Chapter 9. Political Economy of Trade Policy

Empirical exercise

This exercise is to reproduce regression results Branstetter and Feenstra (2002). To complete the exercise, the file “china_fdi.dta” should be stored in Chapter-9.

Documentation

The primary data set is a file, in STATA format, called china_fdi.dta. An extended list and description of the variables are given below.

Variable	Brief Description
pcode	Province Code
pname	Province Name
year	1978-1996
output	Total output
state	State-owned firm output
coll	Output of collectives
indi	Output of individual enterprises
others	Output of other firms
fiech	fie2 + oversea2
other2	Finer breakdown of other output
stock2	Output of stock companies
fie2	Output of Foreign-Invested Enterprises (FIEs)
oversea2	Output of Overseas Chinese FIEs
fiexrat	cx_fo / fiech
cx_fo	(cx_or_fo + cx_pr_fo + cx_ot_fo)
import	Imports from provincial data
export	Exports from provincial data
loan	Foreign loans
fdi	Foreign direct investments
ofdi	Other Foreign Direct Investment (FDI)
fdidum	Dummy variable (1 if fdi > 0 & fdi != .)
cx_tot	Total exports from customs data
cm_tot	Total imports from customs data
cx_or_st	Ordinary trade exports, State-Owned Enterprises (SOEs)
cm_or_st	Ordinary trade imports, SOEs
cx_or_fo	Ordinary trade exports, FIEs
cm_or_fo	Ordinary trade imports, FIEs
cx_or_ot	Ordinary trade exports, others
cm_or_ot	Ordinary trade imports, others
cx_pr_st	Processing trade exports, SOEs
cm_pr_st	Processing trade imports, SOEs
cx_pr_fo	Processing trade exports, FIEs
cm_pr_fo	Processing trade imports, FIEs
cx_pr_ot	Processing trade exports, others
cm_pr_ot	Processing trade imports, others
cx_ot_st	Other trade exports, SOEs
cm_ot_st	Other trade imports, SOEs
cx_ot_fo	Other trade exports, FIEs
cm_ot_fo	Other trade imports, FIEs
cx_ot_ot	Other trade exports, others
cm_ot_ot	Other trade imports, others
totwage	Total wages
soewage	SOE wages
collwage	Urban collective wages
othwage	Other wages
premium	othwage / ((soewage + collwage) / 2)
totalemp	Total provincial employment
urbanemp	Total urban employment (in 10,000 people)
soeemp	SOE employment
collemp	Total (urban) collective employment
ruralemp	Total rural employment
tveemp	Total township and village enterprise employment
jointemp	Total joint-owned employment
fieemp	FIE employment
overemp	Employment by overseas Chinese
indemp	Employment by individual businesses
fieshr	fieemp / (jointemp + fieemp + overemp)
fiechshr	(fieemp + overemp) / (jointemp + fieemp)
statrat1	state / appcons
impute	=1 if output is imputed
coastal	=1 if coastal province
suprox	=1 if Fujian or Guangdong
tariff96	1996 tariff estimates
merge1	Old merge variable for tariffs?
fdirv	Sets fdi=0 if missing
fdistock	Cumulative FDI stock
fdidum2	=1 if fdistock > 0
fierat1	fiech / (output + import)
imprat1	import / (output + import)
fdi_imp1	fdistock * imprat1
tar_imp1	tariff96 * imprat1
lfdistok	Lagged fdistock
tar_imp	tariff96 * import
fdi_imp	fdistock * import
lfdi_imp	Lagged fdistock * import
tar_stat	tariff96 * state
lfdi_sta	Lagged fdistock * state
tar_lfdi	tariff96 * lagged fdistock
stat_imp	state * import
imp_prem	import * newprem
sta_prem	state * newprem
lfdi_pre	lfdistok * newprem
newprem	(othwage - collwage) / other
tar_prem	tariff96 * newprem
statrat3	= statrat2 if y >= 1988, pc != 11,54
fierat3	= fierat2 if y >= 1988, pc != 11,54
imprat3	= imprat2 if y >= 1988, pc != 11,54
fdi_imp3	fdistock * imprat3
tar_imp3	tariff96 * imprat3

Note: Additional interaction terms and various residuals are present in the dataset, often used as instruments for econometric analyses.

Exercise 1

Run the program share_reg.do to reproduce the regression results in Table 9.1. Notice that apparent consumption (appcon3) is included as a control variables in these regressions. What happens if this variable is dropped?

Feenstra’s code

clear
capture log close
log using Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-9\share_reg.log,replace

use Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-9\china_fdi,clear

set matsize 100

reg fiech3 state3 premsta3 tar_cm3 newprem fdi2_cm3 appcons3 pd1-pd30 yd1-yd18  if fiech3>0, r 

reg fiech3 state3 premsta3 tar_cm3 newprem fdi2_cm3 appcons3 pd1-pd30 yd1-yd18 /*
     */ (elecpro elecgdp elecpop elecurb elecrur elecwag elecwags elecwagu cmpr3 /*
     */ cmprgdp  cmprpop cmprelec indewag indewags indewagu gdp pop urbaninc rurinc /*
     */  pd1-pd30 yd1-yd18)  if fiech3>0, r 

reg fiech3 state3 premsta3 tar_cm3 newprem fdi2_cm3 appcons3 pd1-pd30 yd1-yd18 /*
     */ (elecpro elecgdp elecpop elecurb elecrur elecwag elecwags elecwagu cmpr3 /*
     */ cmprgdp  cmprpop cmprelec indewag indewags indewagu gdp pop urbaninc rurinc /*
     */  pd1-pd30 yd1-yd18) [w=gdp]  if fiech3>0, r 

matrix cv=get(VCE)

matrix cv1 = cv[1..3,1..3]

matrix list cv1

reg fiech3 state3 premsta3 tar_cm3 newprem fdi2_cm3 appcons3 pd1-pd30 yd1-yd18 /*
     */ (elecpro elecgdp elecpop elecurb elecrur elecwag elecwags elecwagu cmpr3 /*
     */ cmprgdp  cmprpop cmprelec indewag indewags indewagu gdp pop urbaninc rurinc /*
     */  pd1-pd30 yd1-yd18) [w=gdp]  if fiech3>0 & year>=1988, r 

matrix cv=get(VCE)

matrix cv1 = cv[1..3,1..3]

matrix list cv1

reg fiech3 state3 premsta3 tar_cm3 newprem fdi2_cm3 appcons3 pd1-pd30 yd1-yd18 /*
     */ (elecpro elecgdp elecpop elecurb elecrur elecwag elecwags elecwagu cmpr3 /*
     */ cmprgdp  cmprpop cmprelec indewag indewags indewagu gdp pop urbaninc rurinc /*
     */  pd1-pd30 yd1-yd18) [w=gdp]  if fiech3>0 & year>=1990, r 


matrix cv=get(VCE)

matrix cv1 = cv[1..3,1..3]

matrix list cv1

log close

Output:

