# Packages ----
library(archive)
library(readr)
library(dplyr)
library(tidyr)
library(purrr)
library(knitr)
# Extract ----
fzip <- "first-edition/Chapter-2.zip"
dout <- gsub("\\.zip$", "", fzip)
if (!dir.exists(dout)) {
archive_extract("first-edition/Chapter-2.zip",
dir = "first-edition/Chapter-2"
)
}
# Read ----
fout <- paste0(dout, "/trefler.rds")
fout2 <- paste0(dout, "/trefler_desc.rds")
if (!file.exists(fout)) {
trefler <- read_csv("first-edition/Chapter-2/hov_pub.csv", col_names = F) %>%
rename(
country = X1,
factor = X2,
at = X3,
v = X4,
y = X5,
b = X6,
ypc = X7,
pop = X8
)
# Transform ----
# see https://www.stata.com/manuals/rsummarize.pdf
# https://www.stata.com/manuals/degen.pdf
# https://www.stata.com/manuals/degen.pdf
# Create an auxiliary table for delta values
delta_values <- tibble(
country = c(
"Bangladesh", "Pakistan", "Indonesia", "Sri Lanka", "Thailand",
"Colombia", "Panama", "Yugoslavia", "Portugal", "Uruguay", "Greece",
"Ireland", "Spain", "Israel", "Hong Kong", "New Zealand", "Austria",
"Singapore", "Italy", "UK", "Japan", "Belgium", "Trinidad", "Netherlands",
"Finland", "Denmark", "West Germany", "France", "Sweden", "Norway",
"Switzerland", "Canada", "USA"
),
delta = c(
0.03, 0.09, 0.10, 0.09, 0.17, 0.16, 0.28, 0.29, 0.14, 0.11, 0.45,
0.55, 0.42, 0.49, 0.40, 0.38, 0.60, 0.48, 0.60, 0.58, 0.70, 0.65, 0.47,
0.72, 0.65, 0.73, 0.78, 0.74, 0.57, 0.69, 0.79, 0.55, 1
)
)
trefler <- trefler %>%
mutate(ypc_max = max(ypc)) %>%
mutate(
ratio = case_when(
country != "Italy" ~ ypc / ypc_max,
country == "Italy" ~ (ypc / ypc_max) + 0.0001
)
) %>%
select(-ypc_max) %>%
arrange(ratio) %>%
group_by(ratio) %>%
mutate(indexc = cur_group_id()) %>%
group_by(factor) %>%
mutate(indexf = cur_group_id()) %>%
ungroup() %>%
left_join(delta_values)
# Labels ----
# Create a separate table with the variables description
trefler_desc <- tibble(
variable = c(
"country", "factor", "at", "v", "y", "b", "ypc", "indexc",
"indexf"
),
description = c(
"Name of the country", "Name of the factor",
"Factor content of trade F=A*T", "Endowment", "GDP, World Bank, y=p*Q",
"Trade balance, World Bank b=p*T", "GDP per capita, PWT",
"Country indentifier", "Factor Indentifier"
)
)
# Save ----
saveRDS(trefler, fout)
saveRDS(trefler_desc, fout2)
} else {
trefler <- readRDS(fout)
trefler_desc <- readRDS(fout2)
}Chapter 2. The Heckscher-Ohlin Model”
In these exercises, you will reproduce some of the empirical results from Trefler (1993, 1995). To complete the exercise, the Excel file hov_pub.csv should be stored in the directory: c:\Empirical_Exercise\Chapter_2\hov_pub.csv. After this, run the STATA program hov_pub.do, which will create a new STATA data file trefler.dta.
