[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

# st: Re: statalist-digest V4 #3365

 From Kit Baum To statalist@hsphsun2.harvard.edu Subject st: Re: statalist-digest V4 #3365 Date Mon, 16 Mar 2009 09:33:27 -0400

```<>
```
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
implies
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
implies
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   |   http://ideas.repec.org/e/pba1.html
An Introduction to Stata Programming   |   http://www.stata-press.com/books/isp.html
An Introduction to Modern Econometrics Using Stata   |   http://www.stata-press.com/books/imeus.html

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?
```
```
*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/
```

 © Copyright 1996–2021 StataCorp LLC   |   Terms of use   |   Privacy   |   Contact us   |   What's new   |   Site index