clear
cd "E:\Econ 107\LAB7\data"
use cps08.dta\[AHE=\beta_0+\beta_1Age+\beta_2 Female+\beta_3 Bachelor\]
Codes
reg ahe age female bachelor, robust
outreg2 using LAB7.doc, replaceResults
Linear regression Number of obs = 7,711
F(3, 7707) = 555.48
Prob > F = 0.0000
R-squared = 0.1998
Root MSE = 9.0718
------------------------------------------------------------------------------
| Robust
ahe | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | .5852144 .0365302 16.02 0.000 .5136052 .6568236
female | -3.664026 .2076129 -17.65 0.000 -4.071003 -3.257048
bachelor | 8.083001 .2126945 38.00 0.000 7.666062 8.49994
_cons | -.6356977 1.083075 -0.59 0.557 -2.758818 1.487423
------------------------------------------------------------------------------\[AHE=-0.6356977+0.5852144Age-3.664026 Female+8.083001 Bachelor\]
Take differential:
\[dAHE=0.5852144dAge\]
Age increases from 25 to 26, which is one unit, ahe increases by 0.5852144.
Age increases from 33 to 34, which is one unit, ahe increases by 0.5852144.
\[log(AHE)=\beta_0+\beta_1Age+\beta_2 Female+\beta_3 Bachelor\]
Codes
gen logahe=ln(ahe)
reg logahe age female bachelor, robust
outreg2 using LAB7.docResults
Linear regression Number of obs = 7,711
F(3, 7707) = 629.21
Prob > F = 0.0000
R-squared = 0.2007
Root MSE = .46938
------------------------------------------------------------------------------
| Robust
logahe | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | .027327 .0018604 14.69 0.000 .0236802 .0309738
female | -.1859238 .0108425 -17.15 0.000 -.2071781 -.1646696
bachelor | .4281274 .0108477 39.47 0.000 .406863 .4493919
_cons | 1.87634 .0558599 33.59 0.000 1.76684 1.985841
------------------------------------------------------------------------------\[log(AHE)=1.87634+0.027327Age-0.1859238 Female+0.4281274 Bachelor\]
Take differential:
\[\frac{dAHE}{AHE}=0.027327dAge\]
Age increases from 25 to 26, which is one unit, ahe increases by 2.7327%.
Age increases from 33 to 34, which is one unit, ahe increases by 2.7327%.
\[log(AHE)=\beta_0+\beta_1log(Age)+\beta_2 Female+\beta_3 Bachelor\]
Codes
gen logage=ln(age)
reg logahe logage female bachelor, robust
outreg2 using LAB7.docResults
Linear regression Number of obs = 7,711
F(3, 7707) = 629.58
Prob > F = 0.0000
R-squared = 0.2008
Root MSE = .46935
------------------------------------------------------------------------------
| Robust
logahe | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
logage | .8039051 .0544678 14.76 0.000 .6971334 .9106768
female | -.1858896 .0108414 -17.15 0.000 -.2071417 -.1646374
bachelor | .4282541 .010847 39.48 0.000 .406991 .4495173
_cons | -.0345257 .1846056 -0.19 0.852 -.3964029 .3273515
------------------------------------------------------------------------------\[log(AHE)=-0.0345257+0.8039051log(Age)-0.1858896 Female+0.4282541 Bachelor\]
Take differential:
\[\frac{dAHE}{AHE}=0.8039051\frac{dAge}{Age}\]
Age increases from 25 to 26, which is \((26-25)/25\times 100%=4%\), ahe increases by \(4\times 0.8039051=3.2156\).
Age increases from 33 to 34, which is \((34-33)/33\times 100%=3%\), ahe increases by \(3\times 0.8039051=2.4117\).
\[log(AHE)=\beta_0+\beta_1Age+\beta_2 Female+\beta_3 Bachelor+\beta_4Age^2\]
Codes
gen age2=age^2
reg logahe age female bachelor age2, robust
outreg2 using LAB7.docResults
Linear regression Number of obs = 7,711
F(4, 7706) = 472.33
Prob > F = 0.0000
R-squared = 0.2008
Root MSE = .46937
------------------------------------------------------------------------------
| Robust
logahe | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | .0813725 .0433885 1.88 0.061 -.0036807 .1664257
female | -.1858687 .0108411 -17.14 0.000 -.2071203 -.1646172
bachelor | .428378 .0108492 39.48 0.000 .4071105 .4496455
age2 | -.0009148 .0007353 -1.24 0.213 -.0023561 .0005265
_cons | 1.08543 .6353251 1.71 0.088 -.15998 2.33084
------------------------------------------------------------------------------\[log(AHE)=1.08543+0.0813725Age-0.1858687 Female+0.428378 Bachelor-0.0009148Age^2\]
Take differential:
\[\frac{dAHE}{AHE}=(0.0813725-0.0018296Age^*)dAge\]
Let \(Age^*=\frac{Age_1+Age_0}{2}\)
Age increases from 25 to 26, which is one unit, ahe increases by \(0.0813725-0.0018296*25.5=3.47%\)
Age increases from 33 to 34, which is one unit, ahe increases by \(0.0813725-0.0018296*33.5=2%\).
Done
Codes
reg logahe age if female==0 & bachelor==0, robust
predict loglin
reg logahe logage if female==0 & bachelor==0, robust
predict loglog
reg logahe age age2 if female==0 & bachelor==0, robust
predict logquad
twoway lfitci loglin age \\Twoway linear prediction plots with CIs
twoway lfitci loglog age
twoway lfitci logquad age