[Taka Sakamoto]

Does this work?

[Erik Ruzek]

Hi Taka. Provided that your data is wide and you have a separate lag variable, then yes, this is how you would include it in the SEM. It seems to be working as expected given the reduction in the path coefficients from post #13 above to the model you attached in post #14.

[Taka Sakamoto]

Dear Erik:

Thank you so much for reaching out. So, it's just a box of a lagged dependent variable, which is connected to the dependent variable by an arrow? The sem result without the lagged dependent variable is attached to this message.

Thank you again for your kind help.

Best,

Taka


SEM_4.stsem

[Taka Sakamoto]

I am also attaching the sem results.

Thank you!

. sem (sme -> koenpov50disposable, ) (sme -> gfcfgrow, ) (sme -> hfcegrow, ) (sme -> gdpgrow, ) (koenpov50dispo
> sable -> gfcfgrow, ) (koenpov50disposable -> hfcegrow, ) (koenpov50disposable -> gdpgrow, ) (gfcfgrow -> gdpg
> row, ) (hfcegrow -> gdpgrow, ) (glag -> gdpgrow, ) if id~=10, vce(cluster id) cov( e.hfcegrow*e.gfcfgrow) noc
> apslatent
(1335 observations with missing values excluded)

Endogenous variables
  Observed: koenpov50disposable gfcfgrow hfcegrow gdpgrow

Exogenous variables
  Observed: sme glag

Fitting target model:
Iteration 0:  Log pseudolikelihood = -2262.6426  (not concave)
Iteration 1:  Log pseudolikelihood = -2262.4895  (not concave)
Iteration 2:  Log pseudolikelihood =  -2259.847  (not concave)
Iteration 3:  Log pseudolikelihood = -2257.1386  (not concave)
Iteration 4:  Log pseudolikelihood = -2256.0635  (not concave)
Iteration 5:  Log pseudolikelihood = -2255.5181  (not concave)
Iteration 6:  Log pseudolikelihood = -2254.1203  (not concave)
Iteration 7:  Log pseudolikelihood = -2253.3798  (not concave)
Iteration 8:  Log pseudolikelihood = -2252.7327  (not concave)
Iteration 9:  Log pseudolikelihood = -2252.3961  (not concave)
Iteration 10: Log pseudolikelihood = -2250.8392  (not concave)
Iteration 11: Log pseudolikelihood = -2248.7603  (not concave)
Iteration 12: Log pseudolikelihood = -2248.3286  (not concave)
Iteration 13: Log pseudolikelihood = -2247.9495  (not concave)
Iteration 14: Log pseudolikelihood = -2247.6572  (not concave)
Iteration 15: Log pseudolikelihood = -2247.3977  (not concave)
Iteration 16: Log pseudolikelihood = -2247.1616  (not concave)
Iteration 17: Log pseudolikelihood = -2246.9071  (not concave)
Iteration 18: Log pseudolikelihood = -2246.4795  (not concave)
Iteration 19: Log pseudolikelihood = -2245.7546  (not concave)
Iteration 20: Log pseudolikelihood = -2245.1134  (not concave)
Iteration 21: Log pseudolikelihood = -2192.9761  (not concave)
Iteration 22: Log pseudolikelihood = -2185.5261  (not concave)
Iteration 23: Log pseudolikelihood = -2184.5722  (not concave)
Iteration 24: Log pseudolikelihood = -2183.1804  (not concave)
Iteration 25: Log pseudolikelihood = -2182.1387  (not concave)
Iteration 26: Log pseudolikelihood = -2181.6071  (not concave)
Iteration 27: Log pseudolikelihood = -2181.0636  (not concave)
Iteration 28: Log pseudolikelihood = -2180.5443  (not concave)
Iteration 29: Log pseudolikelihood = -2180.0301  (not concave)
Iteration 30: Log pseudolikelihood = -2179.5082  (not concave)
Iteration 31: Log pseudolikelihood = -2178.9891  (not concave)
Iteration 32: Log pseudolikelihood = -2178.4754  (not concave)
