Chapter 8. Import Quotas and Export Subsidies

Empirical exercise

This exercise is to reproduce regression results Feenstra (1988a). To complete the exercise, the files “car_7990.dta, truck_7990.dta” should be stored in Chapter-8.

Documentation

Data Description for Feenstra (1988a):

1. car.dta: This STATA file contains car’s various characteristics, such as weight (wght), width (wdth), height (hght), horse power (hs), four-wheel (four), transmission (tran), power steering (ps) and air condition (ac) for 1979-1990. It also includes each model’s sales (quan) and price.
2. truck.dta: This STATA file contains truck’s various characteristics, such as weight (wght), width (wdth), height (hght), horse power (hs), four-wheel (four), transmission (tran), power steering (ps) and air condition (ac) for 1979-1990. It also includes each model’s sale (quan) and price, though sales are missing after 1985.

Exercise 1

Run the programs pindex_c.do, pindex_t.do, unit_value.do to reproduce the price indexes and unit-values for cars and trucks in Table 8.3. What formula is used for the price indexes, and how does this differ from the unit-values?

Feenstra’s code

pindex_c.do

clear
capture log close
log using Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\pindex_c.log,replace

use Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\car_7990,clear
keep year model type price quan

preserve
keep if year==80
keep model type price quan
ren price price_80
ren quan quan_80
sort model
save Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\car_80,replace
restore

sort model
merge model using Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\car_80
keep if _merge==3
drop _merge

sort year model
egen value_80=sum(price_80*quan_80), by(year)
egen value_cp=sum(price*quan_80),by(year)
gen lasp=value_cp/value_80

egen value_c=sum(price*quan), by(year)
egen value_cq=sum(price_80*quan), by(year)
gen pasp=value_c/value_cq
 
gen pindex=(lasp*pasp)^0.5

collapse (mean) pindex, by(year)
list

log close

Output:

. clear

. capture log close

. log using Z:\home\pacha\github\advanced-international-trade\first-edition\Chapte
> r-8\pindex_c.log,replace
(note: file Z:\home\pacha\github\advanced-international-trade\first-edition\Chapte
> r-8\pindex_c.log not found)
----------------------------------------------------------------------------------
      name:  <unnamed>
       log:  Z:\home\pacha\github\advanced-international-trade\first-edition\Chapt
> er-8\pindex_c.log
  log type:  text
 opened on:  19 Jun 2024, 18:40:59

. 
. use Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\ca
> r_7990,clear

. keep year model type price quan

. 
. preserve

. keep if year==80
(260 observations deleted)

. keep model type price quan

. ren price price_80

. ren quan quan_80

. sort model

. save Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\c
> ar_80,replace
file Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\car
> _80.dta saved

. restore

. 
. sort model

. merge model using Z:\home\pacha\github\advanced-international-trade\first-editio
> n\Chapter-8\car_80
(note: you are using old merge syntax; see [R] merge for new syntax)
variable model does not uniquely identify observations in the master data

. keep if _merge==3
(55 observations deleted)

. drop _merge

. 
. sort year model

. egen value_80=sum(price_80*quan_80), by(year)

. egen value_cp=sum(price*quan_80),by(year)

. gen lasp=value_cp/value_80

. 
. egen value_c=sum(price*quan), by(year)

. egen value_cq=sum(price_80*quan), by(year)

. gen pasp=value_c/value_cq

.  
. gen pindex=(lasp*pasp)^0.5

. 
. collapse (mean) pindex, by(year)

. list

     +-----------------+
     | year     pindex |
     |-----------------|
  1. |   79      .9663 |
  2. |   80          1 |
  3. |   81   1.197522 |
  4. |   82   1.289163 |
  5. |   83   1.312988 |
     |-----------------|
  6. |   84   1.389093 |
  7. |   85   1.477987 |
  8. |   86   1.668846 |
  9. |   87   1.885685 |
 10. |   88    2.04798 |
     |-----------------|
 11. |   89   2.082082 |
 12. |   90    2.10851 |
     +-----------------+

. 
. log close
      name:  <unnamed>
       log:  Z:\home\pacha\github\advanced-international-trade\first-edition\Chapt
> er-8\pindex_c.log
  log type:  text
 closed on:  19 Jun 2024, 18:41:01
----------------------------------------------------------------------------------

. 
end of do-file

pindex_t.do

clear
capture log close
log using Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\pindex_t.log,replace

use Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\truck_7990,clear
keep year model type price quan

preserve
keep if year==80
keep model type price quan
ren price price_80
ren quan quan_80
sort model
save Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\truck_80,replace
restore

sort model
merge model using Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\truck_80
keep if _merge==3
drop _merge

sort year model
egen value_80=sum(price_80*quan_80), by(year)
egen value_cp=sum(price*quan_80),by(year)
gen lasp=value_cp/value_80

egen value_c=sum(price*quan), by(year)
egen value_cq=sum(price_80*quan), by(year)
gen pasp=value_c/value_cq
 
gen pindex=(lasp*pasp)^0.5

collapse (mean) pindex, by(year)
list

log close

Output:

. clear

. capture log close

. log using Z:\home\pacha\github\advanced-international-trade\first-edition\Chapte
> r-8\pindex_t.log,replace
(note: file Z:\home\pacha\github\advanced-international-trade\first-edition\Chapte
> r-8\pindex_t.log not found)
----------------------------------------------------------------------------------
      name:  <unnamed>
       log:  Z:\home\pacha\github\advanced-international-trade\first-edition\Chapt
> er-8\pindex_t.log
  log type:  text
 opened on:  19 Jun 2024, 18:59:29

. 
. use Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\tr
> uck_7990,clear

. keep year model type price quan

. 
. preserve

. keep if year==80
(110 observations deleted)

. keep model type price quan

. ren price price_80

. ren quan quan_80

. sort model

. save Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\t
> ruck_80,replace
file Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\tru
> ck_80.dta saved

. restore

. 
. sort model

. merge model using Z:\home\pacha\github\advanced-international-trade\first-editio
> n\Chapter-8\truck_80
(note: you are using old merge syntax; see [R] merge for new syntax)
variable model does not uniquely identify observations in the master data

. keep if _merge==3
(38 observations deleted)

. drop _merge

. 
. sort year model

. egen value_80=sum(price_80*quan_80), by(year)

. egen value_cp=sum(price*quan_80),by(year)

. gen lasp=value_cp/value_80

. 
. egen value_c=sum(price*quan), by(year)

. egen value_cq=sum(price_80*quan), by(year)

. gen pasp=value_c/value_cq
(21 missing values generated)

.  
. gen pindex=(lasp*pasp)^0.5
(21 missing values generated)

. 
. collapse (mean) pindex, by(year)

. list

     +-----------------+
     | year     pindex |
     |-----------------|
  1. |   79    .970215 |
  2. |   80          1 |
  3. |   81   1.278085 |
  4. |   82   1.309353 |
  5. |   83   1.210055 |
     |-----------------|
  6. |   84   1.230847 |
  7. |   85   1.252268 |
  8. |   86          . |
  9. |   87          . |
 10. |   88          . |
     |-----------------|
 11. |   89          . |
 12. |   90          . |
     +-----------------+

. 
. log close
      name:  <unnamed>
       log:  Z:\home\pacha\github\advanced-international-trade\first-edition\Chapt
> er-8\pindex_t.log
  log type:  text
 closed on:  19 Jun 2024, 18:59:31
----------------------------------------------------------------------------------

. 
end of do-file

unit_value.do

clear
capture log close
log using Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\unit_value.log,replace

use Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\car_7990,clear

gen value=price*quan
egen aquan=mean(quan), by(year)
egen avalue=mean(value), by(year)
gen uvalue=avalue/aquan
collapse (mean) uvalue, by(year)
list
clear

use Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\truck_7990,clear
gen value=price*quan
egen aquan=mean(quan), by(year)
egen avalue=mean(value), by(year)
gen uvalue=avalue/aquan
collapse (mean) uvalue, by(year)
list
clear

log close
exit

Output:

. clear

. capture log close

. log using Z:\home\pacha\github\advanced-international-trade\first-edition\Chapte
> r-8\unit_value.log,replace
(note: file Z:\home\pacha\github\advanced-international-trade\first-edition\Chapte
> r-8\unit_value.log not found)
----------------------------------------------------------------------------------
      name:  <unnamed>
       log:  Z:\home\pacha\github\advanced-international-trade\first-edition\Chapt
> er-8\unit_value.log
  log type:  text
 opened on:  19 Jun 2024, 19:13:08

. 
. use Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\ca
> r_7990,clear

. 
. gen value=price*quan

. egen aquan=mean(quan), by(year)

. egen avalue=mean(value), by(year)

. gen uvalue=avalue/aquan

. collapse (mean) uvalue, by(year)

. list

     +-----------------+
     | year     uvalue |
     |-----------------|
  1. |   79   4945.603 |
  2. |   80   5174.757 |
  3. |   81   6210.741 |
  4. |   82   6834.219 |
  5. |   83   7069.203 |
     |-----------------|
  6. |   84   7518.311 |
  7. |   85   8153.146 |
  8. |   86   9391.989 |
  9. |   87   10396.91 |
 10. |   88    10840.6 |
     |-----------------|
 11. |   89   10492.76 |
 12. |   90   11112.68 |
     +-----------------+

. clear

. 
. use Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\tr
> uck_7990,clear

. gen value=price*quan

. egen aquan=mean(quan), by(year)

. egen avalue=mean(value), by(year)

. gen uvalue=avalue/aquan
(45 missing values generated)

. collapse (mean) uvalue, by(year)

. list

     +-----------------+
     | year     uvalue |
     |-----------------|
  1. |   79   4794.177 |
  2. |   80   4937.291 |
  3. |   81   6313.539 |
  4. |   82   6426.264 |
  5. |   83   6134.027 |
     |-----------------|
  6. |   84   6246.728 |
  7. |   85   6249.927 |
  8. |   86          . |
  9. |   87          . |
 10. |   88          . |
     |-----------------|
 11. |   89          . |
 12. |   90          . |
     +-----------------+

. clear

. 
. log close
      name:  <unnamed>
       log:  Z:\home\pacha\github\advanced-international-trade\first-edition\Chapt
> er-8\unit_value.log
  log type:  text
 closed on:  19 Jun 2024, 19:13:10
----------------------------------------------------------------------------------

. exit

end of do-file

My code

pindex_c.do

# Packages ----

library(archive)
library(haven)
library(dplyr)
library(tidyr)

# Extract ----

fzip <- "first-edition/Chapter-8.zip"
dout <- gsub("\\.zip$", "", fzip)

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

# Read and transform ----

fout <- paste0(dout, "/feenstra_88.rds")

if (!file.exists(fout)) {
  feenstra_88 <- list(
    car_7990 = read_dta(paste0(dout, "/car_7990.dta")),
    truck_7990 = read_dta(paste0(dout, "/truck_7990.dta"))
  )

  saveRDS(feenstra_88, fout)
} else {
  feenstra_88 <- readRDS(fout)
}

car_7990 <- feenstra_88$car_7990 %>%
  select(year, model, type, price, quan) %>%
  arrange(year, model)

car_80 <- car_7990 %>%
  filter(year == 80) %>%
  select(model, type, price, quan) %>%
  rename(price_80 = price, quan_80 = quan)

car_7990 <- car_7990 %>%
  inner_join(car_80) %>%
  group_by(year) %>%
  mutate(
    value_80 = sum(price_80 * quan_80),
    value_cp = sum(price * quan_80)
  ) %>%
  ungroup() %>%
  mutate(lasp = value_cp / value_80)

car_7990 <- car_7990 %>%
  group_by(year) %>%
  mutate(
    value_c = sum(price * quan),
    value_cq = sum(price_80 * quan)
  ) %>%
  ungroup() %>%
  mutate(pasp = value_c / value_cq)

car_7990 %>%
  mutate(pindex = sqrt(lasp * pasp)) %>%
  group_by(year) %>%
  summarise(pindex = mean(pindex))

# A tibble: 12 × 2
    year pindex
   <dbl>  <dbl>
 1    79  0.966
 2    80  1    
 3    81  1.20 
 4    82  1.29 
 5    83  1.31 
 6    84  1.39 
 7    85  1.48 
 8    86  1.67 
 9    87  1.89 
10    88  2.05 
11    89  2.08 
12    90  2.11 

pindex_t.do

truck_7990 <- feenstra_88$truck_7990 %>%
  select(year, model, type, price, quan) %>%
  arrange(year, model)

truck_80 <- truck_7990 %>%
  filter(year == 80) %>%
  select(model, type, price, quan) %>%
  rename(price_80 = price, quan_80 = quan)

truck_7990 <- truck_7990 %>%
  inner_join(truck_80) %>%
  group_by(year) %>%
  mutate(
    value_80 = sum(price_80 * quan_80),
    value_cp = sum(price * quan_80)
  ) %>%
  ungroup() %>%
  mutate(lasp = value_cp / value_80)

truck_7990 <- truck_7990 %>%
  group_by(year) %>%
  mutate(
    value_c = sum(price * quan),
    value_cq = sum(price_80 * quan)
  ) %>%
  ungroup() %>%
  mutate(pasp = value_c / value_cq)

truck_7990 %>%
  mutate(pindex = sqrt(lasp * pasp)) %>%
  group_by(year) %>%
  summarise(pindex = mean(pindex))

# A tibble: 12 × 2
    year  pindex
   <dbl>   <dbl>
 1    79   0.970
 2    80   1    
 3    81   1.28 
 4    82   1.31 
 5    83   1.21 
 6    84   1.23 
 7    85   1.25 
 8    86 NaN    
 9    87 NaN    
10    88 NaN    
11    89 NaN    
12    90 NaN    

unit_value.do

car_7990 <- feenstra_88$car_7990 %>%
  mutate(value = price * quan) %>%
  group_by(year) %>%
  mutate(
    aquan = mean(quan),
    avalue = mean(value),
    uvalue = avalue / aquan
  )

truck_7990 <- feenstra_88$truck_7990 %>%
  mutate(value = price * quan) %>%
  group_by(year) %>%
  mutate(
    aquan = mean(quan),
    avalue = mean(value),
    uvalue = avalue / aquan
  )

car_7990 %>%
  group_by(year) %>%
  summarise(uvalue = mean(uvalue))

# A tibble: 12 × 2
    year uvalue
   <dbl>  <dbl>
 1    79  4946.
 2    80  5175.
 3    81  6211.
 4    82  6834.
 5    83  7069.
 6    84  7518.
 7    85  8153.
 8    86  9392.
 9    87 10397.
10    88 10841.
11    89 10493.
12    90 11113.

truck_7990 %>%
  group_by(year) %>%
  summarise(uvalue = mean(uvalue))

# A tibble: 12 × 2
    year uvalue
   <dbl>  <dbl>
 1    79  4794.
 2    80  4937.
 3    81  6314.
 4    82  6426.
 5    83  6134.
 6    84  6247.
 7    85  6250.
 8    86   NaN 
 9    87   NaN 
10    88   NaN 
11    89   NaN 
12    90   NaN 

Exercise 2

Run the program car_reg.do to reproduce the column (1) in Table 8.4, and the program truck_reg.do to reproduce column (2). What weights are being used in the regression, and how does this affect the results?

Feenstra’s code

car_reg.do

clear
capture log close
log using Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\car_reg.log,replace

use Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\car_7990,clear
drop if year>=86

tab year, gen(yd)

program define nlcar
version 7.0
if "`1'"=="?"{
global S_1 "a3 a4 a5 a6 a7 b2 b3 b4 b5 b6 b7 c1 c2 c3 c4 c5 c6 c7 c8"
global a3=1
global a4=1
global a5=1
global a6=1
global a7=1
global b2=.1
global b3=.1
global b4=.1
global b5=.1
global b6=.1
global b7=.1
global c1=.1
global c2=.1
global c3=.1
global c4=.1
global c5=.1
global c6=.1
global c7=.1
global c8=.1
exit
}
replace `1'=$a3*yd3+$a4*yd4+$a5*yd5+$a6*yd6+$a7*yd7/*
*/+exp($b2*yd2+$b3*yd3+$b4*yd4+$b5*yd5+$b6*yd6+$b7*yd7/*
*/+$c1*wght+$c2*wdth+$c3*hght+$c4*hp+$c5*tran+$c6*ps+$c7*ac+$c8)

end

nl car price

gen winv=1/exp(_b[b2]*yd2+_b[b3]*yd3+_b[b4]*yd4+_b[b5]*yd5+_b[b6]*yd6+_b[b7]*yd7/*
*/+_b[c1]*wght+_b[c2]*wdth+_b[c3]*hght+_b[c4]*hp+_b[c5]*tran+_b[c6]*ps+_b[c7]*ac+_b[c8])

gen nprice=price*winv
gen nyd3=yd3*winv
gen nyd4=yd4*winv
gen nyd5=yd5*winv
gen nyd6=yd6*winv
gen nyd7=yd7*winv

program define nlncar
    version 7.0
    if "`1'"=="?"{
        global S_1 "a3 a4 a5 a6 a7 b2 b3 b4 b5 b6 b7 c1 c2 c3 c4 c5 c6 c7 c8"
        global a3=1
        global a4=1
        global a5=1 
        global a6=1
        global a7=1
        global b2=.1    
        global b3=.1
        global b4=.1
        global b5=.1
        global b6=.1    
        global b7=.1
        global c1=.1
        global c2=.1
        global c3=.1
        global c4=.1
        global c5=.1
        global c6=.1
        global c7=.1
        global c8=.1
        exit
    }
    replace `1'=$a3*nyd3+$a4*nyd4+$a5*nyd5+$a6*nyd6+$a7*nyd7/*
*/+winv*exp($b2*yd2+$b3*yd3+$b4*yd4+$b5*yd5+$b6*yd6+$b7*yd7/*
*/+$c1*wght+$c2*wdth+$c3*hght+$c4*hp+$c5*tran+$c6*ps+$c7*ac+$c8)

end

nl ncar nprice
clear
program drop _all
log close
exit

Output:

. clear

. capture log close

. log using Z:\home\pacha\github\advanced-international-trade\first-edition\Chapte
> r-8\car_reg.log,replace
(note: file Z:\home\pacha\github\advanced-international-trade\first-edition\Chapte
> r-8\car_reg.log not found)
----------------------------------------------------------------------------------
      name:  <unnamed>
       log:  Z:\home\pacha\github\advanced-international-trade\first-edition\Chapt
> er-8\car_reg.log
  log type:  text
 opened on:  19 Jun 2024, 19:28:58

. 
. use Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\ca
> r_7990,clear

. drop if year>=86
(105 observations deleted)

. 
. tab year, gen(yd)

       year |      Freq.     Percent        Cum.
------------+-----------------------------------
         79 |         21       11.73       11.73
         80 |         24       13.41       25.14
         81 |         24       13.41       38.55
         82 |         24       13.41       51.96
         83 |         26       14.53       66.48
         84 |         29       16.20       82.68
         85 |         31       17.32      100.00
------------+-----------------------------------
      Total |        179      100.00

. 
. program define nlcar
  1. version 7.0
  2. if "`1'"=="?"{
  3. global S_1 "a3 a4 a5 a6 a7 b2 b3 b4 b5 b6 b7 c1 c2 c3 c4 c5 c6 c7 c8"
  4. global a3=1
  5. global a4=1
  6. global a5=1
  7. global a6=1
  8. global a7=1
  9. global b2=.1
 10. global b3=.1
 11. global b4=.1
 12. global b5=.1
 13. global b6=.1
 14. global b7=.1
 15. global c1=.1
 16. global c2=.1
 17. global c3=.1
 18. global c4=.1
 19. global c5=.1
 20. global c6=.1
 21. global c7=.1
 22. global c8=.1
 23. exit
 24. }
 25. replace `1'=$a3*yd3+$a4*yd4+$a5*yd5+$a6*yd6+$a7*yd7/*
> */+exp($b2*yd2+$b3*yd3+$b4*yd4+$b5*yd5+$b6*yd6+$b7*yd7/*
> */+$c1*wght+$c2*wdth+$c3*hght+$c4*hp+$c5*tran+$c6*ps+$c7*ac+$c8)
 26. 
. end

. 
. nl car price
(obs = 179)

Iteration 0:   residual SS =  1.16e+10
...
Iteration 9:   residual SS =  8.39e+07
Iteration 10:  residual SS =  8.39e+07

      Source |       SS       df       MS            Number of obs =       179
-------------+------------------------------         F( 19,   160) =   1158.52
       Model |  1.1541e+10    19   607414473         Prob > F      =    0.0000
    Residual |    83888568   160   524303.55         R-squared     =    0.9928
-------------+------------------------------         Adj R-squared =    0.9919
       Total |  1.1625e+10   179  64942813.2         Root MSE      =  724.0881
                                                     Res. dev.     =  2845.293
(car)
------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          a3 |  -294.7452   723.3322    -0.41   0.684    -1723.255    1133.765
          a4 |  -304.9631   714.5517    -0.43   0.670    -1716.132    1106.206
          a5 |  -137.3977   700.8446    -0.20   0.845    -1521.497    1246.701
          a6 |   72.87527   695.4052     0.10   0.917    -1300.482    1446.232
          a7 |  -103.4007   742.9475    -0.14   0.889    -1570.649    1363.848
          b2 |   .0099678   .0362994     0.27   0.784      -.06172    .0816555
          b3 |   .1522578   .1022847     1.49   0.139    -.0497444      .35426
          b4 |   .1899382   .0965319     1.97   0.051    -.0007027    .3805792
          b5 |   .1540892   .0959124     1.61   0.110    -.0353283    .3435068
          b6 |    .172972   .0944704     1.83   0.069    -.0135977    .3595417
          b7 |   .2274326   .0945034     2.41   0.017     .0407977    .4140675
          c1 |  -.0007315   .1021984    -0.01   0.994    -.2025632    .2011002
          c2 |   .3681958   .1019742     3.61   0.000     .1668067    .5695849
          c3 |  -.1431584   .0519385    -2.76   0.007    -.2457317    -.040585
          c4 |   .6070451   .0665196     9.13   0.000     .4756756    .7384147
          c5 |   .1315757   .0264479     4.97   0.000     .0793437    .1838078
          c6 |   .0515819   .0218212     2.36   0.019     .0084872    .0946766
          c7 |   .1635465   .0228493     7.16   0.000     .1184213    .2086717
          c8 |    6.73024   .5719055    11.77   0.000     5.600783    7.859697
------------------------------------------------------------------------------
 (SEs, P values, CIs, and correlations are asymptotic approximations)

