Problem with Instrumental Variable Regression

[Zainab Mariam]

Hello,

I am using Stata 14. The data type of my research is panel data (unbalanced), the time period is 22 years, 5084 firms. My model includes 10 explanatory variables (x1, x2, …, x10) where 9 of these 10 explanatory variables are lagged one year, while only one explanatory variable is in the current time/present period (i.e., not lagged. It is in time t). In other words, the nine explanatory variables (x1, x2, x3, x4, x5, x6, x7, x8, x9) are lagged one year, while the explanatory variable x10 is in the current time.

The dependent variable y of my research is a limited dependent variable and truncated between zero and one. Thus, I applied the Tobit model by typing in Stata the following:

xttobit y L.(x1 x2 x3 x4 x5 x6 x7 x8 x9) x10, ll(0) ul(1)

The explanatory variable x1 is endogenous. Thus, I will use the Instrumental Variable Tobit (IVTobit) method. Accordingly, the first issue is about the static model and my first question is: can I use the command ‘ivtobit’ for panel data i.e., without the prefix ‘xt’? Is there ‘xtivtobit’ command to deal with a panel data model with a limited dependent variable and with the endogenous explanatory variable x1? If no, I kindly ask you please to guide me on what I should do.

The second issue is regarding the dynamic model i.e., the model includes the lagged dependent variable y as a regressor. The dependent variable y of my research is a limited dependent variable and truncated between zero and one. Thus, my second question is: what should I do in this case? how to apply the Instrumental Variable Tobit (IVTobit) method in dynamic panel data (the lagged dependent variable y is an explanatory variable) and the dependent variable y is a limited dependent variable and truncated between zero and one? What is the command?

The third issue is regarding having two endogenous variables in the dynamic model i.e., the lagged dependent variable y is endogenous regressor and the explanatory variable x1 is endogenous. Thus, my third question is: what should I do in this case? how to apply the Instrumental Variable Tobit (IVTobit) method in dynamic panel data (the lagged dependent variable y is an explanatory variable) and the dependent variable y is a limited dependent variable and truncated between zero and one? What is the command?

My fourth question is: do I have to use internal or external instrumental variables? can I use lagged values of the endogenous variable as an instrumental variable?

Thank you in advance.

[Zainab Mariam]

Eagerly waiting for a response, please!

[Andrew Musau]

You raise too many issues in your post, some of which I do not think have been properly resolved in the econometric literature. Here is a partial answer and guidance to move forward.

1. Take a look at the difference between truncated data and censored data as these are two distinct but often conflated processes. tobit can be used if your outcome is censored (although it has its problems with its assumptions).

2. There is no parametric conditional fixed effects Tobit estimator as there does not exist a sufficient statistic that allows the fixed effects to be conditioned out of the likelihood. Nevertheless, Bill Greene uses simulations to show that if the \(T\) dimension is sufficiently large, there is not much incidental parameters bias if one uses the unconditional FE estimator (i.e., tobit with dummies).

3. In linear FE, the lagged dependent variable (LDV) bias is declining in \(T\), so again this suggests that unconditional FE Tobit with an LDV may be OK. But I am speculating here, this goes back to my comment that such an application has not been sufficiently studied in the literature.

4. The points on unconditional FE Tobit naturally extend to instrumental-variables Tobit with dummies.

Reference:
Greene, W. “Fixed Effects and Bias Due to the Incidental Parameters Problem in the Tobit Model.” Econometric Reviews, 23 (2004), 125-147.

[Minhaj uddin]

Hello, Miss Zainab
As you have discussed in detail in one of your posts with Prof. Sebastian about applying GMM to the above dataset. I want to know if you have treated your truncated dependent variable (like taking log or log odd) before applying GMM. If yes, How?

Your response prompt would be a great help to me.

Thank you!

[Minhaj uddin]

Hello, @Zainab Mariam
As you have discussed in detail in one of your posts with Prof. Sebastian about applying GMM to the above dataset. I want to know if you have treated your truncated dependent variable (like taking log or log odd) before applying GMM. If yes, How?

Your response would be a great help to me.

Thank you!