Help! Unexpected impact of controlling an omitted variable

Hi everyone,

I'm estimating production function using firm-level panel data (6 years) to obtain firms' productivity. To illustrate, please have a look at the following code and results:

Code:

 reg log_output log_labor log_capital log_materials 

      Source |       SS           df       MS      Number of obs   =    77,674
-------------+----------------------------------   F(3, 77670)     >  99999.00
       Model |  232153.056         3   77384.352   Prob > F        =    0.0000
    Residual |  14296.2403    77,670  .184063864   R-squared       =    0.9420
-------------+----------------------------------   Adj R-squared   =    0.9420
       Total |  246449.296    77,673  3.17290817   Root MSE        =    .42903

-------------------------------------------------------------------------------
   log_output |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
    log_labor |   .2786241   .0016469   169.18   0.000     .2753962    .2818521
  log_capital |   .1249548   .0011086   112.72   0.000      .122782    .1271276
log_materials |   .6145012   .0010075   609.93   0.000     .6125266    .6164759
        _cons |   2.023493   .0077761   260.22   0.000     2.008252    2.038734
-------------------------------------------------------------------------------

One of my concerns is the problem of so-called firm attrition or selection bias: firm with too low capital stock or output (thus, profit) will leave the market, make the data truncated because they show only survivals.
I can generate a dummy variable (exit_dummy), it equals 1 if a firm survive through 6 years of panel data, equals 0 if they exit during those years.
Because exit_dummy is negatively related to all current independent variables, especially log of capital, as you can see from here:

Code:

. corr exit_dummy log_labor log_capital log_materials
(obs=77,677)

             | exit_d~y log_la~r log_ca~l log_ma~s
-------------+------------------------------------
  exit_dummy |   1.0000
   log_labor |  -0.0668   1.0000
 log_capital |  -0.0918   0.6461   1.0000
log_materi~s |  -0.0732   0.5564   0.6777   1.0000

Hence, I expect that inputs, especially log of capital, is downwards biased without taking "exit_dummy" into account.

Now I add exit_dummy to the regression, and this is the results:

Code:

reg log_output log_labor log_capital log_materials exit_dummy 

      Source |       SS           df       MS      Number of obs   =    77,674
-------------+----------------------------------   F(4, 77669)     >  99999.00
       Model |   232160.76         4  58040.1901   Prob > F        =    0.0000
    Residual |  14288.5358    77,669  .183967038   R-squared       =    0.9420
-------------+----------------------------------   Adj R-squared   =    0.9420
       Total |  246449.296    77,673  3.17290817   Root MSE        =    .42891

-------------------------------------------------------------------------------
   log_output |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
    log_labor |   .2785518   .0016465   169.18   0.000     .2753246     .281779
  log_capital |   .1246052   .0011096   112.30   0.000     .1224304    .1267799
log_materials |   .6144147   .0010073   609.96   0.000     .6124404     .616389
   exit_dummy |   -.054435   .0084116    -6.47   0.000    -.0709217   -.0379483
        _cons |   2.029817   .0078352   259.06   0.000      2.01446    2.045174
-------------------------------------------------------------------------------

What you can see is all estimators of inputs decrease slightly after exit_dummy included, which is contrast to the prediction from theory (they should increase after including a explanatory variable that is negatively correlated to other explanatory variables).
Given that, I don't intend to put exit_dummy into this regression to control selection bias, I use another method which uses exit_dummy in a multi-stage regression, I also obatain the unexpted results after controlling selection bias, so I use this simple example (based on my dataset) to show the same kind of unexpected results for my case.

Anyone can please help me make sense out of this unexpected results?
Thanks a lot in advance.