. clear

. capture log close

. log using Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-9\share_reg.log,replace
(note: file Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-9\share_reg.log not found)
------------------------------------------------------------------------------------------------------------------------
      name:  <unnamed>
       log:  Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-9\share_reg.log
  log type:  text
 opened on:  27 Oct 2024, 17:14:23

. 
. use Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-9\china_fdi,clear

. 
. set matsize 100

Current memory allocation

                    current                                 memory usage
    settable          value     description                 (1M = 1024k)
    --------------------------------------------------------------------
    set maxvar         5000     max. variables allowed           1.909M
    set memory           50M    max. data space                 50.000M
    set matsize         100     max. RHS vars in models          0.085M
                                                            -----------
                                                                51.994M

. 
. reg fiech3 state3 premsta3 tar_cm3 newprem fdi2_cm3 appcons3 pd1-pd30 yd1-yd18  if fiech3>0, r 
note: pd25 omitted because of collinearity
note: pd28 omitted because of collinearity
note: yd1 omitted because of collinearity
note: yd2 omitted because of collinearity
note: yd3 omitted because of collinearity
note: yd4 omitted because of collinearity
note: yd5 omitted because of collinearity
note: yd6 omitted because of collinearity
note: yd8 omitted because of collinearity

Linear regression                                      Number of obs =     297
                                                       F( 45,   251) =   13.17
                                                       Prob > F      =  0.0000
                                                       R-squared     =  0.8517
                                                       Root MSE      =  70.771

------------------------------------------------------------------------------
             |               Robust
      fiech3 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      state3 |  -.4120043   .1252756    -3.29   0.001    -.6587296   -.1652789
    premsta3 |    .418439   .2349873     1.78   0.076    -.0443591    .8812372
     tar_cm3 |  -.1462319   2.698182    -0.05   0.957    -5.460194     5.16773
     newprem |  -118.4885   63.81774    -1.86   0.065     -244.175    7.197995
    fdi2_cm3 |   3.67e-07   2.21e-07     1.66   0.099    -6.89e-08    8.03e-07
    appcons3 |   .1085887   .0181638     5.98   0.000     .0728158    .1443616
         pd1 |   138.6463   53.32884     2.60   0.010     33.61727    243.6753
         pd2 |   111.7079   53.14862     2.10   0.037     7.033765    216.3819
         pd3 |   47.80944   46.13068     1.04   0.301     -43.0431     138.662
         pd4 |   38.63599   36.39048     1.06   0.289    -33.03362    110.3056
         pd5 |   33.63291    33.2422     1.01   0.313    -31.83628     99.1021
         pd6 |   56.76019   96.64213     0.59   0.558    -133.5726     247.093
         pd7 |   63.22479   44.37549     1.42   0.155    -24.17098    150.6206
         pd8 |   91.16894    58.7561     1.55   0.122    -24.54885    206.8867
         pd9 |   334.7459   91.91022     3.64   0.000     153.7324    515.7594
        pd10 |   91.62152   56.68167     1.62   0.107    -20.01078    203.2538
        pd11 |  -23.90319   42.97933    -0.56   0.579    -108.5493    60.74289
        pd12 |   15.61683   44.60963     0.35   0.727    -72.24007    103.4737
        pd13 |   97.31858   42.69299     2.28   0.023     13.23643    181.4007
        pd14 |   32.84924   34.97525     0.94   0.349    -36.03311    101.7316
        pd15 |  -12.67496   71.00855    -0.18   0.858    -152.5235    127.1735
        pd16 |   43.48629   48.61576     0.89   0.372    -52.26052    139.2331
        pd17 |   78.74117   55.86131     1.41   0.160    -31.27545    188.7578
        pd18 |   42.05588   42.98484     0.98   0.329    -42.60106    126.7128
        pd19 |   5.776277   104.8443     0.06   0.956    -200.7105     212.263
        pd20 |   38.00421    36.7446     1.03   0.302    -34.36282    110.3712
        pd21 |    14.8177     32.051     0.46   0.644    -48.30546    77.94086
        pd22 |   76.34966   66.17087     1.15   0.250    -53.97124    206.6706
        pd23 |   33.08723   29.60536     1.12   0.265    -25.21934    91.39381
        pd24 |   44.62833   38.59018     1.16   0.249     -31.3735    120.6302
        pd25 |  (omitted)
        pd26 |   39.83218    37.3268     1.07   0.287    -33.68146    113.3458
        pd27 |   45.07108   33.09393     1.36   0.174     -20.1061    110.2483
        pd28 |  (omitted)
        pd29 |  -3.537009    27.8295    -0.13   0.899    -58.34611    51.27209
        pd30 |    42.1159   31.27092     1.35   0.179    -19.47094    103.7027
         yd1 |  (omitted)
         yd2 |  (omitted)
         yd3 |  (omitted)
         yd4 |  (omitted)
         yd5 |  (omitted)
         yd6 |  (omitted)
         yd7 |  -7.813549   31.83694    -0.25   0.806    -70.51514    54.88804
         yd8 |  (omitted)
         yd9 |    4.66118   19.13492     0.24   0.808    -33.02428    42.34664
        yd10 |   8.009458   18.69165     0.43   0.669      -28.803    44.82192
        yd11 |   4.120545   19.32224     0.21   0.831    -33.93384    42.17493
        yd12 |   15.40138   20.54087     0.75   0.454    -25.05304    55.85579
        yd13 |   18.11733   19.94841     0.91   0.365    -21.17027    57.40493
        yd14 |   21.38019   23.03616     0.93   0.354    -23.98861    66.74899
        yd15 |    37.6667   27.87403     1.35   0.178    -17.23009    92.56349
        yd16 |   29.59672   34.22505     0.86   0.388    -37.80815    97.00159
        yd17 |   9.661191   37.11564     0.26   0.795    -63.43658    82.75896
        yd18 |   114.3398   43.81527     2.61   0.010     28.04735    200.6322
       _cons |   8.138607   42.66315     0.19   0.849    -75.88476    92.16198
------------------------------------------------------------------------------

