Interpreting Lagged First Differences Linear Regression Coefficents

I am running a Linear Regression Model about housing prices and certain macro variables. My model is as follows: $$House Price_{t+1}=\beta_0 + \beta_1 rent_t+\beta_2 unemployment_t+\beta_1 volume_t+\beta_1 income_t+\beta_1 interest_t$$

I found out that Housing Prices (using Case-Shiller Price Index SA) are nonstationary. So I thought what if I changed it to first differences. But now I am confused on the interpretation of those variables. For arguments sake, lets say the parameter estimates are as follows:

Rent: 100
Unemployment: -.03
Volume: 5 (originally measured in Millions)
Income: 4
Interest: -.05

Therefore the following interpretations would apply? Data is quarterly data:

A one dollar increase in the change in Rent this quarter results in a 100 change in the index next quarter

A one percent increase in the change in unemployment rate this quarter results in a .03 change in the index next quarter

A one million increase this quarter in the change in volume results in a 5 unit increase in the index next quarter

Is this methodology right? I don't think it sounds right at all or makes sense which is why I am here.

• If it's the first difference, wouldn't it be an effect on the change of index instead of simply on the index? "A \$1 increase in rent is associated with a +100 change in the change of the index next quarter? Analogically, if the index is car speed, then it is the increase on acceleration, not speed level. – carl_pch Mar 10 '17 at 20:41
• Did yout take the first difference of all variables? or just the house prices? or just the right-hand-side variables? – Richard Hardy Mar 11 '17 at 8:36