# Dummy variables and their interaction (urgent help required)

#### andy1234

##### New Member
Dear All,

I have a question concerning the dummy and dummy interactions. Firm Performance is a continuous variable (variable of interest) and firms which offers different plans are categories as follows: Plan 1, Plan 2 and Plan 3 are dummy plans (reference category, zero plans). While, interaction terms are Plan 1*Performance, Plan 2*Performance, and Plan 3*Performance. However, dependent variable as the natural logarithm of expense.

Dependent Vairabe
Log of expense Model 1 Model 2 Model 3

PERFORMANCE 0.1231*** 0.123 0.105**
Plan 1 (Dummy) 0.923** 0.837** 0.637**
Plan 2 (Dummy) 1.388*** 1.032** 0.932**
Plan 3 (Dummy) 2.622** 2.905*** 2.123***
Plan 1*Performance 0.11** 0.11**
PLan 2*Performance 0.228* 0.198*
Plan 3* Performance 0.232** 0.201**
Control Variables 2 2 6

For Model 1

Stata Code:
regress c Performance plan1 plan2 plan3 Performance firmsize

For Model 2
Stata Code:
regress c Performance plan1 plan2 plan3 i.plan1#c.Performance i.plan2#c.Performance i.plan3#c.Performance Performance firmsize

For Model 3
Stata Code:
regress c Performance plan1 plan2 plan3 i.plan1#c.Performance i.plan2#c.Performance i.plan3#c.Performance Performance firmsize

I am very interested in analyzing the effect of performance on expense.

Also, we can claim in Model 1 that firms which give 1 plan give higher 92.3% higher pay than firm which gives no plans (since there are no interaction terms)

How do we interpret the coefficient of plan 1, plan 2 in model 2. As no of plan increases, the expense also increases, can we claim that and how do we interpret the coefficients in Model 2. In Model 2, can we say that firm which grant Plan 1 gives 83.7% increase in expense? or due to interaction terms, we can not say that

In model 2, for plan1* performance interaction term, can we say a 10% increase (or percentage point increase ) in performance leads to 1.1% increase in expense in plan 1. Please help me with interpretation (or do we need to take natural logarithm).

Lastly, if My performance variable becomes insignificant how can Interpret this. Firms which do not choose any plans (reference category), what is the impact of performance on expense in Model 2 and Model 3? Please help me.

Michael

#### andy1234

##### New Member
Code:
Log of expense (Dependent Vairabe)	Model 1	Model 2	Model 3
PERFORMANCE	0.1231***	0.123	0.105**
Plan 1 (Dummy)	0.923**	0.837**	0.637**
Plan 2 (Dummy)	1.388***	1.032**	0.932**
Plan 3 (Dummy)	2.622**	2.905***	2.123***
Plan 1*Performance		      0.11**	0.11**
PLan 2*Performance		0.228*	0.198*
Plan 3* Performance		0.232**	0.201**
Control Variables	2	2	6

#### rogojel

##### TS Contributor
hi,
I find it the easiest to spell out the regression equation. It is then clear, what effect each term has. In your case the logarithm will complicate things a bit, essentially you will have to change the interpretation from mean to median.

E.g if your equation is log e = a0+a1*P+a2*D1+a3*D1*P then this is a shorthand for two equations

log e=a0+a1*P for the base case (D1=0) and
log e=(a0+a2) + (a1+a3)*P for D1=1

So, the coefficient of the dummy changes the intersection point with the vertical axis, the interaction term changes the slope of the regression line.
As the intersection is often not really sensible (we have no firms with 0 performance) it is a good idea to standardise the variables X->(X-meanX).

regards