Read and transform the data
Feenstra’s code
* This is to read the data into Stata *
set mem 30m
* insheet using c:\Empirical_Exercise\Chapter_2\trefler.csv *
insheet using "Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-2\hov_pub.csv"
rename v1 country
rename v2 factor
rename v3 AT
rename v4 V
rename v5 Y
rename v6 B
rename v7 YPC
rename v8 POP
* create country index *
quietly summarize YPC
local maxYPC=_result(6)
gen ratio=YPC/`maxYPC'
replace ratio=ratio+0.0001 if country=="Italy"
sort ratio
egen indexc=group(ratio)
* create factor index *
sort factor
egen indexf=group(factor)
* include delta *
gen delta=1
replace delta=0.03 if country=="Bangladesh"
replace delta=0.09 if country=="Pakistan"
replace delta=0.10 if country=="Indonesia"
replace delta=0.09 if country=="Sri Lanka"
replace delta=0.17 if country=="Thailand"
replace delta=0.16 if country=="Colombia"
replace delta=0.28 if country=="Panama"
replace delta=0.29 if country=="Yugoslavia"
replace delta=0.14 if country=="Portugal"
replace delta=0.11 if country=="Uruguay"
replace delta=0.45 if country=="Greece"
replace delta=0.55 if country=="Ireland"
replace delta=0.42 if country=="Spain"
replace delta=0.49 if country=="Israel"
replace delta=0.40 if country=="Hong Kong"
replace delta=0.38 if country=="New Zealand"
replace delta=0.60 if country=="Austria"
replace delta=0.48 if country=="Singapore"
replace delta=0.60 if country=="Italy"
replace delta=0.58 if country=="UK"
replace delta=0.70 if country=="Japan"
replace delta=0.65 if country=="Belgium"
replace delta=0.47 if country=="Trinidad"
replace delta=0.72 if country=="Netherlands"
replace delta=0.65 if country=="Finland"
replace delta=0.73 if country=="Denmark"
replace delta=0.78 if country=="West Germany"
replace delta=0.74 if country=="France"
replace delta=0.57 if country=="Sweden"
replace delta=0.69 if country=="Norway"
replace delta=0.79 if country=="Switzerland"
replace delta=0.55 if country=="Canada"
replace delta=1 if country=="USA"
compress
label var country "Name of the country"
label var factor "Name of the factor"
label var AT "Factor content of trade F=A*T"
label var V "Endowment"
label var Y "GDP, World Bank, y=p*Q"
label var B "Trade balance, World Bank b=p*T"
label var YPC "GDP per capita, PWT"
label var indexc "Country indentifier"
label var indexf "Factor Indentifier"
* save c:\Empirical_Exercise\Chapter_2\trefler,replace *
save "Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-2\trefler", replace
exitMy code
Exercise 1
Given identical technologies across countries, run the program sign_rank_1.do to conduct the sign test, rank test, and test for missing trade. Use the results in sign_rank_1.log to replicate columns (2) and (4) in Table 2.5.
Feenstra’s code
* This program is to conduct sign test, Rank test and Missing trade test *
capture log close
* log using c:\Empirical_Exercise\Chapter_2\sign_rank_1.log, replace *
log using "Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-2\sign_rank_1.log", replace
set mem 30m
* use C:\Empirical_Exercise\Chapter_2\trefler, clear *
use "Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-2\trefler", clear
* number of country in the dataset *
egen C=max(indexc)
egen F=max(indexf)
* Calculate the world level of Yw, Bw and Vw *
egen Yww=sum(Y)
gen Yw=Yww/F
egen Bww=sum(B)
gen Bw=Bww/F
egen Vfw=sum(V), by(indexf)
* Calculate country share Sc *
gen Sc=(Y-B)/(Yw-Bw)