. 
. gen winv=1/exp(_b[b2]*yd2+_b[b3]*yd3+_b[b4]*yd4+_b[b5]*yd5+_b[b6]*yd6+_b[b7]*yd7
> /*
> */+_b[c1]*wght+_b[c2]*wdth+_b[c3]*hght+_b[c4]*hp+_b[c5]*tran+_b[c6]*ps+_b[c7]*ac
> +_b[c8])

. 
. gen nprice=price*winv

. gen nyd3=yd3*winv

. gen nyd4=yd4*winv

. gen nyd5=yd5*winv

. gen nyd6=yd6*winv

. gen nyd7=yd7*winv

. 
. program define nlncar
  1.         version 7.0
  2.         if "`1'"=="?"{
  3.                 global S_1 "a3 a4 a5 a6 a7 b2 b3 b4 b5 b6 b7 c1 c2 c3 c4 c5 c
> 6 c7 c8"
  4.                 global a3=1
  5.                 global a4=1
  6.                 global a5=1     
  7.                 global a6=1
  8.                 global a7=1
  9.                 global b2=.1    
 10.                 global b3=.1
 11.                 global b4=.1
 12.                 global b5=.1
 13.                 global b6=.1    
 14.                 global b7=.1
 15.                 global c1=.1
 16.                 global c2=.1
 17.                 global c3=.1
 18.                 global c4=.1
 19.                 global c5=.1
 20.                 global c6=.1
 21.                 global c7=.1
 22.                 global c8=.1
 23.                 exit
 24.         }
 25.         replace `1'=$a3*nyd3+$a4*nyd4+$a5*nyd5+$a6*nyd6+$a7*nyd7/*
> */+winv*exp($b2*yd2+$b3*yd3+$b4*yd4+$b5*yd5+$b6*yd6+$b7*yd7/*
> */+$c1*wght+$c2*wdth+$c3*hght+$c4*hp+$c5*tran+$c6*ps+$c7*ac+$c8)
 26. 
. end

. 
. nl ncar nprice
(obs = 179)

Iteration 0:   residual SS =  174.4452
...
Iteration 13:  residual SS =  1.672068
Iteration 14:  residual SS =  1.672068

      Source |       SS       df       MS            Number of obs =       179
-------------+------------------------------         F( 19,   160) =    871.41
       Model |  173.025768    19  9.10661939         Prob > F      =    0.0000
    Residual |  1.67206775   160  .010450423         R-squared     =    0.9904
-------------+------------------------------         Adj R-squared =    0.9893
       Total |  174.697836   179  .975965565         Root MSE      =  .1022273
                                                     Res. dev.     = -328.5451
(ncar)
------------------------------------------------------------------------------
      nprice |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          a3 |   410.4256   619.1744     0.66   0.508    -812.3829    1633.234
          a4 |    378.927   650.2562     0.58   0.561     -905.265    1663.119
          a5 |   770.6115   601.2054     1.28   0.202    -416.7099    1957.933
          a6 |   624.3817   618.9925     1.01   0.315    -598.0676    1846.831
          a7 |  -122.9148   719.4492    -0.17   0.865    -1543.756    1297.927
          b2 |   .0089535   .0309918     0.29   0.773    -.0522522    .0701592
          b3 |   .0474345   .1093808     0.43   0.665    -.1685818    .2634509
          b4 |   .0938457    .108274     0.87   0.387    -.1199848    .3076761
          b5 |   .0195742   .1052628     0.19   0.853    -.1883094    .2274579
          b6 |   .0918745   .1019572     0.90   0.369     -.109481      .29323
          b7 |   .2189293   .1012639     2.16   0.032      .018943    .4189156
          c1 |   .0254744   .1207686     0.21   0.833    -.2130317    .2639805
          c2 |   .3565755   .1083292     3.29   0.001      .142636     .570515
          c3 |  -.0630705   .0554954    -1.14   0.257    -.1726685    .0465275
          c4 |   .6899452   .0852231     8.10   0.000      .521638    .8582524
          c5 |   .1428588   .0244762     5.84   0.000     .0945207    .1911968
          c6 |   .0581011   .0272835     2.13   0.035     .0042188    .1119834
          c7 |   .1473354    .033027     4.46   0.000     .0821103    .2125606
          c8 |   6.328371   .5830815    10.85   0.000     5.176842    7.479899
------------------------------------------------------------------------------
 (SEs, P values, CIs, and correlations are asymptotic approximations)

. clear

. program drop _all

. log close
      name:  <unnamed>
       log:  Z:\home\pacha\github\advanced-international-trade\first-edition\Chapt
> er-8\car_reg.log
  log type:  text
 closed on:  19 Jun 2024, 19:29:06
----------------------------------------------------------------------------------

. exit

end of do-file

My code

truck_reg.do

library(minpack.lm) # for nlsLM()

car_7990 <- feenstra_88$car_7990 %>%
  filter(year < 86) %>%
  mutate(yd = factor(year)) %>%
  group_by(yd) %>%
  mutate(id = row_number()) %>%
  ungroup()

car_7990 %>%
  group_by(yd) %>%
  summarise(freq = n()) %>%
  ungroup() %>%
  mutate(
    percent = freq / sum(freq) * 100,
    cum = cumsum(percent)
  )

# A tibble: 7 × 4
  yd     freq percent   cum
  <fct> <int>   <dbl> <dbl>
1 79       21    11.7  11.7
2 80       24    13.4  25.1
3 81       24    13.4  38.5
4 82       24    13.4  52.0
5 83       26    14.5  66.5
6 84       29    16.2  82.7
7 85       31    17.3 100  

# expand the yd variable to 0/1 columns
# in R, you cannot multiply a factor/categorical variable

car_7990 <- car_7990 %>%
  mutate(yd_ind = as.integer(yd)) %>%
  mutate(yd_ind = as.factor(yd_ind - min(yd_ind) + 1))

car_7990_dummy <- model.matrix(~ yd_ind - 1, data = car_7990)
colnames(car_7990_dummy) <- gsub("_ind", "", colnames(car_7990_dummy))

car_7990 <- car_7990 %>%
  bind_cols(as.data.frame(car_7990_dummy))

# fit the non-linear specification with initial values
# nls() fails, so I use nlsLM() that implements the Levenberg-Marquardt
# algorithm

initial_values <- list(
  a3 = 1, a4 = 1, a5 = 1, a6 = 1, a7 = 1,
  b2 = 0.1, b3 = 0.1, b4 = 0.1, b5 = 0.1, b6 = 0.1, b7 = 0.1,
  c1 = 0.1, c2 = 0.1, c3 = 0.1, c4 = 0.1, c5 = 0.1, c6 = 0.1, c7 = 0.1,
  c8 = 0.1
)

fit <- nlsLM(
  price ~ a3 * yd3 + a4 * yd4 + a5 * yd5 + a6 * yd6 + a7 * yd7 +
    exp(
      b2 * yd2 + b3 * yd3 + b4 * yd4 + b5 * yd5 + b6 * yd6 + b7 * yd7 +
        c1 * wght + c2 * wdth + c3 * hght + c4 * hp + c5 * tran + c6 * ps +
        c7 * ac + c8
    ),
  data = car_7990,
  start = initial_values
)

summary(fit)

Formula: price ~ a3 * yd3 + a4 * yd4 + a5 * yd5 + a6 * yd6 + a7 * yd7 + 
    exp(b2 * yd2 + b3 * yd3 + b4 * yd4 + b5 * yd5 + b6 * yd6 + 
        b7 * yd7 + c1 * wght + c2 * wdth + c3 * hght + c4 * hp + 
        c5 * tran + c6 * ps + c7 * ac + c8)

Parameters:
     Estimate Std. Error t value Pr(>|t|)    
a3 -2.947e+02  7.233e+02  -0.407 0.684236    
a4 -3.049e+02  7.145e+02  -0.427 0.670137    
a5 -1.374e+02  7.008e+02  -0.196 0.844867    
a6  7.293e+01  6.954e+02   0.105 0.916608    
a7 -1.033e+02  7.429e+02  -0.139 0.889554    
b2  9.967e-03  3.630e-02   0.275 0.783991    
b3  1.523e-01  1.023e-01   1.489 0.138586    
b4  1.899e-01  9.653e-02   1.968 0.050842 .  
b5  1.541e-01  9.591e-02   1.607 0.110130    
b6  1.730e-01  9.447e-02   1.831 0.068972 .  
b7  2.274e-01  9.450e-02   2.407 0.017243 *  
c1 -6.998e-04  1.022e-01  -0.007 0.994545    
c2  3.682e-01  1.020e-01   3.610 0.000409 ***
c3 -1.432e-01  5.194e-02  -2.756 0.006522 ** 
c4  6.070e-01  6.652e-02   9.126 2.93e-16 ***
c5  1.316e-01  2.645e-02   4.975 1.67e-06 ***
c6  5.158e-02  2.182e-02   2.364 0.019283 *  
c7  1.635e-01  2.285e-02   7.157 2.81e-11 ***
c8  6.730e+00  5.719e-01  11.768  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 724.1 on 160 degrees of freedom

Number of iterations to convergence: 19 
Achieved convergence tolerance: 1.49e-08

fit_coef <- coef(fit)

car_7990 <- car_7990 %>%
  mutate(
    winv = 1 / exp(fit_coef["b2"] * yd2 + fit_coef["b3"] * yd3 +
      fit_coef["b4"] * yd4 + fit_coef["b5"] * yd5 + fit_coef["b6"] * yd6 +
      fit_coef["b7"] * yd7 + fit_coef["c1"] * wght + fit_coef["c2"] * wdth +
      fit_coef["c3"] * hght + fit_coef["c4"] * hp + fit_coef["c5"] * tran +
      fit_coef["c6"] * ps + fit_coef["c7"] * ac + fit_coef["c8"]),
    nprice = price * winv,
    nyd3 = yd3 * winv,
    nyd4 = yd4 * winv,
    nyd5 = yd5 * winv,
    nyd6 = yd6 * winv,
    nyd7 = yd7 * winv
  )

fit2 <- nlsLM(
  nprice ~ a3 * nyd3 + a4 * nyd4 + a5 * nyd5 + a6 * nyd6 + a7 * nyd7 +
    winv * exp(
      b2 * yd2 + b3 * yd3 + b4 * yd4 + b5 * yd5 + b6 * yd6 + b7 * yd7 +
        c1 * wght + c2 * wdth + c3 * hght + c4 * hp + c5 * tran + c6 * ps +
        c7 * ac + c8
    ),
  data = car_7990,
  start = initial_values,
  # increase the number of iterations to avoid convergence issues
  control = nls.lm.control(maxiter = 100)
)

summary(fit2)

Formula: nprice ~ a3 * nyd3 + a4 * nyd4 + a5 * nyd5 + a6 * nyd6 + a7 * 
    nyd7 + winv * exp(b2 * yd2 + b3 * yd3 + b4 * yd4 + b5 * yd5 + 
    b6 * yd6 + b7 * yd7 + c1 * wght + c2 * wdth + c3 * hght + 
    c4 * hp + c5 * tran + c6 * ps + c7 * ac + c8)

Parameters:
     Estimate Std. Error t value Pr(>|t|)    
a3  4.105e+02  6.192e+02   0.663  0.50834    
a4  3.789e+02  6.503e+02   0.583  0.56087    
a5  7.706e+02  6.012e+02   1.282  0.20176    
a6  6.244e+02  6.190e+02   1.009  0.31465    
a7 -1.229e+02  7.194e+02  -0.171  0.86455    
b2  8.954e-03  3.099e-02   0.289  0.77303    
b3  4.743e-02  1.094e-01   0.434  0.66515    
b4  9.384e-02  1.083e-01   0.867  0.38740    
b5  1.957e-02  1.053e-01   0.186  0.85274    
b6  9.188e-02  1.020e-01   0.901  0.36887    
b7  2.189e-01  1.013e-01   2.162  0.03211 *  
c1  2.548e-02  1.208e-01   0.211  0.83316    
c2  3.566e-01  1.083e-01   3.292  0.00123 ** 
c3 -6.306e-02  5.550e-02  -1.136  0.25748    
c4  6.899e-01  8.522e-02   8.096 1.36e-13 ***
c5  1.429e-01  2.448e-02   5.837 2.88e-08 ***
c6  5.810e-02  2.728e-02   2.130  0.03474 *  
c7  1.473e-01  3.303e-02   4.461 1.53e-05 ***
c8  6.328e+00  5.831e-01  10.853  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.1022 on 160 degrees of freedom

Number of iterations to convergence: 18 
Achieved convergence tolerance: 1.49e-08

Exercise 3

Pooling car and truck data, run system_7985.do to reproduce columns (3) and (4) in Table 8.4 with the constraints specified in equation (8.22). How are these constraints built into the program for the nonlinear regression?

Feenstra’s code

capture log close
log using Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\system_7985.log,replace

use Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\truck_7990,clear
gen ve=2
rename wdth wdth_t
rename hght hght_t
rename weight wght_t
rename hp hp_t
rename four four_t
rename tran tran_t
rename ps ps_t
rename ac ac_t
drop if year>=86

save Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\truck_temp,replace

use Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\car_7990,clear
drop if year>=86
gen ve=1
rename wdth wdth_c
rename hght hght_c
rename wght wght_c
rename hp hp_c
rename four four_c
rename tran tran_c
rename ps ps_c
rename ac ac_c

append using Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\truck_temp

replace wdth_c=0 if wdth_c==.
replace hght_c=0 if hght_c==.
replace wght_c=0 if wght_c==.
replace hp_c=0 if hp_c==.
replace four_c=0 if four_c==.
replace tran_c=0 if tran_c==.
replace ps_c=0 if ps_c==.
replace ac_c=0 if ac_c==.
replace wdth_t=0 if wdth_t==.
replace hght_t=0 if hght_t==.
replace wght_t=0 if wght_t==.
replace hp_t=0 if hp_t==.
replace four_t=0 if four_t==.
replace tran_t=0 if tran_t==.
replace ps_t=0 if ps_t==.
replace ac_t=0 if ac_t==.

tab year, gen(yd)

gen cyd2=yd2
gen tyd2=yd2
replace cyd2=0 if type=="JT"
replace tyd2=0 if type~="JT"

gen cyd3=yd3
gen tyd3=yd3
replace cyd3=0 if type=="JT"
replace tyd3=0 if type~="JT"

gen cyd4=yd4
gen tyd4=yd4
replace cyd4=0 if type=="JT"
replace tyd4=0 if type~="JT"

gen cyd5=yd5
gen tyd5=yd5
replace cyd5=0 if type=="JT"
replace tyd5=0 if type~="JT"

gen cyd6=yd6
gen tyd6=yd6
replace cyd6=0 if type=="JT"
replace tyd6=0 if type~="JT"

gen cyd7=yd7
gen tyd7=yd7
replace cyd7=0 if type=="JT"
replace tyd7=0 if type~="JT"

program define nlct_1
version 7.0
if "`1'"=="?"{
global S_1 "a3 a4 a5 a6 a7 b2 b3 b4 b5 b6 b7 c1 c2 c3 c4 c5 c6 c7 c8 c9 d1 d2 d3 d4 d5 d6 d7 d8"
global a3=1
global a4=1
global a5=1
global a6=1
global a7=1
global b2=.1
global b3=.1
global b4=.1
global b5=.1
global b6=.1
global b7=.1
global c1=.1
global c2=.1
global c3=.1
global c4=.1
global c5=.1
global c6=.1
global c7=.1
global c8=.1
global c9=.1
global d1=.1
global d2=.1
global d3=.1
global d4=.1
global d5=.1
global d6=.1
global d7=.1
global d8=.1
exit
}

replace `1'=$a3*cyd3+$a4*cyd4+$a5*cyd5+$a6*cyd6+$a7*cyd7/*
*/+exp($b2*cyd2+$b3*cyd3+$b4*cyd4+$b5*cyd5+$b6*cyd6+$b7*cyd7/*
*/+$c1*wght_c+$c2*wdth_c+$c3*hght_c+$c4*hp_c+$c5*tran_c+$c6*ps_c+$c7*ac_c/*
*/+$c8)+exp($b2*tyd2+($b3+.16)*tyd3+($b4+.16)*tyd4+($b5+.16)*tyd5+($b6+.16)*tyd6+$c9*tyd7/*
*/+$d1*wght_t+$d2*wdth_t+$d3*hght_t+$d4*hp_t+$d5*tran_t+$d6*ps_t+$d7*four_t+$d8)

end

nl ct_1 price

gen winv=1/exp(_b[b2]*cyd2+_b[b3]*cyd3+_b[b4]*cyd4+_b[b5]*cyd5+_b[b6]*cyd6+_b[b7]*cyd7/*
*/+_b[c1]*wght_c+_b[c2]*wdth_c+_b[c3]*hght_c+_b[c4]*hp_c+_b[c5]*tran_c+_b[c6]*ps_c/*
*/+_b[c7]*ac_c+_b[c8])

replace winv=1/exp((_b[b2]+0.16)*tyd2+(_b[b3]+.16)*tyd3+(_b[b4]+.16)*tyd4/*
*/+(_b[b5]+.16)*tyd5+(_b[b6]+.16)*tyd6+_b[c9]*tyd7/*
*/+_b[d1]*wght_t+_b[d2]*wdth_t+_b[d3]*hght_t+_b[d4]*hp_t/*
*/+_b[d5]*tran_t+_b[d6]*ps_t+_b[d7]*four_t+_b[d8]) if ve==2

gen nprice=price*winv


program define nlct_2
version 7.0
if "`1'"=="?"{
global S_1 "a3 a4 a5 a6 a7 b2 b3 b4 b5 b6 b7 c1 c2 c3 c4 c5 c6 c7 c8 c9 d1 d2 d3 d4 d5 d6 d7 d8"
global a3=1
global a4=1
global a5=1
global a6=1
global a7=1
global b2=.1
global b3=.1
global b4=.1
global b5=.1
global b6=.1
global b7=.1
global c1=.1
global c2=.1
global c3=.1
global c4=.1
global c5=.1
global c6=.1
global c7=.1
global c8=.1
global c9=.1
global d1=.1
global d2=.1
global d3=.1
global d4=.1
global d5=.1
global d6=.1
global d7=.1
global d8=.1
exit
}
replace `1'=winv*($a3*cyd3+$a4*cyd4+$a5*cyd5+$a6*cyd6+$a7*cyd7)/*
*/+winv*exp($b2*cyd2+$b3*cyd3+$b4*cyd4+$b5*cyd5+$b6*cyd6+$b7*cyd7/*
*/+$c1*wght_c+$c2*wdth_c+$c3*hght_c+$c4*hp_c+$c5*tran_c+$c6*ps_c+$c7*ac_c/*
*/+$c8)+winv*exp($b2*tyd2+($b3+.16)*tyd3+($b4+.16)*tyd4+($b5+.16)*tyd5+($b6+.16)*tyd6+$c9*tyd7/*
*/+$d1*wght_t+$d2*wdth_t+$d3*hght_t+$d4*hp_t+$d5*tran_t+$d6*ps_t+$d7*four_t+$d8)

end

nl ct_2 nprice

program drop _all
log close
exit

Output:

. capture log close

. log using Z:\home\pacha\github\advanced-international-trade\first-edition\Chapte
> r-8\system_7985.log,replace
----------------------------------------------------------------------------------
      name:  <unnamed>
       log:  Z:\home\pacha\github\advanced-international-trade\first-edition\Chapt
> er-8\system_7985.log
  log type:  text
 opened on:  19 Jun 2024, 21:59:23

. 
. use Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\tr
> uck_7990,clear

. gen ve=2

. rename wdth wdth_t

. rename hght hght_t

. rename weight wght_t

. rename hp hp_t

. rename four four_t

. rename tran tran_t

. rename ps ps_t

. rename ac ac_t

. drop if year>=86
(45 observations deleted)

. 
. save Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\t
> ruck_temp,replace
file Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\tru
> ck_temp.dta saved

. 
. use Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\ca
> r_7990,clear

. drop if year>=86
(105 observations deleted)

. gen ve=1

. rename wdth wdth_c

. rename hght hght_c

. rename wght wght_c

. rename hp hp_c

. rename four four_c

. rename tran tran_c

. rename ps ps_c

. rename ac ac_c

. 
. append using Z:\home\pacha\github\advanced-international-trade\first-edition\Cha
> pter-8\truck_temp

. 
. replace wdth_c=0 if wdth_c==.
(75 real changes made)

. replace hght_c=0 if hght_c==.
(75 real changes made)

. replace wght_c=0 if wght_c==.
(75 real changes made)

. replace hp_c=0 if hp_c==.
(75 real changes made)

. replace four_c=0 if four_c==.
(75 real changes made)

