Stata Command: including interaction terms of the endogenous variable in 2SLS using xtivreg

Zhenghan Zhang

Join Date: May 2023
Posts: 2

Stata Command: including interaction terms of the endogenous variable in 2SLS using xtivreg

22 May 2023, 01:04

Hi,

I am wondering if anyone had any experience in including an interaction term in 2SLS using xtivreg?

I am now having a successful 2SLS, not including any interaction terms as follows:

Code:

xtivreg PatMV_real_log Lev CAPX_AT Size rd_log sale_log number_log (inverse_D = toughness_normalized) i.fyear, fe

inverse_D is the endogenous variable and toughness is the instrumental variable

This is successful, and I have the results like this:

Code:

Fixed-effects (within) IV regression            Number of obs     =      5,066
Group variable: all_cluster                     Number of groups  =        554

R-squared:                                      Obs per group:
     Within  =      .                                         min =          1
     Between = 0.2823                                         avg =        9.1
     Overall = 0.3891                                         max =         31

                                                Wald chi2(37)     =   19922.00
corr(u_i, Xb) = 0.0856                          Prob > chi2       =     0.0000

------------------------------------------------------------------------------
PatMV_real~g | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
   inverse_D |   13.87709   5.667382     2.45   0.014     2.769226    24.98496
         Lev |   .0032969   .0029638     1.11   0.266     -.002512    .0091058
     CAPX_AT |   1.526791   .6927957     2.20   0.028     .1689361    2.884645
        Size |   .0862929   .0621718     1.39   0.165    -.0355617    .2081474
      rd_log |   -.084102   .3179503    -0.26   0.791    -.7072731     .539069
    sale_log |   .1517564   .0322944     4.70   0.000     .0884605    .2150523
  number_log |   .0404435   .0334691     1.21   0.227    -.0251548    .1060417
             |
       fyear |
       1986  |  -.1775167    .298694    -0.59   0.552    -.7629462    .4079129
       1987  |  -.0519888   .3001776    -0.17   0.862    -.6403262    .5363485
       1988  |  -.0481431   .3076404    -0.16   0.876    -.6511073     .554821
       1989  |   .0163748   .2844115     0.06   0.954    -.5410614     .573811
       1990  |  -.0718744   .2990964    -0.24   0.810    -.6580925    .5143437
       1991  |  -.2075746   .3433348    -0.60   0.545    -.8804984    .4653492
       1992  |  -.2268283   .3502615    -0.65   0.517    -.9133282    .4596715
       1993  |   .1302594   .3597807     0.36   0.717    -.5748978    .8354166
       1994  |    .394627    .391701     1.01   0.314    -.3730928    1.162347
       1995  |  -.2333602   .4519216    -0.52   0.606     -1.11911    .6523898
       1996  |   .1275317   .4482286     0.28   0.776    -.7509803    1.006044
       1997  |  -.1892146     .55809    -0.34   0.735    -1.283051    .9046217
       1998  |  -.3070482   .5836953    -0.53   0.599     -1.45107    .8369736
       1999  |  -.6370051   .6263369    -1.02   0.309    -1.864603    .5905927
       2000  |  -.8418151   .6641659    -1.27   0.205    -2.143556    .4599261
       2001  |  -1.119607   .7252079    -1.54   0.123    -2.540988    .3017744
       2002  |  -1.545625   .8150542    -1.90   0.058    -3.143102    .0518518
       2003  |  -1.636655   .8022847    -2.04   0.041    -3.209104   -.0642054
       2004  |  -1.786408   .8443835    -2.12   0.034    -3.441369   -.1314466
       2005  |  -1.878826   .8648506    -2.17   0.030    -3.573902   -.1837496
       2006  |  -2.023935   .8749888    -2.31   0.021    -3.738882   -.3089884
       2007  |  -2.223262   .9041965    -2.46   0.014    -3.995455   -.4510695
       2008  |  -2.062127   .8859147    -2.33   0.020    -3.798488   -.3257664
       2009  |   -2.24123   .9245712    -2.42   0.015    -4.053357   -.4291043
       2010  |  -2.249556   .9657848    -2.33   0.020    -4.142459   -.3566523
       2011  |  -2.138431    .923046    -2.32   0.021    -3.947568   -.3292945
       2012  |  -2.460573   .9528901    -2.58   0.010    -4.328203    -.592943
       2013  |  -3.264231   .9082721    -3.59   0.000    -5.044412   -1.484051
       2014  |  -4.738765   .8172058    -5.80   0.000    -6.340459   -3.137071
       2015  |  -7.135273     .62943   -11.34   0.000    -8.368933   -5.901613
             |
       _cons |   1.398011    .499853     2.80   0.005     .4183173    2.377705
-------------+----------------------------------------------------------------
     sigma_u |  1.6160709
     sigma_e |  1.3406031
         rho |   .5923664   (fraction of variance due to u_i)
------------------------------------------------------------------------------
 F test that all u_i=0: F(553,4475) =     4.74            Prob > F    = 0.0000
------------------------------------------------------------------------------
Instrumented: inverse_D
 Instruments: Lev CAPX_AT Size rd_log sale_log number_log 1986.fyear
              1987.fyear 1988.fyear 1989.fyear 1990.fyear 1991.fyear
              1992.fyear 1993.fyear 1994.fyear 1995.fyear 1996.fyear
              1997.fyear 1998.fyear 1999.fyear 2000.fyear 2001.fyear
              2002.fyear 2003.fyear 2004.fyear 2005.fyear 2006.fyear
              2007.fyear 2008.fyear 2009.fyear 2010.fyear 2011.fyear
              2012.fyear 2013.fyear 2014.fyear 2015.fyear toughness_normalized