* Calculate epsilon(fc) and sigma^2(f) according to eq.2 in Trefler (1995)*
gen Efc=AT-(V-Sc*Vfw)
* Construct the average epsilon for a given factor *
egen total=sum(Efc),by(indexf)
gen ave=total/C
* Construct sigma^2 and the weight *
egen tot=sum((Efc-ave)^2), by(indexf)
gen sigma2f=tot/(C-1)
codebook sigma2f
gen sigmaf=sqrt(sigma2f)
gen weight=sigmaf*sqrt(Sc)
* Using the weight, convert all the data *
gen trAT=AT/(sigmaf*sqrt(Sc))
gen trV=V/(sigmaf*sqrt(Sc))
gen trY=Y/sqrt(Sc)
gen trB=B/sqrt(Sc)
gen trVfw=Vfw/sigmaf
gen AThat=trV-Sc*trVfw
gen AThat2=(V-Sc*Vfw)/weight
* Correlation, should be .28 *
corr trAT AThat2
*************
* Sign Test *
*************
sort indexc
by indexc: count if trAT*AThat2>0
count if trAT*AThat2>0
display _result(1)/_N
*****************
* Missing Trade *
*****************
* Checking for the missing trade, should be .032 *
quietly summarize trAT
local varAT=_result(4)
quietly summarize AThat
local varHat=_result(4)
quietly summarize AThat2
local varHat2=_result(4)
display `varAT'/`varHat'
display `varAT'/`varHat2'
**************
* Rank Tests *
**************
keep country indexc indexf trAT AThat2
sort indexc indexf
reshape wide trAT AThat2, i(indexc) j(indexf)
local i=1
while `i'<9{
local j=`i'+1
while `j'<=9{
gen rank`i'`j'=((trAT`i'-trAT`j')*(AThat2`i'-AThat2`j')>0)
local j=`j'+1
}
local i=`i'+1
}
keep country indexc rank*
reshape long rank, i(indexc) j(factor)
egen r1=sum(rank), by(indexc)
gen r2=r1/36
collapse r2,by(indexc country)
sum r2
list
log close
exitMy code
# Transform ----
trefler <- readRDS(fout) %>%
# Number of country in the dataset
mutate(
c = max(indexc),
f = max(indexf)
) %>%
# Calculate the world level of Yw, Bw and Vw
mutate(
yww = sum(y),
yw = yww / f,
bww = sum(b),
bw = bww / f
) %>%
group_by(indexf) %>%
mutate(
vfw = sum(v)
) %>%
ungroup() %>%
# Calculate country share Sc
mutate(
sc = (y - b) / (yw - bw)
) %>%
# Calculate epsilon(fc) and sigma^2(f) according to eq.2 in Trefler (1995)
mutate(
efc = at - (v - sc * vfw)
) %>%
# Construct the average epsilon for a given factor
group_by(indexf) %>%
mutate(ave = sum(efc) / c) %>%
# Construct sigma^2 and the weight
mutate(
sigma2f = sum((efc - ave)^2) / (c - 1),
sigmaf = sqrt(sigma2f),
weight = sigmaf * sqrt(sc)
) %>%
ungroup() %>%
# Using the weight, convert all the data
mutate(
trat = at / (sigmaf * sqrt(sc)),
athat2 = (v - (sc * vfw)) / weight
) %>%
arrange(country)
# Correlation, should be .28
trefler %>%
select(trat, athat2) %>%
cor() trat athat2
trat 1.0000000 0.2822883
athat2 0.2822883 1.0000000# Sign Test ----
trefler %>%
group_by(country, indexc) %>%
summarize(
p = sum(trat * athat2 > 0) / n()
)# A tibble: 33 × 3
# Groups: country [33]
country indexc p
<chr> <int> <dbl>
1 Austria 17 0.556
2 Bangladesh 1 0.333
3 Belgium 22 0.667
4 Canada 32 0.556
5 Colombia 6 0.333
6 Denmark 26 0.444
7 Finland 25 0.333
8 France 28 0.333
9 Greece 11 0.111
10 Hong Kong 15 0.667
# ℹ 23 more rowstrefler %>%
summarize(
p = sum(trat * athat2 > 0) / n()
)# A tibble: 1 × 1
p
<dbl>
1 0.498# Missing Trade ----
# Checking for the missing trade, should be .032
trefler %>%
summarize(
varat = var(trat),
varhat2 = var(athat2)
) %>%
mutate(
varat_varhat2 = varat / varhat2
)# A tibble: 1 × 3
varat varhat2 varat_varhat2
<dbl> <dbl> <dbl>
1 1.61 50.3 0.0320# Rank Tests ----
trefler_wide <- trefler %>%
select(country, indexc, indexf, trat, athat2) %>%
arrange(indexc, indexf) %>%
pivot_wider(
names_from = indexf,
values_from = c(trat, athat2)
)
