Segmented regression and estimate slopes

[Jen Ward]

Hi,

I have a time series and am interested in fitting a segmented regression model to my data to estimate whether there is a change in trends/slopes before and after the introduction of a new policy

I am basing my analyses on this paper: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5407170/ so I enter 3 predictor terms in the model: time, ban (called ban and coded as 0 before policy introduction, and 1 after that), and a time*ban interaction. I can't share my data so I am using a sample data example, which reflects what I do on my own data:

clear *
use http://www.stata-press.com/data/r16/wpi1.dta

g time = _n
g ban = time>=101 //policy introduced in 1st quarter 1985

regress wpi c.time##i.ban

My understanding is that the coefficient of time captures the trend pre-policy, while the interaction term (time*ban) captures the change post-policy.

My question is how can I estimate the actual slope post-policy introduction and its standard error?

Thanks for your help!

[Rich Goldstein]

you may have to replay your regression with the "coeflegend" option but you can use the -lincom- command for this - just add the two; here is an example using the auto data:

. sysuse auto
(1978 automobile data)
r; t=0.01 15:11:58

. regre price c.weight##i.foreign

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(3, 70)        =     26.20
       Model |   335885357         3   111961786   Prob > F        =    0.0000
    Residual |   299180039        70  4274000.55   R-squared       =    0.5289
-------------+----------------------------------   Adj R-squared   =    0.5087
       Total |   635065396        73  8699525.97   Root MSE        =    2067.4

------------------------------------------------------------------------------
       price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
      weight |   2.994814   .4163132     7.19   0.000     2.164503    3.825124
             |
     foreign |
   Domestic  |          0  (base)
    Foreign  |  -2171.597   2829.409    -0.77   0.445    -7814.676    3471.482
             |
     foreign#|
    c.weight |
    Foreign  |   2.367227   1.121973     2.11   0.038      .129522    4.604931
             |
       _cons |  -3861.719   1410.404    -2.74   0.008    -6674.681   -1048.757
------------------------------------------------------------------------------
r; t=0.14 15:12:09

. regre price c.weight##i.foreign, coeflegend

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(3, 70)        =     26.20
       Model |   335885357         3   111961786   Prob > F        =    0.0000
    Residual |   299180039        70  4274000.55   R-squared       =    0.5289
-------------+----------------------------------   Adj R-squared   =    0.5087
       Total |   635065396        73  8699525.97   Root MSE        =    2067.4

------------------------------------------------------------------------------
       price | Coefficient  Legend
-------------+----------------------------------------------------------------
      weight |   2.994814  _b[weight]
             |
     foreign |
   Domestic  |          0  _b[0b.foreign]
    Foreign  |  -2171.597  _b[1.foreign]
             |
     foreign#|
    c.weight |
    Foreign  |   2.367227  _b[1.foreign#c.weight]
             |
       _cons |  -3861.719  _b[_cons]
------------------------------------------------------------------------------
r; t=0.02 15:12:17

. lincom  _b[weight]+_b[1.foreign#c.weight]

 ( 1)  weight + 1.foreign#c.weight = 0

------------------------------------------------------------------------------
       price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         (1) |    5.36204   1.041877     5.15   0.000     3.284083    7.439997
------------------------------------------------------------------------------

[Jared Greathouse]

Look up the itsa command by Ariel Linden.

[Jen Ward]

Thank you both, this is very helpful.

Rich Goldstein is there a way for me to see what formula is used by -lincom- to estimate the standard error of slope 2?

[Rich Goldstein]

I'm not completely sure I understand what you are asking, but there are two places to start: (1) the manual which you can look at by clicking on the link at the top of the help file; (2) the ado file itself which you an locate with the -which- command

[Jen Ward]

Thanks Rich Goldstein