. 
. reg fiech3 state3 premsta3 tar_cm3 newprem fdi2_cm3 appcons3 pd1-pd30 yd1-yd18 /*
>      */ (elecpro elecgdp elecpop elecurb elecrur elecwag elecwags elecwagu cmpr3 /*
>      */ cmprgdp  cmprpop cmprelec indewag indewags indewagu gdp pop urbaninc rurinc /*
>      */  pd1-pd30 yd1-yd18)  if fiech3>0, r 

Instrumental variables (2SLS) regression               Number of obs =     280
                                                       F( 43,   236) =   11.69
                                                       Prob > F      =  0.0000
                                                       R-squared     =  0.7437
                                                       Root MSE      =   94.71

------------------------------------------------------------------------------
             |               Robust
      fiech3 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      state3 |  -1.301465   .4036078    -3.22   0.001    -2.096599   -.5063307
    premsta3 |   2.188291   .8745997     2.50   0.013     .4652708    3.911311
     tar_cm3 |    -7.4778   3.316947    -2.25   0.025    -14.01241   -.9431926
     newprem |   -967.166   435.0548    -2.22   0.027    -1824.253    -110.079
    fdi2_cm3 |   3.73e-07   1.73e-07     2.15   0.032     3.18e-08    7.14e-07
    appcons3 |   .1501362   .0251856     5.96   0.000     .1005188    .1997536
         pd1 |   22.49351   84.71518     0.27   0.791    -144.4011    189.3881
         pd2 |  (omitted)
         pd3 |  -101.9567    68.5424    -1.49   0.138    -236.9898    33.07639
         pd4 |  -62.65556   118.8012    -0.53   0.598     -296.702    171.3908
         pd5 |  -261.3773   128.8722    -2.03   0.044    -515.2641   -7.490483
         pd6 |  (omitted)
         pd7 |  -95.03245   83.30879    -1.14   0.255    -259.1563    69.09143
         pd8 |  -32.86181   81.23209    -0.40   0.686    -192.8945    127.1708
         pd9 |     324.31   65.47577     4.95   0.000     195.3183    453.3016
        pd10 |   24.40901   44.81474     0.54   0.586    -63.87903     112.697
        pd11 |  -240.2662   82.48247    -2.91   0.004    -402.7622    -77.7702
        pd12 |  -185.4254   106.2032    -1.75   0.082    -394.6528    23.80195
        pd13 |  -38.63878   118.8187    -0.33   0.745    -272.7195     195.442
        pd14 |  -136.9162   106.3078    -1.29   0.199    -346.3496    72.51729
        pd15 |  (omitted)
        pd16 |  -75.15068   69.47177    -1.08   0.280    -212.0147    61.71335
        pd17 |   14.33876   50.61352     0.28   0.777    -85.37326    114.0508
        pd18 |   -116.985   87.18557    -1.34   0.181    -288.7464    54.77642
        pd19 |  -40.35602   124.3852    -0.32   0.746    -285.4032    204.6911
        pd20 |  -179.2321   101.3529    -1.77   0.078     -378.904    20.43983
        pd21 |  -119.2624   149.9743    -0.80   0.427    -414.7219     176.197
        pd22 |   10.03015   64.99138     0.15   0.877    -118.0072    138.0675
        pd23 |  -157.3637   121.3052    -1.30   0.196    -396.3431    81.61573
        pd24 |  -170.5148   103.4955    -1.65   0.101    -374.4078    33.37831
        pd25 |  (omitted)
        pd26 |  -136.5358   112.6071    -1.21   0.227    -358.3793    85.30762
        pd27 |  -130.0935   103.6251    -1.26   0.211    -334.2418    74.05478
        pd28 |  -213.2504   156.1108    -1.37   0.173    -520.7991    94.29841
        pd29 |  -371.6727   159.8529    -2.33   0.021    -686.5936   -56.75185
        pd30 |  -131.4453   106.1748    -1.24   0.217    -340.6168    77.72623
         yd1 |  (omitted)
         yd2 |  (omitted)
         yd3 |  (omitted)
         yd4 |  (omitted)
         yd5 |  (omitted)
         yd6 |  (omitted)
         yd7 |  (omitted)
         yd8 |  -23.25973   50.76326    -0.46   0.647    -123.2667    76.74728
         yd9 |  -12.41766   50.90956    -0.24   0.808    -112.7129    87.87757
        yd10 |   15.76796   48.88126     0.32   0.747    -80.53139    112.0673
        yd11 |   43.42377   51.59704     0.84   0.401    -58.22585    145.0734
        yd12 |    79.3707   56.02184     1.42   0.158    -30.99606    189.7375
        yd13 |   77.22576   55.69696     1.39   0.167    -32.50098    186.9525
        yd14 |   98.32196   60.62045     1.62   0.106    -21.10439    217.7483
        yd15 |    129.245   67.84135     1.91   0.058    -4.407003     262.897
        yd16 |   134.9046   72.58903     1.86   0.064    -8.100661    277.9098
        yd17 |   92.58514   67.73654     1.37   0.173    -40.86038    226.0307
        yd18 |   218.5723   79.71104     2.74   0.007     61.53622    375.6084
       _cons |   469.3039   197.0992     2.38   0.018     81.00532    857.6025
------------------------------------------------------------------------------