# This would be too long
# trefler_wide <- trefler_wide %>%
# mutate(
# rank12 = (trat_1 - trat_2) * (athat2_1 - athat2_2) > 0,
# rank13 = (trat_1 - trat_3) * (athat2_1 - athat2_3) > 0,
# ...
# rank89 = (trat_8 - trat_9) * (athat2_8 - athat2_9) > 0,
# )
# create all relevant trat_1 - trat_2, trat_1 - trat_3, etc.
ranks <- expand_grid(
x = 1:8,
y = 1:9
) %>%
filter(x < y)
# The syntax here is based on internal R developer functions, but these
# allow to create columns with minimal lines of code and avoids more complicated
# bracket syntax
trefler_rank <- map2_df(
pull(ranks, x),
pull(ranks, y),
function(x, y) {
trefler_wide %>%
mutate(
name = paste0("rank", x, y),
value = (!!sym(paste0("trat_", x)) - !!sym(paste0("trat_", y))) *
(!!sym(paste0("athat2_", x)) - !!sym(paste0("athat2_", y))) > 0
) %>%
select(country, indexc, name, value)
}
) %>%
group_by(country, indexc) %>%
summarise(r1 = sum(value)) %>%
mutate(r2 = r1 / 36)
trefler_rank# A tibble: 33 × 4
# Groups: country [33]
country indexc r1 r2
<chr> <int> <int> <dbl>
1 Austria 17 19 0.528
2 Bangladesh 1 27 0.75
3 Belgium 22 22 0.611
4 Canada 32 32 0.889
5 Colombia 6 29 0.806
6 Denmark 26 19 0.528
7 Finland 25 17 0.472
8 France 28 3 0.0833
9 Greece 11 17 0.472
10 Hong Kong 15 30 0.833
# ℹ 23 more rowstrefler_rank %>%
pull(r2) %>%
mean()[1] 0.6026936Extra step: formatting the table
trefler %>%
group_by(country, indexc) %>%
summarize(
p = sum(trat * athat2 > 0) / n()
) %>%
arrange(indexc) %>% # same order as in the book
select(country, sign_hov = p) %>%
left_join(
trefler_rank %>%
select(country, rank_hov = r2)
) %>%
bind_rows(
trefler %>%
summarize(
p = sum(trat * athat2 > 0) / n()
) %>%
mutate(
country = "All countries",
rank_hov = mean(pull(trefler_rank, r2))
) %>%
select(country, sign_hov = p, rank_hov)
) %>%
mutate_if(is.numeric, round, 2) %>% # same no of decimals as in the book
kable()| country | sign_hov | rank_hov |
|---|---|---|
| Bangladesh | 0.33 | 0.75 |
| Pakistan | 0.33 | 0.72 |
| Indonesia | 0.22 | 0.67 |
| Sri Lanka | 0.22 | 0.42 |
| Thailand | 0.22 | 0.69 |
| Colombia | 0.33 | 0.81 |
| Panama | 0.33 | 0.56 |
| Yugoslavia | 0.56 | 0.44 |
| Portugal | 0.22 | 0.53 |
| Uruguay | 1.00 | 0.72 |
| Greece | 0.11 | 0.47 |
| Ireland | 0.67 | 0.53 |
| Spain | 0.22 | 0.39 |
| Israel | 0.67 | 0.39 |
| Hong Kong | 0.67 | 0.83 |
| New Zealand | 0.44 | 0.53 |
| Austria | 0.56 | 0.53 |
| Singapore | 0.56 | 0.61 |
| Italy | 0.67 | 0.78 |
| UK | 0.67 | 0.58 |
| Japan | 0.78 | 0.78 |
| Belgium | 0.67 | 0.61 |
| Trinidad | 0.67 | 0.50 |
| Netherlands | 0.44 | 0.53 |
| Finland | 0.33 | 0.47 |
| Denmark | 0.44 | 0.53 |
| West Germany | 0.56 | 0.81 |
| France | 0.33 | 0.08 |
| Sweden | 0.44 | 0.67 |
| Norway | 0.44 | 0.61 |
| Switzerland | 0.89 | 0.56 |
| Canada | 0.56 | 0.89 |
| USA | 0.89 | 0.92 |
| All countries | 0.50 | 0.60 |
Exercise 2
Given uniform technological differences across countries, run the program sign_rank_2.do to redo the sign test, rank test, and missing trade. Use the results in sign_rank_2.log to replicate column (3) and (5), given column (6) in Table 2.5.
