Dear statalist
I am trying to estimate the elasticity of my outcome variable y with respect to income.
y is censored at 0, and it is between 0 and almost one, which suggests the use of the Tobit model(under the usual assumption on residuals) . However, for the sake of simplicity, I am presenting OLS here
my data for the variable y and income are reported below. I also include the log of income for reference, as I used it in the model (i.e. ln_income).
input float(y ln_income income)
.6291617 6.839435 933.9615
.9945465 7.655005 2111.1853
.9926049 6.69821 810.9529
0 7.633141 2065.5273
0 7.138404 1259.4164
0 8.019789 3040.534
.981214 6.830252 925.424
.8981348 6.331939 562.2459
.9946473 7.226309 1375.1375
0 5.830486 340.5242
0 -4.6051702 .01
I found this technical note: https://www.stata.com/stata14/fracti...utcome-models/ suggesting to use margins, dyex in the context of fractional regression given that the dependent variable is already a proportion and so is already on a percentage scale (same as mine).
When I apply this
regress prob_mod_sev income [pw=wt]
margins [pw=wt], dyex(income)
I get
---------------------------------------------------------------------------------
| Delta-method
| dy/ex std. err. t P>|t| [95% conf. interval]
----------------+----------------------------------------------------------------
income | -.0018123 .0004174 -4.34 0.000 -.0026304 -.0009943
---------------------------------------------------------------------------------
Differently from the technical note, in my case, the elasticity is computed with margins, dydx because the independent variable of interest appears in log (i.e. ln_income), so it is already on a percentage scale
regress prob_mod_sev ln_income [pw=wt]
margins [pw=wt], dydx(ln_income)
which gives me:
------------------------------------------------------------------------------------
| Delta-method
| dy/dx std. err. t P>|t| [95% conf. interval]
-------------------+----------------------------------------------------------------
ln_income | -.0238224 .0002898 -82.20 0.000 -.0243904 -.0232544
------------------------------------------------------------------------------------
SO I have two main concerns:
1. how to reconcile the two results that in principle should be the same (or at least scaled by 100, not by 10 for sure) and which one should I trust?
2. with reference to the second model: how to interpret the elasticity given my context? so a 1% increase in income would bring a reduction in y by 0.02% or 2%. And with reference to the first?
Thanks in advance for any help you can provide on this
Anna
I am trying to estimate the elasticity of my outcome variable y with respect to income.
y is censored at 0, and it is between 0 and almost one, which suggests the use of the Tobit model(under the usual assumption on residuals) . However, for the sake of simplicity, I am presenting OLS here
my data for the variable y and income are reported below. I also include the log of income for reference, as I used it in the model (i.e. ln_income).
input float(y ln_income income)
.6291617 6.839435 933.9615
.9945465 7.655005 2111.1853
.9926049 6.69821 810.9529
0 7.633141 2065.5273
0 7.138404 1259.4164
0 8.019789 3040.534
.981214 6.830252 925.424
.8981348 6.331939 562.2459
.9946473 7.226309 1375.1375
0 5.830486 340.5242
0 -4.6051702 .01
I found this technical note: https://www.stata.com/stata14/fracti...utcome-models/ suggesting to use margins, dyex in the context of fractional regression given that the dependent variable is already a proportion and so is already on a percentage scale (same as mine).
When I apply this
regress prob_mod_sev income [pw=wt]
margins [pw=wt], dyex(income)
I get
---------------------------------------------------------------------------------
| Delta-method
| dy/ex std. err. t P>|t| [95% conf. interval]
----------------+----------------------------------------------------------------
income | -.0018123 .0004174 -4.34 0.000 -.0026304 -.0009943
---------------------------------------------------------------------------------
Differently from the technical note, in my case, the elasticity is computed with margins, dydx because the independent variable of interest appears in log (i.e. ln_income), so it is already on a percentage scale
regress prob_mod_sev ln_income [pw=wt]
margins [pw=wt], dydx(ln_income)
which gives me:
------------------------------------------------------------------------------------
| Delta-method
| dy/dx std. err. t P>|t| [95% conf. interval]
-------------------+----------------------------------------------------------------
ln_income | -.0238224 .0002898 -82.20 0.000 -.0243904 -.0232544
------------------------------------------------------------------------------------
SO I have two main concerns:
1. how to reconcile the two results that in principle should be the same (or at least scaled by 100, not by 10 for sure) and which one should I trust?
2. with reference to the second model: how to interpret the elasticity given my context? so a 1% increase in income would bring a reduction in y by 0.02% or 2%. And with reference to the first?
Thanks in advance for any help you can provide on this
Anna