. 
. reg fiech3 state3 premsta3 tar_cm3 newprem fdi2_cm3 appcons3 pd1-pd30 yd1-yd18 /*
>      */ (elecpro elecgdp elecpop elecurb elecrur elecwag elecwags elecwagu cmpr3 /*
>      */ cmprgdp  cmprpop cmprelec indewag indewags indewagu gdp pop urbaninc rurinc /*
>      */  pd1-pd30 yd1-yd18) [w=gdp]  if fiech3>0, r 
(analytic weights assumed)
(sum of wgt is   2.4017e+05)

Instrumental variables (2SLS) regression               Number of obs =     280
                                                       F( 43,   236) =   26.43
                                                       Prob > F      =  0.0000
                                                       R-squared     =  0.7550
                                                       Root MSE      =  171.68

------------------------------------------------------------------------------
             |               Robust
      fiech3 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      state3 |  -1.660521   .4807088    -3.45   0.001    -2.607549   -.7134923
    premsta3 |   3.618218   1.160893     3.12   0.002     1.331182    5.905255
     tar_cm3 |  -15.85201    5.11311    -3.10   0.002    -25.92518   -5.778843
     newprem |  -3333.269    1085.09    -3.07   0.002     -5470.97   -1195.569
    fdi2_cm3 |   5.17e-07   1.25e-07     4.12   0.000     2.70e-07    7.65e-07
    appcons3 |   .1497793   .0216163     6.93   0.000     .1071937    .1923649
         pd1 |   151.3819   205.4259     0.74   0.462     -253.321    556.0847
         pd2 |  (omitted)
         pd3 |  -136.5562   231.6549    -0.59   0.556    -592.9319    319.8195
         pd4 |    131.699   236.2008     0.56   0.578    -333.6322    597.0303
         pd5 |  -519.0087   313.4677    -1.66   0.099    -1136.561    98.54363
         pd6 |  (omitted)
         pd7 |  -94.63755   227.7186    -0.42   0.678    -543.2584    353.9833
         pd8 |  -97.71278   248.7448    -0.39   0.695    -587.7566     392.331
         pd9 |   504.7952   252.3469     2.00   0.047     7.654983    1001.935
        pd10 |   11.20123   247.3212     0.05   0.964     -476.038    498.4405
        pd11 |  -384.5489   224.5097    -1.71   0.088    -826.8481    57.75023
        pd12 |  -170.7961   215.2741    -0.79   0.428    -594.9006    253.3083
        pd13 |   234.0235   204.0305     1.15   0.253    -167.9302    635.9771
        pd14 |  -4.280486   199.6937    -0.02   0.983    -397.6905    389.1295
        pd15 |  -61.50421   250.3792    -0.25   0.806    -554.7679    431.7595
        pd16 |  -48.59471   226.6831    -0.21   0.830    -495.1755    397.9861
        pd17 |   3.428437   244.1047     0.01   0.989    -477.4742     484.331
        pd18 |  -83.46781   215.5776    -0.39   0.699      -508.17    341.2344
        pd19 |   335.7746   280.9931     1.19   0.233    -217.8006    889.3499
        pd20 |  -237.5962   238.2537    -1.00   0.320    -706.9719    231.7795
        pd21 |   254.9373   222.6991     1.14   0.253    -183.7948    693.6694
        pd22 |   -172.099   259.6178    -0.66   0.508    -683.5633    339.3653
        pd23 |  -4.580315   199.7805    -0.02   0.982    -398.1613    389.0006
        pd24 |   -248.713   253.6054    -0.98   0.328    -748.3327    250.9066
        pd25 |  (omitted)
        pd26 |   89.16112   207.6892     0.43   0.668    -320.0004    498.3226
        pd27 |   -212.042   251.1014    -0.84   0.399    -706.7285    282.6444
        pd28 |  (omitted)
        pd29 |  -622.8209   321.3912    -1.94   0.054    -1255.983    10.34126
        pd30 |  -171.1686   225.7568    -0.76   0.449    -615.9247    273.5874
         yd1 |  (omitted)
         yd2 |  (omitted)
         yd3 |  (omitted)
         yd4 |  (omitted)
         yd5 |  (omitted)
         yd6 |  (omitted)
         yd7 |   43.01289   141.6405     0.30   0.762    -236.0284    322.0542
         yd8 |  (omitted)
         yd9 |   20.60074   86.75487     0.24   0.813    -150.3122    191.5136
        yd10 |   140.6733   92.57702     1.52   0.130    -41.70964    323.0562
        yd11 |    249.315   113.0118     2.21   0.028      26.6742    471.9558
        yd12 |   297.7457   121.7527     2.45   0.015     57.88479    537.6067
        yd13 |   301.1773   125.5635     2.40   0.017     53.80884    548.5457
        yd14 |   364.4928   141.5999     2.57   0.011      85.5315    643.4542
        yd15 |   432.1373   159.4536     2.71   0.007      118.003    746.2716
        yd16 |   462.5475   187.6808     2.46   0.014     92.80381    832.2912
        yd17 |   408.6656   200.4563     2.04   0.043     13.75323     803.578
        yd18 |   580.9932   201.3976     2.88   0.004     184.2265      977.76
       _cons |   898.3402   356.9691     2.52   0.013     195.0871    1601.593
------------------------------------------------------------------------------

. 
. matrix cv=get(VCE)

. 
. matrix cv1 = cv[1..3,1..3]

. 
. matrix list cv1

symmetric cv1[3,3]
              state3    premsta3     tar_cm3
  state3   .23108091
premsta3   -.5216955   1.3476718
 tar_cm3    1.511459  -3.9109265   26.143895

. 
. reg fiech3 state3 premsta3 tar_cm3 newprem fdi2_cm3 appcons3 pd1-pd30 yd1-yd18 /*
>      */ (elecpro elecgdp elecpop elecurb elecrur elecwag elecwags elecwagu cmpr3 /*
>      */ cmprgdp  cmprpop cmprelec indewag indewags indewagu gdp pop urbaninc rurinc /*
>      */  pd1-pd30 yd1-yd18) [w=gdp]  if fiech3>0 & year>=1988, r 
(analytic weights assumed)
(sum of wgt is   2.1445e+05)