. replace tran_c=0 if tran_c==.
(75 real changes made)

. replace ps_c=0 if ps_c==.
(75 real changes made)

. replace ac_c=0 if ac_c==.
(75 real changes made)

. replace wdth_t=0 if wdth_t==.
(179 real changes made)

. replace hght_t=0 if hght_t==.
(179 real changes made)

. replace wght_t=0 if wght_t==.
(179 real changes made)

. replace hp_t=0 if hp_t==.
(179 real changes made)

. replace four_t=0 if four_t==.
(179 real changes made)

. replace tran_t=0 if tran_t==.
(179 real changes made)

. replace ps_t=0 if ps_t==.
(179 real changes made)

. replace ac_t=0 if ac_t==.
(179 real changes made)

. 
. tab year, gen(yd)

       year |      Freq.     Percent        Cum.
------------+-----------------------------------
         79 |         31       12.20       12.20
         80 |         34       13.39       25.59
         81 |         35       13.78       39.37
         82 |         35       13.78       53.15
         83 |         36       14.17       67.32
         84 |         40       15.75       83.07
         85 |         43       16.93      100.00
------------+-----------------------------------
      Total |        254      100.00

. 
. gen cyd2=yd2

. gen tyd2=yd2

. replace cyd2=0 if type=="JT"
(8 real changes made)

. replace tyd2=0 if type~="JT"
(26 real changes made)

. 
. gen cyd3=yd3

. gen tyd3=yd3

. replace cyd3=0 if type=="JT"
(9 real changes made)

. replace tyd3=0 if type~="JT"
(26 real changes made)

. 
. gen cyd4=yd4

. gen tyd4=yd4

. replace cyd4=0 if type=="JT"
(9 real changes made)

. replace tyd4=0 if type~="JT"
(26 real changes made)

. 
. gen cyd5=yd5

. gen tyd5=yd5

. replace cyd5=0 if type=="JT"
(7 real changes made)

. replace tyd5=0 if type~="JT"
(29 real changes made)

. 
. gen cyd6=yd6

. gen tyd6=yd6

. replace cyd6=0 if type=="JT"
(7 real changes made)

. replace tyd6=0 if type~="JT"
(33 real changes made)

. 
. gen cyd7=yd7

. gen tyd7=yd7

. replace cyd7=0 if type=="JT"
(7 real changes made)

. replace tyd7=0 if type~="JT"
(36 real changes made)

. 
. program define nlct_1
  1. version 7.0
  2. if "`1'"=="?"{
  3. global S_1 "a3 a4 a5 a6 a7 b2 b3 b4 b5 b6 b7 c1 c2 c3 c4 c5 c6 c7 c8 c9 d1 d2
>  d3 d4 d5 d6 d7 d8"
  4. global a3=1
  5. global a4=1
  6. global a5=1
  7. global a6=1
  8. global a7=1
  9. global b2=.1
 10. global b3=.1
 11. global b4=.1
 12. global b5=.1
 13. global b6=.1
 14. global b7=.1
 15. global c1=.1
 16. global c2=.1
 17. global c3=.1
 18. global c4=.1
 19. global c5=.1
 20. global c6=.1
 21. global c7=.1
 22. global c8=.1
 23. global c9=.1
 24. global d1=.1
 25. global d2=.1
 26. global d3=.1
 27. global d4=.1
 28. global d5=.1
 29. global d6=.1
 30. global d7=.1
 31. global d8=.1
 32. exit
 33. }
 34. 
. replace `1'=$a3*cyd3+$a4*cyd4+$a5*cyd5+$a6*cyd6+$a7*cyd7/*
> */+exp($b2*cyd2+$b3*cyd3+$b4*cyd4+$b5*cyd5+$b6*cyd6+$b7*cyd7/*
> */+$c1*wght_c+$c2*wdth_c+$c3*hght_c+$c4*hp_c+$c5*tran_c+$c6*ps_c+$c7*ac_c/*
> */+$c8)+exp($b2*tyd2+($b3+.16)*tyd3+($b4+.16)*tyd4+($b5+.16)*tyd5+($b6+.16)*tyd6
> +$c9*tyd7/*
> */+$d1*wght_t+$d2*wdth_t+$d3*hght_t+$d4*hp_t+$d5*tran_t+$d6*ps_t+$d7*four_t+$d8)
 35. 
. end

. 
. nl ct_1 price
(obs = 254)

Iteration 0:   residual SS =  1.51e+10
...
Iteration 24:  residual SS =  1.01e+08
Iteration 25:  residual SS =  1.01e+08

      Source |       SS       df       MS            Number of obs =       254
-------------+------------------------------         F( 28,   226) =   1210.09
       Model |  1.5069e+10    28   538194036         Prob > F      =    0.0000
    Residual |   100515047   226  444756.844         R-squared     =    0.9934
-------------+------------------------------         Adj R-squared =    0.9926
       Total |  1.5170e+10   254  59724204.9         Root MSE      =  666.9009
                                                     Res. dev.     =  3994.496
(ct_1)
------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          a3 |   254.0918   317.1045     0.80   0.424    -370.7678    878.9513
          a4 |   505.1058   325.6388     1.55   0.122    -136.5708    1146.782
          a5 |   708.9466   317.3172     2.23   0.026       83.668    1334.225
          a6 |   1082.054   322.4415     3.36   0.001     446.6773     1717.43
          a7 |   1063.014   373.9703     2.84   0.005     326.0995    1799.929
          b2 |   .0040633   .0329008     0.12   0.902    -.0607683    .0688948
          b3 |   .0756038    .049061     1.54   0.125    -.0210716    .1722792
          b4 |   .0828575   .0490467     1.69   0.093    -.0137897    .1795048
          b5 |   .0327776    .050707     0.65   0.519    -.0671415    .1326967
          b6 |   .0351224   .0514768     0.68   0.496    -.0663135    .1365582
          b7 |   .0825554   .0557608     1.48   0.140    -.0273221    .1924329
          c1 |   .0326037   .1117298     0.29   0.771    -.1875618    .2527691
          c2 |    .385946   .1204171     3.21   0.002     .1486621    .6232299
          c3 |  -.1929238   .0568197    -3.40   0.001     -.304888   -.0809596
          c4 |    .715212   .0736084     9.72   0.000     .5701655    .8602585
          c5 |   .1578585     .03381     4.67   0.000     .0912354    .2244816
          c6 |   .0641097   .0247061     2.59   0.010     .0154259    .1127934
          c7 |   .1829447   .0242773     7.54   0.000     .1351059    .2307836
          c8 |   6.599831   .7305317     9.03   0.000     5.160306    8.039356
          c9 |   .1171992   .0634238     1.85   0.066    -.0077785    .2421769
          d1 |   .4917133   .0795807     6.18   0.000     .3348983    .6485283
          d2 |   .2622177   .1757206     1.49   0.137    -.0840426    .6084779
          d3 |  -.0451278   .0677055    -0.67   0.506    -.1785426     .088287
          d4 |   .3030767   .1701249     1.78   0.076    -.0321571    .6383106
          d5 |   .0397822   .0362731     1.10   0.274    -.0316947     .111259
          d6 |   .0967659   .0501832     1.93   0.055    -.0021208    .1956526
          d7 |   .3052359   .0715711     4.26   0.000     .1642038     .446268
          d8 |   6.299805   .9622249     6.55   0.000     4.403726    8.195885
------------------------------------------------------------------------------
 (SEs, P values, CIs, and correlations are asymptotic approximations)

. 
. gen winv=1/exp(_b[b2]*cyd2+_b[b3]*cyd3+_b[b4]*cyd4+_b[b5]*cyd5+_b[b6]*cyd6+_b[b7
> ]*cyd7/*
> */+_b[c1]*wght_c+_b[c2]*wdth_c+_b[c3]*hght_c+_b[c4]*hp_c+_b[c5]*tran_c+_b[c6]*ps
> _c/*
> */+_b[c7]*ac_c+_b[c8])

. 
. replace winv=1/exp((_b[b2]+0.16)*tyd2+(_b[b3]+.16)*tyd3+(_b[b4]+.16)*tyd4/*
> */+(_b[b5]+.16)*tyd5+(_b[b6]+.16)*tyd6+_b[c9]*tyd7/*
> */+_b[d1]*wght_t+_b[d2]*wdth_t+_b[d3]*hght_t+_b[d4]*hp_t/*
> */+_b[d5]*tran_t+_b[d6]*ps_t+_b[d7]*four_t+_b[d8]) if ve==2
(75 real changes made)

. 
. gen nprice=price*winv

. 
. 
. program define nlct_2
  1. version 7.0
  2. if "`1'"=="?"{
  3. global S_1 "a3 a4 a5 a6 a7 b2 b3 b4 b5 b6 b7 c1 c2 c3 c4 c5 c6 c7 c8 c9 d1 d2
>  d3 d4 d5 d6 d7 d8"
  4. global a3=1
  5. global a4=1
  6. global a5=1
  7. global a6=1
  8. global a7=1
  9. global b2=.1
 10. global b3=.1
 11. global b4=.1
 12. global b5=.1
 13. global b6=.1
 14. global b7=.1
 15. global c1=.1
 16. global c2=.1
 17. global c3=.1
 18. global c4=.1
 19. global c5=.1
 20. global c6=.1
 21. global c7=.1
 22. global c8=.1
 23. global c9=.1
 24. global d1=.1
 25. global d2=.1
 26. global d3=.1
 27. global d4=.1
 28. global d5=.1
 29. global d6=.1
 30. global d7=.1
 31. global d8=.1
 32. exit
 33. }
 34. replace `1'=winv*($a3*cyd3+$a4*cyd4+$a5*cyd5+$a6*cyd6+$a7*cyd7)/*
> */+winv*exp($b2*cyd2+$b3*cyd3+$b4*cyd4+$b5*cyd5+$b6*cyd6+$b7*cyd7/*
> */+$c1*wght_c+$c2*wdth_c+$c3*hght_c+$c4*hp_c+$c5*tran_c+$c6*ps_c+$c7*ac_c/*
> */+$c8)+winv*exp($b2*tyd2+($b3+.16)*tyd3+($b4+.16)*tyd4+($b5+.16)*tyd5+($b6+.16)
> *tyd6+$c9*tyd7/*
> */+$d1*wght_t+$d2*wdth_t+$d3*hght_t+$d4*hp_t+$d5*tran_t+$d6*ps_t+$d7*four_t+$d8)
 35. 
. end

. 
. nl ct_2 nprice
(obs = 254)

Iteration 0:   residual SS =  353.5865
...
Iteration 20:  residual SS =  2.957295
Iteration 21:  residual SS =  2.957295

      Source |       SS       df       MS            Number of obs =       254
-------------+------------------------------         F( 28,   226) =    958.75
       Model |  351.277591    28  12.5456282         Prob > F      =    0.0000
    Residual |  2.95729549   226  .013085378         R-squared     =    0.9917
-------------+------------------------------         Adj R-squared =    0.9906
       Total |  354.234886   254  1.39462554         Root MSE      =  .1143913
                                                     Res. dev.     = -410.2562
(ct_2)
------------------------------------------------------------------------------
      nprice |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          a3 |   367.9829    239.059     1.54   0.125    -103.0867    839.0525
          a4 |    600.553   254.2261     2.36   0.019     99.59628     1101.51
          a5 |   887.9399   243.5428     3.65   0.000     408.0348    1367.845
          a6 |   1104.433   251.0245     4.40   0.000     609.7847     1599.08
          a7 |   855.7993   366.2444     2.34   0.020     134.1088     1577.49
          b2 |   .0130387   .0303131     0.43   0.668    -.0466937    .0727711
          b3 |   .0674477   .0425176     1.59   0.114     -.016334    .1512294
          b4 |   .0701234   .0441821     1.59   0.114    -.0169382     .157185
          b5 |  -.0005627   .0470779    -0.01   0.990    -.0933305    .0922051
          b6 |   .0179989   .0473905     0.38   0.704    -.0753848    .1113826
          b7 |   .1007712   .0641587     1.57   0.118    -.0256545    .2271969
          c1 |   .0492474   .1311096     0.38   0.708    -.2091061     .307601
          c2 |   .3908689   .1383663     2.82   0.005     .1182159     .663522
          c3 |  -.0618204   .0611492    -1.01   0.313    -.1823158     .058675
          c4 |   .8103277   .1038045     7.81   0.000     .6057792    1.014876
          c5 |   .1779391   .0355273     5.01   0.000     .1079319    .2479463
          c6 |   .0693687   .0304968     2.27   0.024     .0092743     .129463
          c7 |   .1567051   .0360384     4.35   0.000     .0856908    .2277193
          c8 |   5.839036   .8621144     6.77   0.000     4.140226    7.537847
          c9 |   .1059852   .0550545     1.93   0.055    -.0025007    .2144711
          d1 |   .4759918   .1172145     4.06   0.000     .2450187    .7069649
          d2 |   .2120021   .1419991     1.49   0.137    -.0678094    .4918136
          d3 |  -.0270369    .074052    -0.37   0.715    -.1729575    .1188837
          d4 |     .24435   .1516866     1.61   0.109    -.0545508    .5432508
          d5 |   .0530065   .0356148     1.49   0.138     -.017173     .123186
          d6 |   .0575178   .0639555     0.90   0.369    -.0685076    .1835431
          d7 |   .2971909   .0566882     5.24   0.000      .185486    .4088959
          d8 |   6.630805   .7652819     8.66   0.000     5.122804    8.138805
------------------------------------------------------------------------------
 (SEs, P values, CIs, and correlations are asymptotic approximations)

. 
. program drop _all

. log close
      name:  <unnamed>
       log:  Z:\home\pacha\github\advanced-international-trade\first-edition\Chapt
> er-8\system_7985.log
  log type:  text
 closed on:  19 Jun 2024, 21:59:28
----------------------------------------------------------------------------------

. exit

end of do-file

My code

truck_7990 <- feenstra_88$truck_7990 %>%
  filter(year < 86) %>%
  mutate(ve = 2) %>%
  rename(
    wdth_t = wdth, hght_t = hght, wght_t = weight, hp_t = hp, four_t = four,
    tran_t = tran, ps_t = ps, ac_t = ac
  )

car_7990 <- feenstra_88$car_7990 %>%
  filter(year < 86) %>%
  mutate(ve = 1) %>%
  rename(
    wdth_c = wdth, hght_c = hght, wght_c = wght, hp_c = hp, four_c = four,
    tran_c = tran, ps_c = ps, ac_c = ac
  )

truck_7990 <- truck_7990 %>%
  bind_rows(car_7990) %>%
  mutate(
    wdth_c = ifelse(is.na(wdth_c), 0, wdth_c),
    hght_c = ifelse(is.na(hght_c), 0, hght_c),
    wght_c = ifelse(is.na(wght_c), 0, wght_c),
    hp_c = ifelse(is.na(hp_c), 0, hp_c),
    four_c = ifelse(is.na(four_c), 0, four_c),
    tran_c = ifelse(is.na(tran_c), 0, tran_c),
    ps_c = ifelse(is.na(ps_c), 0, ps_c),
    ac_c = ifelse(is.na(ac_c), 0, ac_c),
    wdth_t = ifelse(is.na(wdth_t), 0, wdth_t),
    hght_t = ifelse(is.na(hght_t), 0, hght_t),
    wght_t = ifelse(is.na(wght_t), 0, wght_t),
    hp_t = ifelse(is.na(hp_t), 0, hp_t),
    four_t = ifelse(is.na(four_t), 0, four_t),
    tran_t = ifelse(is.na(tran_t), 0, tran_t),
    ps_t = ifelse(is.na(ps_t), 0, ps_t),
    ac_t = ifelse(is.na(ac_t), 0, ac_t)
  )

truck_7990 %>%
  group_by(year) %>%
  summarise(freq = n()) %>%
  ungroup() %>%
  mutate(
    percent = freq / sum(freq) * 100,
    cum = cumsum(percent)
  )

# A tibble: 7 × 4
   year  freq percent   cum
  <dbl> <int>   <dbl> <dbl>
1    79    31    12.2  12.2
2    80    34    13.4  25.6
3    81    35    13.8  39.4
4    82    35    13.8  53.1
5    83    36    14.2  67.3
6    84    40    15.7  83.1
7    85    43    16.9 100  

# expand the yd variable

truck_7990 <- truck_7990 %>%
  mutate(yd = as.factor(year - min(year) + 1))

truck_7990_dummy <- model.matrix(~ yd - 1, data = truck_7990)

truck_7990 <- truck_7990 %>%
  bind_cols(as.data.frame(truck_7990_dummy))

# generate the cyd and tyd variables

truck_7990 <- truck_7990 %>%
  mutate(
    cyd2 = case_when(type == "JT" ~ 0, TRUE ~ yd2),
    tyd2 = case_when(type != "JT" ~ 0, TRUE ~ yd2),
    cyd3 = case_when(type == "JT" ~ 0, TRUE ~ yd3),
    tyd3 = case_when(type != "JT" ~ 0, TRUE ~ yd3),
    cyd4 = case_when(type == "JT" ~ 0, TRUE ~ yd4),
    tyd4 = case_when(type != "JT" ~ 0, TRUE ~ yd4),
    cyd5 = case_when(type == "JT" ~ 0, TRUE ~ yd5),
    tyd5 = case_when(type != "JT" ~ 0, TRUE ~ yd5),
    cyd6 = case_when(type == "JT" ~ 0, TRUE ~ yd6),
    tyd6 = case_when(type != "JT" ~ 0, TRUE ~ yd6),
    cyd7 = case_when(type == "JT" ~ 0, TRUE ~ yd7),
    tyd7 = case_when(type != "JT" ~ 0, TRUE ~ yd7)
  )

# fit the models

initial_values <- list(
  a3 = 1, a4 = 1, a5 = 1, a6 = 1, a7 = 1,
  b2 = 0.1, b3 = 0.1, b4 = 0.1, b5 = 0.1, b6 = 0.1, b7 = 0.1,
  c1 = 0.1, c2 = 0.1, c3 = 0.1, c4 = 0.1, c5 = 0.1, c6 = 0.1, c7 = 0.1,
  c8 = 0.1, c9 = 0.1,
  d1 = 0.1, d2 = 0.1, d3 = 0.1, d4 = 0.1, d5 = 0.1, d6 = 0.1, d7 = 0.1,
  d8 = 0.1
)

fit <- nlsLM(
  price ~ a3 * cyd3 + a4 * cyd4 + a5 * cyd5 + a6 * cyd6 + a7 * cyd7 +
    exp(b2 * cyd2 + b3 * cyd3 + b4 * cyd4 + b5 * cyd5 + b6 * cyd6 + b7 * cyd7 +
      c1 * wght_c + c2 * wdth_c + c3 * hght_c + c4 * hp_c + c5 * tran_c +
      c6 * ps_c + c7 * ac_c + c8) +
    exp(b2 * tyd2 + (b3 + 0.16) * tyd3 + (b4 + 0.16) * tyd4 +
      (b5 + 0.16) * tyd5 + (b6 + 0.16) * tyd6 + c9 * tyd7 +
      d1 * wght_t + d2 * wdth_t + d3 * hght_t + d4 * hp_t + d5 * tran_t +
      d6 * ps_t + d7 * four_t + d8),
  data = truck_7990,
  start = initial_values
)

summary(fit)

Formula: price ~ a3 * cyd3 + a4 * cyd4 + a5 * cyd5 + a6 * cyd6 + a7 * 
    cyd7 + exp(b2 * cyd2 + b3 * cyd3 + b4 * cyd4 + b5 * cyd5 + 
    b6 * cyd6 + b7 * cyd7 + c1 * wght_c + c2 * wdth_c + c3 * 
    hght_c + c4 * hp_c + c5 * tran_c + c6 * ps_c + c7 * ac_c + 
    c8) + exp(b2 * tyd2 + (b3 + 0.16) * tyd3 + (b4 + 0.16) * 
    tyd4 + (b5 + 0.16) * tyd5 + (b6 + 0.16) * tyd6 + c9 * tyd7 + 
    d1 * wght_t + d2 * wdth_t + d3 * hght_t + d4 * hp_t + d5 * 
    tran_t + d6 * ps_t + d7 * four_t + d8)

Parameters:
     Estimate Std. Error t value Pr(>|t|)    
a3  2.542e+02  3.171e+02   0.802 0.423598    
a4  5.052e+02  3.256e+02   1.552 0.122150    
a5  7.090e+02  3.173e+02   2.235 0.026415 *  
a6  1.082e+03  3.224e+02   3.356 0.000926 ***
a7  1.063e+03  3.739e+02   2.843 0.004876 ** 
b2  4.065e-03  3.290e-02   0.124 0.901779    
b3  7.559e-02  4.906e-02   1.541 0.124732    
b4  8.284e-02  4.904e-02   1.689 0.092555 .  
b5  3.276e-02  5.070e-02   0.646 0.518840    
b6  3.510e-02  5.147e-02   0.682 0.495934    
b7  8.254e-02  5.576e-02   1.480 0.140197    
c1  3.261e-02  1.117e-01   0.292 0.770715    
c2  3.860e-01  1.204e-01   3.205 0.001545 ** 
c3 -1.929e-01  5.683e-02  -3.395 0.000811 ***
c4  7.152e-01  7.362e-02   9.715  < 2e-16 ***
c5  1.579e-01  3.382e-02   4.668 5.21e-06 ***
c6  6.412e-02  2.471e-02   2.595 0.010082 *  
c7  1.830e-01  2.428e-02   7.535 1.16e-12 ***
c8  6.599e+00  7.307e-01   9.032  < 2e-16 ***
c9  1.172e-01  6.342e-02   1.848 0.065932 .  
d1  4.917e-01  7.958e-02   6.179 2.97e-09 ***
d2  2.621e-01  1.757e-01   1.492 0.137107    
d3 -4.513e-02  6.770e-02  -0.667 0.505752    
d4  3.031e-01  1.701e-01   1.782 0.076158 .  
d5  3.978e-02  3.627e-02   1.097 0.273899    
d6  9.676e-02  5.018e-02   1.928 0.055072 .  
d7  3.052e-01  7.156e-02   4.265 2.94e-05 ***
d8  6.300e+00  9.620e-01   6.549 3.85e-10 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 666.9 on 226 degrees of freedom