And now, I want to add an interaction term: log_analysts. I found that in previous posts that integrating interaction terms into a new variable is recommended, so I did:

Code:

gen int_log_analysts = c.inverse_D#c.log_analysts

gen int_log_analysts_iv = c.toughness_normalized#c.log_analysts

And then I suppose that my code should be:

Code:

xtivreg PatMV_real_log Lev CAPX_AT Size rd_log sale_log number_log log_analysts (inverse_D int_log_analysts= toughness_normalized int_log_analysts_iv) i.fyear, fe

I wonder if this is correct. In particular, I want to know if variable 'log_analysts' should exist outside the parenthesis, and more importantly: does this mean that I am using one instrumental variable 'toughness' on one endogenous variable 'inverse_D'? I was worried that this implies using 2 instruments on 2 endogenous variables, with 2x2 = 4 first stage estimations.

For more information, I am trying to mimic the code using ivreg2:

Code:

ivreg2 y w (x c.x#c.w= z c.z#c.w)

where w is the interaction term variable, x is the endogenous variable and z is the instrument. I don't know if it will be the same in xtivreg though. Any other suggestions or recommendations will be much appreciated.

Many Thanks,
Harry

Tags: None

Jeff Wooldridge

Join Date: Apr 2014

Posts: 2204
#2

22 May 2023, 17:17

Everything works the same with xtivreg. In fact, I think you can use factor notation now rather than having to define the interaction. One thing I would do is center the variable w (in the ivreg2 command) about its average before interacting it with x and z. That will make the coefficient on z in the first stage easier to interpret and, more importantly, force the coefficient on x to be the average partial effect.

You are correct that the w variable belongs outside the parentheses at it is an exogenous variable and acts as its own instrument.
Comment
Zhenghan Zhang

Join Date: May 2023

Posts: 2
#3

25 May 2023, 00:33

Originally posted by Jeff Wooldridge View Post

Everything works the same with xtivreg. In fact, I think you can use factor notation now rather than having to define the interaction. One thing I would do is center the variable w (in the ivreg2 command) about its average before interacting it with x and z. That will make the coefficient on z in the first stage easier to interpret and, more importantly, force the coefficient on x to be the average partial effect.

You are correct that the w variable belongs outside the parentheses at it is an exogenous variable and acts as its own instrument.

