regression help

Hi,

I am trying to figure out the relationship between pay roll taxes and unemployment. I have done some research that suggests that productivity can influence the results, so if firms increase productivity, then unemployment will not increase.

I ran the regression in the form

unemployment= beta_1(increase in payroll tax)+ beta_2(unemployment*productivity)+ beta_3(gov spending on labour market programs)

does that make sense? or is it wrong to have unemployment in the regression as an explanatory variable? I think it might be.

[FONT=Verdana, Arial, Tahoma, Calibri, Geneva, sans-serif]Is there another functional form that I can use, that will determine how productivity influences the relationship between unemployment and pay roll taxes?[/FONT]


Thank you,

WlND said:

Hi,

I am trying to figure out the relationship between pay roll taxes and unemployment. I have done some research that suggests that productivity can influence the results, so if firms increase productivity, then unemployment will not increase.

I ran the regression in the form

unemployment= beta_1(increase in payroll tax)+ beta_2(unemployment*productivity)+ beta_3(gov spending on labour market programs)

does that make sense? or is it wrong to have unemployment in the regression as an explanatory variable? I think it might be.

Is there another functional form that I can use, that will determine how productivity influences the relationship between unemployment and pay roll taxes?


Thank you,

Click to expand...

First, I surprised you didn't put in a constant term but then maybe the data suggests that.

Let
u = unemployment
i = increase in payroll tax
p = productivity
g = gov spending on labour market programs
So your equation is
\(\displaystyle u\, =\, \beta_1\, i\, +\, \beta_2\, u\, p\, +\, \beta_3\, g\)
or
\(\displaystyle u\, =\, \frac{\alpha_1\, i\, +\alpha_2\, g}{1\, +\, \alpha_3\, p}\)

You can run the regression like that but it isn't linear (in the coefficients). Over a 'sufficiently small' range, the \(\displaystyle 1+\alpha_3p\) in the denominator could be turned into a linear regression formula of a quadratic or cubic in p, i.e.
\(\displaystyle u\, =\, (\alpha_1\, i\, +\alpha_2\, g) * (1\, +\, \alpha_3\, p\, +\, \alpha_4\, p^2)\)
Multiply that out to get coefficients of i, q, pi, pg, p²i, p²g. I would also add a coefficient for p [equivalent to that constant term I mentioned before] for a total of 7 linear regression terms or 8 if you added a 'true' constant term. Or, maybe just drop the p squared terms for a total of 6?