Instrumental variables (2SLS) regression               Number of obs =     210
                                                       F( 39,   170) =   23.69
                                                       Prob > F      =  0.0000
                                                       R-squared     =  0.8734
                                                       Root MSE      =   130.7

------------------------------------------------------------------------------
             |               Robust
      fiech3 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      state3 |  -1.320297    .497583    -2.65   0.009    -2.302534   -.3380597
    premsta3 |   2.553575   1.187916     2.15   0.033     .2086084    4.898541
     tar_cm3 |  -11.46246   6.712541    -1.71   0.090    -24.71313    1.788208
     newprem |   -2519.84   1256.346    -2.01   0.046    -4999.888    -39.7934
    fdi2_cm3 |   4.85e-07   1.50e-07     3.23   0.001     1.89e-07    7.81e-07
    appcons3 |   .1486559    .024088     6.17   0.000     .1011058     .196206
         pd1 |   163.2254   169.4229     0.96   0.337    -171.2181    497.6689
         pd2 |  (omitted)
         pd3 |  -34.73277   188.4823    -0.18   0.854    -406.7999    337.3344
         pd4 |   51.19367    183.792     0.28   0.781    -311.6148    414.0022
         pd5 |  -368.2653   282.3617    -1.30   0.194     -925.652    189.1214
         pd6 |  (omitted)
         pd7 |  -8.148863   187.4163    -0.04   0.965    -378.1118     361.814
         pd8 |   42.97417   207.3155     0.21   0.836    -366.2702    452.2185
         pd9 |   598.6921   241.8478     2.48   0.014     121.2806    1076.104
        pd10 |   63.07135   209.5412     0.30   0.764    -350.5666    476.7093
        pd11 |  -339.0711   190.8114    -1.78   0.077     -715.736    37.59373
        pd12 |  -64.59059    172.208    -0.38   0.708    -404.5321    275.3509
        pd13 |   196.2458   173.3039     1.13   0.259     -145.859    538.3505
        pd14 |   33.28636   161.2055     0.21   0.837     -284.936    351.5087
        pd15 |  -35.32299   218.3816    -0.16   0.872    -466.4118    395.7658
        pd16 |   7.898497   190.3217     0.04   0.967    -367.7998    383.5968
        pd17 |   58.21349    208.674     0.28   0.781    -353.7125    470.1395
        pd18 |  -7.502736   175.9845    -0.04   0.966    -354.8991    339.8936
        pd19 |   192.1812   346.1707     0.56   0.580    -491.1656     875.528
        pd20 |  -160.9523   206.8624    -0.78   0.438    -569.3022    247.3976
        pd21 |   192.3007   199.4306     0.96   0.336    -201.3787    585.9802
        pd22 |    -48.786   215.9674    -0.23   0.822    -475.1092    377.5372
        pd23 |   27.90071   159.6185     0.17   0.861    -287.1889    342.9903
        pd24 |  -136.5801   218.0904    -0.63   0.532    -567.0941     293.934
        pd25 |  (omitted)
        pd26 |   164.0468   177.9983     0.92   0.358    -187.3247    515.4184
        pd27 |  -238.2111   238.5003    -1.00   0.319    -709.0147    232.5925
        pd28 |  (omitted)
        pd29 |  -464.9702   303.1842    -1.53   0.127    -1063.461    133.5205
        pd30 |  -152.6274   201.0469    -0.76   0.449    -549.4973    244.2425
         yd1 |  (omitted)
         yd2 |  (omitted)
         yd3 |  (omitted)
         yd4 |  (omitted)
         yd5 |  (omitted)
         yd6 |  (omitted)
         yd7 |  (omitted)
         yd8 |  (omitted)
         yd9 |  (omitted)
        yd10 |  (omitted)
        yd11 |  (omitted)
        yd12 |   42.70326   47.13385     0.91   0.366    -50.33976    135.7463
        yd13 |   45.25918   45.69599     0.99   0.323    -44.94548    135.4638
        yd14 |   97.22254   61.23666     1.59   0.114    -23.65965    218.1047
        yd15 |   155.5728   85.44523     1.82   0.070    -13.09748    324.2432
        yd16 |   186.4389   125.9879     1.48   0.141    -62.26333    435.1412
        yd17 |   136.0366   144.7728     0.94   0.349    -149.7474    421.8206
        yd18 |   315.0861   143.2271     2.20   0.029     32.35332    597.8188
       _cons |   842.7119   438.2943     1.92   0.056    -22.48842    1707.912
------------------------------------------------------------------------------

. 
. matrix cv=get(VCE)

. 
. matrix cv1 = cv[1..3,1..3]

. 
. matrix list cv1

symmetric cv1[3,3]
              state3    premsta3     tar_cm3
  state3   .24758885
premsta3  -.55788145   1.4111448
 tar_cm3   1.8692088  -4.6693021   45.058204

. 
. reg fiech3 state3 premsta3 tar_cm3 newprem fdi2_cm3 appcons3 pd1-pd30 yd1-yd18 /*
>      */ (elecpro elecgdp elecpop elecurb elecrur elecwag elecwags elecwagu cmpr3 /*
>      */ cmprgdp  cmprpop cmprelec indewag indewags indewagu gdp pop urbaninc rurinc /*
>      */  pd1-pd30 yd1-yd18) [w=gdp]  if fiech3>0 & year>=1990, r 
(analytic weights assumed)
(sum of wgt is   1.8621e+05)

Instrumental variables (2SLS) regression               Number of obs =     158
                                                       F( 37,   120) =   24.51
                                                       Prob > F      =  0.0000
                                                       R-squared     =  0.9150
                                                       Root MSE      =  115.63

