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re: st: ldv when the dv is first-differenced: d.variable and l.variable

From   Kit Baum <>
Subject   re: st: ldv when the dv is first-differenced: d.variable and l.variable
Date   Mon, 16 Mar 2009 09:35:04 -0400

Sorry for the previous subject line.

On Mar 16, 2009, at 02:33 , Carlos wrote:

If the dependent variable is first-differenced (i.e, change in
unemployment -I'm using the d.variable command) and one would like to
control for the lagged dependent
variable on the right-hand side of the regression, should one lag the
"first-differenced variable" (i.e, lagged change in unemployment) or
should one lag the level variable (lagged unemployment -using the
time-series command l.variable).  To be
clearer say you have:

d.unemployment  = dependent variable

Should one use  "l.unemployment" as the
Lagged DV in the right-hand side or should one lagged the
first-differenced variable?

It is useful to do the algebra. In the case where you have L.x on the RHS,

D.x = alpha + beta L.x + eps
x_t = alpha + (1+beta) x_t-1 + eps
For this linear first-order difference equation to be stable, beta must be less than one. (Note that the model as written is a form of the "Dickey-Fuller" regression used to test for a unit root in x).

In the other case,
D.x = alpha + beta LD.x + eps
x_t = alpha + (1+beta) x_t-1 - beta x_t-2 + eps
This equation contains a unit root by construction, no matter what beta is, as the sum of the lag coefficients is unity. The equation will be stable in differences if beta is within the unit circle, but implies nonstationary behavior for the level of x.

Kit Baum   |   Boston College Economics and DIW Berlin   |
An Introduction to Stata Programming   |
An Introduction to Modern Econometrics Using Stata   |

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