Feenstra’s code
* This program is to conduct sign test, Rank test and Missing trade test *
* using delta *
capture log close
* log using c:\Empirical_Exercise\Chapter_2\sign_rank_2.log, replace *
log using "Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-2\sign_rank_2.log", replace
set mem 30m
* use c:\Empirical_Exercise\Chapter_2\trefler, clear *
use "Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-2\trefler", clear
* number of country in the dataset *
egen C=max(indexc)
egen F=max(indexf)
* Calculate the world level of Yw, Bw and Vw *
egen Yww=sum(Y)
gen Yw=Yww/F
egen Bww=sum(B)
gen Bw=Bww/F
egen Vfw=sum(V), by(indexf)
egen Vw=sum(delta*V), by(indexf)
* Calculate country share Sc *
gen Sc=(Y-B)/(Yw-Bw)
* Calculate epsilon(fc) and sigma^2(f) according to eq.2 in Trefler (1995)
gen Efc=delta*AT-(delta*V-Sc*Vw)
* Construct the average epsilon for a given factor *
egen total=sum(Efc),by(indexf)
gen ave=total/C
* Construct sigma^2 and the weight *
egen tot=sum((Efc-ave)^2), by(indexf)
gen sigma2f=tot/(C-1)
codebook sigma2f
gen sigmaf=sqrt(sigma2f)
gen weight=sigmaf*sqrt(Sc)
* Using the weight, convert all the data *
gen trAT=delta*AT/weight
gen AThat2=(delta*V-Sc*Vw)/weight
* Correlation *
corr trAT AThat2
*************
* Sign Test *
*************
sort indexc
by indexc: count if trAT*AThat2>0
count if trAT*AThat2>0
display _result(1)/_N
*****************
* Missing Trade *
*****************
quietly summarize trAT
local varAT=_result(4)
quietly summarize AThat
local varHat=_result(4)
quietly summarize AThat2
local varHat2=_result(4)
display `varAT'/`varHat'
display `varAT'/`varHat2'
*************
* Rank Test *
*************
keep country indexc indexf trAT AThat2
sort indexc indexf
reshape wide trAT AThat2, i(indexc) j(indexf)
local i=1
while `i'<9{
local j=`i'+1
while `j'<=9{
gen rank`i'`j'=((trAT`i'-trAT`j')*(AThat2`i'-AThat2`j')>0)
local j=`j'+1
}
local i=`i'+1
}
keep country indexc rank*
reshape long rank, i(indexc) j(factor)
egen r1=sum(rank), by(indexc)
gen r2=r1/36
collapse r2,by(indexc country)
sum r2
list
log close
exitMy code
# Transform ----
trefler <- readRDS(fout) %>%
# Number of country in the dataset
mutate(
c = max(indexc),
f = max(indexf)
) %>%
# Calculate the world level of Yw, Bw and Vw
mutate(
yww = sum(y),
yw = yww / f,
bww = sum(b),
bw = bww / f
) %>%
group_by(indexf) %>%
mutate(
vfw = sum(v),
vw = sum(delta * v)
) %>%
ungroup() %>%
# Calculate country share Sc
mutate(
sc = (y - b) / (yw - bw)
) %>%
# Calculate epsilon(fc) and sigma^2(f) according to eq.2 in Trefler (1995)
mutate(
efc = delta * at - (delta * v - sc * vw)
) %>%
# Construct the average epsilon for a given factor
group_by(indexf) %>%
mutate(ave = sum(efc) / c) %>%
# Construct sigma^2 and the weight
mutate(
sigma2f = sum((efc - ave)^2) / (c - 1),
sigmaf = sqrt(sigma2f),
weight = sigmaf * sqrt(sc)
) %>%
ungroup() %>%
# Using the weight, convert all the data
mutate(
trat = delta * at / weight,