Hi Jeff,

Thanks for the reply! I'm currently using STATA 17.0 SE, and

Code:

. xtivreg PatMV_real_log Lev CAPX_AT Size rd_log sale_log number_log c.log_analysts ( > inverse_D c.inverse_D#c.log_analysts= toughness_normalized c.toughness_normalized#c > .log_analysts) i.fyear, fe depvars may not be interactions

Other than that things seemed to be working. Thanks a lot!
Comment

Paola Jaimes

Join Date: Jan 2021
Posts: 6

10 Jul 2023, 17:48

Hello!

I am currently conducting an analysis aimed at understanding the differential effects of my variable, ln_legal_ha, across two distinct regions: the overall region, and another region specifically within ZME zones (where zme_dummy = 1). In order to carry out this analysis, I have executed two separate 2SLS regression models, making use of the xtivreg2 command in Stata. This approach closely aligns with the model proposed in this ongoing discussion.

However, I have noticed differences in the Kleibergen-Paap rk Wald F statistic between these two models and I'm trying to discern what might be leading to these discrepancies. To my understanding, the Kleibergen-Paap rk Wald F statistic is utilized within the context of instrumental variable regression to test the null hypothesis that our instruments are weak, meaning that they are uncorrelated with the endogenous regressors. The interpretation of this statistic suggests that a larger value is indicative of stronger instruments. Therefore, the drop that I am witnessing in the statistic is a cause for concern.

Any guidance or insights on this matter would be greatly appreciated.

These are my results: ( I am using Stata 18)

Code:

 xtivreg2 ln_rate_displacement (ln_legal_ha = instrument2) terror coca_crop_ha year_dummy* , fe cluster(m
> un_code) first
Warning - collinearities detected
Vars dropped:       year_dummy21

FIXED EFFECTS ESTIMATION
------------------------
Number of groups =      1122                    Obs per group: min =        21
                                                               avg =      21.0
                                                               max =        21
Warning - collinearities detected
Vars dropped:  year_dummy21

First-stage regressions
-----------------------


FIXED EFFECTS ESTIMATION
------------------------
Number of groups =      1122                    Obs per group: min =        21
                                                               avg =      21.0
                                                               max =        21

First-stage regression of ln_legal_ha:

Statistics robust to heteroskedasticity and clustering on mun_code
Number of obs =                  23562
Number of clusters (mun_code) =   1122
------------------------------------------------------------------------------
             |               Robust
 ln_legal_ha | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
 instrument2 |    .613449   .0996371     6.16   0.000     .4181533    .8087447
      terror |   .0205875   .0252284     0.82   0.414    -.0288619    .0700368
coca_crop_ha |   .0000477   .0000297     1.60   0.109    -.0000106    .0001059
 year_dummy1 |  -.0292766   .0314515    -0.93   0.352    -.0909237    .0323706
 year_dummy2 |  -.0565373   .0299063    -1.89   0.059    -.1151557    .0020811
 year_dummy3 |  -.0914659   .0298665    -3.06   0.002    -.1500064   -.0329255
 year_dummy4 |  -.0789681   .0288944    -2.73   0.006    -.1356032    -.022333
 year_dummy5 |   -.073261    .027846    -2.63   0.009     -.127841   -.0186809
 year_dummy6 |  -.0994106   .0269124    -3.69   0.000    -.1521609   -.0466604
 year_dummy7 |  -.0522922   .0290662    -1.80   0.072    -.1092639    .0046796
 year_dummy8 |  -.0689375   .0301594    -2.29   0.022     -.128052    -.009823
 year_dummy9 |  -.0175844   .0295243    -0.60   0.551    -.0754541    .0402854
year_dummy10 |  -.0382615    .024036    -1.59   0.111    -.0853736    .0088507
year_dummy11 |  -.0832753   .0288057    -2.89   0.004    -.1397365   -.0268141
year_dummy12 |  -.0128858   .0278011    -0.46   0.643    -.0673778    .0416062
year_dummy13 |  -.0153934    .023063    -0.67   0.504    -.0605985    .0298116
year_dummy14 |  -.0005325   .0244218    -0.02   0.983     -.048401     .047336
year_dummy15 |  -.0400893   .0242562    -1.65   0.098     -.087633    .0074545
year_dummy16 |   .0378343   .0247247     1.53   0.126    -.0106278    .0862964
year_dummy17 |   .0916008   .0236791     3.87   0.000      .045188    .1380135
year_dummy18 |   .0131319    .020486     0.64   0.522    -.0270222    .0532859
year_dummy19 |   .0145469   .0183182     0.79   0.427    -.0213582    .0504519
year_dummy20 |  -.0399248   .0188167    -2.12   0.034    -.0768068   -.0030428
year_dummy21 |          0  (omitted)
------------------------------------------------------------------------------
F test of excluded instruments:
  F(  1,  1121) =    37.91
  Prob > F      =   0.0000
Sanderson-Windmeijer multivariate F test of excluded instruments:
  F(  1,  1121) =    37.91
  Prob > F      =   0.0000



