Before I begin, I would like to say that I have already read many, many articles by Stata, Statalist, Richard Williams, and others about margins (and learned a great deal). However uncertainty arises in that: 1) most examples of interpreting margins involve models dealing with probability (logit, probit, etc) and it’s hard for me to make an analogous interpretation with panel data, and/or 2) involved an SSC (e.g. -mcp-, -spost13-) which I am unable to download due to networking restrictions. I realize questions about margins come up a lot.
Stata/MP 14.2 – (via remote access)
Data: Census Bureau Longitudinal Business Database: microdata on millions of establishments with info on id, year, industry, payroll, and employment.
Research Goal: Numerous studies show that workers at smaller firms make less than those with comparable skills working at larger firms, this is called the Firm Size-Wage Effect. However these studies make the assumption that if a small firm magically grew to the size of a large firm, the average wages would also grow to magically match those at the large firm. The ultimate goal is to see if as smaller firms grow, do they become more like larger firms.
From what I could understand, the -margins- command (MERs in particular) was the best way to find the slope of the derivative for intrafirm growth’s effect on average payroll.
Note:
Size_cat: categories of number of employees (10 is the most employees)
emp_change: (empt- empt-1)/((empt+empt-1)*.5)
- this measure is widely used in economics because “it is identical to log changes up to a second-order Taylor Series expansion”
-ranges from -2 to 2
growth==1: An indication that a firm’s mean employment change over the previous three years was positive.
***I apologize that this is a picture. Networking restrictions do not allow me to export Stata results either by the internet or copy/paste. Please do not FAQ me for this. ***
Perhaps the safest interpretation of these estimates would be that if all firms were adjusted to be in size category 3, then their average payroll would decrease 33.7% with a 1 percent increase in employment (since emp_change has log-like properties, I (blindly) assume that it can be interpreted like log-transformed variables). However, that isn't very interesting in the context of my research.
I’m sort of stuck at this point not knowing what to compare what with what in order to meet my research goal. I apologize for the open-endedness of this question, but I can't come up with a guess that even sounds close. Does anybody have a suggestions or could point me in the right direction? (Hopefully you don't just post a link to an article about margins, I feel I've already read all of them).
Stata/MP 14.2 – (via remote access)
Data: Census Bureau Longitudinal Business Database: microdata on millions of establishments with info on id, year, industry, payroll, and employment.
Research Goal: Numerous studies show that workers at smaller firms make less than those with comparable skills working at larger firms, this is called the Firm Size-Wage Effect. However these studies make the assumption that if a small firm magically grew to the size of a large firm, the average wages would also grow to magically match those at the large firm. The ultimate goal is to see if as smaller firms grow, do they become more like larger firms.
- As previous studies have, I want to find the differences in average payroll based on firm size categories (the easy part).
- See if the relationship between intrafirm growth and its average payroll changes coincide with the findings in #1.
- In other words, let’s say in #1 I find that firms with 10 to 15 (50 to 100) employees have an average pay of $20,000 ($40,000)- then in #2 I would want to find if the firms with 10 to 15 employees that grow to having 50 to 100 employees, does their average payroll double. I’d want to determine this across many size categories. I’m only using size categories to help account for a nonlinear relationship between the DV and IVs, and using them is more intuitive to understand for me. It would be nice if there was a more fluid approach than using lumpy size categories.
From what I could understand, the -margins- command (MERs in particular) was the best way to find the slope of the derivative for intrafirm growth’s effect on average payroll.
Note:
Size_cat: categories of number of employees (10 is the most employees)
emp_change: (empt- empt-1)/((empt+empt-1)*.5)
- this measure is widely used in economics because “it is identical to log changes up to a second-order Taylor Series expansion”
-ranges from -2 to 2
growth==1: An indication that a firm’s mean employment change over the previous three years was positive.
***I apologize that this is a picture. Networking restrictions do not allow me to export Stata results either by the internet or copy/paste. Please do not FAQ me for this. ***
Code:
xtreg log_avg_pay size_cat##c.num_years c.emp_change#c.emp_change size_cat##c.emp_change c.log_emp#c.log_emp if growth==1, fe vce(cluster lbdnum)
Code:
margins, dydx(emp_change) at(size_cat=(1/10))
Perhaps the safest interpretation of these estimates would be that if all firms were adjusted to be in size category 3, then their average payroll would decrease 33.7% with a 1 percent increase in employment (since emp_change has log-like properties, I (blindly) assume that it can be interpreted like log-transformed variables). However, that isn't very interesting in the context of my research.
I’m sort of stuck at this point not knowing what to compare what with what in order to meet my research goal. I apologize for the open-endedness of this question, but I can't come up with a guess that even sounds close. Does anybody have a suggestions or could point me in the right direction? (Hopefully you don't just post a link to an article about margins, I feel I've already read all of them).
Attached Files