Number of iterations to convergence: 30 
Achieved convergence tolerance: 1.49e-08

truck_7990 <- truck_7990 %>%
  mutate(
    winv = case_when(
      ve == 1 ~ 1 / exp(coef(fit)["b2"] * cyd2 + coef(fit)["b3"] * cyd3 +
        coef(fit)["b4"] * cyd4 + coef(fit)["b5"] * cyd5 +
        coef(fit)["b6"] * cyd6 + coef(fit)["b7"] * cyd7 +
        coef(fit)["c1"] * wght_c + coef(fit)["c2"] * wdth_c +
        coef(fit)["c3"] * hght_c + coef(fit)["c4"] * hp_c +
        coef(fit)["c5"] * tran_c + coef(fit)["c6"] * ps_c +
        coef(fit)["c7"] * ac_c + coef(fit)["c8"]),
      ve == 2 ~ 1 / exp((coef(fit)["b2"] + 0.16) * tyd2 +
        (coef(fit)["b3"] + 0.16) * tyd3 + (coef(fit)["b4"] + 0.16) * tyd4 +
        (coef(fit)["b5"] + 0.16) * tyd5 + (coef(fit)["b6"] + 0.16) * tyd6 +
        coef(fit)["c9"] * tyd7 + coef(fit)["d1"] * wght_t +
        coef(fit)["d2"] * wdth_t + coef(fit)["d3"] * hght_t +
        coef(fit)["d4"] * hp_t + coef(fit)["d5"] * tran_t +
        coef(fit)["d6"] * ps_t + coef(fit)["d7"] * four_t +
        coef(fit)["d8"])
    ),
    nprice = price * winv
  )

fit2 <- nlsLM(
  nprice ~ winv * (a3 * cyd3 + a4 * cyd4 + a5 * cyd5 + a6 * cyd6 + a7 * cyd7) +
    winv * exp(b2 * cyd2 + b3 * cyd3 + b4 * cyd4 + b5 * cyd5 + b6 * cyd6 +
      b7 * cyd7 + c1 * wght_c + c2 * wdth_c + c3 * hght_c + c4 * hp_c +
      c5 * tran_c + c6 * ps_c + c7 * ac_c + c8) +
    winv * exp(b2 * tyd2 + (b3 + 0.16) * tyd3 + (b4 + 0.16) * tyd4 +
      (b5 + 0.16) * tyd5 + (b6 + 0.16) * tyd6 + c9 * tyd7 + d1 * wght_t +
      d2 * wdth_t + d3 * hght_t + d4 * hp_t + d5 * tran_t + d6 * ps_t +
      d7 * four_t + d8),
  data = truck_7990,
  start = initial_values
)

summary(fit2)

Formula: nprice ~ winv * (a3 * cyd3 + a4 * cyd4 + a5 * cyd5 + a6 * cyd6 + 
    a7 * cyd7) + winv * exp(b2 * cyd2 + b3 * cyd3 + b4 * cyd4 + 
    b5 * cyd5 + b6 * cyd6 + b7 * cyd7 + c1 * wght_c + c2 * wdth_c + 
    c3 * hght_c + c4 * hp_c + c5 * tran_c + c6 * ps_c + c7 * 
    ac_c + c8) + winv * exp(b2 * tyd2 + (b3 + 0.16) * tyd3 + 
    (b4 + 0.16) * tyd4 + (b5 + 0.16) * tyd5 + (b6 + 0.16) * tyd6 + 
    c9 * tyd7 + d1 * wght_t + d2 * wdth_t + d3 * hght_t + d4 * 
    hp_t + d5 * tran_t + d6 * ps_t + d7 * four_t + d8)

Parameters:
     Estimate Std. Error t value Pr(>|t|)    
a3  3.679e+02  2.391e+02   1.539 0.125219    
a4  6.005e+02  2.543e+02   2.362 0.019041 *  
a5  8.879e+02  2.436e+02   3.645 0.000332 ***
a6  1.104e+03  2.511e+02   4.399 1.68e-05 ***
a7  8.556e+02  3.663e+02   2.336 0.020379 *  
b2  1.304e-02  3.031e-02   0.430 0.667488    
b3  6.745e-02  4.252e-02   1.586 0.114086    
b4  7.013e-02  4.419e-02   1.587 0.113886    
b5 -5.484e-04  4.708e-02  -0.012 0.990718    
b6  1.801e-02  4.740e-02   0.380 0.704268    
b7  1.008e-01  6.416e-02   1.571 0.117554    
c1  4.925e-02  1.311e-01   0.376 0.707523    
c2  3.908e-01  1.383e-01   2.825 0.005153 ** 
c3 -6.182e-02  6.114e-02  -1.011 0.313088    
c4  8.103e-01  1.038e-01   7.807 2.17e-13 ***
c5  1.779e-01  3.552e-02   5.009 1.10e-06 ***
c6  6.936e-02  3.049e-02   2.275 0.023864 *  
c7  1.567e-01  3.604e-02   4.348 2.08e-05 ***
c8  5.839e+00  8.619e-01   6.775 1.07e-10 ***
c9  1.060e-01  5.506e-02   1.925 0.055494 .  
d1  4.760e-01  1.172e-01   4.060 6.76e-05 ***
d2  2.121e-01  1.420e-01   1.493 0.136773    
d3 -2.704e-02  7.406e-02  -0.365 0.715380    
d4  2.443e-01  1.517e-01   1.611 0.108659    
d5  5.301e-02  3.562e-02   1.488 0.138112    
d6  5.751e-02  6.396e-02   0.899 0.369534    
d7  2.972e-01  5.670e-02   5.242 3.64e-07 ***
d8  6.630e+00  7.655e-01   8.661 8.98e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.1144 on 226 degrees of freedom

Number of iterations to convergence: 31 
Achieved convergence tolerance: 1.49e-08

Exercise 4

Run the programs unit_quality.do, qindex_c.do, qindex_t.do to reproduce the quality indexes and unit-qualities for cars and trucks in Table 8.3. What formula is used for the quality of each model and the quality indexes, and how does this differ from the unit-quality?

Feenstra’s code

unit_quality.do

capture log close
log using Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\unit_quality.log,replace

use Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\truck_7990,clear
drop if year>=86
gen ve=2
rename quan quan_t
rename wdth wdth_t
rename hght hght_t
rename weight wght_t
rename hp hp_t
rename four four_t
rename tran tran_t
rename ps ps_t
rename ac ac_t

save Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\truck_temp,replace

use Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\car_7990,clear
drop if year>=86
gen ve=1
rename quan quan_c
rename wdth wdth_c
rename hght hght_c
rename wght wght_c
rename hp hp_c
rename four four_c
rename tran tran_c
rename ps ps_c
rename ac ac_c

append using Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\truck_temp

replace wdth_c=0 if wdth_c==.
replace hght_c=0 if hght_c==.
replace wght_c=0 if wght_c==.
replace hp_c=0 if hp_c==.
replace four_c=0 if four_c==.
replace tran_c=0 if tran_c==.
replace ps_c=0 if ps_c==.
replace ac_c=0 if ac_c==.
replace wdth_t=0 if wdth_t==.
replace hght_t=0 if hght_t==.
replace wght_t=0 if wght_t==.
replace hp_t=0 if hp_t==.
replace four_t=0 if four_t==.
replace tran_t=0 if tran_t==.
replace ps_t=0 if ps_t==.
replace ac_t=0 if ac_t==.

tab year, gen(yd)

gen cyd2=yd2
gen tyd2=yd2
replace cyd2=0 if type=="JT"
replace tyd2=0 if type~="JT"

gen cyd3=yd3
gen tyd3=yd3
replace cyd3=0 if type=="JT"
replace tyd3=0 if type~="JT"

gen cyd4=yd4
gen tyd4=yd4
replace cyd4=0 if type=="JT"
replace tyd4=0 if type~="JT"

gen cyd5=yd5
gen tyd5=yd5
replace cyd5=0 if type=="JT"
replace tyd5=0 if type~="JT"

gen cyd6=yd6
gen tyd6=yd6
replace cyd6=0 if type=="JT"
replace tyd6=0 if type~="JT"

gen cyd7=yd7
gen tyd7=yd7
replace cyd7=0 if type=="JT"
replace tyd7=0 if type~="JT"

program define nlct_1
version 7.0
if "`1'"=="?"{
global S_1 "a3 a4 a5 a6 a7 b2 b3 b4 b5 b6 b7 c1 c2 c3 c4 c5 c6 c7 c8 c9 d1 d2 d3 d4 d5 d6 d7 d8"
global a3=1
global a4=1
global a5=1
global a6=1
global a7=1
global b2=.1
global b3=.1
global b4=.1
global b5=.1
global b6=.1
global b7=.1
global c1=.1
global c2=.1
global c3=.1
global c4=.1
global c5=.1
global c6=.1
global c7=.1
global c8=.1
global c9=.1
global d1=.1
global d2=.1
global d3=.1
global d4=.1
global d5=.1
global d6=.1
global d7=.1
global d8=.1
exit
}

replace `1'=$a3*cyd3+$a4*cyd4+$a5*cyd5+$a6*cyd6+$a7*cyd7/*
*/+exp($b2*cyd2+$b3*cyd3+$b4*cyd4+$b5*cyd5+$b6*cyd6+$b7*cyd7/*
*/+$c1*wght_c+$c2*wdth_c+$c3*hght_c+$c4*hp_c+$c5*tran_c+$c6*ps_c+$c7*ac_c/*
*/+$c8)+exp($b2*tyd2+($b3+.16)*tyd3+($b4+.16)*tyd4+($b5+.16)*tyd5+($b6+.16)*tyd6+$c9*tyd7/*
*/+$d1*wght_t+$d2*wdth_t+$d3*hght_t+$d4*hp_t+$d5*tran_t+$d6*ps_t+$d7*four_t+$d8)

end

nl ct_1 price

gen winv=1/exp(_b[b2]*cyd2+_b[b3]*cyd3+_b[b4]*cyd4+_b[b5]*cyd5+_b[b6]*cyd6+_b[b7]*cyd7/*
*/+_b[c1]*wght_c+_b[c2]*wdth_c+_b[c3]*hght_c+_b[c4]*hp_c+_b[c5]*tran_c+_b[c6]*ps_c/*
*/+_b[c7]*ac_c+_b[c8])

replace winv=1/exp((_b[b2]+0.16)*tyd2+(_b[b3]+.16)*tyd3+(_b[b4]+.16)*tyd4/*
*/+(_b[b5]+.16)*tyd5+(_b[b6]+.16)*tyd6+_b[c9]*tyd7/*
*/+_b[d1]*wght_t+_b[d2]*wdth_t+_b[d3]*hght_t+_b[d4]*hp_t/*
*/+_b[d5]*tran_t+_b[d6]*ps_t+_b[d7]*four_t+_b[d8]) if ve==2

gen nprice=price*winv


program define nlct_2
version 7.0
if "`1'"=="?"{
global S_1 "a3 a4 a5 a6 a7 b2 b3 b4 b5 b6 b7 c1 c2 c3 c4 c5 c6 c7 c8 c9 d1 d2 d3 d4 d5 d6 d7 d8"
global a3=1
global a4=1
global a5=1
global a6=1
global a7=1
global b2=.1
global b3=.1
global b4=.1
global b5=.1
global b6=.1
global b7=.1
global c1=.1
global c2=.1
global c3=.1
global c4=.1
global c5=.1
global c6=.1
global c7=.1
global c8=.1
global c9=.1
global d1=.1
global d2=.1
global d3=.1
global d4=.1
global d5=.1
global d6=.1
global d7=.1
global d8=.1
exit
}
replace `1'=winv*($a3*cyd3+$a4*cyd4+$a5*cyd5+$a6*cyd6+$a7*cyd7)/*
*/+winv*exp($b2*cyd2+$b3*cyd3+$b4*cyd4+$b5*cyd5+$b6*cyd6+$b7*cyd7/*
*/+$c1*wght_c+$c2*wdth_c+$c3*hght_c+$c4*hp_c+$c5*tran_c+$c6*ps_c+$c7*ac_c/*
*/+$c8)+winv*exp($b2*tyd2+($b3+.16)*tyd3+($b4+.16)*tyd4+($b5+.16)*tyd5+($b6+.16)*tyd6+$c9*tyd7/*
*/+$d1*wght_t+$d2*wdth_t+$d3*hght_t+$d4*hp_t+$d5*tran_t+$d6*ps_t+$d7*four_t+$d8)

end

nl ct_2 nprice


preserve
keep if ve==1

gen quality=exp(_b[c8]+_b[b2]+_b[c1]*wght_c+_b[c2]*wdth_c+_b[c3]*hght_c+_b[c4]*hp_c/*
*/+_b[c5]*tran_c+_b[c6]*ps_c+_b[c7]*ac_c)

save Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\quality_c,replace

gen nvalue=quality*quan_c
egen aquan=mean(quan_c), by(year)
egen anvalue=mean(nvalue),by(year)
gen uquality=anvalue/aquan
collapse (mean)uquality, by(year)
list
restore

preserve
keep if ve==2

gen quality=exp(_b[d8]+_b[b2]+_b[d1]*wght_t+_b[d2]*wdth_t+_b[d3]*hght_t+_b[d4]*hp_t/*
*/+_b[d5]*tran_t+_b[d6]*ps_t+_b[d7]*four_t)

save Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\quality_t,replace

gen nvalue=quality*quan_t
egen aquan=mean(quan_t),by(year)
egen anvalue=mean(nvalue), by(year)
gen uquality=anvalue/aquan
collapse (mean)uquality, by(year)
list
restore

program drop _all
log close
exit

Output:

. capture log close

. log using Z:\home\pacha\github\advanced-international-trade\first-edition\Chapte
> r-8\unit_quality.log,replace
(note: file Z:\home\pacha\github\advanced-international-trade\first-edition\Chapte
> r-8\unit_quality.log not found)
----------------------------------------------------------------------------------
      name:  <unnamed>
       log:  Z:\home\pacha\github\advanced-international-trade\first-edition\Chapt
> er-8\unit_quality.log
  log type:  text
 opened on:  19 Jun 2024, 23:03:32

. 
. use Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\tr
> uck_7990,clear

. drop if year>=86
(45 observations deleted)

. gen ve=2

. rename quan quan_t

. rename wdth wdth_t

. rename hght hght_t

. rename weight wght_t

. rename hp hp_t

. rename four four_t

. rename tran tran_t

. rename ps ps_t

. rename ac ac_t

. 
. save Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\t
> ruck_temp,replace
file Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\tru
> ck_temp.dta saved

. 
. use Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\ca
> r_7990,clear

. drop if year>=86
(105 observations deleted)

. gen ve=1

. rename quan quan_c

. rename wdth wdth_c

. rename hght hght_c

. rename wght wght_c

. rename hp hp_c

. rename four four_c

. rename tran tran_c

. rename ps ps_c

. rename ac ac_c

. 
. append using Z:\home\pacha\github\advanced-international-trade\first-edition\Cha
> pter-8\truck_temp

. 
. replace wdth_c=0 if wdth_c==.
(75 real changes made)

. replace hght_c=0 if hght_c==.
(75 real changes made)

. replace wght_c=0 if wght_c==.
(75 real changes made)

. replace hp_c=0 if hp_c==.
(75 real changes made)

. replace four_c=0 if four_c==.
(75 real changes made)

. replace tran_c=0 if tran_c==.
(75 real changes made)

. replace ps_c=0 if ps_c==.
(75 real changes made)

. replace ac_c=0 if ac_c==.
(75 real changes made)

. replace wdth_t=0 if wdth_t==.
(179 real changes made)

. replace hght_t=0 if hght_t==.
(179 real changes made)

. replace wght_t=0 if wght_t==.
(179 real changes made)

. replace hp_t=0 if hp_t==.
(179 real changes made)

. replace four_t=0 if four_t==.
(179 real changes made)

. replace tran_t=0 if tran_t==.
(179 real changes made)

. replace ps_t=0 if ps_t==.
(179 real changes made)

. replace ac_t=0 if ac_t==.
(179 real changes made)

. 
. tab year, gen(yd)

       year |      Freq.     Percent        Cum.
------------+-----------------------------------
         79 |         31       12.20       12.20
         80 |         34       13.39       25.59
         81 |         35       13.78       39.37
         82 |         35       13.78       53.15
         83 |         36       14.17       67.32
         84 |         40       15.75       83.07
         85 |         43       16.93      100.00
------------+-----------------------------------
      Total |        254      100.00

. 
. gen cyd2=yd2

. gen tyd2=yd2

. replace cyd2=0 if type=="JT"
(8 real changes made)

. replace tyd2=0 if type~="JT"
(26 real changes made)

. 
. gen cyd3=yd3

. gen tyd3=yd3

. replace cyd3=0 if type=="JT"
(9 real changes made)

. replace tyd3=0 if type~="JT"
(26 real changes made)

. 
. gen cyd4=yd4

. gen tyd4=yd4

. replace cyd4=0 if type=="JT"
(9 real changes made)

. replace tyd4=0 if type~="JT"
(26 real changes made)

. 
. gen cyd5=yd5

. gen tyd5=yd5

. replace cyd5=0 if type=="JT"
(7 real changes made)

. replace tyd5=0 if type~="JT"
(29 real changes made)

. 
. gen cyd6=yd6

. gen tyd6=yd6

. replace cyd6=0 if type=="JT"
(7 real changes made)

. replace tyd6=0 if type~="JT"
(33 real changes made)

. 
. gen cyd7=yd7

. gen tyd7=yd7

. replace cyd7=0 if type=="JT"
(7 real changes made)

. replace tyd7=0 if type~="JT"
(36 real changes made)

. 
. program define nlct_1
  1. version 7.0
  2. if "`1'"=="?"{
  3. global S_1 "a3 a4 a5 a6 a7 b2 b3 b4 b5 b6 b7 c1 c2 c3 c4 c5 c6 c7 c8 c9 d1 d2
>  d3 d4 d5 d6 d7 d8"
  4. global a3=1
  5. global a4=1
  6. global a5=1
  7. global a6=1
  8. global a7=1
  9. global b2=.1
 10. global b3=.1
 11. global b4=.1
 12. global b5=.1
 13. global b6=.1
 14. global b7=.1
 15. global c1=.1
 16. global c2=.1
 17. global c3=.1
 18. global c4=.1
 19. global c5=.1
 20. global c6=.1
 21. global c7=.1
 22. global c8=.1
 23. global c9=.1
 24. global d1=.1
 25. global d2=.1
 26. global d3=.1
 27. global d4=.1
 28. global d5=.1
 29. global d6=.1
 30. global d7=.1
 31. global d8=.1
 32. exit
 33. }
 34. 
. replace `1'=$a3*cyd3+$a4*cyd4+$a5*cyd5+$a6*cyd6+$a7*cyd7/*
> */+exp($b2*cyd2+$b3*cyd3+$b4*cyd4+$b5*cyd5+$b6*cyd6+$b7*cyd7/*
> */+$c1*wght_c+$c2*wdth_c+$c3*hght_c+$c4*hp_c+$c5*tran_c+$c6*ps_c+$c7*ac_c/*
> */+$c8)+exp($b2*tyd2+($b3+.16)*tyd3+($b4+.16)*tyd4+($b5+.16)*tyd5+($b6+.16)*tyd6
> +$c9*tyd7/*
> */+$d1*wght_t+$d2*wdth_t+$d3*hght_t+$d4*hp_t+$d5*tran_t+$d6*ps_t+$d7*four_t+$d8)
 35. 
. end

. 
. nl ct_1 price
(obs = 254)

Iteration 0:   residual SS =  1.51e+10
...
Iteration 24:  residual SS =  1.01e+08
Iteration 25:  residual SS =  1.01e+08

