/1-a)x₁-(a/1-a)x₂+error term
and
model 2: y=constant+(a/1-a-b)x₁₊(b/1-a-b)x₂-(a+b/1-a-b)x₃+error term

I have succesfully got the regression results for the coefficient, and I would also like to calculate value for a using coefficients attained in regression model 1, and also values for a and b using coefficients attained in regression model 2, however I can't find any ways of calculating.

Results for both models are:

regress ln_yl2017 ln_Sk ln_n005,robust

Linear regression Number of obs = 1,216
F(2, 1213) = 73.67
Prob > F = 0.0000
R-squared = 0.1570
Root MSE = .34053

------------------------------------------------------------------------------
| Robust
ln_yl2017 | Coefficient std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
ln_Sk | .4220417 .0475839 8.87 0.000 .3286858 .5153975
ln_n005 | -.7741964 .0801613 -9.66 0.000 -.9314667 -.6169262
_cons | 23.44511 .227626 103.00 0.000 22.99852 23.89169

regress ln_yl2017 ln_Sk ln_Sh ln_n005,robust

Linear regression Number of obs = 1,216
F(3, 1212) = 51.74
Prob > F = 0.0000
R-squared = 0.1577
Root MSE = .34054

------------------------------------------------------------------------------
| Robust
ln_yl2017 | Coefficient std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
ln_Sk | .4145648 .0465565 8.90 0.000 .3232246 .505905
ln_Sh | .0546034 .0492135 1.11 0.267 -.0419497 .1511566
ln_n005 | -.778283 .0814161 -9.56 0.000 -.9380152 -.6185509
_cons | 23.36464 .2528492 92.41 0.000 22.86857 23.86071

Thank you in advance to everyone who can help.
Tiffany

[George Ford]

what sort of theoretical model produced these empirical relationships?

[KiuYuetTiffany Lee]

what sort of theoretical model produced these empirical relationships?

Hi George, I'm trying to replicate methodology following Mankiw, Romer and Weil (1992), their coefficient being estimated would give implication of a and b.

[George Ford]

clear

set obs 1000

g x1 = rnormal()
g x2 = rnormal()

global a  0.75
global b  0.20

g e = rnormal()
g y =  1 + ($a/(1-$a))*(x1 - x2) + e
g y2 = 1 + ($a/(1-$a))*x1 - ($a/(1-$a))*x2  + e
correl y y2

g dx1x2 = x1 - x2

reg y dx1x2
di _b[dx1x2]/(1 + _b[dx1x2])

reg y2 dx1x2
di _b[dx1x2]/(1 + _b[dx1x2])

nl (y = {b0} + x1*({a}/(1-{a})) - x2*({a}/(1-{a})))
nl (y = {b0} + dx1x2*({a}/(1-{a})))

[KiuYuetTiffany Lee]

clear

set obs 1000

g x1 = rnormal()
g x2 = rnormal()

global a 0.75
global b 0.20

g e = rnormal()
g y = 1 + ($a/(1-$a))*(x1 - x2) + e
g y2 = 1 + ($a/(1-$a))*x1 - ($a/(1-$a))*x2 + e
correl y y2

g dx1x2 = x1 - x2

reg y dx1x2
di _b[dx1x2]/(1 + _b[dx1x2])

reg y2 dx1x2
di _b[dx1x2]/(1 + _b[dx1x2])

nl (y = {b0} + x1*({a}/(1-{a})) - x2*({a}/(1-{a})))
nl (y = {b0} + dx1x2*({a}/(1-{a})))

Hi George, definately gonna give it a try. Thank you very much!

[George Ford]

g y3 = 1 + x1*$a/(1-$a-$b) + x3*($b/(1-$a-$b)) - x2*(($a+$b)/(1-$a-$b)) + e
nl (y3 = {b0} + x1*{a}/(1-{a}-{b}) + x3*{b}/(1-{a}-{b}) - x2*({a}+{b})/(1-{a}-{b}))