I have following regression:
logCPI = 1,2922 – 0,3525*logGDP + 0,4239*logImport + 0,2115*logNEER + 0,6291*logWAGE + 0,0121*dummy
How should I interpret last variable (dummy variable)? The regression is performed for quarterly data (from 2010:1 to 2017:4). The dummy variable represents FX interventions which should increase CPI (consumer price index). The inverventions took place from 2013:4 to 2017:2 (in this period dummy has value 1).
I would appreciate each advice. Thank you
Best Answer
The simplest thing is to simplify and look at the math.
If $y=\beta{x}+\gamma\delta$, then $\exp(y)=\exp(\beta{x})\times\exp(\gamma\delta),$ where $\delta$ is your dummy and $\gamma$ is your coefficient.
When $\delta=0,\exp(\gamma\delta)=1,$ so your problem reduces down to $\exp(y)=\exp(\beta{x})$. When $\delta=1$, $\exp(\gamma\delta)$ is a positive contant. In this case it is $1.012174$. This is a multiplier that rescales the product of your other variables. Because it is greater than unity, it multiplies the consumer price index by an increasing amount over the factors.
When zero, the consumer price index is predictable from the factors alone. When non-zero, the scale of the factors is $1.012174$ greater than without the intervention.
An alternative way to think of it would be that in the presence of intervention, the effect of the $\beta$ terms is $1.012174$ larger.
$$CPI = \frac{1,2922}{GDP^{0,3525}}\times{Import^{0,4239}}\times{NEER^{0,2115}}\times{WAGE^{0,6291}}\times{1.012174},\text{if }\delta=1$$ and $$CPI = \frac{1,2922}{GDP^{0,3525}}\times{Import^{0,4239}}\times{NEER^{0,2115}}\times{WAGE^{0,6291}}\times{1},\text{if }\delta=0$$