Using margins to calculate MERs after tobit with interaction terms - interpreting the results
Hi,
I am currently conducting some research on innovation output (endogenous variable). Innovation output is presented by share of turnover generated with new products in relation to total sales. As the endogenous variable is bounded from below by zero and from above by 100 percent, I thought about applying a Tobit model. In fact, I do find a corner solution with a fair share of observations at the lower bound. This led me to applying a Tobit Type 1 model.
Since I am researching firm level data, it is of iterest to me, wether certain types of firms generate innovation output more efficiently - that is with less input. I have two types of firms that I indicated with a dumy variable (Type 1=0, Type 2=1). To see wether there is a relationship between output, input and firm type, I introduced a interaciton term.
I thus have the following variables:
endogenous: outp exogenous: c.inp and i.type (I obviously have a few more covariates, but let us stay with these for simplicity reasons)
I specified the following model:
tobit outp c.inp##i.type, ll(0)
margins type, at(inp=(0(0.1)1))
marginsplot
With this I try to figure out, wether firm Type 1 or Type 2 generate more output per unit input. However, I am not sure, wether I may interpret the result in the fashion depicted.
Or should I use the dydx option instead?
Such as:
tobit outp c.inp##i.type, ll(0)
margins, dydx(*)
or
tobit outp c.inp##i.type, ll(0)
margins, dydx(type) at(inp=(0(0.1)1))
In the end of the day, I would like to circumvent the somewhat complicated interpretation of the effects of the covariates on a latent variably y* and instead show the impact on the true variable y.
I hope I made myself comprehensable! Any help is greatly appreciated!
Thank you, m
Jonas
I am currently conducting some research on innovation output (endogenous variable). Innovation output is presented by share of turnover generated with new products in relation to total sales. As the endogenous variable is bounded from below by zero and from above by 100 percent, I thought about applying a Tobit model. In fact, I do find a corner solution with a fair share of observations at the lower bound. This led me to applying a Tobit Type 1 model.
Since I am researching firm level data, it is of iterest to me, wether certain types of firms generate innovation output more efficiently - that is with less input. I have two types of firms that I indicated with a dumy variable (Type 1=0, Type 2=1). To see wether there is a relationship between output, input and firm type, I introduced a interaciton term.
I thus have the following variables:
endogenous: outp exogenous: c.inp and i.type (I obviously have a few more covariates, but let us stay with these for simplicity reasons)
I specified the following model:
tobit outp c.inp##i.type, ll(0)
margins type, at(inp=(0(0.1)1))
marginsplot
With this I try to figure out, wether firm Type 1 or Type 2 generate more output per unit input. However, I am not sure, wether I may interpret the result in the fashion depicted.
Or should I use the dydx option instead?
Such as:
tobit outp c.inp##i.type, ll(0)
margins, dydx(*)
or
tobit outp c.inp##i.type, ll(0)
margins, dydx(type) at(inp=(0(0.1)1))
In the end of the day, I would like to circumvent the somewhat complicated interpretation of the effects of the covariates on a latent variably y* and instead show the impact on the true variable y.
I hope I made myself comprehensable! Any help is greatly appreciated!
Thank you, m
Jonas
