Change of sign on coefficient and and r squared when supressing constant. How to interpret the results?

[Mark Baskett]

Hi

I am trying to estimate a system of equations concerning the effect of FDI on Business cycle synchronisation.

The system is as follows.

(Business Synchronization) _{i j} = (Trade Intensity)_{i j} + (FDI Intensity)_{i j} + (Structural Dissimilarity) + Z_{1i j} + u _{i j}

(FDI Intensity)_{i j} = (Trade Intensity)_{i j} +(Structural Dissimilarity)_{i j} + Z2_{i j} + u _{i j}

(Trade Intensity) _{i j} = (FDI Intensity)_{i j} + (Structural Dissimilarity)_{i j} +Z_{3 i j} +u _ij

(Structual Dissimilarity) _{i j} = (FDI Intensity)_{i j} +(Trade Intensity)_{i j} + Z4 _{I J} +u _{i j}

Where i denotes country I . j denotes country j. Z Denotes exogenous determinants of the dependent variable for that equation


When I don't suppress the constant, here is the STATA output using three stage least squares estimator

Three-stage least-squares regression
----------------------------------------------------------------------
Equation          Obs  Parms        RMSE    "R-sq"       chi2        P
----------------------------------------------------------------------
synch             183      4    .0233448    0.2415     111.42   0.0000
fdi               183      4    .0397629    0.2064     158.99   0.0000
trade             183      4     .024307    0.4589     446.22   0.0000
dissim            183      4    .1277664    0.4433     276.77   0.0000
----------------------------------------------------------------------

----------------------------------------------------------------------------------
                 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-----------------+----------------------------------------------------------------
synch            |
           trade |   .3203797   .1389368     2.31   0.021     .0480685    .5926909
             fdi |   .1204827   .0971815     1.24   0.215    -.0699895    .3109549
          dissim |   .0359573   .0156557     2.30   0.022     .0052726     .066642
            euro |   .0305018   .0059332     5.14   0.000      .018873    .0421306
           _cons |  -.0918088   .0071617   -12.82   0.000    -.1058456   -.0777721
-----------------+----------------------------------------------------------------
fdi              |
           trade |   1.519969   .1435987    10.58   0.000     1.238521    1.801417
          dissim |   .0828209   .0245547     3.37   0.001     .0346944    .1309473
          border |     -.0434   .0120242    -3.61   0.000    -.0669669    -.019833
            euro |  -.0008237   .0042045    -0.20   0.845    -.0090643     .007417
           _cons |  -.0327858   .0113729    -2.88   0.004    -.0550763   -.0104953
-----------------+----------------------------------------------------------------
trade            |
             fdi |   .5812198   .0360878    16.11   0.000     .5104889    .6519506
          dissim |  -.0639277   .0115948    -5.51   0.000    -.0866531   -.0412024
          border |    .025972   .0053825     4.83   0.000     .0154225    .0365215
     logdistance |  -.0068376   .0013158    -5.20   0.000    -.0094165   -.0042587
           _cons |   .0509309   .0066589     7.65   0.000     .0378797     .063982
-----------------+----------------------------------------------------------------
dissim           |
           trade |   1.568267   .9418691     1.67   0.096    -.2777621    3.414297
             fdi |  -2.857465   .9470738    -3.02   0.003    -4.713695   -1.001234
          gdpgap |   .2480874   .0182323    13.61   0.000     .2123528     .283822
loggdpcapitaprod |   .4634245   .0879656     5.27   0.000      .291015     .635834
           _cons |  -4.171305   .8046478    -5.18   0.000    -5.748385   -2.594224
----------------------------------------------------------------------------------
Endogenous variables:  synch trade fdi dissim
Exogenous variables:   logdistance loggdpcapitaprod gdpgap loggdpprod euro
     lang landlocked border logfreedom
------------------------------------------------------------------------------

When I suppress the constant here is the output.

----------------------------------------------------------------------
Equation          Obs  Parms        RMSE    "R-sq"       chi2        P
----------------------------------------------------------------------
synch             183      4    .0475851    0.5097     552.74   0.0000
fdi               183      4    .0377404    0.5349     400.96   0.0000
trade             183      4    .0285063    0.5361     578.89   0.0000
dissim            183      4     .167015    0.8399    1957.54   0.0000
----------------------------------------------------------------------

----------------------------------------------------------------------------------
                 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-----------------+----------------------------------------------------------------
synch            |
           trade |  -1.290544   .1589516    -8.12   0.000    -1.602084    -.979005
             fdi |   .9583024   .1368436     7.00   0.000     .6900939    1.226511
          dissim |  -.1607618   .0085147   -18.88   0.000    -.1774502   -.1440734
            euro |   .0361279   .0072658     4.97   0.000     .0218871    .0503687
-----------------+----------------------------------------------------------------
fdi              |
           trade |   1.202404   .0902235    13.33   0.000     1.025569    1.379239
          dissim |   .0144295   .0075185     1.92   0.055    -.0003066    .0291656
          border |  -.0109175   .0093866    -1.16   0.245     -.029315    .0074799
            euro |    .006046   .0043691     1.38   0.166    -.0025172    .0146093
-----------------+----------------------------------------------------------------
trade            |
             fdi |   .7297148   .0377461    19.33   0.000     .6557339    .8036958
          dissim |  -.0347674   .0072208    -4.81   0.000    -.0489199   -.0206149
          border |   .0131548   .0052226     2.52   0.012     .0029188    .0233909
     logdistance |   .0036213   .0006443     5.62   0.000     .0023585    .0048842
-----------------+----------------------------------------------------------------
dissim           |
           trade |  -5.162866   .5351785    -9.65   0.000    -6.211796   -4.113935
             fdi |   3.246299    .435652     7.45   0.000     2.392437    4.100161
          gdpgap |   .1619648   .0152134    10.65   0.000     .1321472    .1917824
loggdpcapitaprod |   .0181678   .0029277     6.21   0.000     .0124296     .023906
----------------------------------------------------------------------------------
Endogenous variables:  synch trade fdi dissim
Exogenous variables:   logdistance loggdpcapitaprod gdpgap loggdpprod euro
     lang landlocked border logfreedom
------------------------------------------------------------------------------

As can be seen, when suppressing the constant for each equation, R squared seems to increase for each equation and a number of variables become more significant. However, the coefficient for trade becomes negative. This however goes against what economic theory predicts. Theory would predict that countries that have high trade intensity would be suspect to business cycle synchronisation.

Should I thus suppress the constant and go with the model with the higher r squared and more significant variables or should I go with what the theory predicts?

Thanks

Mark