Summary results for first-stage regressions
-------------------------------------------

                                           (Underid)            (Weak id)
Variable     | F(  1,  1121)  P-val | SW Chi-sq(  1) P-val | SW F(  1,  1121)
ln_legal_ha  |      37.91    0.0000 |       37.98   0.0000 |       37.91

NB: first-stage test statistics cluster-robust

Stock-Yogo weak ID F test critical values for single endogenous regressor:
                                   10% maximal IV size             16.38
                                   15% maximal IV size              8.96
                                   20% maximal IV size              6.66
                                   25% maximal IV size              5.53
Source: Stock-Yogo (2005).  Reproduced by permission.
NB: Critical values are for i.i.d. errors only.

Underidentification test
Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified)
Ha: matrix has rank=K1 (identified)
Kleibergen-Paap rk LM statistic          Chi-sq(1)=35.03    P-val=0.0000

Weak identification test
Ho: equation is weakly identified
Cragg-Donald Wald F statistic                                     982.44
Kleibergen-Paap Wald rk F statistic                                37.91

Stock-Yogo weak ID test critical values for K1=1 and L1=1:
                                   10% maximal IV size             16.38
                                   15% maximal IV size              8.96
                                   20% maximal IV size              6.66
                                   25% maximal IV size              5.53
Source: Stock-Yogo (2005).  Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.

Weak-instrument-robust inference
Tests of joint significance of endogenous regressors B1 in main equation
Ho: B1=0 and orthogonality conditions are valid
Anderson-Rubin Wald test           F(1,1121)=     72.07     P-val=0.0000
Anderson-Rubin Wald test           Chi-sq(1)=     72.21     P-val=0.0000
Stock-Wright LM S statistic        Chi-sq(1)=     64.74     P-val=0.0000

NB: Underidentification, weak identification and weak-identification-robust
    test statistics cluster-robust

Number of clusters             N_clust  =       1122
Number of observations               N  =      23562
Number of regressors                 K  =         23
Number of endogenous regressors      K1 =          1
Number of instruments                L  =         23
Number of excluded instruments       L1 =          1

IV (2SLS) estimation
--------------------

Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity and clustering on mun_code

Number of clusters (mun_code) =   1122                Number of obs =    23562
                                                      F( 23,  1121) =   106.44
                                                      Prob > F      =   0.0000
Total (centered) SS     =  120880.6954                Centered R2   =   0.1764
Total (uncentered) SS   =  120880.6954                Uncentered R2 =   0.1764
Residual SS             =  99557.80502                Root MSE      =    2.106