------------------------------------------------------------------------------
             |               Robust
      fiech3 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      state3 |  -1.037144    .485102    -2.14   0.035    -1.997612   -.0766754
    premsta3 |   1.837028   1.160133     1.58   0.116    -.4599559    4.134011
     tar_cm3 |  -9.974153   7.575814    -1.32   0.190    -24.97374    5.025432
     newprem |  -2125.903   1396.838    -1.52   0.131    -4891.545    639.7383
    fdi2_cm3 |   5.11e-07   1.60e-07     3.19   0.002     1.94e-07    8.29e-07
    appcons3 |   .1446918   .0269515     5.37   0.000     .0913298    .1980538
         pd1 |   175.8829   154.8554     1.14   0.258    -130.7201    482.4859
         pd2 |  (omitted)
         pd3 |  -23.40224   173.3892    -0.13   0.893    -366.7008    319.8963
         pd4 |  -33.34945   158.2301    -0.21   0.833     -346.634    279.9351
         pd5 |  -183.8552   209.1258    -0.88   0.381    -597.9097    230.1993
         pd6 |  (omitted)
         pd7 |   43.79854   168.3807     0.26   0.795    -289.5835    377.1806
         pd8 |    99.2044   192.0972     0.52   0.607    -281.1347    479.5435
         pd9 |    677.295   252.7652     2.68   0.008     176.8374    1177.752
        pd10 |   61.92765   195.3322     0.32   0.752    -324.8165    448.6718
        pd11 |  -330.9045   175.7311    -1.88   0.062    -678.8399    17.03093
        pd12 |  -30.48932   156.9822    -0.19   0.846    -341.3031    280.3245
        pd13 |   201.1421   166.0392     1.21   0.228     -127.604    529.8881
        pd14 |   42.74646    144.145     0.30   0.767    -242.6506    328.1435
        pd15 |  -82.50432    214.247    -0.39   0.701    -506.6984    341.6897
        pd16 |   15.49172   176.6563     0.09   0.930    -334.2755    365.2589
        pd17 |   42.55748   199.6531     0.21   0.832    -352.7417    437.8567
        pd18 |   9.402431   160.6178     0.06   0.953    -308.6096    327.4145
        pd19 |   167.9075   418.6528     0.40   0.689    -660.9959     996.811
        pd20 |  -120.0367   187.6748    -0.64   0.524    -491.6197    251.5464
        pd21 |   170.3136    193.863     0.88   0.381    -213.5217    554.1488
        pd22 |  -24.40219   200.0268    -0.12   0.903    -420.4413    371.6369
        pd23 |      59.87   143.5248     0.42   0.677     -224.299     344.039
        pd24 |  -82.74678   202.1043    -0.41   0.683    -482.8992    317.4057
        pd25 |  (omitted)
        pd26 |   180.1916   173.7741     1.04   0.302    -163.8691    524.2523
        pd27 |  -231.2034   255.1446    -0.91   0.367    -736.3719    273.9651
        pd28 |  (omitted)
        pd29 |  -404.6779   325.7161    -1.24   0.217    -1049.573    240.2173
        pd30 |  -173.7454   217.6256    -0.80   0.426    -604.6289    257.1381
         yd1 |  (omitted)
         yd2 |  (omitted)
         yd3 |  (omitted)
         yd4 |  (omitted)
         yd5 |  (omitted)
         yd6 |  (omitted)
         yd7 |  (omitted)
         yd8 |  (omitted)
         yd9 |  (omitted)
        yd10 |  (omitted)
        yd11 |  (omitted)
        yd12 |  (omitted)
        yd13 |  -99.68378   152.6417    -0.65   0.515    -401.9037    202.5361
        yd14 |  -51.76248   127.3657    -0.41   0.685    -303.9377    200.4127
        yd15 |   1.204476   98.69447     0.01   0.990    -194.2037    196.6127
        yd16 |   35.94405   57.09284     0.63   0.530    -77.09581    148.9839
        yd17 |  (omitted)
        yd18 |   171.8328   55.21844     3.11   0.002     62.50408    281.1614
       _cons |   826.6987   609.2366     1.36   0.177    -379.5473    2032.945
------------------------------------------------------------------------------

. 
. 
. matrix cv=get(VCE)

. 
. matrix cv1 = cv[1..3,1..3]

. 
. matrix list cv1

symmetric cv1[3,3]
              state3    premsta3     tar_cm3
  state3   .23532398
premsta3  -.52880818   1.3459097
 tar_cm3   1.8540186  -4.6583376   57.392959

. 
. log close
      name:  <unnamed>
       log:  Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-9\share_reg.log
  log type:  text
 closed on:  27 Oct 2024, 17:14:31
------------------------------------------------------------------------------------------------------------------------

. 
end of do-file

My code

# Packages ----

library(archive)
library(haven)
library(dplyr)
library(broom)
library(ivreg) # for 2SLS regression
library(sandwich) # for robust standard errors
library(purrr)
library(knitr)

# Extract ----

fzip <- "first-edition/Chapter-9.zip"
dout <- gsub("\\.zip$", "", fzip)

if (!dir.exists(dout)) {
  archive_extract(fzip, dir = dout)
}

# Read and transform ----

fout <- paste0(dout, "/china_fdi.rds")

if (!file.exists(fout)) {
  china_fdi <- read_dta(paste0(dout, "/china_fdi.dta"))

  saveRDS(china_fdi, fout)
} else {
  china_fdi <- readRDS(fout)
}

rhs_vars <- paste(c("state3", "premsta3", "tar_cm3", "newprem", "fdi2_cm3",
  "appcons3"), collapse = " + ")
pd_vars <- paste("pd", 1:30, sep = "", collapse = " + ")
yd_vars <- paste("yd", 1:18, sep = "", collapse = " + ")

formula_str <- paste("fiech3 ~",  rhs_vars, "+", pd_vars, "+", yd_vars)

fit1 <- lm(formula_str, data = filter(china_fdi, fiech3 > 0))

tidy(fit1)

