The New Jersey-Pennsylvania Study on the Effect of Minimum Wages $\Delta Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + \beta _ { 2 } W _ { 1 , i } + \ldots + \beta _ { 1 + r } W _ { r , i } + u _ { i }$

Essay

The New Jersey-Pennsylvania study on the effect of minimum wages on employment
mentioned in your textbook used a comparison in means "before" and "after" analysis.
The difference-in-difference estimate turned out to be 2.76 with a standard error of 1.36.
The authors also used a difference-in-differences estimator with additional regressors of
the type $\Delta Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + \beta _ { 2 } W _ { 1 , i } + \ldots + \beta _ { 1 + r } W _ { r , i } + u _ { i }$ where $i = 1 , \ldots , 410 . X$ is a binary variable taking on the value one for the 331 observations in New Jersey. Since the authors looked at Burger King, KFC, Wendy's, and Roy Rogers fast food restaurants and the restaurant could be company owned, four $W$ -variables were added. (a)Given that there are four chains and the possibility of a company ownership, why did the
authors not include five W-variables?