SEM equivalence between long and wide panel data

[Ariel Karlinsky]

Hi all,

I'm trying to estimate a simple auto-regressive model with SEM command, using both long and wide data formats, but I can't seem to get it to be identical as I think it should be.

Here's a simple code, where I use the web-data of nlswork, limiting it to only 3 years of data (1968 to 1970):

clear all
webuse nlswork, clear
keep idcode year ln_wage
keep if year <= 70

* SEM in long format
sem (ln_wage <- l1.ln_wage)

* SEM in wide format
reshape wide ln_wage, i(idcode) j(year)
sem (ln_wage68@lag _cons@cons -> ln_wage69, ) (ln_wage69@lag _cons@cons -> ln_wage70, ) , /// 
var(e.ln_wage69@E e.ln_wage70@E) nocapslatent

In the wide format I need to be more explicit in constraining some of the paramters to be equal (I think). For that I constrained the AR coefficients to be identical (lag), the intercepts to be identical (cons) and the error terms to be identical (E).

Here's the output, very similar coefficients but not identical:

long:

Endogenous variables
  Observed: ln_wage

Exogenous variables
  Observed: L.ln_wage

Fitting target model:
Iteration 0:   log likelihood = -794.93331  
Iteration 1:   log likelihood = -794.93331  

Structural equation model                                Number of obs = 1,852
Estimation method: ml

Log likelihood = -794.93331

-------------------------------------------------------------------------------
              |                 OIM
              | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
--------------+----------------------------------------------------------------
Structural    |
  ln_wage     |
      ln_wage |
          L1. |   .7021511   .0160968    43.62   0.000      .670602    .7337002
        _cons |   .5145363   .0251871    20.43   0.000     .4651705    .5639021
--------------+----------------------------------------------------------------
var(e.ln_wage)|   .0623013   .0020473                      .0584151    .0664461
-------------------------------------------------------------------------------
LR test of model vs. saturated: chi2(0) = 0.00                  Prob > chi2 = .

wide

(1513 observations with missing values excluded)

Endogenous variables
  Observed: ln_wage69 ln_wage70

Exogenous variables
  Observed: ln_wage68

Fitting target model:
Iteration 0:   log likelihood = -261.74268  
Iteration 1:   log likelihood = -260.83664  
Iteration 2:   log likelihood = -260.83456  
Iteration 3:   log likelihood = -260.83456  

Structural equation model                                  Number of obs = 719
Estimation method: ml

Log likelihood = -260.83456

 ( 1)  - [ln_wage69]ln_wage68 + [ln_wage70]ln_wage69 = 0
 ( 2)  [/]var(e.ln_wage69) - [/]var(e.ln_wage70) = 0
 ( 3)  [ln_wage69]_cons - [ln_wage70]_cons = 0
---------------------------------------------------------------------------------
                |                 OIM
                | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
----------------+----------------------------------------------------------------
Structural      |
  ln_wage69     |
      ln_wage68 |   .6771415   .0183876    36.83   0.000     .6411025    .7131806
          _cons |   .5610107   .0293061    19.14   0.000     .5035719    .6184496
  --------------+----------------------------------------------------------------
  ln_wage70     |
      ln_wage69 |   .6771415   .0183876    36.83   0.000     .6411025    .7131806
          _cons |   .5610107   .0293061    19.14   0.000     .5035719    .6184496
----------------+----------------------------------------------------------------
var(e.ln_wage69)|   .0578137   .0021561                      .0537386    .0621979
var(e.ln_wage70)|   .0578137   .0021561                      .0537386    .0621979
---------------------------------------------------------------------------------
LR test of model vs. saturated: chi2(4) = 97.42              Prob > chi2 = 0.0000

Any guidance would be greatly appreciated!

[Jeff Pitblado (StataCorp)]

The panels in this dataset are not balanced.
If you drop the panels with < 3 observations, the results will match.

[Ariel Karlinsky]

Thanks!

[Cassidy Perez]

Hi,

I have a question regarding using mediation analysis in Stata, with panel data, in the format country year (128 countries for 16 years).


Name of the variables ( Y - dependent variable; M- Mediator; X - Independent Variable)

Y - v2x_polyarchy; M - l.v2xcs_ccsi; X - l.CSOdisbursementsSector150_pc

sem (l.v2xcs_ccsi <- l.CSOdisbursementsSector150_pc l.CSOdisbAllSectorsexclgov_pc l.totaldisbursementsexclCSO_pc l.log_GDPpc l.v2clrspct l.conflict)(v2x_polyarchy <- l.v2xcs_ccsi l.CSOdisbursementsSector150_pc l.CSOdisbAllSectorsexclgov_pc l.totaldisbursementsexclCSO_pc l.log_GDPpc l.v2clrspct l.conflict), nocapslatent

estat teffects


Our question: Is it appropriate to use sem, with our panel data (country year? If not do you have any alternative options?


However, we are getting weird results; we didnt expect that the direct effect is negative. Can you help us with interpretation?

Mediator: Core Civil Society Index
	Total Effect	Direct Effect	Indirect Effect
CSO democracy assistance p.c	0.005* (0.002)	-0.005*** (0.001)	0.01*** (0.002)[CHK1]