# A tibble: 55 × 5
   term        estimate     std.error statistic  p.value
   <chr>          <dbl>         <dbl>     <dbl>    <dbl>
 1 (Intercept)  1.65e+2 41.6              3.96  9.89e- 5
 2 state3      -4.12e-1  0.0794          -5.19  4.33e- 7
 3 premsta3     4.18e-1  0.138            3.04  2.65e- 3
 4 tar_cm3     -1.46e-1  1.18            -0.124 9.02e- 1
 5 newprem     -1.18e+2 65.2             -1.82  7.02e- 2
 6 fdi2_cm3     3.67e-7  0.0000000750     4.89  1.80e- 6
 7 appcons3     1.09e-1  0.00842         12.9   1.60e-29
 8 pd1          9.65e+1 32.7              2.95  3.47e- 3
 9 pd2          6.96e+1 32.7              2.13  3.41e- 2
10 pd3          5.69e+0 31.9              0.178 8.58e- 1
# ℹ 45 more rows

instruments <- paste(
  c(
    "elecpro", "elecgdp", "elecpop", "elecurb", "elecrur", "elecwag",
    "elecwags", "elecwagu", "cmpr3", "cmprgdp", "cmprpop", "cmprelec",
    "indewag", "indewags", "indewagu", "gdp", "pop", "urbaninc", "rurinc"
  ),
  collapse = " + "
)

formula_str <- paste(
  "fiech3 ~", rhs_vars, "+", pd_vars, "+", yd_vars,
  "|", instruments, "+", pd_vars, "+", yd_vars
)

china_fdi_8495 <- filter(china_fdi, fiech3 > 0)
china_fdi_8895 <- filter(china_fdi, fiech3 > 0 & year >= 1988)
china_fdi_9095 <- filter(china_fdi, fiech3 > 0 & year >= 1990)

fit_8495 <- ivreg(formula_str,
  data = china_fdi_8495,
  weights = china_fdi_8495$gdp
)

fit_8895 <- ivreg(formula_str,
  data = china_fdi_8895,
  weights = china_fdi_8895$gdp
)

fit_9095 <- ivreg(formula_str,
  data = china_fdi_9095,
  weights = china_fdi_9095$gdp
)

The models run correctly, however there is an issue with the summary() and tidy() functions, which fails because of dropped coefficients due to collinearity. Stata also dropped some coefficients, as we can see in the output of the previous regressions.

In order to bypass this issue, we can write a function to report the model summary.

iv_summary <- function(model) {
  coeffs <- coef(model)
  se <- sqrt(diag(vcov(model)))
  t_stats <- coeffs / se
  p_values <- 2 * pt(abs(t_stats), df = model$df.residual, lower.tail = FALSE)
  
  results <- tibble(
    variable = names(coeffs),
    coefficient = coeffs,
    std_error = se,
    t_value = t_stats,
    p_value = p_values
  )
  
  key_vars <- c("state3", "premsta3", "tar_cm3", "newprem", "fdi2_cm3", "appcons3")

  results %>%
    filter(variable %in% key_vars)
}

iv_summary(fit_8495)

# A tibble: 6 × 5
  variable coefficient     std_error t_value  p_value
  <chr>          <dbl>         <dbl>   <dbl>    <dbl>
1 state3      -1.66e+0   0.285         -5.84 1.76e- 8
2 premsta3     3.62e+0   0.764          4.74 3.75e- 6
3 tar_cm3     -1.59e+1   3.73          -4.25 3.06e- 5
4 newprem     -3.33e+3 878.            -3.80 1.87e- 4
5 fdi2_cm3     5.17e-7   0.000000119    4.35 2.05e- 5
6 appcons3     1.50e-1   0.0163         9.22 1.77e-17

iv_summary(fit_8895)

# A tibble: 6 × 5
  variable coefficient std_error t_value  p_value
  <chr>          <dbl>     <dbl>   <dbl>    <dbl>
1 state3      -1.32e+0   2.91e-1   -4.54 1.06e- 5
2 premsta3     2.55e+0   8.27e-1    3.09 2.37e- 3
3 tar_cm3     -1.15e+1   3.91e+0   -2.93 3.81e- 3
4 newprem     -2.52e+3   1.12e+3   -2.25 2.59e- 2
5 fdi2_cm3     4.85e-7   1.03e-7    4.69 5.49e- 6
6 appcons3     1.49e-1   1.49e-2    9.96 1.05e-18

iv_summary(fit_9095)

# A tibble: 6 × 5
  variable coefficient std_error t_value  p_value
  <chr>          <dbl>     <dbl>   <dbl>    <dbl>
1 state3      -1.04e+0   3.09e-1   -3.35 1.07e- 3
2 premsta3     1.84e+0   8.81e-1    2.08 3.92e- 2
3 tar_cm3     -9.97e+0   4.18e+0   -2.39 1.85e- 2
4 newprem     -2.13e+3   1.28e+3   -1.66 1.00e- 1
5 fdi2_cm3     5.11e-7   1.03e-7    4.97 2.25e- 6
6 appcons3     1.45e-1   1.60e-2    9.04 3.30e-15

Exercise 2

Open the excel file standard_errors.xls to see how the results in Table 9.2 are computed. What formula is used for $\alpha$, and for its variance and standard error? Justify these formulas.

Hint: Consider the easier case of taking the difference between $\alpha$ and $\beta$. Then:

$$var(\alpha -\beta )=E[(\alpha -\beta )-(\overline{\alpha }-\overline{beta}){]}^2=Ef(\alpha ,\beta ),$$

where $f(\alpha ,\beta )$ is the quadratic function indicated. To compute this expected value, we take a second-order Taylor series expansion:

$$\begin{array}{rl}f(\alpha ,\beta )& \approx f(\overline{\alpha },\overline{\beta })+f_{\alpha }(\overline{\alpha },\overline{\beta })(\alpha -\overline{\alpha })+f_{\beta }(\overline{\alpha },\overline{\beta })(\beta -\overline{\beta })\\ & +\frac{1}{2}{f}_{\alpha \alpha }(\overline{\alpha },\overline{\beta })(\alpha -\overline{\alpha }{)}^2+\frac{1}{2}{f}_{\beta \beta }(\overline{\alpha },\overline{\beta })(\beta -\overline{\beta }{)}^2\\ & +f_{\alpha \beta }(\overline{\alpha },\overline{\beta })(\alpha -\overline{\alpha })(\beta -\overline{\beta })\end{array}$$

