Solving simultaneity with lagged endogenous variable

[William Dawe]

Dear all,

I am investigating to what extent relative salary (salary relative to teammates, salary relative to compatriots etc.) influences performance in Major League Baseball using panel data of individual players from 1985 until 2014. Due to the nature of baseball, there is attrition whereby no player is observed for the full time period and there are also gaps in the panel for numerous reasons (ie. a player serves suspension, a player takes a year out etc). I intend to estimate this relationship using fixed effects.

This is an obvious case of simultaneity whereby a player's salary influences his performance, whilst his performance also influences salary. Unfortunately, I haven't been able to find appropriate instruments, however, I have read about the use of lagged endogenous variables to solve for simultaneity which work because the dependent variable at time t will have no causal relationship with the independent variable at time t-1. I suspect that this technique won't be necessary for me since, naturally, salary at time t is influenced by performance at time t-1 since a player's salary can only be changed at the beginning of the season where performance statistics for that season are not yet observed. I have two questions: firstly, is this intuition correct and secondly, does the nature of baseball mean that simultaneity does not exist between performance and salary and if not, is there anything else I could potentially do to correct for it? (I understand that it would be impossible to tell me what would work since I haven't disclosed enough information about my investigation but any suggestions would be greatly appreciated)

Kind regards,

William

[Phil Bromiley]

You didn't get a quick answer. You would increase your chances of a useful answer if you include Stata code in code delimiters, Stata output, and sample data using dataex - see FAQ on asking questions.

You have multiple issues. First, you have sample selection - players come into and leave the sample in ways related to performance. Second, you have simultaneity - salary may influence performance and performance may influence salary. Players sometimes have incentive clauses in their compensation which guarantees this problem. I'm also not sure how you measure performance consistently for all positions - are you working one position or related positions (e.g., outfielders) at a time? You probably have additional issues I didn't catch.

I would look at cmp (user written) or SEM/GSEM. I think both will handle both problems. However, you still have an underlying need for exogenous variables to identify the model. It is hard to comment on what variables to use since I don't know what data you have and what you've included in the salary equation.

This is more an econometrics issue than a Stata issue. You should start by looking at some good econometrics texts on these issues.

[William Dawe]

Dear Phil Bromiley,

Many thanks for your response and advice on asking future questions, apologies for not following the FAQ. I'll look more into SEM/GSEM as per your recommendation.