      Source |       SS       df       MS            Number of obs =       254
-------------+------------------------------         F( 28,   226) =   1210.09
       Model |  1.5069e+10    28   538194036         Prob > F      =    0.0000
    Residual |   100515047   226  444756.844         R-squared     =    0.9934
-------------+------------------------------         Adj R-squared =    0.9926
       Total |  1.5170e+10   254  59724204.9         Root MSE      =  666.9009
                                                     Res. dev.     =  3994.496
(ct_1)
------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          a3 |   254.0918   317.1045     0.80   0.424    -370.7678    878.9513
          a4 |   505.1058   325.6388     1.55   0.122    -136.5708    1146.782
          a5 |   708.9466   317.3172     2.23   0.026       83.668    1334.225
          a6 |   1082.054   322.4415     3.36   0.001     446.6773     1717.43
          a7 |   1063.014   373.9703     2.84   0.005     326.0995    1799.929
          b2 |   .0040633   .0329008     0.12   0.902    -.0607683    .0688948
          b3 |   .0756038    .049061     1.54   0.125    -.0210716    .1722792
          b4 |   .0828575   .0490467     1.69   0.093    -.0137897    .1795048
          b5 |   .0327776    .050707     0.65   0.519    -.0671415    .1326967
          b6 |   .0351224   .0514768     0.68   0.496    -.0663135    .1365582
          b7 |   .0825554   .0557608     1.48   0.140    -.0273221    .1924329
          c1 |   .0326037   .1117298     0.29   0.771    -.1875618    .2527691
          c2 |    .385946   .1204171     3.21   0.002     .1486621    .6232299
          c3 |  -.1929238   .0568197    -3.40   0.001     -.304888   -.0809596
          c4 |    .715212   .0736084     9.72   0.000     .5701655    .8602585
          c5 |   .1578585     .03381     4.67   0.000     .0912354    .2244816
          c6 |   .0641097   .0247061     2.59   0.010     .0154259    .1127934
          c7 |   .1829447   .0242773     7.54   0.000     .1351059    .2307836
          c8 |   6.599831   .7305317     9.03   0.000     5.160306    8.039356
          c9 |   .1171992   .0634238     1.85   0.066    -.0077785    .2421769
          d1 |   .4917133   .0795807     6.18   0.000     .3348983    .6485283
          d2 |   .2622177   .1757206     1.49   0.137    -.0840426    .6084779
          d3 |  -.0451278   .0677055    -0.67   0.506    -.1785426     .088287
          d4 |   .3030767   .1701249     1.78   0.076    -.0321571    .6383106
          d5 |   .0397822   .0362731     1.10   0.274    -.0316947     .111259
          d6 |   .0967659   .0501832     1.93   0.055    -.0021208    .1956526
          d7 |   .3052359   .0715711     4.26   0.000     .1642038     .446268
          d8 |   6.299805   .9622249     6.55   0.000     4.403726    8.195885
------------------------------------------------------------------------------
 (SEs, P values, CIs, and correlations are asymptotic approximations)

. 
. gen winv=1/exp(_b[b2]*cyd2+_b[b3]*cyd3+_b[b4]*cyd4+_b[b5]*cyd5+_b[b6]*cyd6+_b[b7
> ]*cyd7/*
> */+_b[c1]*wght_c+_b[c2]*wdth_c+_b[c3]*hght_c+_b[c4]*hp_c+_b[c5]*tran_c+_b[c6]*ps
> _c/*
> */+_b[c7]*ac_c+_b[c8])

. 
. replace winv=1/exp((_b[b2]+0.16)*tyd2+(_b[b3]+.16)*tyd3+(_b[b4]+.16)*tyd4/*
> */+(_b[b5]+.16)*tyd5+(_b[b6]+.16)*tyd6+_b[c9]*tyd7/*
> */+_b[d1]*wght_t+_b[d2]*wdth_t+_b[d3]*hght_t+_b[d4]*hp_t/*
> */+_b[d5]*tran_t+_b[d6]*ps_t+_b[d7]*four_t+_b[d8]) if ve==2
(75 real changes made)

. 
. gen nprice=price*winv

. 
. 
. program define nlct_2
  1. version 7.0
  2. if "`1'"=="?"{
  3. global S_1 "a3 a4 a5 a6 a7 b2 b3 b4 b5 b6 b7 c1 c2 c3 c4 c5 c6 c7 c8 c9 d1 d2
>  d3 d4 d5 d6 d7 d8"
  4. global a3=1
  5. global a4=1
  6. global a5=1
  7. global a6=1
  8. global a7=1
  9. global b2=.1
 10. global b3=.1
 11. global b4=.1
 12. global b5=.1
 13. global b6=.1
 14. global b7=.1
 15. global c1=.1
 16. global c2=.1
 17. global c3=.1
 18. global c4=.1
 19. global c5=.1
 20. global c6=.1
 21. global c7=.1
 22. global c8=.1
 23. global c9=.1
 24. global d1=.1
 25. global d2=.1
 26. global d3=.1
 27. global d4=.1
 28. global d5=.1
 29. global d6=.1
 30. global d7=.1
 31. global d8=.1
 32. exit
 33. }
 34. replace `1'=winv*($a3*cyd3+$a4*cyd4+$a5*cyd5+$a6*cyd6+$a7*cyd7)/*
> */+winv*exp($b2*cyd2+$b3*cyd3+$b4*cyd4+$b5*cyd5+$b6*cyd6+$b7*cyd7/*
> */+$c1*wght_c+$c2*wdth_c+$c3*hght_c+$c4*hp_c+$c5*tran_c+$c6*ps_c+$c7*ac_c/*
> */+$c8)+winv*exp($b2*tyd2+($b3+.16)*tyd3+($b4+.16)*tyd4+($b5+.16)*tyd5+($b6+.16)
> *tyd6+$c9*tyd7/*
> */+$d1*wght_t+$d2*wdth_t+$d3*hght_t+$d4*hp_t+$d5*tran_t+$d6*ps_t+$d7*four_t+$d8)
 35. 
. end

. 
. nl ct_2 nprice
(obs = 254)

Iteration 0:   residual SS =  353.5865
...
Iteration 20:  residual SS =  2.957295
Iteration 21:  residual SS =  2.957295

      Source |       SS       df       MS            Number of obs =       254
-------------+------------------------------         F( 28,   226) =    958.75
       Model |  351.277591    28  12.5456282         Prob > F      =    0.0000
    Residual |  2.95729549   226  .013085378         R-squared     =    0.9917
-------------+------------------------------         Adj R-squared =    0.9906
       Total |  354.234886   254  1.39462554         Root MSE      =  .1143913
                                                     Res. dev.     = -410.2562
(ct_2)
------------------------------------------------------------------------------
      nprice |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          a3 |   367.9829    239.059     1.54   0.125    -103.0867    839.0525
          a4 |    600.553   254.2261     2.36   0.019     99.59628     1101.51
          a5 |   887.9399   243.5428     3.65   0.000     408.0348    1367.845
          a6 |   1104.433   251.0245     4.40   0.000     609.7847     1599.08
          a7 |   855.7993   366.2444     2.34   0.020     134.1088     1577.49
          b2 |   .0130387   .0303131     0.43   0.668    -.0466937    .0727711
          b3 |   .0674477   .0425176     1.59   0.114     -.016334    .1512294
          b4 |   .0701234   .0441821     1.59   0.114    -.0169382     .157185
          b5 |  -.0005627   .0470779    -0.01   0.990    -.0933305    .0922051
          b6 |   .0179989   .0473905     0.38   0.704    -.0753848    .1113826
          b7 |   .1007712   .0641587     1.57   0.118    -.0256545    .2271969
          c1 |   .0492474   .1311096     0.38   0.708    -.2091061     .307601
          c2 |   .3908689   .1383663     2.82   0.005     .1182159     .663522
          c3 |  -.0618204   .0611492    -1.01   0.313    -.1823158     .058675
          c4 |   .8103277   .1038045     7.81   0.000     .6057792    1.014876
          c5 |   .1779391   .0355273     5.01   0.000     .1079319    .2479463
          c6 |   .0693687   .0304968     2.27   0.024     .0092743     .129463
          c7 |   .1567051   .0360384     4.35   0.000     .0856908    .2277193
          c8 |   5.839036   .8621144     6.77   0.000     4.140226    7.537847
          c9 |   .1059852   .0550545     1.93   0.055    -.0025007    .2144711
          d1 |   .4759918   .1172145     4.06   0.000     .2450187    .7069649
          d2 |   .2120021   .1419991     1.49   0.137    -.0678094    .4918136
          d3 |  -.0270369    .074052    -0.37   0.715    -.1729575    .1188837
          d4 |     .24435   .1516866     1.61   0.109    -.0545508    .5432508
          d5 |   .0530065   .0356148     1.49   0.138     -.017173     .123186
          d6 |   .0575178   .0639555     0.90   0.369    -.0685076    .1835431
          d7 |   .2971909   .0566882     5.24   0.000      .185486    .4088959
          d8 |   6.630805   .7652819     8.66   0.000     5.122804    8.138805
------------------------------------------------------------------------------
 (SEs, P values, CIs, and correlations are asymptotic approximations)

. 
. 
. preserve

. keep if ve==1
(75 observations deleted)

. 
. gen quality=exp(_b[c8]+_b[b2]+_b[c1]*wght_c+_b[c2]*wdth_c+_b[c3]*hght_c+_b[c4]*h
> p_c/*
> */+_b[c5]*tran_c+_b[c6]*ps_c+_b[c7]*ac_c)

. 
. save Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\q
> uality_c,replace
file Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\qua
> lity_c.dta saved

. 
. gen nvalue=quality*quan_c

. egen aquan=mean(quan_c), by(year)

. egen anvalue=mean(nvalue),by(year)

. gen uquality=anvalue/aquan

. collapse (mean)uquality, by(year)

. list

     +-----------------+
     | year   uquality |
     |-----------------|
  1. |   79   4360.772 |
  2. |   80   4472.789 |
  3. |   81   4867.316 |
  4. |   82   5252.845 |
  5. |   83   5636.667 |
     |-----------------|
  6. |   84    5862.13 |
  7. |   85   6130.052 |
     +-----------------+

. restore

. 
. preserve

. keep if ve==2
(179 observations deleted)

. 
. gen quality=exp(_b[d8]+_b[b2]+_b[d1]*wght_t+_b[d2]*wdth_t+_b[d3]*hght_t+_b[d4]*h
> p_t/*
> */+_b[d5]*tran_t+_b[d6]*ps_t+_b[d7]*four_t)

. 
. save Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\q
> uality_t,replace
file Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\qua
> lity_t.dta saved

. 
. gen nvalue=quality*quan_t

. egen aquan=mean(quan_t),by(year)

. egen anvalue=mean(nvalue), by(year)

. gen uquality=anvalue/aquan

. collapse (mean)uquality, by(year)

. list

     +-----------------+
     | year   uquality |
     |-----------------|
  1. |   79   4626.836 |
  2. |   80   4637.583 |
  3. |   81   4791.255 |
  4. |   82   4929.792 |
  5. |   83   4997.103 |
     |-----------------|
  6. |   84   5009.971 |
  7. |   85   5432.772 |
     +-----------------+

. restore

. 
. program drop _all

. log close
      name:  <unnamed>
       log:  Z:\home\pacha\github\advanced-international-trade\first-edition\Chapt
> er-8\unit_quality.log
  log type:  text
 closed on:  19 Jun 2024, 23:03:38
----------------------------------------------------------------------------------

. exit

end of do-file

qindex_c.do

clear
capture log close
log using Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\qindex_c.log,replace

use Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\quality_c,clear
keep year model type quality quan_c
ren quan_c quan

preserve
keep if year==80
keep model type quality quan
ren quality quality_80
ren quan quan_80
sort model
save Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\quality_80_c,replace
restore

sort model
merge model using Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\quality_80_c
keep if _merge==3
drop _merge

sort year model
egen value_80=sum(quality_80*quan_80), by(year)
egen value_cp=sum(quality*quan_80), by(year)
gen lasp=value_cp/value_80

egen value_c=sum(quality*quan),by(year)
egen value_cq=sum(quality_80*quan), by(year)
gen pasp=value_c/value_cq

gen qindex=(lasp*pasp)^0.5
collapse (mean) qindex, by(year)

list
log close

Output:

. clear

. capture log close

. log using Z:\home\pacha\github\advanced-international-trade\first-edition\Chapte
> r-8\qindex_c.log,replace
(note: file Z:\home\pacha\github\advanced-international-trade\first-edition\Chapte
> r-8\qindex_c.log not found)
----------------------------------------------------------------------------------
      name:  <unnamed>
       log:  Z:\home\pacha\github\advanced-international-trade\first-edition\Chapt
> er-8\qindex_c.log
  log type:  text
 opened on:  19 Jun 2024, 23:06:51

. 
. use Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\qu
> ality_c,clear

. keep year model type quality quan_c

. ren quan_c quan

. 
. preserve

. keep if year==80
(155 observations deleted)

. keep model type quality quan

. ren quality quality_80

. ren quan quan_80

. sort model

. save Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\q
> uality_80_c,replace
file Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\qua
> lity_80_c.dta saved

. restore

. 
. sort model

. merge model using Z:\home\pacha\github\advanced-international-trade\first-editio
> n\Chapter-8\quality_80_c
(note: you are using old merge syntax; see [R] merge for new syntax)
variable model does not uniquely identify observations in the master data

. keep if _merge==3
(23 observations deleted)

. drop _merge

. 
. sort year model

. egen value_80=sum(quality_80*quan_80), by(year)

. egen value_cp=sum(quality*quan_80), by(year)

. gen lasp=value_cp/value_80

. 
. egen value_c=sum(quality*quan),by(year)

. egen value_cq=sum(quality_80*quan), by(year)

. gen pasp=value_c/value_cq

. 
. gen qindex=(lasp*pasp)^0.5

. collapse (mean) qindex, by(year)

. 
. list

     +-----------------+
     | year     qindex |
     |-----------------|
  1. |   79    .986878 |
  2. |   80          1 |
  3. |   81   1.085813 |
  4. |   82    1.15183 |
  5. |   83   1.212675 |
     |-----------------|
  6. |   84   1.266379 |
  7. |   85   1.305744 |
     +-----------------+

. log close
      name:  <unnamed>
       log:  Z:\home\pacha\github\advanced-international-trade\first-edition\Chapt
> er-8\qindex_c.log
  log type:  text
 closed on:  19 Jun 2024, 23:06:53
----------------------------------------------------------------------------------

. 
end of do-file

qindex_t.do

. clear

. capture log close

. log using Z:\home\pacha\github\advanced-international-trade\first-edition\Chapte
> r-8\qindex_t.log,replace
(note: file Z:\home\pacha\github\advanced-international-trade\first-edition\Chapte
> r-8\qindex_t.log not found)
----------------------------------------------------------------------------------
      name:  <unnamed>
       log:  Z:\home\pacha\github\advanced-international-trade\first-edition\Chapt
> er-8\qindex_t.log
  log type:  text
 opened on:  19 Jun 2024, 23:09:00

. 
. use Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\qu
> ality_t,clear

. keep year model type quality quan_t

. ren quan_t quan

. 
. preserve

. keep if year==80
(65 observations deleted)

. keep model type quality quan

. ren quality quality_80

. ren quan quan_80

. sort model

. save Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\q
> uality_80_t,replace
file Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\qua
> lity_80_t.dta saved

. restore

. 
. sort model

. merge model using Z:\home\pacha\github\advanced-international-trade\first-editio
> n\Chapter-8\quality_80_t
(note: you are using old merge syntax; see [R] merge for new syntax)
variable model does not uniquely identify observations in the master data

. keep if _merge==3
(14 observations deleted)

. drop _merge

. 
. sort year model

. egen value_80=sum(quality_80*quan_80), by(year)

. egen value_cp=sum(quality*quan_80), by(year)

. gen lasp=value_cp/value_80

. 
. egen value_c=sum(quality*quan),by(year)

. egen value_cq=sum(quality_80*quan), by(year)

. gen pasp=value_c/value_cq

. 
. gen qindex=(lasp*pasp)^0.5

. collapse (mean) qindex, by(year)

. 
. list

     +-----------------+
     | year     qindex |
     |-----------------|
  1. |   79   .9956951 |
  2. |   80          1 |
  3. |   81   1.035043 |
  4. |   82   1.058717 |
  5. |   83   1.057227 |
     |-----------------|
  6. |   84   1.053449 |
  7. |   85   1.160353 |
     +-----------------+

. log close
      name:  <unnamed>
       log:  Z:\home\pacha\github\advanced-international-trade\first-edition\Chapt
> er-8\qindex_t.log
  log type:  text
 closed on:  19 Jun 2024, 23:09:01
----------------------------------------------------------------------------------

. 
end of do-file

My code

unit_quality.do

truck_7990 <- feenstra_88$truck_7990 %>%
  filter(year < 86) %>%
  mutate(ve = 2) %>%
  rename(
    quan_t = quan,
    wdth_t = wdth,
    hght_t = hght,
    wght_t = weight,
    hp_t = hp,
    four_t = four,
    tran_t = tran,
    ps_t = ps,
    ac_t = ac
  )

car_7990 <- feenstra_88$car_7990 %>%
  filter(year < 86) %>%
  mutate(ve = 1) %>%
  rename(
    quan_c = quan,
    wdth_c = wdth,
    hght_c = hght,
    wght_c = wght,
    hp_c = hp,
    four_c = four,
    tran_c = tran,
    ps_c = ps,
    ac_c = ac
  )

truck_7990 <- truck_7990 %>%
  bind_rows(car_7990) %>%
  mutate(
    wdth_c = ifelse(is.na(wdth_c), 0, wdth_c),
    hght_c = ifelse(is.na(hght_c), 0, hght_c),
    wght_c = ifelse(is.na(wght_c), 0, wght_c),
    hp_c = ifelse(is.na(hp_c), 0, hp_c),
    four_c = ifelse(is.na(four_c), 0, four_c),
    tran_c = ifelse(is.na(tran_c), 0, tran_c),
    ps_c = ifelse(is.na(ps_c), 0, ps_c),
    ac_c = ifelse(is.na(ac_c), 0, ac_c),
    wdth_t = ifelse(is.na(wdth_t), 0, wdth_t),
    hght_t = ifelse(is.na(hght_t), 0, hght_t),
    wght_t = ifelse(is.na(wght_t), 0, wght_t),
    hp_t = ifelse(is.na(hp_t), 0, hp_t),
    four_t = ifelse(is.na(four_t), 0, four_t),
    tran_t = ifelse(is.na(tran_t), 0, tran_t),
    ps_t = ifelse(is.na(ps_t), 0, ps_t),
    ac_t = ifelse(is.na(ac_t), 0, ac_t)
  )

truck_7990 %>%
  group_by(year) %>%
  summarise(freq = n()) %>%
  ungroup() %>%
  mutate(
    percent = freq / sum(freq) * 100,
    cum = cumsum(percent)
  )

# A tibble: 7 × 4
   year  freq percent   cum
  <dbl> <int>   <dbl> <dbl>
1    79    31    12.2  12.2
2    80    34    13.4  25.6
3    81    35    13.8  39.4
4    82    35    13.8  53.1
5    83    36    14.2  67.3
6    84    40    15.7  83.1
7    85    43    16.9 100  

truck_7990 <- truck_7990 %>%
  mutate(yd = as.factor(year - min(year) + 1))

truck_7990_dummy <- model.matrix(~ yd - 1, data = truck_7990)

truck_7990 <- truck_7990 %>%
  bind_cols(as.data.frame(truck_7990_dummy))

truck_7990 <- truck_7990 %>%
  mutate(
    cyd2 = case_when(
      type == "JT" ~ 0,
      TRUE ~ yd2
    ),
    tyd2 = case_when(
      type != "JT" ~ 0,
      TRUE ~ yd2
    ),
    cyd3 = case_when(
      type == "JT" ~ 0,
      TRUE ~ yd3
    ),
    tyd3 = case_when(
      type != "JT" ~ 0,
      TRUE ~ yd3
    ),
    cyd4 = case_when(
      type == "JT" ~ 0,
      TRUE ~ yd4
    ),
    tyd4 = case_when(
      type != "JT" ~ 0,
      TRUE ~ yd4
    ),
    cyd5 = case_when(
      type == "JT" ~ 0,
      TRUE ~ yd5
    ),
    tyd5 = case_when(
      type != "JT" ~ 0,
      TRUE ~ yd5
    ),
    cyd6 = case_when(
      type == "JT" ~ 0,
      TRUE ~ yd6
    ),
    tyd6 = case_when(
      type != "JT" ~ 0,
      TRUE ~ yd6
    ),
    cyd7 = case_when(
      type == "JT" ~ 0,
      TRUE ~ yd7
    ),
    tyd7 = case_when(
      type != "JT" ~ 0,
      TRUE ~ yd7
    )
  )

initial_values <- list(
  a3 = 1, a4 = 1, a5 = 1, a6 = 1, a7 = 1,
  b2 = 0.1, b3 = 0.1, b4 = 0.1, b5 = 0.1, b6 = 0.1, b7 = 0.1,
  c1 = 0.1, c2 = 0.1, c3 = 0.1, c4 = 0.1, c5 = 0.1, c6 = 0.1, c7 = 0.1,
  c8 = 0.1, c9 = 0.1,
  d1 = 0.1, d2 = 0.1, d3 = 0.1, d4 = 0.1, d5 = 0.1, d6 = 0.1, d7 = 0.1,
  d8 = 0.1
)

fit <- nlsLM(
  price ~ a3 * cyd3 + a4 * cyd4 + a5 * cyd5 + a6 * cyd6 + a7 * cyd7 +
    exp(b2 * cyd2 + b3 * cyd3 + b4 * cyd4 + b5 * cyd5 + b6 * cyd6 +
      b7 * cyd7 + c1 * wght_c + c2 * wdth_c + c3 * hght_c + c4 * hp_c +
      c5 * tran_c + c6 * ps_c + c7 * ac_c + c8) +
    exp(b2 * tyd2 + (b3 + 0.16) * tyd3 + (b4 + 0.16) * tyd4 +
      (b5 + 0.16) * tyd5 + (b6 + 0.16) * tyd6 + c9 * tyd7 + d1 * wght_t +
      d2 * wdth_t + d3 * hght_t + d4 * hp_t + d5 * tran_t + d6 * ps_t +
      d7 * four_t + d8),
  data = truck_7990,
  start = initial_values
)

summary(fit)