It follows that,

$$Ef(\alpha ,\beta )\approx \frac{1}{2}{f}_{\alpha \alpha }(\overline{\alpha },\overline{\beta }){\sigma }_{\alpha }^2+\frac{1}{2}{f}_{\beta \beta }(\overline{\alpha },\overline{\beta }){\sigma }_{\beta }^2+f_{\alpha \beta }(\overline{\alpha },\overline{\beta })\text{cov}(\alpha ,\beta ).$$

So computing the derivatives of the quadratic function $f(\alpha ,\beta )$, we obtain,

$$\text{var}(\alpha -\beta )=E[(\alpha -\beta )-(\overline{\alpha }-\overline{\beta }){]}^2\approx {\sigma }_{\alpha }^2+{\sigma }_{\beta }^2-2\text{cov}(\alpha ,\beta ).$$

Now given the formula for $\alpha$, use the same approach to justify its variance.

My code

There is no official code for this exercise, here is my solution following the Excel file and the workaround for table 9.1 in the previous exercise.

To avoid confusion between the estimated coefficients and the $(\alpha ,\beta )$ in the delta method, we will use $\hat{\gamma }$ to denote estimated coefficients.

We compute $\alpha$ for two variables $x$ and $y$ as:

$$\alpha =({\alpha }_x,{\alpha }_y)=(-{\hat{\gamma }}_2/({\hat{\gamma }}_1+1),\text{sd}(\alpha ))$$

This requires the robust variance-covariance matrix of the coefficients, and $\text{var}(\alpha )$ is computed as:

$$\text{var}(\hat{\alpha })=\frac{\text{var}({\hat{\gamma }}_2)}{({\hat{\gamma }}_1+1{)}^2}+\frac{\text{var}(\gamma {)}_2^2\text{var}({\hat{\gamma }}_1)}{({\hat{\gamma }}_1+1{)}^4}-\frac{2{\hat{\gamma }}_2\text{cov}({\hat{\gamma }}_1,{\hat{\gamma }}_2)}{({\hat{\gamma }}_1+1{)}^3}$$

Taking a third variable $z$, we can compute $\beta$ as:

$$\hat{\beta }=({\hat{\beta }}_x,{\hat{\beta }}_y)=(-{\hat{\gamma }}_3,\text{sd}({\hat{\gamma }}_z))$$

iv_summary_delta <- function(model, period) {
  coefs <- coef(model)
  gamma3 <- coefs["state3"]
  gamma2 <- coefs["premsta3"]
  gamma1 <- coefs["tar_cm3"]

  vars <- c("state3", "premsta3", "tar_cm3")

  vcov_matrix <- vcovHC(model, type = "HC1")[vars, vars]

  alpha <- -gamma2 / (gamma1 + 1)

  var_gamma1 <- vcov_matrix["tar_cm3", "tar_cm3"]
  var_gamma2 <- vcov_matrix["premsta3", "premsta3"]
  var_gamma3 <- vcov_matrix["state3", "state3"]

  cov_gamma1_gamma3 <- vcov_matrix["tar_cm3", "state3"]
  cov_gamma1_gamma2 <- vcov_matrix["tar_cm3", "premsta3"]
  cov_gamma2_gamma3 <- vcov_matrix["premsta3", "state3"]

  var_alpha <- var_gamma2 / (gamma1 + 1)^2 +
    var_gamma1 * gamma2^2 / (gamma1 + 1)^4 -
    2 * cov_gamma1_gamma2 * gamma2 / (gamma1 + 1)^3

  beta <- -gamma3

  cov_alpha_beta <- cov_gamma2_gamma3 / (gamma1 + 1) -
    gamma2 * cov_gamma1_gamma3 / (gamma1 + 1)^2

  var_beta_minus_alpha <- var_alpha + var_gamma3 - 2 * cov_alpha_beta

  se_beta_minus_alpha <- sqrt(var_beta_minus_alpha)

  tibble(
    period = period,
    variable = c("tar_cm3", "premsta3", "state3"),
    coefficients = c(gamma1, gamma2, gamma3),
    cov_tar_cm3 = c(var_gamma1, cov_gamma1_gamma2, cov_gamma1_gamma3),
    cov_premsta3 = c(NA, var_gamma2, cov_gamma2_gamma3),
    cov_state3 = c(NA, NA, var_gamma3),
    var_alpha = c(var_alpha, NA, NA),
    alpha = c(alpha, NA, NA),
    beta = c(beta, NA, NA),
    cov_alpha_beta = c(cov_alpha_beta, NA, NA),
    var_beta_minus_alpha = c(var_beta_minus_alpha, NA, NA),
    se_beta_minus_alpha = c(se_beta_minus_alpha, NA, NA)
  )
}

options(knitr.kable.NA = "")

periods <- c("1984-1995", "1988-1995", "1990-1995")
models <- list(fit_8495, fit_8895, fit_9095)

map2_df(models, periods, iv_summary_delta) %>%
  kable(na = "", digits = 3)

period	variable	coefficients	cov_tar_cm3	cov_premsta3	cov_state3	var_alpha	alpha	beta	cov_alpha_beta	var_beta_minus_alpha	se_beta_minus_alpha
1984-1995	tar_cm3	-15.852	26.144			0.005	0.244	1.661	0.010	0.215	0.464
1984-1995	premsta3	3.618	-3.911	1.348
1984-1995	state3	-1.661	1.511	-0.522	0.231
1988-1995	tar_cm3	-11.462	45.058			0.017	0.244	1.320	0.010	0.245	0.495
1988-1995	premsta3	2.554	-4.669	1.411
1988-1995	state3	-1.320	1.869	-0.558	0.248
1990-1995	tar_cm3	-9.974	57.393			0.023	0.205	1.037	0.017	0.225	0.474
1990-1995	premsta3	1.837	-4.658	1.346
1990-1995	state3	-1.037	1.854	-0.529	0.235