SEM vs. 2sls (ivreg): Replicating Stata example

[Roman Mostazir]

Dear Colleagues,

Need some help here to replicate an example from "ivreg" described here: http://www.stata.com/support/faqs/st...rsive-systems/ . I was attracted to a Note in the page where it says:

Note: This model could also be fit with sem, using maximum likelihood instead of a two-step method.

Example of ivreg:

 
 sysuse auto   
 ivregress 2sls price displacement (trunk=headroom), small 
Instrumental variables (2SLS) regression

      Source |       SS       df       MS              Number of obs =      74
-------------+------------------------------           F(  2,    71) =   11.29
       Model |   108641939     2  54320969.4           Prob > F      =  0.0001
    Residual |   526423457    71  7414414.89           R-squared     =  0.1711
-------------+------------------------------           Adj R-squared =  0.1477
       Total |   635065396    73  8699525.97           Root MSE      =  2722.9

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       trunk |  -222.3396   175.7292    -1.27   0.210    -572.7338    128.0545
displacement |   22.19871   6.071088     3.66   0.000      10.0933    34.30411
       _cons |   4844.184   1620.835     2.99   0.004     1612.331    8076.037
------------------------------------------------------------------------------
Instrumented:  trunk
Instruments:   displacement headroom

As the Note above from the page suggests, the model can be fiitted with SEM and that is what I am interested in. What I would like to know is what would be the relevant SEM code to reproduce the same result. If I type the following:

sem (trunk <- headroom) ///
    (price <- displacement trunk),method(ml)

It poduces the following and they are very different:

------------------------------------------------------------------------------
               |                 OIM
               |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
Structural     |
  trunk <-     |
      headroom |   3.347171   .4405193     7.60   0.000     2.483769    4.210573
         _cons |    3.73786    1.36955     2.73   0.006      1.05359    6.422129
  -------------+----------------------------------------------------------------
  price <-     |
         trunk |   14.33919   87.76796     0.16   0.870    -157.6828    186.3612
  displacement |    15.4894   4.087875     3.79   0.000      7.47731    23.50148
         _cons |    2911.98   1005.215     2.90   0.004     941.7949    4882.165
---------------+----------------------------------------------------------------
   var(e.trunk)|   10.13883   1.666814                      7.346008    13.99345
   var(e.price)|    6477314    1064864                       4693083     8939878
--------------------------------------------------------------------------------

Can anyone help in implementing the 2sls in SEM as the page prescribed? Many thanks.

[Richard Williams]

I think the code is something like

. sem (trunk <- headroom displacement) (price <- displacement trunk), method(ml) cov(e.trunk*e.price) nolog

Endogenous variables

Observed:  trunk price

Exogenous variables

Observed:  headroom displacement

Structural equation model                       Number of obs      =        74
Estimation method  = ml
Log likelihood     = -1387.9682

-------------------------------------------------------------------------------------
                    |                 OIM
                    |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------------+----------------------------------------------------------------
Structural          |
  trunk <-          |
           headroom |    2.43531   .4478109     5.44   0.000     1.557617    3.313003
       displacement |   .0177031   .0041252     4.29   0.000     .0096179    .0257883
              _cons |   2.974509   1.238357     2.40   0.016     .5473744    5.401644
  ------------------+----------------------------------------------------------------
  price <-          |
              trunk |  -222.3396   172.1303    -1.29   0.196    -559.7088    115.0296
       displacement |   22.19871   5.946753     3.73   0.000     10.54329    33.85413
              _cons |   4844.184    1587.64     3.05   0.002     1732.467    7955.901
--------------------+----------------------------------------------------------------
        var(e.trunk)|   8.118382   1.334654                      5.882106    11.20485
        var(e.price)|    7113831    1491621                       4716550    1.07e+07
--------------------+----------------------------------------------------------------
cov(e.trunk,e.price)|    2689.37   1682.547     1.60   0.110    -608.3611    5987.101
-------------------------------------------------------------------------------------
Note: The LR test of model vs. saturated is not reported because the fitted
      model is not full rank.

.

I had to include displacement in the trunk equation (which ivregress is also doing, right?) and then let the residuals for trunk and price be correlated. The only thing that worries me is the note at the end. But the numbers all seem fine (indeed, if you use liml with ivregress, the numbers match perfectly.)

[Roman Mostazir]

Thank you so much Richard for the correct codes. It's been a great help.

[Richard Williams]

You are welcome. It just annoys me that it says the fitted model is not full rank. As far as I can tell, the model is just identified/saturated, and the LR stat should be zero. If you do estat resid, all the residuals are zero.

FYI, a very good book on sem is http://www.stata.com/bookstore/disco...g-using-stata/

[Roman Mostazir]

Thank you Richard, I actually just got the hold of the book and skimming through. But that help was something I needed now to understand the mechanism.

Best.

[Roman Mostazir]

I have one more question regarding SEM. I know I can use the SEM GUI chart builder for my model and estimate and copy the chart to my document. Is there any way to get the chart through commands in .do file as we get "marginsplot" after "margins" command?

[Richard Williams]

If you are asking, can syntax generate the diagram, rather than the other way around -- as far as I know, the answer is no,

[Roman Mostazir]

Thanks again Richard, at least I now know it and will not waste my time to search for it.

[Henry Kohlsdorf]

Hi all:

Sorry for re-opening this old thread. I was wondering why "displacement" must also be included in the equation predicting "trunk" in Richard's post from 30 Jan 2015? This is really just a question about understanding what is going on "under the hood" of 2SLS. Thank you!

[Joro Kolev]

This is what 2SLS does, it models the endogenous right hand side variable as a function of all exogenous variables (both included exogenous, and excluded instruments).

It needs to be done this way to get consistent estimates in fully simultaneous systems.

It does not need to be done this way in triangular systems.

Hi all:

Sorry for re-opening this old thread. I was wondering why "displacement" must also be included in the equation predicting "trunk" in Richard's post from 30 Jan 2015? This is really just a question about understanding what is going on "under the hood" of 2SLS. Thank you!

[Joro Kolev]

Also to straighten the record, because one might conclude false equivalences here. (Everything that Richard Williams said is correct, he even hinted at what I am saying next but did not really spell it out).

1. The correct equivalence is that -sem- applied on triangular systems gives you numerically the same results as -ivregress liml-, if you do like LIML does and include all exogenous variables in the equation for the endogenous right hand side variable (just like Richard did above).

2. Only in exactly identified triangular systems is -sem- equivalent to -ivregress 2sls- and equivalent to -ivregress liml-.