Measuring efficiency with an interaction in a Tobit model?
Hi,
recently asked a question on how to interpret outputs generated with marginal effects after estimating a Tobit model. I am using Stata 13, so I figured I'd use the command margins - which I find very helpful. However, I am still a little bit lost when it comes to interpreting the results. I am researching firm level data in regards to innovation output and would like to understand wether certain companies use innovation input (for example Research and Development expenditures) more efficiently than others.
I have three issues/questions:
(1) Issue: Overcoming the short come of the Tobit output: namely that it shows the impact of changes in the regressors on the latent variable y instead of on the observed variable y*.
(2) Issue: Making sure that I actually estimate efficiency. I am just not sure if I am doing it correctly.
(3) Question: Does it make sense to incorporate a interaction term, or should I merely use single terms and use margins with at/over instead?
To make things a little more tangible (especially compared to my earlier post that failed to gain any attraction due to my stupid asking style; see the link below), I figured a simulate some data and analyze them accordingly:
I generate output bounded from below via the function y=2*x-3*t+4*x*t+5*t*m+rnormal(), where x depicts a metric input variable, t indicates the firm type (coded 0;1), m acts as an indicator for market uncertainty (coded 0;1 for simplicity reasons). The function thus simulates data, where y grows with the input of x, declines when company type 1 is in question, but where company type 1 generates more y per unit x invested, and does so even more, when the market is certain (m=1).
Running the Tobit model does yield the results expected.
Tobit regression results:
However, I have some issues interpreting the marginal effects.
Results marginal effects:
I interpret them as follows: Holding all covariates at their respective mean, company type 2 generates 5.35 units of y per unit x invested, whilst company type 1 only amounts to 1.31 units y per unit x invested. As such, company type 2 are on average more efficient. Moreover, this relationship increases as m increases. Does this make sense? And how can I be sure, that I am acctually measure "efficiency". Any help is gladly appreciated.
Thank you loads,
Jonas
PS: Earlier related question via http://www.statalist.org/forums/foru...ng-the-results
recently asked a question on how to interpret outputs generated with marginal effects after estimating a Tobit model. I am using Stata 13, so I figured I'd use the command margins - which I find very helpful. However, I am still a little bit lost when it comes to interpreting the results. I am researching firm level data in regards to innovation output and would like to understand wether certain companies use innovation input (for example Research and Development expenditures) more efficiently than others.
I have three issues/questions:
(1) Issue: Overcoming the short come of the Tobit output: namely that it shows the impact of changes in the regressors on the latent variable y instead of on the observed variable y*.
(2) Issue: Making sure that I actually estimate efficiency. I am just not sure if I am doing it correctly.
(3) Question: Does it make sense to incorporate a interaction term, or should I merely use single terms and use margins with at/over instead?
To make things a little more tangible (especially compared to my earlier post that failed to gain any attraction due to my stupid asking style; see the link below), I figured a simulate some data and analyze them accordingly:
Code:
***Generate simulated Data *Input gen x=rnormal()^2 *Company Type gen t=round(runiform()) *Market environment gen m=round(runiform()) ***Functional forms gen y=2*x-3*t+4*x*t+5*t*m+rnormal() ***Creating Tobit conditions (left censored at 0) replace y=0 if _n<1000 *Tobit: Let yi be the observed var bounded from below and yi* the latent var tobit y c.x##i.t i.m##i.t, ll(0) *Marginal effect on the censored expected value E(yi) margins, dydx(x) predict(ystar(0,.)) atmeans over(t) margins, dydx(x) predict(ystar(0,.)) at(m=(0 1)) over(t) marginsplot
I generate output bounded from below via the function y=2*x-3*t+4*x*t+5*t*m+rnormal(), where x depicts a metric input variable, t indicates the firm type (coded 0;1), m acts as an indicator for market uncertainty (coded 0;1 for simplicity reasons). The function thus simulates data, where y grows with the input of x, declines when company type 1 is in question, but where company type 1 generates more y per unit x invested, and does so even more, when the market is certain (m=1).
Running the Tobit model does yield the results expected.
Tobit regression results:
Code:
Tobit regression Number of obs = 10000
LR chi2(5) = 15604.32
Prob > chi2 = 0.0000
Log likelihood = -19054.298 Pseudo R2 = 0.2905
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x | 1.963289 .0294802 66.60 0.000 1.905502 2.021076
1.t | -3.409549 .1061183 -32.13 0.000 -3.617562 -3.201536
|
t#c.x |
1 | 3.769483 .0401508 93.88 0.000 3.690779 3.848186
|
1.m | .0056122 .0880544 0.06 0.949 -.1669922 .1782166
|
m#t |
1 1 | 5.580141 .1144427 48.76 0.000 5.35581 5.804471
|
_cons | -.7479231 .0703441 -10.63 0.000 -.8858117 -.6100346
-------------+----------------------------------------------------------------
/sigma | 2.926497 .0126382 2.901723 2.95127
------------------------------------------------------------------------------
Obs. summary: 3129 left-censored observations at y<=0
6871 uncensored observations
0 right-censored observations
However, I have some issues interpreting the marginal effects.
Results marginal effects:
Code:
. margins, dydx(x) predict(ystar(0,.)) atmeans over(t)
Conditional marginal effects Number of obs = 10000
Model VCE : OIM
Expression : E(y*|y>0), predict(ystar(0,.))
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x |
t |
0 | 1.310562 .021878 59.90 0.000 1.267682 1.353442
1 | 5.351779 .0214539 249.46 0.000 5.30973 5.393828
------------------------------------------------------------------------------
. margins, dydx(x) predict(ystar(0,.)) at(m=(0 1)) over(t)
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x |
_at#t |
1 0 | 1.17447 .0196007 59.92 0.000 1.136054 1.212887
1 1 | 2.626861 .024471 107.35 0.000 2.578899 2.674823
2 0 | 1.175705 .0195122 60.25 0.000 1.137462 1.213949
2 1 | 5.033166 .0211266 238.24 0.000 4.991759 5.074574
------------------------------------------------------------------------------
Thank you loads,
Jonas
PS: Earlier related question via http://www.statalist.org/forums/foru...ng-the-results
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