I have data that explores the relationship between Port activity (TEU) and industrial real estate vacancy/availability (avail). Availability is not a stationary variable, so I have taken the first difference to find it as stationary. My data are quarterly.

My model has the difference in log-availability as a function of the first lag in log-teu.

I've specified the following regression and with the following results


Code:
arima d.ln_avail l.ln_teu  l(1).ln_avail if tin(2002q1,), ar(1)
The coefficient on l1.ln_availability is b = -0.143

How do I interpret the coefficient in l1.ln_teu ? Is this a standard elasticity? ("A one percent increase in TEU is associated with a 0.143% decrease in availability in a subsequent quarter")?

Or is there a different interpretation given that the Y variable is a first difference?

Thanks!


Code:
clear

**SET YOUR WORKING DIRECTORY
cd "C:\yourdirectory"

use "baltportsindustrial.dta", clear

**set TS**
tsset qdate, quarterly

**check ac in Y variable***
ac avail
ac ln_avail
ac d.ln_avail


**regression**
arima d.ln_avail l(1).ln_teu l(1).ln_avail if tin(2002q1,), ar(1)

**tests for staionarity in residuals**
predict resid
dfuller resid, nocons lags(2)
dfuller resid, nocons