In my current project, I’m facing some confusion regarding the appropriate sampling and estimation methods and would appreciate some guidance. Here's a simplified outline of the situation:-
I am trying to replicate a methodology of a paper. Following are my hypothesis.
Hypothesis 1. Firms with high proportion of X1 managerial characteristics are more likely to make Y expenditure as compared to firms not having such characteristics
Hypothesis 2. Firms with high proportion of X2 managerial characteristics are less likely to make Y expenditure as compared to firms not having such characteristics
My independent variables are continuous and time variant. It is calculated as proportion of board member with X1 characteristics and proportion of board members with X2 characteristics.
Dependent variables:- I have two dependent variables.
First dependent variable is likelihood of making Y expenditure (time variant and binary) and is coded as 1 if a firms makes Y expenditure in a given year else 0.
Second dependent variable is the amount of Y expenditure.
Data:- I have a panel data ranging for 5 years. In a population of 2011 number of publicly listed firms, 222 firms make Y expenditure. Among these 222 firms making Y expenditure, 135 firms have X1 and X2 characteristics. 87 firms do not have X1 and X2 characteristics. In my sample of 2011 firms, 1031 firms have X1 and X2 characteristics (% of board members) and rest 980 firms does not and hence they simply take zero value.
Here is a summarized version of my data: -
I plan on using the 2 step Heckman selection model for my estimation. In the first stage, I plan on using Probit model to calculate the likelihood of firms with X1 and X2 characteristics making Y expenditure i.e 1’s and 0’s. And in the second stage, I plan on using a fixed effects linear regression (controlling for inverse mills ratio), where my dependent variable is amount of Y expenditure (among firms making Y expenditure).
My questions are as follows: -
1) Given that number of firms making Y expenditure are just 222 in a total sample of 2011 firms. Do I need to reduce the number of firms “NOT” making Y expenditure? Will it create a class imbalance? What are the techniques to solve this problem?
2) How should I select my sample without incurring any sort of bias like for example, selection bias?
3) Do I need to perform a propensity score matching to reduce the number of firms not making Y expenditure?
4) In a paper which I referred to, propensity score matching (PSM) was used to mitigate the endogeneity concerns by creating a control group having similar characteristics as that of firms having X1 and X2 characteristics (In our case, that number is 1031 firms as we can see in the table). However, If I want to create a control group for firms not making Y expenditure, then I will have to deploy PSM based on dependent variable (i.e firms with similar characteristics making Y expenditure) instead of independent variables i.e (firms with similar characteristics as of firm having X1 and X2 characteristics).
I am utterly confused as to how should I go about it. I have a beginner level learning understanding of econometrics, and I am deeply grateful for any help I shall receive from the Stata community.
I am trying to replicate a methodology of a paper. Following are my hypothesis.
Hypothesis 1. Firms with high proportion of X1 managerial characteristics are more likely to make Y expenditure as compared to firms not having such characteristics
Hypothesis 2. Firms with high proportion of X2 managerial characteristics are less likely to make Y expenditure as compared to firms not having such characteristics
My independent variables are continuous and time variant. It is calculated as proportion of board member with X1 characteristics and proportion of board members with X2 characteristics.
Dependent variables:- I have two dependent variables.
First dependent variable is likelihood of making Y expenditure (time variant and binary) and is coded as 1 if a firms makes Y expenditure in a given year else 0.
Second dependent variable is the amount of Y expenditure.
Data:- I have a panel data ranging for 5 years. In a population of 2011 number of publicly listed firms, 222 firms make Y expenditure. Among these 222 firms making Y expenditure, 135 firms have X1 and X2 characteristics. 87 firms do not have X1 and X2 characteristics. In my sample of 2011 firms, 1031 firms have X1 and X2 characteristics (% of board members) and rest 980 firms does not and hence they simply take zero value.
Here is a summarized version of my data: -
| Y expenditure | |||||
| X1 and X2 characteristics |
|
No (coded as 0) | Total | ||
| Present | 135 firms | 896 firms | 1031 firms | ||
| Absent | 87 firms | 893 firms | 980 firms | ||
| Total ___________________222 firms | 1789 firms | 2011 firms | |||
My questions are as follows: -
1) Given that number of firms making Y expenditure are just 222 in a total sample of 2011 firms. Do I need to reduce the number of firms “NOT” making Y expenditure? Will it create a class imbalance? What are the techniques to solve this problem?
2) How should I select my sample without incurring any sort of bias like for example, selection bias?
3) Do I need to perform a propensity score matching to reduce the number of firms not making Y expenditure?
4) In a paper which I referred to, propensity score matching (PSM) was used to mitigate the endogeneity concerns by creating a control group having similar characteristics as that of firms having X1 and X2 characteristics (In our case, that number is 1031 firms as we can see in the table). However, If I want to create a control group for firms not making Y expenditure, then I will have to deploy PSM based on dependent variable (i.e firms with similar characteristics making Y expenditure) instead of independent variables i.e (firms with similar characteristics as of firm having X1 and X2 characteristics).
I am utterly confused as to how should I go about it. I have a beginner level learning understanding of econometrics, and I am deeply grateful for any help I shall receive from the Stata community.