Formula: price ~ a3 * cyd3 + a4 * cyd4 + a5 * cyd5 + a6 * cyd6 + a7 * 
    cyd7 + exp(b2 * cyd2 + b3 * cyd3 + b4 * cyd4 + b5 * cyd5 + 
    b6 * cyd6 + b7 * cyd7 + c1 * wght_c + c2 * wdth_c + c3 * 
    hght_c + c4 * hp_c + c5 * tran_c + c6 * ps_c + c7 * ac_c + 
    c8) + exp(b2 * tyd2 + (b3 + 0.16) * tyd3 + (b4 + 0.16) * 
    tyd4 + (b5 + 0.16) * tyd5 + (b6 + 0.16) * tyd6 + c9 * tyd7 + 
    d1 * wght_t + d2 * wdth_t + d3 * hght_t + d4 * hp_t + d5 * 
    tran_t + d6 * ps_t + d7 * four_t + d8)

Parameters:
     Estimate Std. Error t value Pr(>|t|)    
a3  2.542e+02  3.171e+02   0.802 0.423598    
a4  5.052e+02  3.256e+02   1.552 0.122150    
a5  7.090e+02  3.173e+02   2.235 0.026415 *  
a6  1.082e+03  3.224e+02   3.356 0.000926 ***
a7  1.063e+03  3.739e+02   2.843 0.004876 ** 
b2  4.065e-03  3.290e-02   0.124 0.901779    
b3  7.559e-02  4.906e-02   1.541 0.124732    
b4  8.284e-02  4.904e-02   1.689 0.092555 .  
b5  3.276e-02  5.070e-02   0.646 0.518840    
b6  3.510e-02  5.147e-02   0.682 0.495934    
b7  8.254e-02  5.576e-02   1.480 0.140197    
c1  3.261e-02  1.117e-01   0.292 0.770715    
c2  3.860e-01  1.204e-01   3.205 0.001545 ** 
c3 -1.929e-01  5.683e-02  -3.395 0.000811 ***
c4  7.152e-01  7.362e-02   9.715  < 2e-16 ***
c5  1.579e-01  3.382e-02   4.668 5.21e-06 ***
c6  6.412e-02  2.471e-02   2.595 0.010082 *  
c7  1.830e-01  2.428e-02   7.535 1.16e-12 ***
c8  6.599e+00  7.307e-01   9.032  < 2e-16 ***
c9  1.172e-01  6.342e-02   1.848 0.065932 .  
d1  4.917e-01  7.958e-02   6.179 2.97e-09 ***
d2  2.621e-01  1.757e-01   1.492 0.137107    
d3 -4.513e-02  6.770e-02  -0.667 0.505752    
d4  3.031e-01  1.701e-01   1.782 0.076158 .  
d5  3.978e-02  3.627e-02   1.097 0.273899    
d6  9.676e-02  5.018e-02   1.928 0.055072 .  
d7  3.052e-01  7.156e-02   4.265 2.94e-05 ***
d8  6.300e+00  9.620e-01   6.549 3.85e-10 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 666.9 on 226 degrees of freedom

Number of iterations to convergence: 30 
Achieved convergence tolerance: 1.49e-08

fit_coef <- coef(fit)

truck_7990 <- truck_7990 %>%
  mutate(
    winv = case_when(
      ve == 1 ~ 1 / exp(fit_coef["b2"] * cyd2 + fit_coef["b3"] * cyd3 +
        fit_coef["b4"] * cyd4 + fit_coef["b5"] * cyd5 +
        fit_coef["b6"] * cyd6 + fit_coef["b7"] * cyd7 +
        fit_coef["c1"] * wght_c + fit_coef["c2"] * wdth_c +
        fit_coef["c3"] * hght_c + fit_coef["c4"] * hp_c +
        fit_coef["c5"] * tran_c + fit_coef["c6"] * ps_c +
        fit_coef["c7"] * ac_c + fit_coef["c8"]),
      ve == 2 ~ 1 / exp((fit_coef["b2"] + 0.16) * tyd2 +
        (fit_coef["b3"] + 0.16) * tyd3 + (fit_coef["b4"] + 0.16) * tyd4 +
        (fit_coef["b5"] + 0.16) * tyd5 + (fit_coef["b6"] + 0.16) * tyd6 +
        fit_coef["c9"] * tyd7 + fit_coef["d1"] * wght_t +
        fit_coef["d2"] * wdth_t + fit_coef["d3"] * hght_t +
        fit_coef["d4"] * hp_t + fit_coef["d5"] * tran_t +
        fit_coef["d6"] * ps_t + fit_coef["d7"] * four_t + fit_coef["d8"])
    ),
    nprice = price * winv
  )

fit2 <- nlsLM(
  nprice ~ winv * (a3 * cyd3 + a4 * cyd4 + a5 * cyd5 + a6 * cyd6 + a7 * cyd7) +
    winv * exp(b2 * cyd2 + b3 * cyd3 + b4 * cyd4 + b5 * cyd5 + b6 * cyd6 +
      b7 * cyd7 + c1 * wght_c + c2 * wdth_c + c3 * hght_c + c4 * hp_c +
      c5 * tran_c + c6 * ps_c + c7 * ac_c + c8) +
    winv * exp(b2 * tyd2 + (b3 + 0.16) * tyd3 + (b4 + 0.16) * tyd4 +
      (b5 + 0.16) * tyd5 + (b6 + 0.16) * tyd6 + c9 * tyd7 + d1 * wght_t +
      d2 * wdth_t + d3 * hght_t + d4 * hp_t + d5 * tran_t + d6 * ps_t +
      d7 * four_t + d8),
  data = truck_7990,
  start = initial_values
)

summary(fit2)

Formula: nprice ~ winv * (a3 * cyd3 + a4 * cyd4 + a5 * cyd5 + a6 * cyd6 + 
    a7 * cyd7) + winv * exp(b2 * cyd2 + b3 * cyd3 + b4 * cyd4 + 
    b5 * cyd5 + b6 * cyd6 + b7 * cyd7 + c1 * wght_c + c2 * wdth_c + 
    c3 * hght_c + c4 * hp_c + c5 * tran_c + c6 * ps_c + c7 * 
    ac_c + c8) + winv * exp(b2 * tyd2 + (b3 + 0.16) * tyd3 + 
    (b4 + 0.16) * tyd4 + (b5 + 0.16) * tyd5 + (b6 + 0.16) * tyd6 + 
    c9 * tyd7 + d1 * wght_t + d2 * wdth_t + d3 * hght_t + d4 * 
    hp_t + d5 * tran_t + d6 * ps_t + d7 * four_t + d8)

Parameters:
     Estimate Std. Error t value Pr(>|t|)    
a3  3.679e+02  2.391e+02   1.539 0.125219    
a4  6.005e+02  2.543e+02   2.362 0.019041 *  
a5  8.879e+02  2.436e+02   3.645 0.000332 ***
a6  1.104e+03  2.511e+02   4.399 1.68e-05 ***
a7  8.556e+02  3.663e+02   2.336 0.020379 *  
b2  1.304e-02  3.031e-02   0.430 0.667488    
b3  6.745e-02  4.252e-02   1.586 0.114086    
b4  7.013e-02  4.419e-02   1.587 0.113886    
b5 -5.484e-04  4.708e-02  -0.012 0.990718    
b6  1.801e-02  4.740e-02   0.380 0.704268    
b7  1.008e-01  6.416e-02   1.571 0.117554    
c1  4.925e-02  1.311e-01   0.376 0.707523    
c2  3.908e-01  1.383e-01   2.825 0.005153 ** 
c3 -6.182e-02  6.114e-02  -1.011 0.313088    
c4  8.103e-01  1.038e-01   7.807 2.17e-13 ***
c5  1.779e-01  3.552e-02   5.009 1.10e-06 ***
c6  6.936e-02  3.049e-02   2.275 0.023864 *  
c7  1.567e-01  3.604e-02   4.348 2.08e-05 ***
c8  5.839e+00  8.619e-01   6.775 1.07e-10 ***
c9  1.060e-01  5.506e-02   1.925 0.055494 .  
d1  4.760e-01  1.172e-01   4.060 6.76e-05 ***
d2  2.121e-01  1.420e-01   1.493 0.136773    
d3 -2.704e-02  7.406e-02  -0.365 0.715380    
d4  2.443e-01  1.517e-01   1.611 0.108659    
d5  5.301e-02  3.562e-02   1.488 0.138112    
d6  5.751e-02  6.396e-02   0.899 0.369534    
d7  2.972e-01  5.670e-02   5.242 3.64e-07 ***
d8  6.630e+00  7.655e-01   8.661 8.98e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.1144 on 226 degrees of freedom

Number of iterations to convergence: 31 
Achieved convergence tolerance: 1.49e-08

fit2_coef <- coef(fit2)

truck_7990_2 <- truck_7990 %>%
  filter(ve == 1) %>%
  mutate(
    quality = exp(fit2_coef["c8"] + fit2_coef["b2"] + fit2_coef["c1"] * wght_c +
      fit2_coef["c2"] * wdth_c + fit2_coef["c3"] * hght_c +
      fit2_coef["c4"] * hp_c + fit2_coef["c5"] * tran_c +
      fit2_coef["c6"] * ps_c + fit2_coef["c7"] * ac_c),
    nvalue = quality * quan_c
  )

truck_7990_2 %>%
  group_by(year) %>%
  summarise(
    aquan = mean(quan_c),
    anvalue = mean(nvalue)
  ) %>%
  ungroup() %>%
  mutate(uquality = anvalue / aquan) %>%
  group_by(year) %>%
  summarise(mean_uquality = mean(uquality))

# A tibble: 7 × 2
   year mean_uquality
  <dbl>         <dbl>
1    79         4361.
2    80         4473.
3    81         4868.
4    82         5253.
5    83         5637.
6    84         5862.
7    85         6130.

truck_7990_3 <- truck_7990 %>%
  filter(ve == 2) %>%
  mutate(
    quality = exp(fit2_coef["d8"] + fit2_coef["b2"] + fit2_coef["d1"] * wght_t +
      fit2_coef["d2"] * wdth_t + fit2_coef["d3"] * hght_t +
      fit2_coef["d4"] * hp_t + fit2_coef["d5"] * tran_t +
      fit2_coef["d6"] * ps_t + fit2_coef["d7"] * four_t),
    nvalue = quality * quan_t
  )

truck_7990_3 %>%
  group_by(year) %>%
  summarise(
    aquan = mean(quan_t),
    anvalue = mean(nvalue)
  ) %>%
  ungroup() %>%
  mutate(uquality = anvalue / aquan) %>%
  group_by(year) %>%
  summarise(mean_uquality = mean(uquality))

# A tibble: 7 × 2
   year mean_uquality
  <dbl>         <dbl>
1    79         4627.
2    80         4637.
3    81         4791.
4    82         4930.
5    83         4997.
6    84         5010.
7    85         5433.

qindex_c.do

truck_7990_2_80 <- truck_7990_2 %>%
  filter(year == 80) %>%
  select(model, type, quality, quan_c) %>%
  rename(
    quality_80 = quality,
    quan_80 = quan_c
  )

truck_7990_2 %>%
  select(year, model, type, quality, quan_c) %>%
  inner_join(truck_7990_2_80, by = c("model", "type")) %>%
  group_by(year, model) %>%
  mutate(
    value_80 = sum(quality_80 * quan_80),
    value_cp = sum(quality * quan_80),
    lasp = value_cp / value_80
  ) %>%
  group_by(year) %>%
  mutate(
    value_c = sum(quality * quan_c),
    value_cq = sum(quality_80 * quan_c),
    pasp = value_c / value_cq,
    qindex = sqrt(lasp * pasp)
  ) %>%
  summarise(mean_qindex = mean(qindex))

# A tibble: 7 × 2
   year mean_qindex
  <dbl>       <dbl>
1    79       0.985
2    80       1    
3    81       1.09 
4    82       1.14 
5    83       1.20 
6    84       1.26 
7    85       1.33 

qindex_t.do

truck_7990_3_80 <- truck_7990_3 %>%
  filter(year == 80) %>%
  select(model, type, quality, quan_t) %>%
  rename(
    quality_80 = quality,
    quan_80 = quan_t
  )

truck_7990_3 %>%
  select(year, model, type, quality, quan_t) %>%
  inner_join(truck_7990_3_80, by = c("model", "type")) %>%
  group_by(year, model) %>%
  mutate(
    value_80 = sum(quality_80 * quan_80),
    value_tp = sum(quality * quan_80),
    lasp = value_tp / value_80
  ) %>%
  group_by(year) %>%
  mutate(
    value_t = sum(quality * quan_t),
    value_tq = sum(quality_80 * quan_t),
    pasp = value_t / value_tq,
    qindex = sqrt(lasp * pasp)
  ) %>%
  summarise(mean_qindex = mean(qindex))

# A tibble: 7 × 2
   year mean_qindex
  <dbl>       <dbl>
1    79       0.983
2    80       1    
3    81       1.03 
4    82       1.06 
5    83       1.05 
6    84       1.07 
7    85       1.17 

Exercise 5

Pooling car and truck data, run system_nocom.do and system_wcon.do to reproduce columns (1) – (4) in Table 8.5, with constraints specified in equation (8.22).

Feenstra’s code

system_nocom.do

I think there is a typo in the original code, in specific in the lines:

gen cyd10=yd10
gen tyd10=yd10
replace cyd7=10 if type=="JT"
replace tyd7=10 if type~="JT"

gen cyd11=yd11
gen tyd11=yd11
replace cyd7=11 if type=="JT"
replace tyd7=11 if type~="JT"

gen cyd12=yd12
gen tyd12=yd12
replace cyd7=12 if type=="JT"
replace tyd7=12 if type~="JT"

To me, it is not clear why overwriting cyd7 three times instead of replacing with “12” in one step. I corrected cyd10, cyd11, and cyd12 below.

capture log close
log using Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\system_nocon.log,replace

set matsize 400

use Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\truck_7990,clear
gen ve=2
rename wdth wdth_t
rename hght hght_t
rename weight wght_t
rename hp hp_t
rename four four_t
rename tran tran_t
rename ps ps_t
rename ac ac_t

save Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\truck_temp,replace

use Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\car_7990,clear
gen ve=1
rename wdth wdth_c
rename hght hght_c
rename wght wght_c
rename hp hp_c
rename four four_c
rename tran tran_c
rename ps ps_c
rename ac ac_c

append using Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\truck_temp

replace wdth_c=0 if wdth_c==.
replace hght_c=0 if hght_c==.
replace wght_c=0 if wght_c==.
replace hp_c=0 if hp_c==.
replace four_c=0 if four_c==.
replace tran_c=0 if tran_c==.
replace ps_c=0 if ps_c==.
replace ac_c=0 if ac_c==.
replace wdth_t=0 if wdth_t==.
replace hght_t=0 if hght_t==.
replace wght_t=0 if wght_t==.
replace hp_t=0 if hp_t==.
replace four_t=0 if four_t==.
replace tran_t=0 if tran_t==.
replace ps_t=0 if ps_t==.
replace ac_t=0 if ac_t==.

tab year, gen(yd)

gen cyd2=yd2
gen tyd2=yd2
replace cyd2=0 if type=="JT"
replace tyd2=0 if type~="JT"

gen cyd3=yd3
gen tyd3=yd3
replace cyd3=0 if type=="JT"
replace tyd3=0 if type~="JT"

gen cyd4=yd4
gen tyd4=yd4
replace cyd4=0 if type=="JT"
replace tyd4=0 if type~="JT"

gen cyd5=yd5
gen tyd5=yd5
replace cyd5=0 if type=="JT"
replace tyd5=0 if type~="JT"

gen cyd6=yd6
gen tyd6=yd6
replace cyd6=0 if type=="JT"
replace tyd6=0 if type~="JT"

gen cyd7=yd7
gen tyd7=yd7
replace cyd7=0 if type=="JT"
replace tyd7=0 if type~="JT"

gen cyd8=yd8
gen tyd8=yd8
replace cyd8=0 if type=="JT"
replace tyd8=0 if type~="JT"

gen cyd9=yd9
gen tyd9=yd9
replace cyd9=0 if type=="JT"
replace tyd9=0 if type~="JT"

gen cyd10=yd10
gen tyd10=yd10
replace cyd10=0 if type=="JT"
replace tyd10=0 if type~="JT"

gen cyd11=yd11
gen tyd11=yd11
replace cyd11=0 if type=="JT"
replace tyd11=0 if type~="JT"

gen cyd12=yd12
gen tyd12=yd12
replace cyd12=0 if type=="JT"
replace tyd12=0 if type~="JT"

program define nlct_1
version 7.0
if "`1'"=="?"{
global S_1 "a3 a4 a5 a6 a7 a8 a9 a10 a11 a12 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12 c1 c2 c3 c4 c5 c6 c7 c8 d1 d2 d3 d4 d5 d6 d7 d8 e2 e3 e4 e5 e6 e7 e8 e9 e10 e11 e12"
global a3=1
global a4=1
global a5=1
global a6=1
global a7=1
global a8=1
global a9=1
global a10=1
global a11=1
global a12=1
global b2=.1
global b3=.1
global b4=.1
global b5=.1
global b6=.1
global b7=.1
global b8=.1
global b9=.1
global b10=.1
global b11=.1
global b12=.1
global c1=.1
global c2=.1
global c3=.1
global c4=.1
global c5=.1
global c6=.1
global c7=.1
global c8=.1
global d1=.1
global d2=.1
global d3=.1
global d4=.1
global d5=.1
global d6=.1
global d7=.1
global d8=.1
global e2=.1
global e3=.1
global e4=.1
global e5=.1
global e6=.1
global e7=.1
global e8=.1
global e9=.1
global e10=.1
global e11=.1
global e12=.1
exit
}

replace `1'=$a3*cyd3+$a4*cyd4+$a5*cyd5+$a6*cyd6+$a7*cyd7/*
*/+$a8*cyd8+$a9*cyd9+$a10*cyd10+$a11*cyd11+$a12*cyd12/*
*/+exp($b2*cyd2+$b3*cyd3+$b4*cyd4+$b5*cyd5+$b6*cyd6+$b7*cyd7/*
*/+$b8*cyd8+$b9*cyd9+$b10*cyd10+$b11*cyd11+$b12*cyd12/*
*/+$c1*wght_c+$c2*wdth_c+$c3*hght_c+$c4*hp_c+$c5*tran_c+$c6*ps_c+$c7*ac_c/*
*/+$c8)+exp($e2*tyd2+$e3*tyd3+$e4*tyd4+$e5*tyd5+$e6*tyd6+$e7*tyd7/*
*/+$e8*tyd8+$e9*tyd9+$e10*tyd10+$e11*tyd11+$e12*tyd12/*
*/+$d1*wght_t+$d2*wdth_t+$d3*hght_t+$d4*hp_t+$d5*tran_t+$d6*ps_t+$d7*four_t+$d8)

end

nl ct_1 price

gen winv=1/exp(_b[b2]*cyd2+_b[b3]*cyd3+_b[b4]*cyd4+_b[b5]*cyd5+_b[b6]*cyd6+_b[b7]*cyd7/*
*/+_b[b8]*cyd8+_b[b9]*cyd9+_b[b10]*cyd10+_b[b11]*cyd11+_b[b12]*cyd12/*
*/+_b[c1]*wght_c+_b[c2]*wdth_c+_b[c3]*hght_c+_b[c4]*hp_c+_b[c5]*tran_c+_b[c6]*ps_c/*
*/+_b[c7]*ac_c+_b[c8])

replace winv=1/exp(_b[e2]*tyd2+_b[e3]*tyd3+_b[e4]*tyd4+_b[e5]*tyd5+_b[e6]*tyd6/*
*/+_b[e7]*tyd7+_b[e8]*tyd8+_b[e9]*tyd9+_b[e10]*tyd10+_b[e11]*tyd11+_b[e12]*tyd12/*
*/+_b[d1]*wght_t+_b[d2]*wdth_t+_b[d3]*hght_t+_b[d4]*hp_t/*
*/+_b[d5]*tran_t+_b[d6]*ps_t+_b[d7]*four_t+_b[d8]) if ve==2

gen nprice=price*winv


program define nlct_2
version 7.0
if "`1'"=="?"{
global S_1 "a3 a4 a5 a6 a7 a8 a9 a10 a11 a12 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12 c1 c2 c3 c4 c5 c6 c7 c8 d1 d2 d3 d4 d5 d6 d7 d8 e2 e3 e4 e5 e6 e7 e8 e9 e10 e11 e12"
global a3=1
global a4=1
global a5=1
global a6=1
global a7=1
global a8=1
global a9=1
global a10=1
global a11=1
global a12=1
global b2=.1
global b3=.1
global b4=.1
global b5=.1
global b6=.1
global b7=.1
global b8=.1
global b9=.1
global b10=.1
global b11=.1
global b12=.1
global c1=.1
global c2=.1
global c3=.1
global c4=.1
global c5=.1
global c6=.1
global c7=.1
global c8=.1
global d1=.1
global d2=.1
global d3=.1
global d4=.1
global d5=.1
global d6=.1
global d7=.1
global d8=.1
global e2=.1
global e3=.1
global e4=.1
global e5=.1
global e6=.1
global e7=.1
global e8=.1
global e9=.1
global e10=.1
global e11=.1
global e12=.1
exit
}

replace `1'=winv*($a3*cyd3+$a4*cyd4+$a5*cyd5+$a6*cyd6+$a7*cyd7/*
*/+$a8*cyd8+$a9*cyd9+$a10*cyd10+$a11*cyd11+$a12*cyd12)/*
*/+winv*exp($b2*cyd2+$b3*cyd3+$b4*cyd4+$b5*cyd5+$b6*cyd6+$b7*cyd7/*
*/+$b8*cyd8+$b9*cyd9+$b10*cyd10+$b11*cyd11+$b12*cyd12/*
*/+$c1*wght_c+$c2*wdth_c+$c3*hght_c+$c4*hp_c+$c5*tran_c+$c6*ps_c+$c7*ac_c/*
*/+$c8)+winv*exp($e2*tyd2+$e3*tyd3+$e4*tyd4+$e5*tyd5+$e6*tyd6+$e7*tyd7/*
*/+$e8*tyd8+$e9*tyd9+$e10*tyd10+$e11*tyd11+$e12*tyd12/*
*/+$d1*wght_t+$d2*wdth_t+$d3*hght_t+$d4*hp_t+$d5*tran_t+$d6*ps_t+$d7*four_t+$d8)

end

nl ct_2 nprice

program drop _all
log close
exit

Output:

. capture log close

. log using Z:\home\pacha\github\advanced-international-trade\first-edition\Chapte
> r-8\system_nocon.log,replace
(note: file Z:\home\pacha\github\advanced-international-trade\first-edition\Chapte
> r-8\system_nocon.log not found)
----------------------------------------------------------------------------------
      name:  <unnamed>
       log:  Z:\home\pacha\github\advanced-international-trade\first-edition\Chapt
> er-8\system_nocon.log
  log type:  text
 opened on:  24 Jun 2024, 00:33:59

. 
. set matsize 400

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         400     max. RHS vars in models          1.254M
                                                            -----------
                                                                53.163M

. 
. use Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\tr
> uck_7990,clear

. gen ve=2

. rename wdth wdth_t

. rename hght hght_t

. rename weight wght_t

. rename hp hp_t

. rename four four_t

. rename tran tran_t

. rename ps ps_t

. rename ac ac_t

. 
. save Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\t
> ruck_temp,replace
(note: file Z:\home\pacha\github\advanced-international-trade\first-edition\Chapte
> r-8\truck_temp.dta not found)
file Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\tru
> ck_temp.dta saved

. 
. use Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-8\ca
> r_7990,clear

. gen ve=1

. rename wdth wdth_c

. rename hght hght_c

. rename wght wght_c

. rename hp hp_c

. rename four four_c

. rename tran tran_c

. rename ps ps_c

. rename ac ac_c

. 
. append using Z:\home\pacha\github\advanced-international-trade\first-edition\Cha
> pter-8\truck_temp

. 
. replace wdth_c=0 if wdth_c==.
(120 real changes made)

. replace hght_c=0 if hght_c==.
(120 real changes made)

. replace wght_c=0 if wght_c==.
(120 real changes made)

. replace hp_c=0 if hp_c==.
(120 real changes made)

. replace four_c=0 if four_c==.
(120 real changes made)

. replace tran_c=0 if tran_c==.
(120 real changes made)

. replace ps_c=0 if ps_c==.
(120 real changes made)

. replace ac_c=0 if ac_c==.
(120 real changes made)

. replace wdth_t=0 if wdth_t==.
(284 real changes made)

. replace hght_t=0 if hght_t==.
(284 real changes made)

. replace wght_t=0 if wght_t==.
(284 real changes made)

. replace hp_t=0 if hp_t==.
(284 real changes made)

. replace four_t=0 if four_t==.
(284 real changes made)

. replace tran_t=0 if tran_t==.
(284 real changes made)

. replace ps_t=0 if ps_t==.
(284 real changes made)

. replace ac_t=0 if ac_t==.
(284 real changes made)

. 
. tab year, gen(yd)

       year |      Freq.     Percent        Cum.
------------+-----------------------------------
         79 |         31        7.67        7.67
         80 |         34        8.42       16.09
         81 |         35        8.66       24.75
         82 |         35        8.66       33.42
         83 |         36        8.91       42.33
         84 |         40        9.90       52.23
         85 |         43       10.64       62.87
         86 |         33        8.17       71.04
         87 |         35        8.66       79.70
         88 |         30        7.43       87.13
         89 |         26        6.44       93.56
         90 |         26        6.44      100.00
------------+-----------------------------------
      Total |        404      100.00

. 
. gen cyd2=yd2

. gen tyd2=yd2

. replace cyd2=0 if type=="JT"
(8 real changes made)

. replace tyd2=0 if type~="JT"
(26 real changes made)

. 
. gen cyd3=yd3

. gen tyd3=yd3

. replace cyd3=0 if type=="JT"
(9 real changes made)

. replace tyd3=0 if type~="JT"
(26 real changes made)

. 
. gen cyd4=yd4

. gen tyd4=yd4

. replace cyd4=0 if type=="JT"
(9 real changes made)

. replace tyd4=0 if type~="JT"
(26 real changes made)

. 
. gen cyd5=yd5

. gen tyd5=yd5

. replace cyd5=0 if type=="JT"
(7 real changes made)

. replace tyd5=0 if type~="JT"
(29 real changes made)

. 
. gen cyd6=yd6

. gen tyd6=yd6

. replace cyd6=0 if type=="JT"
(7 real changes made)

. replace tyd6=0 if type~="JT"
(33 real changes made)

. 
. gen cyd7=yd7

. gen tyd7=yd7

. replace cyd7=0 if type=="JT"
(7 real changes made)

. replace tyd7=0 if type~="JT"
(36 real changes made)

. 
. gen cyd8=yd8

. gen tyd8=yd8

. replace cyd8=0 if type=="JT"
(7 real changes made)

. replace tyd8=0 if type~="JT"
(26 real changes made)

. 
. gen cyd9=yd9

. gen tyd9=yd9

. replace cyd9=0 if type=="JT"
(6 real changes made)

. replace tyd9=0 if type~="JT"
(29 real changes made)

. 
. gen cyd10=yd10

. gen tyd10=yd10

. replace cyd10=0 if type=="JT"
(5 real changes made)

. replace tyd10=0 if type~="JT"
(25 real changes made)

. 
. gen cyd11=yd11

. gen tyd11=yd11

. replace cyd11=0 if type=="JT"
(6 real changes made)

. replace tyd11=0 if type~="JT"
(20 real changes made)

. 
. gen cyd12=yd12

. gen tyd12=yd12

. replace cyd12=0 if type=="JT"
(5 real changes made)

. replace tyd12=0 if type~="JT"
(21 real changes made)

. 
. program define nlct_1
  1. version 7.0
  2. if "`1'"=="?"{
  3. global S_1 "a3 a4 a5 a6 a7 a8 a9 a10 a11 a12 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 
> b12 c1 c2 c3 c4 c5 c6 c7 c8 d1 d2 d3 d4 d5 d6 d7 d8 e2 e3 e4 e5 e6 e7 e8 e9 e10 
> e11 e12"
  4. global a3=1
  5. global a4=1
  6. global a5=1
  7. global a6=1
  8. global a7=1
  9. global a8=1
 10. global a9=1
 11. global a10=1
 12. global a11=1
 13. global a12=1
 14. global b2=.1
 15. global b3=.1
 16. global b4=.1
 17. global b5=.1
 18. global b6=.1
 19. global b7=.1
 20. global b8=.1
 21. global b9=.1
 22. global b10=.1
 23. global b11=.1
 24. global b12=.1
 25. global c1=.1
 26. global c2=.1
 27. global c3=.1
 28. global c4=.1
 29. global c5=.1
 30. global c6=.1
 31. global c7=.1
 32. global c8=.1
 33. global d1=.1
 34. global d2=.1
 35. global d3=.1
 36. global d4=.1
 37. global d5=.1
 38. global d6=.1
 39. global d7=.1
 40. global d8=.1
 41. global e2=.1
 42. global e3=.1
 43. global e4=.1
 44. global e5=.1
 45. global e6=.1
 46. global e7=.1
 47. global e8=.1
 48. global e9=.1
 49. global e10=.1
 50. global e11=.1
 51. global e12=.1
 52. exit
 53. }
 54. 
. replace `1'=$a3*cyd3+$a4*cyd4+$a5*cyd5+$a6*cyd6+$a7*cyd7/*
> */+$a8*cyd8+$a9*cyd9+$a10*cyd10+$a11*cyd11+$a12*cyd12/*
> */+exp($b2*cyd2+$b3*cyd3+$b4*cyd4+$b5*cyd5+$b6*cyd6+$b7*cyd7/*
> */+$b8*cyd8+$b9*cyd9+$b10*cyd10+$b11*cyd11+$b12*cyd12/*
> */+$c1*wght_c+$c2*wdth_c+$c3*hght_c+$c4*hp_c+$c5*tran_c+$c6*ps_c+$c7*ac_c/*
> */+$c8)+exp($e2*tyd2+$e3*tyd3+$e4*tyd4+$e5*tyd5+$e6*tyd6+$e7*tyd7/*
> */+$e8*tyd8+$e9*tyd9+$e10*tyd10+$e11*tyd11+$e12*tyd12/*
> */+$d1*wght_t+$d2*wdth_t+$d3*hght_t+$d4*hp_t+$d5*tran_t+$d6*ps_t+$d7*four_t+$d8)
 55. 
. end

. 
. nl ct_1 price
(obs = 404)

Iteration 0:   residual SS =  3.69e+10
...
Iteration 59:  residual SS =  3.48e+08
Iteration 60:  residual SS =  3.48e+08

      Source |       SS       df       MS            Number of obs =       404
-------------+------------------------------         F( 45,   358) =    134.73
       Model |  5.8946e+09    45   130990377         Prob > F      =    0.0000
    Residual |   348069386   358  972260.856         R-squared     =    0.9442
-------------+------------------------------         Adj R-squared =    0.9372
       Total |  6.2426e+09   403  15490412.8         Root MSE      =  986.0329
                                                     Res. dev.     =  6667.767
(ct_1)
------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          a3 |  -591.4105   1021.533    -0.58   0.563    -2600.371     1417.55
          a4 |  -1145.046   1057.554    -1.08   0.280    -3224.844    934.7527
          a5 |  -824.1875    1016.79    -0.81   0.418    -2823.819    1175.444
          a6 |  -592.6532   1010.202    -0.59   0.558    -2579.329    1394.023
          a7 |  -1306.657     1083.9    -1.21   0.229    -3438.268    824.9532
          a8 |  -98.11828   1087.933    -0.09   0.928    -2237.661    2041.425
          a9 |  -257.0587   1177.715    -0.22   0.827    -2573.168     2059.05
         a10 |  -413.3716   1310.795    -0.32   0.753    -2991.198    2164.455
         a11 |  -1220.982   1430.616    -0.85   0.394     -4034.45    1592.486
         a12 |  -1076.411   1450.708    -0.74   0.459    -3929.392    1776.569
          b2 |   .0197206   .0474133     0.42   0.678    -.0735229    .1129641
          b3 |   .2183407   .1415785     1.54   0.124    -.0600893    .4967707
          b4 |   .3398839   .1306741     2.60   0.010     .0828985    .5968693
          b5 |     .30743    .128895     2.39   0.018     .0539436    .5609165
          b6 |    .338236   .1254585     2.70   0.007     .0915077    .5849643
          b7 |   .4292664   .1225126     3.50   0.001     .1883316    .6702011
          b8 |   .3855295   .1262504     3.05   0.002     .1372438    .6338152
          b9 |   .4743625   .1264804     3.75   0.000     .2256246    .7231004
         b10 |   .5337515   .1278549     4.17   0.000     .2823104    .7851925
         b11 |   .6487194   .1271098     5.10   0.000     .3987437    .8986951
         b12 |   .6188886   .1311527     4.72   0.000      .360962    .8768152
          c1 |   .4598504   .0886104     5.19   0.000      .285588    .6341127
          c2 |   .1780578   .0341819     5.21   0.000     .1108352    .2452803
          c3 |  -.3850267   .0481769    -7.99   0.000     -.479772   -.2902814
          c4 |   .2680433   .0393044     6.82   0.000     .1907467    .3453399
          c5 |   .0679777   .0194236     3.50   0.001      .029779    .1061764
          c6 |   .0932556    .021253     4.39   0.000     .0514591     .135052
          c7 |   .1534133    .021252     7.22   0.000     .1116189    .1952077
          c8 |   8.572183   .0409525   209.32   0.000     8.491646    8.652721
          d1 |   1.024883   .2198255     4.66   0.000     .5925712    1.457194
          d2 |   .5861134   .7924544     0.74   0.460    -.9723374    2.144564
          d3 |   -.149842   .2155522    -0.70   0.487    -.5737496    .2740656
          d4 |   1.150419    .347234     3.31   0.001     .4675444    1.833294
          d5 |   .3132963   .1385789     2.26   0.024     .0407654    .5858273
          d6 |   .0163816   .1407749     0.12   0.907     -.260468    .2932313
          d7 |   226.2423   4.491789    50.37   0.000     217.4087    235.0759
          d8 |  -223.6678          .        .       .            .           .
          e2 |  -9.321882          .        .       .            .           .
          e3 |   225.8105   4.416818    51.13   0.000     217.1244    234.4967
          e4 |    225.818   4.410297    51.20   0.000     217.1447    234.4914
          e5 |   225.3464   4.385453    51.38   0.000      216.722    233.9709
          e6 |   225.4068   4.379008    51.47   0.000      216.795    234.0186
          e7 |   225.3594   4.388533    51.35   0.000     216.7288    233.9899
          e8 |   225.6487   4.417134    51.08   0.000     216.9619    234.3355
          e9 |   225.5402   4.407819    51.17   0.000     216.8718    234.2087
         e10 |   226.0232   4.412848    51.22   0.000     217.3448    234.7015
         e11 |   226.0775   4.462525    50.66   0.000     217.3015    234.8536
         e12 |    226.117   4.421014    51.15   0.000     217.4226    234.8115
------------------------------------------------------------------------------
* Parameter e2 taken as constant term in model & ANOVA table
 (SEs, P values, CIs, and correlations are asymptotic approximations)

. 
. gen winv=1/exp(_b[b2]*cyd2+_b[b3]*cyd3+_b[b4]*cyd4+_b[b5]*cyd5+_b[b6]*cyd6+_b[b7
> ]*cyd7/*
> */+_b[b8]*cyd8+_b[b9]*cyd9+_b[b10]*cyd10+_b[b11]*cyd11+_b[b12]*cyd12/*
> */+_b[c1]*wght_c+_b[c2]*wdth_c+_b[c3]*hght_c+_b[c4]*hp_c+_b[c5]*tran_c+_b[c6]*ps
> _c/*
> */+_b[c7]*ac_c+_b[c8])

. 
. replace winv=1/exp(_b[e2]*tyd2+_b[e3]*tyd3+_b[e4]*tyd4+_b[e5]*tyd5+_b[e6]*tyd6/*
> */+_b[e7]*tyd7+_b[e8]*tyd8+_b[e9]*tyd9+_b[e10]*tyd10+_b[e11]*tyd11+_b[e12]*tyd12
> /*
> */+_b[d1]*wght_t+_b[d2]*wdth_t+_b[d3]*hght_t+_b[d4]*hp_t/*
> */+_b[d5]*tran_t+_b[d6]*ps_t+_b[d7]*four_t+_b[d8]) if ve==2
(120 real changes made, 18 to missing)

. 
. gen nprice=price*winv
(18 missing values generated)

. 
. 
. program define nlct_2
  1. version 7.0
  2. if "`1'"=="?"{
  3. global S_1 "a3 a4 a5 a6 a7 a8 a9 a10 a11 a12 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 
> b12 c1 c2 c3 c4 c5 c6 c7 c8 d1 d2 d3 d4 d5 d6 d7 d8 e2 e3 e4 e5 e6 e7 e8 e9 e10 
> e11 e12"
  4. global a3=1
  5. global a4=1
  6. global a5=1
  7. global a6=1
  8. global a7=1
  9. global a8=1
 10. global a9=1
 11. global a10=1
 12. global a11=1
 13. global a12=1
 14. global b2=.1
 15. global b3=.1
 16. global b4=.1
 17. global b5=.1
 18. global b6=.1
 19. global b7=.1
 20. global b8=.1
 21. global b9=.1
 22. global b10=.1
 23. global b11=.1
 24. global b12=.1
 25. global c1=.1
 26. global c2=.1
 27. global c3=.1
 28. global c4=.1
 29. global c5=.1
 30. global c6=.1
 31. global c7=.1
 32. global c8=.1
 33. global d1=.1
 34. global d2=.1
 35. global d3=.1
 36. global d4=.1
 37. global d5=.1
 38. global d6=.1
 39. global d7=.1
 40. global d8=.1
 41. global e2=.1
 42. global e3=.1
 43. global e4=.1
 44. global e5=.1
 45. global e6=.1
 46. global e7=.1
 47. global e8=.1
 48. global e9=.1
 49. global e10=.1
 50. global e11=.1
 51. global e12=.1
 52. exit
 53. }
 54. 
. replace `1'=winv*($a3*cyd3+$a4*cyd4+$a5*cyd5+$a6*cyd6+$a7*cyd7/*
> */+$a8*cyd8+$a9*cyd9+$a10*cyd10+$a11*cyd11+$a12*cyd12)/*
> */+winv*exp($b2*cyd2+$b3*cyd3+$b4*cyd4+$b5*cyd5+$b6*cyd6+$b7*cyd7/*
> */+$b8*cyd8+$b9*cyd9+$b10*cyd10+$b11*cyd11+$b12*cyd12/*
> */+$c1*wght_c+$c2*wdth_c+$c3*hght_c+$c4*hp_c+$c5*tran_c+$c6*ps_c+$c7*ac_c/*
> */+$c8)+winv*exp($e2*tyd2+$e3*tyd3+$e4*tyd4+$e5*tyd5+$e6*tyd6+$e7*tyd7/*
> */+$e8*tyd8+$e9*tyd9+$e10*tyd10+$e11*tyd11+$e12*tyd12/*
> */+$d1*wght_t+$d2*wdth_t+$d3*hght_t+$d4*hp_t+$d5*tran_t+$d6*ps_t+$d7*four_t+$d8)
 55. 
. end

. 
. nl ct_2 nprice
(obs = 386)

Iteration 0:   residual SS =  3793.244
...
Iteration 51:  residual SS =  11.84729
Iteration 52:  residual SS =  11.84729

      Source |       SS       df       MS            Number of obs =       386
-------------+------------------------------         F( 46,   339) =   1272.95
       Model |  2046.39509    46  44.4868497         Prob > F      =    0.0000
    Residual |  11.8472856   339  .034947745         R-squared     =    0.9942
-------------+------------------------------         Adj R-squared =    0.9935
       Total |  2058.24237   385  5.34608409         Root MSE      =  .1869432
                                                     Res. dev.     = -249.3025
(ct_2)
------------------------------------------------------------------------------
      nprice |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          a3 |   129.1587   649.8698     0.20   0.843    -1149.127    1407.444
          a4 |  -332.9346   853.5884    -0.39   0.697    -2011.931    1346.062
          a5 |  -39.00799   816.3593    -0.05   0.962    -1644.776     1566.76
          a6 |  -49.30975   887.7125    -0.06   0.956    -1795.428    1696.809
          a7 |  -251.5048   1055.969    -0.24   0.812    -2328.582    1825.572
          a8 |   475.7476   1105.123     0.43   0.667    -1698.014    2649.509
          a9 |   1305.252   1054.533     1.24   0.217    -769.0007    3379.505
         a10 |   1500.556   1475.416     1.02   0.310    -1401.567    4402.679
         a11 |   275.3094    1918.11     0.14   0.886    -3497.586    4048.205
         a12 |  -369.0768   2256.641    -0.16   0.870    -4807.859    4069.706
          b2 |  -.0382212   .0476313    -0.80   0.423    -.1319113    .0554688
          b3 |   .1007584   .1545476     0.65   0.515    -.2032345    .4047514
          b4 |   .3643006   .1549828     2.35   0.019     .0594514    .6691497
          b5 |   .3350521   .1522164     2.20   0.028     .0356445    .6344596
          b6 |    .448507   .1460037     3.07   0.002     .1613198    .7356943
          b7 |   .5008198   .1605704     3.12   0.002     .1849799    .8166597
          b8 |   .5229822   .1722726     3.04   0.003     .1841243      .86184
          b9 |   .3892165   .1802644     2.16   0.032     .0346389    .7437941
         b10 |   .5894213   .2041663     2.89   0.004     .1878289    .9910137
         b11 |   .8546564    .199235     4.29   0.000      .462764    1.246549
         b12 |   1.000789   .1993482     5.02   0.000     .6086733    1.392904
          c1 |   1.059199   .3598464     2.94   0.003     .3513857    1.767012
          c2 |   .1615223   .1132255     1.43   0.155    -.0611907    .3842354
          c3 |  -.6524711   .2018085    -3.23   0.001    -1.049426   -.2555164
          c4 |   .2672449   .1289842     2.07   0.039     .0135347    .5209551
          c5 |   .2030882   .0598443     3.39   0.001     .0853753    .3208011
          c6 |   .2113444   .0828113     2.55   0.011     .0484557    .3742331
          c7 |   .1550375   .0660018     2.35   0.019     .0252129    .2848621
          c8 |   8.340437    .114401    72.91   0.000     8.115411    8.565462
          d1 |   1.111578   .2140655     5.19   0.000     .6905136    1.532641
          d2 |  -.4348055    .168151    -2.59   0.010    -.7655563   -.1040547
          d3 |   .0754878   .0932058     0.81   0.419    -.1078468    .2588223
          d4 |    .559007    .181628     3.08   0.002     .2017472    .9162667
          d5 |   .1239908   .0427616     2.90   0.004     .0398792    .2081023
          d6 |  -.0185416   .0827602    -0.22   0.823    -.1813297    .1442466
          d7 |  -.5680364   .7627409    -0.74   0.457    -2.068338    .9322647
          d8 |   7.995761   .1883688    42.45   0.000     7.625242     8.36628
          e2 |         .1          .        .       .            .           .
          e3 |  -.3274455   .7327471    -0.45   0.655    -1.768749    1.113858
          e4 |  -.3156744   .7324389    -0.43   0.667    -1.756372    1.125023
          e5 |  -.5595854   .7452185    -0.75   0.453     -2.02542    .9062493
          e6 |  -.5473584   .7454929    -0.73   0.463    -2.013733    .9190161
          e7 |  -.6603122   .7473731    -0.88   0.378    -2.130385    .8097605
          e8 |  -.4940828   .7382813    -0.67   0.504    -1.946272    .9581066
          e9 |  -.4857295   .7335855    -0.66   0.508    -1.928682    .9572232
         e10 |  -.2352299   .7308603    -0.32   0.748    -1.672822    1.202362
         e11 |  -.1529434   .7360252    -0.21   0.836    -1.600695    1.294808
         e12 |  -.0194963   .7348633    -0.03   0.979    -1.464963     1.42597
------------------------------------------------------------------------------
* Parameter e2 taken as constant term in model & ANOVA table
 (SEs, P values, CIs, and correlations are asymptotic approximations)