Iteration 33: Log pseudolikelihood = -2177.9604  (not concave)
Iteration 34: Log pseudolikelihood = -2177.4429  (not concave)
Iteration 35: Log pseudolikelihood = -2176.9259  (not concave)
Iteration 36: Log pseudolikelihood = -2176.4092  (not concave)
Iteration 37: Log pseudolikelihood = -2175.8914  (not concave)
Iteration 38: Log pseudolikelihood = -2175.3724  (not concave)
Iteration 39: Log pseudolikelihood = -2174.8527  (not concave)
Iteration 40: Log pseudolikelihood = -2174.3321  (not concave)
Iteration 41: Log pseudolikelihood = -2173.8102  (not concave)
Iteration 42: Log pseudolikelihood = -2173.2871  (not concave)
Iteration 43: Log pseudolikelihood = -2172.7626  (not concave)
Iteration 44: Log pseudolikelihood = -2172.2367  (not concave)
Iteration 45: Log pseudolikelihood = -2171.7092  (not concave)
Iteration 46: Log pseudolikelihood =   -2171.18  (not concave)
Iteration 47: Log pseudolikelihood = -2170.6492  (not concave)
Iteration 48: Log pseudolikelihood = -2170.1165  (not concave)
Iteration 49: Log pseudolikelihood = -2169.5818  (not concave)
Iteration 50: Log pseudolikelihood = -2169.0452  (not concave)
Iteration 51: Log pseudolikelihood = -2168.5064  (not concave)
Iteration 52: Log pseudolikelihood = -2167.9655  (not concave)
Iteration 53: Log pseudolikelihood = -2167.4223  (not concave)
Iteration 54: Log pseudolikelihood = -2166.8768  (not concave)
Iteration 55: Log pseudolikelihood = -2166.3288  (not concave)
Iteration 56: Log pseudolikelihood = -2165.7783  (not concave)
Iteration 57: Log pseudolikelihood = -2165.2252  (not concave)
Iteration 58: Log pseudolikelihood = -2164.6695  (not concave)
Iteration 59: Log pseudolikelihood =  -2164.111  (not concave)
Iteration 60: Log pseudolikelihood = -2163.5497  (not concave)
Iteration 61: Log pseudolikelihood = -2162.9856  (not concave)
Iteration 62: Log pseudolikelihood = -2162.4185  (not concave)
Iteration 63: Log pseudolikelihood = -2161.8485  (not concave)
Iteration 64: Log pseudolikelihood = -2161.2754  (not concave)
Iteration 65: Log pseudolikelihood = -2160.6991  (not concave)
Iteration 66: Log pseudolikelihood = -2160.1198  (not concave)
Iteration 67: Log pseudolikelihood = -2159.5372  (not concave)
Iteration 68: Log pseudolikelihood = -2158.9514  (not concave)
Iteration 69: Log pseudolikelihood = -2158.3623  (not concave)
Iteration 70: Log pseudolikelihood = -2157.7699  (not concave)
Iteration 71: Log pseudolikelihood = -2157.1741  (not concave)
Iteration 72: Log pseudolikelihood = -2156.5749  (not concave)
Iteration 73: Log pseudolikelihood = -2155.9724  (not concave)
Iteration 74: Log pseudolikelihood = -2155.3664  (not concave)
Iteration 75: Log pseudolikelihood =  -2154.757  (not concave)
Iteration 76: Log pseudolikelihood = -2154.1442  (not concave)
Iteration 77: Log pseudolikelihood =  -2153.528  (not concave)
Iteration 78: Log pseudolikelihood = -2152.9084  (not concave)
Iteration 79: Log pseudolikelihood = -2152.2854  (not concave)
Iteration 80: Log pseudolikelihood =  -2151.659  (not concave)
Iteration 81: Log pseudolikelihood = -2151.0292  (not concave)
Iteration 82: Log pseudolikelihood = -2150.3962  (not concave)
Iteration 83: Log pseudolikelihood = -2149.7599  (not concave)
Iteration 84: Log pseudolikelihood = -2149.1205  (not concave)
Iteration 85: Log pseudolikelihood = -2148.4779  (not concave)
