Consider two variables with levels over two time periods $\{y^i_t,x^i_t\},\{y^i_{t+1},x^i_{t+1}\}$.

For example, it could be profit and cost data of various firms over two quarters.

Suppose I take the differences of these levels over the two periods and produce new variables.


In other words, for each firm, I now have the difference in profit and cost for the two consecutive quarters. Here DProfit and DCost are meant to represent "D"elta.

I perform a linear regression with the following specification:


Is the following interpretation correct for the coefficients?:

Fix $i=$Apple Inc. Then $\hat\beta_{Apple Inc.}$ tells us for a unit increase in the change in cost between the 2 quarters result in $\hat\beta_{Apple Inc.}$ increase in the change in profit.

Is there a more sensible way of writing or interpreting the coefficients?


1 Answer 1


Two things:

1) You should not assign a specific $i$ value to a regression coefficient. The same estimated coefficient applies to all $i$'s, so you should write it as $\beta_1$, not $\beta_i$.

2) An easier to read interpretation would be: "If a firm's cost increases by 1 unit between two consecutive periods, the firm's revenue is expected to increase by $\beta_1$ units, on average." If the sign of the estimated $\beta_1$ is negative, you can change "increase" to "decrease".


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.