------------------------------------------------------------------------------
             |               Robust
ln_rate_di~t | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
 ln_legal_ha |   1.253122   .2381549     5.26   0.000      .786347    1.719897
      terror |   .4320092    .044179     9.78   0.000     .3454199    .5185985
coca_crop_ha |    .000149   .0000396     3.76   0.000     .0000714    .0002266
 year_dummy1 |   3.430221   .1247621    27.49   0.000     3.185692    3.674751
 year_dummy2 |   3.897132   .1231214    31.65   0.000     3.655819    4.138446
 year_dummy3 |   3.553965   .1264553    28.10   0.000     3.306117    3.801813
 year_dummy4 |   3.550806   .1183822    29.99   0.000     3.318781    3.782831
 year_dummy5 |   3.613434   .1148947    31.45   0.000     3.388244    3.838623
 year_dummy6 |   3.642814   .1135996    32.07   0.000     3.420163    3.865465
 year_dummy7 |    3.67309   .1084828    33.86   0.000     3.460467    3.885712
 year_dummy8 |   3.304358   .1058579    31.22   0.000     3.096881    3.511836
 year_dummy9 |   2.529605   .1000324    25.29   0.000     2.333546    2.725665
year_dummy10 |   1.795675   .0932082    19.27   0.000      1.61299     1.97836
year_dummy11 |   1.780305   .0963259    18.48   0.000      1.59151      1.9691
year_dummy12 |   1.925373   .0963339    19.99   0.000     1.736562    2.114184
year_dummy13 |   2.112034   .0930321    22.70   0.000     1.929695    2.294374
year_dummy14 |   2.060556   .0927674    22.21   0.000     1.878735    2.242376
year_dummy15 |   1.720606   .0924471    18.61   0.000     1.539413    1.901799
year_dummy16 |   1.129815   .0879648    12.84   0.000     .9574075    1.302223
year_dummy17 |   .5553081   .0830768     6.68   0.000     .3924805    .7181356
year_dummy18 |   .4999019   .0823196     6.07   0.000     .3385584    .6612453
year_dummy19 |   .0147657   .0736492     0.20   0.841     -.129584    .1591154
year_dummy20 |  -.4479701   .0763393    -5.87   0.000    -.5975924   -.2983479
year_dummy21 |          0  (omitted)
------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic):             35.025
                                                   Chi-sq(1) P-val =    0.0000
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic):              982.443
                         (Kleibergen-Paap rk Wald F statistic):         37.907
Stock-Yogo weak ID test critical values: 10% maximal IV size             16.38
                                         15% maximal IV size              8.96
                                         20% maximal IV size              6.66
                                         25% maximal IV size              5.53
Source: Stock-Yogo (2005).  Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
------------------------------------------------------------------------------
Hansen J statistic (overidentification test of all instruments):         0.000
                                                 (equation exactly identified)
------------------------------------------------------------------------------
Instrumented:         ln_legal_ha
Included instruments: terror coca_crop_ha year_dummy1 year_dummy2 year_dummy3
                      year_dummy4 year_dummy5 year_dummy6 year_dummy7
                      year_dummy8 year_dummy9 year_dummy10 year_dummy11
                      year_dummy12 year_dummy13 year_dummy14 year_dummy15
                      year_dummy16 year_dummy17 year_dummy18 year_dummy19
                      year_dummy20
Excluded instruments: instrument2
Dropped collinear:    year_dummy21
------------------------------------------------------------------------------

.
. // in zme zones
.
. gen instrument_zme = instrument2 * zme_dummy
(1 missing value generated)

. gen lnlegal_zme = ln_legal_ha * zme_dummy
(1 missing value generated)

.
. xtivreg2 ln_rate_displacement coca_crop_ha zme_dummy year_dummy* terror (ln_legal_ha lnlegal_zme = instr
> ument2 instrument_zme), fe cluster(mun_code) first
Warning - collinearities detected
Vars dropped:       zme_dummy year_dummy21

FIXED EFFECTS ESTIMATION
------------------------
Number of groups =      1122                    Obs per group: min =        21
                                                               avg =      21.0
                                                               max =        21
Warning - collinearities detected
Vars dropped:  zme_dummy year_dummy21

First-stage regressions
-----------------------


FIXED EFFECTS ESTIMATION
------------------------
Number of groups =      1122                    Obs per group: min =        21
                                                               avg =      21.0
                                                               max =        21

First-stage regression of ln_legal_ha:

Statistics robust to heteroskedasticity and clustering on mun_code
Number of obs =                  23562
Number of clusters (mun_code) =   1122
--------------------------------------------------------------------------------
               |               Robust
   ln_legal_ha | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
   instrument2 |   .4109556   .1040751     3.95   0.000     .2069612    .6149499
instrument_zme |   .6767629   .2380131     2.84   0.004     .2102406    1.143285
  coca_crop_ha |   .0000424   .0000286     1.48   0.138    -.0000137    .0000984
     zme_dummy |          0  (omitted)
   year_dummy1 |  -.0285822   .0314254    -0.91   0.363    -.0901782    .0330137
   year_dummy2 |  -.0557878    .029883    -1.87   0.062    -.1143605     .002785
   year_dummy3 |  -.0910839   .0298398    -3.05   0.002    -.1495719   -.0325958
   year_dummy4 |  -.0787427   .0288616    -2.73   0.006    -.1353134   -.0221721
   year_dummy5 |  -.0730655   .0278593    -2.62   0.009    -.1276717   -.0184593
   year_dummy6 |  -.0994101   .0269065    -3.69   0.000    -.1521488   -.0466714
   year_dummy7 |  -.0522725   .0290816    -1.80   0.072    -.1092743    .0047294
   year_dummy8 |  -.0690675   .0301716    -2.29   0.022    -.1282059    -.009929
   year_dummy9 |  -.0178076   .0295455    -0.60   0.547    -.0757188    .0401036
  year_dummy10 |  -.0384256     .02404    -1.60   0.110    -.0855457    .0086945
  year_dummy11 |  -.0827822    .028785    -2.88   0.004    -.1392028   -.0263617
  year_dummy12 |  -.0120192   .0276638    -0.43   0.664    -.0662421    .0422038
  year_dummy13 |   -.014817   .0229478    -0.65   0.518    -.0597964    .0301624
  year_dummy14 |  -.0000993   .0243058    -0.00   0.997    -.0477404    .0475418
  year_dummy15 |  -.0397557   .0241909    -1.64   0.100    -.0871715    .0076601
  year_dummy16 |   .0379377    .024713     1.54   0.125    -.0105015     .086377
  year_dummy17 |   .0913747   .0236661     3.86   0.000     .0449874     .137762
  year_dummy18 |   .0128727   .0204837     0.63   0.530    -.0272767    .0530221
  year_dummy19 |   .0141505   .0183203     0.77   0.440    -.0217585    .0500596
  year_dummy20 |  -.0403134   .0188564    -2.14   0.033    -.0772734   -.0033535
  year_dummy21 |          0  (omitted)
        terror |   .0159255   .0244313     0.65   0.515    -.0319615    .0638126
--------------------------------------------------------------------------------
F test of excluded instruments:
  F(  2,  1121) =    20.34
  Prob > F      =   0.0000
Sanderson-Windmeijer multivariate F test of excluded instruments:
  F(  1,  1121) =    26.07
  Prob > F      =   0.0000


FIXED EFFECTS ESTIMATION
------------------------
Number of groups =      1122                    Obs per group: min =        21
                                                               avg =      21.0
                                                               max =        21

First-stage regression of lnlegal_zme:

Statistics robust to heteroskedasticity and clustering on mun_code
Number of obs =                  23562
Number of clusters (mun_code) =   1122
--------------------------------------------------------------------------------
               |               Robust
   lnlegal_zme | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
   instrument2 |   -.013011   .0093928    -1.39   0.166    -.0314215    .0053995
instrument_zme |   1.129027   .2146203     5.26   0.000     .7083559    1.549698
  coca_crop_ha |   .0000109   .0000166     0.65   0.514    -.0000217    .0000435
     zme_dummy |          0  (omitted)
   year_dummy1 |  -.0092521   .0193666    -0.48   0.633    -.0472121    .0287078
   year_dummy2 |  -.0212773   .0180335    -1.18   0.238    -.0566243    .0140697
   year_dummy3 |  -.0378648    .017972    -2.11   0.035    -.0730913   -.0026384
   year_dummy4 |  -.0308286   .0182999    -1.68   0.092    -.0666977    .0050404
   year_dummy5 |   -.017589   .0126131    -1.39   0.163    -.0423116    .0071337
   year_dummy6 |  -.0343534   .0133573    -2.57   0.010    -.0605346   -.0081723
   year_dummy7 |  -.0186262   .0140504    -1.33   0.185    -.0461659    .0089135
   year_dummy8 |  -.0103816   .0156303    -0.66   0.507    -.0410181     .020255
   year_dummy9 |   .0099454   .0165377     0.60   0.548    -.0224696    .0423604
  year_dummy10 |  -.0016365   .0147883    -0.11   0.912    -.0306226    .0273495
  year_dummy11 |  -.0268412   .0170884    -1.57   0.116    -.0603357    .0066532
  year_dummy12 |  -.0075724   .0140665    -0.54   0.590    -.0351436    .0199989
  year_dummy13 |   -.010816   .0133215    -0.81   0.417    -.0369272    .0152951
  year_dummy14 |  -.0223117   .0148615    -1.50   0.133    -.0514413    .0068179
  year_dummy15 |  -.0180329   .0169097    -1.07   0.286    -.0511771    .0151114
  year_dummy16 |   .0165845   .0128369     1.29   0.196    -.0085767    .0417458
  year_dummy17 |    .049236   .0129781     3.79   0.000      .023798     .074674
  year_dummy18 |   .0148787   .0102042     1.46   0.145    -.0051224    .0348797
  year_dummy19 |   .0091065   .0064517     1.41   0.158    -.0035392    .0217522
  year_dummy20 |  -.0218001   .0106351    -2.05   0.040    -.0426457   -.0009546
  year_dummy21 |          0  (omitted)
        terror |   .0256446   .0160596     1.60   0.110    -.0058334    .0571226
--------------------------------------------------------------------------------
F test of excluded instruments:
  F(  2,  1121) =    14.77
  Prob > F      =   0.0000
Sanderson-Windmeijer multivariate F test of excluded instruments:
  F(  1,  1121) =    49.55
  Prob > F      =   0.0000



Summary results for first-stage regressions
-------------------------------------------

                                           (Underid)            (Weak id)
Variable     | F(  2,  1121)  P-val | SW Chi-sq(  1) P-val | SW F(  1,  1121)
ln_legal_ha  |      20.34    0.0000 |       26.12   0.0000 |       26.07
lnlegal_zme  |      14.77    0.0000 |       49.64   0.0000 |       49.55

NB: first-stage test statistics cluster-robust

Stock-Yogo weak ID F test critical values for single endogenous regressor:
                                   10% maximal IV size             19.93
                                   15% maximal IV size             11.59
                                   20% maximal IV size              8.75
                                   25% maximal IV size              7.25
Source: Stock-Yogo (2005).  Reproduced by permission.
NB: Critical values are for i.i.d. errors only.

Underidentification test
Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified)
Ha: matrix has rank=K1 (identified)
Kleibergen-Paap rk LM statistic          Chi-sq(1)=16.04    P-val=0.0001

Weak identification test
Ho: equation is weakly identified
Cragg-Donald Wald F statistic                                     296.42
Kleibergen-Paap Wald rk F statistic                                 8.48

Stock-Yogo weak ID test critical values for K1=2 and L1=2:
                                   10% maximal IV size              7.03
                                   15% maximal IV size              4.58
                                   20% maximal IV size              3.95
                                   25% maximal IV size              3.63
Source: Stock-Yogo (2005).  Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.

Weak-instrument-robust inference
Tests of joint significance of endogenous regressors B1 in main equation
Ho: B1=0 and orthogonality conditions are valid
Anderson-Rubin Wald test           F(2,1121)=     36.24     P-val=0.0000
Anderson-Rubin Wald test           Chi-sq(2)=     72.62     P-val=0.0000
Stock-Wright LM S statistic        Chi-sq(2)=     64.83     P-val=0.0000

NB: Underidentification, weak identification and weak-identification-robust
    test statistics cluster-robust

Number of clusters             N_clust  =       1122
Number of observations               N  =      23562
Number of regressors                 K  =         24
Number of endogenous regressors      K1 =          2
Number of instruments                L  =         24
Number of excluded instruments       L1 =          2

IV (2SLS) estimation
--------------------

Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity and clustering on mun_code