Iteration 86: Log pseudolikelihood = -2147.8323  (not concave)
Iteration 87: Log pseudolikelihood = -2147.1838  (not concave)
Iteration 88: Log pseudolikelihood = -2146.5324  (not concave)
Iteration 89: Log pseudolikelihood = -2145.8783  (not concave)
Iteration 90: Log pseudolikelihood = -2145.2216  (not concave)
Iteration 91: Log pseudolikelihood = -2144.5625  (not concave)
Iteration 92: Log pseudolikelihood =  -2143.901  (not concave)
Iteration 93: Log pseudolikelihood = -2143.2374  (not concave)
Iteration 94: Log pseudolikelihood = -2142.5718  (not concave)
Iteration 95: Log pseudolikelihood = -2141.9044  (not concave)
Iteration 96: Log pseudolikelihood = -2141.2355  (not concave)
Iteration 97: Log pseudolikelihood = -2140.5652  (not concave)
Iteration 98: Log pseudolikelihood = -2139.8937  (not concave)
Iteration 99: Log pseudolikelihood = -2139.2214  (not concave)
Iteration 100: Log pseudolikelihood = -2138.5484  (not concave)
Iteration 101: Log pseudolikelihood = -2137.8751  (not concave)
Iteration 102: Log pseudolikelihood = -2137.2016  (not concave)
Iteration 103: Log pseudolikelihood = -2136.5284  (not concave)
Iteration 104: Log pseudolikelihood = -2135.8556  (not concave)
Iteration 105: Log pseudolikelihood = -2135.1836  (not concave)
Iteration 106: Log pseudolikelihood = -2134.5126  (not concave)
Iteration 107: Log pseudolikelihood = -2133.8431  (not concave)
Iteration 108: Log pseudolikelihood = -2133.1752  (not concave)
Iteration 109: Log pseudolikelihood = -2132.5094  (not concave)
Iteration 110: Log pseudolikelihood = -2131.8458  (not concave)
Iteration 111: Log pseudolikelihood = -2131.1849  (not concave)
Iteration 112: Log pseudolikelihood = -2130.5268  (not concave)
Iteration 113: Log pseudolikelihood = -2129.8719  (not concave)
Iteration 114: Log pseudolikelihood = -2129.2204  (not concave)
Iteration 115: Log pseudolikelihood = -2128.5725  (not concave)
Iteration 116: Log pseudolikelihood = -2127.9285  (not concave)
Iteration 117: Log pseudolikelihood = -2127.2885  (not concave)
Iteration 118: Log pseudolikelihood = -2126.6528  (not concave)
Iteration 119: Log pseudolikelihood = -2126.0215  (not concave)
Iteration 120: Log pseudolikelihood = -2125.3946  (not concave)
Iteration 121: Log pseudolikelihood = -2124.7723  (not concave)
Iteration 122: Log pseudolikelihood = -2124.1547  (not concave)
Iteration 123: Log pseudolikelihood = -2123.5416  (not concave)
Iteration 124: Log pseudolikelihood = -2122.9332  (not concave)
Iteration 125: Log pseudolikelihood = -2122.3295  (not concave)
Iteration 126: Log pseudolikelihood = -2121.7302  (not concave)
Iteration 127: Log pseudolikelihood = -2121.1355  (not concave)
Iteration 128: Log pseudolikelihood = -2120.5451  (not concave)
Iteration 129: Log pseudolikelihood = -2119.9589  (not concave)
Iteration 130: Log pseudolikelihood = -2119.3768  (not concave)
Iteration 131: Log pseudolikelihood = -2118.7987  (not concave)
Iteration 132: Log pseudolikelihood = -2118.2245  (not concave)
Iteration 133: Log pseudolikelihood = -2117.6538  
Iteration 134: Log pseudolikelihood = -2083.5987  (backed up)
Iteration 135: Log pseudolikelihood = -2069.5068  
Iteration 136: Log pseudolikelihood = -2066.4491  
Iteration 137: Log pseudolikelihood = -2066.4102  
Iteration 138: Log pseudolikelihood = -2066.4101  