. 
. program drop _all

. log close
      name:  <unnamed>
       log:  Z:\home\pacha\github\advanced-international-trade\first-edition\Chapt
> er-8\system_nocon.log
  log type:  text
 closed on:  24 Jun 2024, 00:34:17
----------------------------------------------------------------------------------

. exit

end of do-file

My code

system_nocom.do

truck_7990 <- feenstra_88$truck_7990 %>%
  mutate(ve = 2) %>%
  rename(
    wdth_t = wdth, hght_t = hght, wght_t = weight, hp_t = hp, four_t = four,
    tran_t = tran, ps_t = ps, ac_t = ac
  )

car_7990 <- feenstra_88$car_7990 %>%
  mutate(ve = 1) %>%
  rename(
    wdth_c = wdth, hght_c = hght, wght_c = wght, hp_c = hp, four_c = four,
    tran_c = tran, ps_c = ps, ac_c = ac
  )

truck_7990 <- truck_7990 %>%
  bind_rows(car_7990) %>%
  mutate(
    wdth_c = ifelse(is.na(wdth_c), 0, wdth_c),
    hght_c = ifelse(is.na(hght_c), 0, hght_c),
    wght_c = ifelse(is.na(wght_c), 0, wght_c),
    hp_c = ifelse(is.na(hp_c), 0, hp_c),
    four_c = ifelse(is.na(four_c), 0, four_c),
    tran_c = ifelse(is.na(tran_c), 0, tran_c),
    ps_c = ifelse(is.na(ps_c), 0, ps_c),
    ac_c = ifelse(is.na(ac_c), 0, ac_c),
    wdth_t = ifelse(is.na(wdth_t), 0, wdth_t),
    hght_t = ifelse(is.na(hght_t), 0, hght_t),
    wght_t = ifelse(is.na(wght_t), 0, wght_t),
    hp_t = ifelse(is.na(hp_t), 0, hp_t),
    four_t = ifelse(is.na(four_t), 0, four_t),
    tran_t = ifelse(is.na(tran_t), 0, tran_t),
    ps_t = ifelse(is.na(ps_t), 0, ps_t),
    ac_t = ifelse(is.na(ac_t), 0, ac_t)
  )

truck_7990 %>%
  group_by(year) %>%
  summarise(freq = n()) %>%
  ungroup() %>%
  mutate(
    percent = freq / sum(freq) * 100,
    cum = cumsum(percent)
  )

# A tibble: 12 × 4
    year  freq percent    cum
   <dbl> <int>   <dbl>  <dbl>
 1    79    31    7.67   7.67
 2    80    34    8.42  16.1 
 3    81    35    8.66  24.8 
 4    82    35    8.66  33.4 
 5    83    36    8.91  42.3 
 6    84    40    9.90  52.2 
 7    85    43   10.6   62.9 
 8    86    33    8.17  71.0 
 9    87    35    8.66  79.7 
10    88    30    7.43  87.1 
11    89    26    6.44  93.6 
12    90    26    6.44 100   

truck_7990 <- truck_7990 %>%
  mutate(yd = as.factor(year - min(year) + 1))

truck_7990_dummy <- model.matrix(~ yd - 1, data = truck_7990)

truck_7990 <- truck_7990 %>%
  bind_cols(as.data.frame(truck_7990_dummy))

truck_7990 <- truck_7990 %>%
  mutate(
    cyd2 = case_when(
      type == "JT" ~ 0,
      TRUE ~ yd2
    ),
    tyd2 = case_when(
      type != "JT" ~ 0,
      TRUE ~ yd2
    ),
    cyd3 = case_when(
      type == "JT" ~ 0,
      TRUE ~ yd3
    ),
    tyd3 = case_when(
      type != "JT" ~ 0,
      TRUE ~ yd3
    ),
    cyd4 = case_when(
      type == "JT" ~ 0,
      TRUE ~ yd4
    ),
    tyd4 = case_when(
      type != "JT" ~ 0,
      TRUE ~ yd4
    ),
    cyd5 = case_when(
      type == "JT" ~ 0,
      TRUE ~ yd5
    ),
    tyd5 = case_when(
      type != "JT" ~ 0,
      TRUE ~ yd5
    ),
    cyd6 = case_when(
      type == "JT" ~ 0,
      TRUE ~ yd6
    ),
    tyd6 = case_when(
      type != "JT" ~ 0,
      TRUE ~ yd6
    ),
    cyd7 = case_when(
      type == "JT" ~ 0,
      TRUE ~ yd7
    ),
    tyd7 = case_when(
      type != "JT" ~ 0,
      TRUE ~ yd7
    ),
    cyd8 = case_when(
      type == "JT" ~ 0,
      TRUE ~ yd8
    ),
    tyd8 = case_when(
      type != "JT" ~ 0,
      TRUE ~ yd8
    ),
    cyd9 = case_when(
      type == "JT" ~ 0,
      TRUE ~ yd9
    ),
    tyd9 = case_when(
      type != "JT" ~ 0,
      TRUE ~ yd9
    ),
    cyd10 = case_when(
      type == "JT" ~ 0,
      TRUE ~ yd10
    ),
    tyd10 = case_when(
      type != "JT" ~ 0,
      TRUE ~ yd10
    ),
    cyd11 = case_when(
      type == "JT" ~ 0,
      TRUE ~ yd11
    ),
    tyd11 = case_when(
      type != "JT" ~ 0,
      TRUE ~ yd11
    ),
    cyd12 = case_when(
      type == "JT" ~ 0,
      TRUE ~ yd12
    ),
    tyd12 = case_when(
      type != "JT" ~ 0,
      TRUE ~ yd12
    )
  )

initial_values <- list(
  a3 = 1, a4 = 1, a5 = 1, a6 = 1, a7 = 1, a8 = 1, a9 = 1, a10 = 1, a11 = 1,
  a12 = 1,
  b2 = 0.1, b3 = 0.1, b4 = 0.1, b5 = 0.1, b6 = 0.1, b7 = 0.1, b8 = 0.1,
  b9 = 0.1, b10 = 0.1, b11 = 0.1, b12 = 0.1,
  c1 = 0.1, c2 = 0.1, c3 = 0.1, c4 = 0.1, c5 = 0.1, c6 = 0.1, c7 = 0.1,
  c8 = 0.1,
  d1 = 0.1, d2 = 0.1, d3 = 0.1, d4 = 0.1, d5 = 0.1, d6 = 0.1, d7 = 0.1,
  d8 = 0.1,
  e2 = 0.1, e3 = 0.1, e4 = 0.1, e5 = 0.1, e6 = 0.1, e7 = 0.1, e8 = 0.1,
  e9 = 0.1, e10 = 0.1, e11 = 0.1, e12 = 0.1
)

fit <- nlsLM(
  price ~ a3 * cyd3 + a4 * cyd4 + a5 * cyd5 + a6 * cyd6 + a7 * cyd7 +
    a8 * cyd8 + a9 * cyd9 + a10 * cyd10 + a11 * cyd11 + a12 * cyd12 +
    exp(b2 * cyd2 + b3 * cyd3 + b4 * cyd4 + b5 * cyd5 + b6 * cyd6 + b7 * cyd7 +
      b8 * cyd8 + b9 * cyd9 + b10 * cyd10 + b11 * cyd11 + b12 * cyd12 +
      c1 * wght_c + c2 * wdth_c + c3 * hght_c + c4 * hp_c + c5 * tran_c +
      c6 * ps_c + c7 * ac_c + c8) +
    exp(e2 * tyd2 + e3 * tyd3 + e4 * tyd4 + e5 * tyd5 + e6 * tyd6 + e7 * tyd7 +
      e8 * tyd8 + e9 * tyd9 + e10 * tyd10 + e11 * tyd11 + e12 * tyd12 +
      d1 * wght_t + d2 * wdth_t + d3 * hght_t + d4 * hp_t + d5 * tran_t +
      d6 * ps_t + d7 * four_t + d8),
  data = truck_7990,
  start = initial_values,
  # adjust parameters to account to slow convergence
  control = nls.lm.control(maxiter = 1000, maxfev = 10000)
)

summary(fit)

Formula: price ~ a3 * cyd3 + a4 * cyd4 + a5 * cyd5 + a6 * cyd6 + a7 * 
    cyd7 + a8 * cyd8 + a9 * cyd9 + a10 * cyd10 + a11 * cyd11 + 
    a12 * cyd12 + exp(b2 * cyd2 + b3 * cyd3 + b4 * cyd4 + b5 * 
    cyd5 + b6 * cyd6 + b7 * cyd7 + b8 * cyd8 + b9 * cyd9 + b10 * 
    cyd10 + b11 * cyd11 + b12 * cyd12 + c1 * wght_c + c2 * wdth_c + 
    c3 * hght_c + c4 * hp_c + c5 * tran_c + c6 * ps_c + c7 * 
    ac_c + c8) + exp(e2 * tyd2 + e3 * tyd3 + e4 * tyd4 + e5 * 
    tyd5 + e6 * tyd6 + e7 * tyd7 + e8 * tyd8 + e9 * tyd9 + e10 * 
    tyd10 + e11 * tyd11 + e12 * tyd12 + d1 * wght_t + d2 * wdth_t + 
    d3 * hght_t + d4 * hp_t + d5 * tran_t + d6 * ps_t + d7 * 
    four_t + d8)

Parameters:
      Estimate Std. Error t value Pr(>|t|)    
a3  -232.06287  893.96625  -0.260 0.795332    
a4  -632.87850  914.45900  -0.692 0.489338    
a5  -367.97647  876.38040  -0.420 0.674825    
a6   -48.30074  863.33409  -0.056 0.955416    
a7  -749.19564  928.78692  -0.807 0.420413    
a8   187.75024  939.25918   0.200 0.841679    
a9   333.01836 1009.60725   0.330 0.741708    
a10  243.82112 1132.40125   0.215 0.829646    
a11 -211.61067 1212.77220  -0.174 0.861583    
a12   11.61149 1219.90438   0.010 0.992411    
b2     0.01556    0.04777   0.326 0.744779    
b3     0.16598    0.13240   1.254 0.210804    
b4     0.27475    0.12216   2.249 0.025124 *  
b5     0.24519    0.11990   2.045 0.041592 *  
b6     0.26695    0.11691   2.283 0.022994 *  
b7     0.36389    0.11358   3.204 0.001478 ** 
b8     0.33385    0.11688   2.856 0.004537 ** 
b9     0.40608    0.11768   3.451 0.000626 ***
b10    0.46226    0.11912   3.881 0.000124 ***
b11    0.55678    0.11831   4.706 3.62e-06 ***
b12    0.51644    0.12254   4.214 3.18e-05 ***
c1     0.47758    0.08994   5.310 1.93e-07 ***
c2     0.21440    0.04811   4.457 1.12e-05 ***
c3    -0.39686    0.04746  -8.362 1.41e-15 ***
c4     0.28379    0.03979   7.132 5.56e-12 ***
c5     0.06936    0.02017   3.439 0.000653 ***
c6     0.09921    0.02178   4.555 7.20e-06 ***
c7     0.16038    0.02163   7.415 8.94e-13 ***
c8     8.38888    0.20671  40.583  < 2e-16 ***
d1     0.88011    0.21681   4.059 6.05e-05 ***
d2     0.47431    0.54808   0.865 0.387397    
d3    -0.15194    0.16103  -0.944 0.346051    
d4     0.89964    0.34067   2.641 0.008636 ** 
d5     0.25704    0.11574   2.221 0.026994 *  
d6     0.02296    0.10258   0.224 0.822986    
d7     0.64556    0.26226   2.462 0.014309 *  
d8     3.42341    3.80931   0.899 0.369421    
e2    -0.75842    1.13213  -0.670 0.503352    
e3     0.38740    0.33106   1.170 0.242720    
e4     0.35839    0.31518   1.137 0.256252    
e5     0.10602    0.32166   0.330 0.741881    
e6     0.13491    0.32069   0.421 0.674237    
e7     0.04074    0.30751   0.132 0.894680    
e8     0.20083    0.31805   0.631 0.528160    
e9     0.09907    0.31555   0.314 0.753733    
e10    0.40385    0.36546   1.105 0.269884    
e11    0.43926    0.34766   1.263 0.207252    
e12    0.48634    0.35567   1.367 0.172359    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 971.1 on 356 degrees of freedom

Number of iterations to convergence: 46 
Achieved convergence tolerance: 1.49e-08

fit_coef <- coef(fit)

truck_7990 <- truck_7990 %>%
  mutate(
    winv = case_when(
      ve == 1 ~ 1 / exp(fit_coef["b2"] * cyd2 + fit_coef["b3"] * cyd3 +
        fit_coef["b4"] * cyd4 + fit_coef["b5"] * cyd5 + fit_coef["b6"] * cyd6 +
        fit_coef["b7"] * cyd7 + fit_coef["b8"] * cyd8 + fit_coef["b9"] * cyd9 +
        fit_coef["b10"] * cyd10 + fit_coef["b11"] * cyd11 +
        fit_coef["b12"] * cyd12 + fit_coef["c1"] * wght_c +
        fit_coef["c2"] * wdth_c + fit_coef["c3"] * hght_c +
        fit_coef["c4"] * hp_c + fit_coef["c5"] * tran_c +
        fit_coef["c6"] * ps_c + fit_coef["c7"] * ac_c + fit_coef["c8"]),
      ve == 2 ~ 1 / exp(fit_coef["e2"] * tyd2 + fit_coef["e3"] * tyd3 +
        fit_coef["e4"] * tyd4 + fit_coef["e5"] * tyd5 + fit_coef["e6"] * tyd6 +
        fit_coef["e7"] * tyd7 + fit_coef["e8"] * tyd8 + fit_coef["e9"] * tyd9 +
        fit_coef["e10"] * tyd10 + fit_coef["e11"] * tyd11 +
        fit_coef["e12"] * tyd12 + fit_coef["d1"] * wght_t +
        fit_coef["d2"] * wdth_t + fit_coef["d3"] * hght_t +
        fit_coef["d4"] * hp_t + fit_coef["d5"] * tran_t +
        fit_coef["d6"] * ps_t + fit_coef["d7"] * four_t + fit_coef["d8"]),
    ),
    nprice = price * winv
  )

fit2 <- nlsLM(
  nprice ~winv * (a3 * cyd3 + a4 * cyd4 + a5 * cyd5 + a6 * cyd6 + a7 * cyd7 +
    a8 * cyd8 + a9 * cyd9 + a10 * cyd10 + a11 * cyd11 + a12 * cyd12) +
    winv * exp(b2 * cyd2 + b3 * cyd3 + b4 * cyd4 + b5 * cyd5 + b6 * cyd6 +
      b7 * cyd7 + b8 * cyd8 + b9 * cyd9 + b10 * cyd10 + b11 * cyd11 +
      b12 * cyd12 + c1 * wght_c + c2 * wdth_c + c3 * hght_c + c4 * hp_c +
      c5 * tran_c + c6 * ps_c + c7 * ac_c + c8) +
    winv * exp(e2 * tyd2 + e3 * tyd3 + e4 * tyd4 + e5 * tyd5 + e6 * tyd6 +
      e7 * tyd7 + e8 * tyd8 + e9 * tyd9 + e10 * tyd10 + e11 * tyd11 +
      e12 * tyd12 + d1 * wght_t + d2 * wdth_t + d3 * hght_t + d4 * hp_t +
      d5 * tran_t + d6 * ps_t + d7 * four_t + d8),
  data = truck_7990,
  start = initial_values,
  control = nls.lm.control(maxiter = 1000, maxfev = 10000)
)

summary(fit2)

Formula: nprice ~ winv * (a3 * cyd3 + a4 * cyd4 + a5 * cyd5 + a6 * cyd6 + 
    a7 * cyd7 + a8 * cyd8 + a9 * cyd9 + a10 * cyd10 + a11 * cyd11 + 
    a12 * cyd12) + winv * exp(b2 * cyd2 + b3 * cyd3 + b4 * cyd4 + 
    b5 * cyd5 + b6 * cyd6 + b7 * cyd7 + b8 * cyd8 + b9 * cyd9 + 
    b10 * cyd10 + b11 * cyd11 + b12 * cyd12 + c1 * wght_c + c2 * 
    wdth_c + c3 * hght_c + c4 * hp_c + c5 * tran_c + c6 * ps_c + 
    c7 * ac_c + c8) + winv * exp(e2 * tyd2 + e3 * tyd3 + e4 * 
    tyd4 + e5 * tyd5 + e6 * tyd6 + e7 * tyd7 + e8 * tyd8 + e9 * 
    tyd9 + e10 * tyd10 + e11 * tyd11 + e12 * tyd12 + d1 * wght_t + 
    d2 * wdth_t + d3 * hght_t + d4 * hp_t + d5 * tran_t + d6 * 
    ps_t + d7 * four_t + d8)

Parameters:
      Estimate Std. Error t value Pr(>|t|)    
a3   6.538e+02  2.721e+02   2.403 0.016762 *  
a4   1.301e+03  2.979e+02   4.365 1.67e-05 ***
a5   1.423e+03  2.842e+02   5.007 8.72e-07 ***
a6   1.938e+03  2.927e+02   6.620 1.32e-10 ***
a7   1.971e+03  2.748e+02   7.172 4.31e-12 ***
a8   2.478e+03  3.573e+02   6.936 1.91e-11 ***
a9   2.834e+03  2.997e+02   9.459  < 2e-16 ***
a10  3.732e+03  5.234e+02   7.130 5.63e-12 ***
a11  4.650e+03  5.096e+02   9.125  < 2e-16 ***
a12  5.719e+03  5.764e+02   9.922  < 2e-16 ***
b2  -5.319e-03  6.580e-02  -0.081 0.935618    
b3  -1.247e-02  9.428e-02  -0.132 0.894871    
b4  -9.225e-02  1.060e-01  -0.870 0.384779    
b5  -1.341e-01  1.021e-01  -1.314 0.189793    
b6  -1.575e-01  1.045e-01  -1.507 0.132733    
b7  -9.892e-02  9.792e-02  -1.010 0.313095    
b8  -6.148e-02  1.125e-01  -0.546 0.585133    
b9   6.130e-02  1.017e-01   0.603 0.546933    
b10 -1.094e-02  1.215e-01  -0.090 0.928310    
b11 -1.361e-01  1.382e-01  -0.985 0.325535    
b12 -3.865e-01  1.695e-01  -2.281 0.023133 *  
c1   4.558e-01  2.257e-01   2.019 0.044207 *  
c2   5.981e-01  2.570e-01   2.327 0.020522 *  
c3  -2.753e-01  1.126e-01  -2.444 0.015028 *  
c4   6.650e-01  1.146e-01   5.804 1.43e-08 ***
c5   1.549e-01  5.320e-02   2.911 0.003831 ** 
c6   1.789e-01  5.407e-02   3.309 0.001031 ** 
c7   1.813e-01  5.576e-02   3.252 0.001257 ** 
c8   5.149e+00  1.476e+00   3.489 0.000547 ***
d1   4.063e-01  6.114e-02   6.645 1.14e-10 ***
d2   1.191e-02  4.744e-02   0.251 0.801843    
d3   6.573e-02  3.308e-02   1.987 0.047646 *  
d4   2.526e-01  4.697e-02   5.378 1.37e-07 ***
d5   3.851e-02  1.365e-02   2.820 0.005068 ** 
d6  -2.048e-02  3.637e-02  -0.563 0.573782    
d7   2.448e-01  3.168e-02   7.726 1.14e-13 ***
d8   7.326e+00  3.043e-01  24.072  < 2e-16 ***
e2   2.753e-02  1.555e-02   1.771 0.077445 .  
e3   2.568e-01  2.406e-02  10.670  < 2e-16 ***
e4   2.587e-01  2.458e-02  10.524  < 2e-16 ***
e5   1.887e-01  2.371e-02   7.960 2.32e-14 ***
e6   1.903e-01  2.388e-02   7.968 2.21e-14 ***
e7   1.387e-01  2.473e-02   5.606 4.16e-08 ***
e8   1.847e-01  2.676e-02   6.901 2.37e-11 ***
e9   1.956e-01  2.944e-02   6.643 1.15e-10 ***
e10  2.804e-01  3.795e-02   7.390 1.06e-12 ***
e11  3.098e-01  3.738e-02   8.289 2.36e-15 ***
e12  3.654e-01  3.774e-02   9.682  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.1613 on 356 degrees of freedom

Number of iterations to convergence: 28 
Achieved convergence tolerance: 1.49e-08