Differencing Models

[kruupy]

Hi All,

I have some models (the numbers in brackets are the time period, t):

Y(1) = c(1) + b(1) x(1) + e(1)
Y(2) = c(c2) + b(2) x(2) + e(2)

If I difference these equations, usually I would get:

equation[1] : [Y(2)-Y(1)] = [c(2)-c(1)] + b [x(2) - x(1)] + e

The above is derived under the assumption that b(1) = b(2). If b(1) is not equal to b(2), the differencing should yield:

equation[2] : [Y(2)-Y(1)] = [c(2)-c(1)] + b(2) x(2) - b(1) x(1) + e

So my question is, if I estimate equation [2] and find that b(2) and b(1) are not statistically significant, but I estimate equation [1] and find that b is statistically significant. Is the significance of the differenced term enough evidence to conclude that b(1) = b(2)?

Cheers and Thanks.