Structural equation model                                  Number of obs = 177
Estimation method: ml

Log pseudolikelihood = -2066.4101

                                                 (Std. err. adjusted for 19 clusters in id)
-------------------------------------------------------------------------------------------
                          |               Robust
                          | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
--------------------------+----------------------------------------------------------------
Structural                |
  koenpov50disposable     |
                      sme |  -5.822986   .8712099    -6.68   0.000    -7.530526   -4.115446
                    _cons |   13.03499   .8077138    16.14   0.000      11.4519    14.61808
  ------------------------+----------------------------------------------------------------
  gfcfgrow                |
      koenpov50disposable |   -.333957   .1269714    -2.63   0.009    -.5828164   -.0850975
                      sme |  -2.566266   1.239707    -2.07   0.038    -4.996046   -.1364859
                    _cons |   7.488948   1.989902     3.76   0.000     3.588812    11.38908
  ------------------------+----------------------------------------------------------------
  hfcegrow                |
      koenpov50disposable |  -.2413382   .0949944    -2.54   0.011    -.4275237   -.0551527
                      sme |  -1.814667   .6257952    -2.90   0.004    -3.041203   -.5881313
                    _cons |   5.684201   1.191705     4.77   0.000     3.348501      8.0199
  ------------------------+----------------------------------------------------------------
  gdpgrow                 |
      koenpov50disposable |   .0080278   .0358674     0.22   0.823    -.0622711    .0783267
                 gfcfgrow |   .1493272   .0390934     3.82   0.000     .0727056    .2259489
                 hfcegrow |   .4479617   .0838816     5.34   0.000     .2835568    .6123665
                      sme |   .7827605   .3281325     2.39   0.017     .1396326    1.425889
                     glag |   .0819549   .0497431     1.65   0.099    -.0155398    .1794496
                    _cons |  -.1974798   .6302928    -0.31   0.754    -1.432831    1.037871
--------------------------+----------------------------------------------------------------
var(e.koenpov50disposable)|   3.719823   .9241743                      2.285835    6.053405
           var(e.gfcfgrow)|   30.25573   6.205864                      20.24019     45.2273
           var(e.hfcegrow)|   3.572638   .4817815                      2.742848    4.653463
            var(e.gdpgrow)|   1.308238   .2180295                       .943684    1.813624
--------------------------+----------------------------------------------------------------
cov(e.gfcfgrow,e.hfcegrow)|   5.959297   1.093574     5.45   0.000     3.815932    8.102663
-------------------------------------------------------------------------------------------
.

[Taka Sakamoto]

Dear Erik:

This is the sem result without the lagged dependent variable.

[Erik Ruzek]

This is helpful, Taka. The lagged variable (glag) does not strongly predict gpdgrow. You can see that the coefficients for the other variables going into gpdgrow are quite similar across the two models. This is a bit unexpected to me. In my world (education and psychology), lags tend to be powerful predictors of their next sequentially observed occasion. However, I do not know your topic area. Perhaps GDP growth in year 1 is not strongly related to GDP growth in year 2. You will have to rely on your expertise to sort this out.

[Taka Sakamoto]

Thank you, Erik. I'm glad that I now know how to model a lagged dependent variable in sem, thanks to you.

And thank you also for noticing the results about the lagged dependent variable. I have to look into it. I attach the results of simple regression results here. Though it's oversimple, the results seem to be in line with the sem results.

Thank you again for your help.

Best,

Taka

. reg gdpgrow glag gfcfgrow hfcegrow sme koenpov50disposable if id~=10 & year>1974,vce(cl id)

Linear regression                               Number of obs     =        174
                                                F(5, 18)          =      48.87
                                                Prob > F          =     0.0000
                                                R-squared         =     0.6602
                                                Root MSE          =     1.1497

                                           (Std. err. adjusted for 19 clusters in id)
-------------------------------------------------------------------------------------
                    |               Robust
            gdpgrow | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
--------------------+----------------------------------------------------------------
               glag |   .0949109   .0538594     1.76   0.095    -.0182435    .2080654
           gfcfgrow |   .1512483   .0421274     3.59   0.002     .0627419    .2397547
           hfcegrow |   .4151266   .0878155     4.73   0.000     .2306331    .5996202
                sme |   .6291386   .3505369     1.79   0.089    -.1073121    1.365589
koenpov50disposable |    -.00512   .0376068    -0.14   0.893    -.0841288    .0738889
              _cons |   .0789032   .6710112     0.12   0.908    -1.330839    1.488645
-------------------------------------------------------------------------------------

[Taka Sakamoto]

And annual GDP growth looks like this in affluent countries.