Number of clusters (mun_code) =   1122                Number of obs =    23562
                                                      F( 24,  1121) =    97.11
                                                      Prob > F      =   0.0000
Total (centered) SS     =  120880.6954                Centered R2   =   0.1191
Total (uncentered) SS   =  120880.6954                Uncentered R2 =   0.1191
Residual SS             =  106485.1948                Root MSE      =    2.178

------------------------------------------------------------------------------
             |               Robust
ln_rate_di~t | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
 ln_legal_ha |   1.769159   .4884995     3.62   0.000      .811718    2.726601
 lnlegal_zme |  -.9746277   .4931153    -1.98   0.048    -1.941116   -.0081395
coca_crop_ha |   .0001436   .0000425     3.38   0.001     .0000602    .0002269
   zme_dummy |          0  (omitted)
 year_dummy1 |   3.435183   .1280892    26.82   0.000     3.184133    3.686233
 year_dummy2 |   3.904351   .1268376    30.78   0.000     3.655754    4.152948
 year_dummy3 |   3.563639   .1309439    27.22   0.000     3.306994    3.820285
 year_dummy4 |   3.561144   .1221877    29.14   0.000      3.32166    3.800627
 year_dummy5 |   3.633779   .1214572    29.92   0.000     3.395727    3.871831
 year_dummy6 |   3.660631   .1191296    30.73   0.000     3.427141     3.89412
 year_dummy7 |   3.681889   .1137976    32.35   0.000     3.458849    3.904928
 year_dummy8 |   3.330026   .1120078    29.73   0.000     3.110495    3.549557
 year_dummy9 |   2.548736   .1050657    24.26   0.000     2.342811     2.75466
year_dummy10 |   1.814091    .096257    18.85   0.000     1.625431    2.002751
year_dummy11 |   1.796316   .0999536    17.97   0.000     1.600411    1.992222
year_dummy12 |   1.923233   .1005084    19.14   0.000      1.72624    2.120226
year_dummy13 |   2.108499   .0951483    22.16   0.000     1.922012    2.294986
year_dummy14 |    2.03838   .0943668    21.60   0.000     1.853425    2.223336
year_dummy15 |   1.723176   .0940175    18.33   0.000     1.538905    1.907447
year_dummy16 |   1.126287   .0910478    12.37   0.000     .9478367    1.304737
year_dummy17 |    .556393   .0851906     6.53   0.000     .3894226    .7233634
year_dummy18 |   .5080478   .0851735     5.96   0.000     .3411109    .6749848
year_dummy19 |   .0167788   .0764369     0.22   0.826    -.1330348    .1665924
year_dummy20 |  -.4479825   .0784852    -5.71   0.000    -.6018107   -.2941544
year_dummy21 |          0  (omitted)
      terror |   .4539593   .0466707     9.73   0.000     .3624865    .5454321
------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic):             16.036
                                                   Chi-sq(1) P-val =    0.0001
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic):              296.417
                         (Kleibergen-Paap rk Wald F statistic):          8.479
Stock-Yogo weak ID test critical values: 10% maximal IV size              7.03
                                         15% maximal IV size              4.58
                                         20% maximal IV size              3.95
                                         25% maximal IV size              3.63
Source: Stock-Yogo (2005).  Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
------------------------------------------------------------------------------
Hansen J statistic (overidentification test of all instruments):         0.000
                                                 (equation exactly identified)
------------------------------------------------------------------------------
Instrumented:         ln_legal_ha lnlegal_zme
Included instruments: coca_crop_ha year_dummy1 year_dummy2 year_dummy3
                      year_dummy4 year_dummy5 year_dummy6 year_dummy7
                      year_dummy8 year_dummy9 year_dummy10 year_dummy11
                      year_dummy12 year_dummy13 year_dummy14 year_dummy15
                      year_dummy16 year_dummy17 year_dummy18 year_dummy19
                      year_dummy20 terror
Excluded instruments: instrument2 instrument_zme
Dropped collinear:    zme_dummy year_dummy21
------------------------------------------------------------------------------

.
end of do-file

Last edited by Paola Jaimes; 10 Jul 2023, 17:57.

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