athat2 = (delta * v - (sc * vw)) / weight
)
# Correlation should be .41
trefler %>%
select(trat, athat2) %>%
cor() trat athat2
trat 1.0000000 0.4099617
athat2 0.4099617 1.0000000# Sign Test ----
trefler %>%
group_by(country, indexc) %>%
summarize(
p = sum(trat * athat2 > 0) / n()
)# A tibble: 33 × 3
# Groups: country [33]
country indexc p
<chr> <int> <dbl>
1 Austria 17 0.667
2 Bangladesh 1 0.778
3 Belgium 22 0.778
4 Canada 32 0.222
5 Colombia 6 0.889
6 Denmark 26 0.444
7 Finland 25 0.444
8 France 28 0.333
9 Greece 11 0.556
10 Hong Kong 15 0.889
# ℹ 23 more rowstrefler %>%
summarize(
p = sum(trat * athat2 > 0) / n()
)# A tibble: 1 × 1
p
<dbl>
1 0.620# Missing Trade ----
# Checking for the missing trade, should be .07
trefler %>%
summarize(
varat = var(trat),
varhat2 = var(athat2)
) %>%
mutate(
varat_varhat2 = varat / varhat2
)# A tibble: 1 × 3
varat varhat2 varat_varhat2
<dbl> <dbl> <dbl>
1 1.34 19.0 0.0706# Rank Tests ----
trefler_wide <- trefler %>%
select(country, indexc, indexf, trat, athat2) %>%
arrange(indexc, indexf) %>%
pivot_wider(
names_from = indexf,
values_from = c(trat, athat2)
)
ranks <- expand_grid(
x = 1:8,
y = 1:9
) %>%
filter(x < y)
trefler_rank <- map2_df(
pull(ranks, x),
pull(ranks, y),
function(x, y) {
trefler_wide %>%
mutate(
name = paste0("rank", x, y),
value = (!!sym(paste0("trat_", x)) - !!sym(paste0("trat_", y))) *
(!!sym(paste0("athat2_", x)) - !!sym(paste0("athat2_", y))) > 0
) %>%
select(country, indexc, name, value)
}
) %>%
group_by(country, indexc) %>%
summarise(r1 = sum(value)) %>%
mutate(r2 = r1 / 36)
trefler_rank# A tibble: 33 × 4
# Groups: country [33]
country indexc r1 r2
<chr> <int> <int> <dbl>
1 Austria 17 16 0.444
2 Bangladesh 1 28 0.778
3 Belgium 22 19 0.528
4 Canada 32 20 0.556
5 Colombia 6 31 0.861
6 Denmark 26 15 0.417
7 Finland 25 18 0.5
8 France 28 7 0.194
9 Greece 11 27 0.75
10 Hong Kong 15 26 0.722
# ℹ 23 more rowstrefler_rank %>%
pull(r2) %>%
mean()[1] 0.6153199Extra step: formatting the table
trefler %>%
group_by(country, indexc) %>%
summarize(
p = sum(trat * athat2 > 0) / n()
) %>%
arrange(indexc) %>% # same order as in the book
select(country, sign_hov = p) %>%
left_join(
trefler_rank %>%
select(country, rank_hov = r2)
) %>%
bind_rows(
trefler %>%
summarize(
p = sum(trat * athat2 > 0) / n()
) %>%
mutate(
country = "All countries",
rank_hov = mean(pull(trefler_rank, r2))
) %>%
select(country, sign_hov = p, rank_hov)
) %>%
mutate_if(is.numeric, round, 2) %>% # same no of decimals as in the book
kable()| country | sign_hov | rank_hov |
|---|---|---|
| Bangladesh | 0.78 | 0.78 |
| Pakistan | 0.67 | 0.78 |
| Indonesia | 0.67 | 0.67 |
| Sri Lanka | 0.56 | 0.67 |
| Thailand | 0.67 | 0.72 |
| Colombia | 0.89 | 0.86 |
| Panama | 0.78 | 0.78 |
| Yugoslavia | 0.67 | 0.61 |
| Portugal | 0.78 | 0.58 |
| Uruguay | 0.11 | 0.53 |
| Greece | 0.56 | 0.75 |
| Ireland | 0.44 | 0.39 |
| Spain | 0.78 | 0.69 |
| Israel | 0.89 | 0.69 |
| Hong Kong | 0.89 | 0.72 |
| New Zealand | 0.22 | 0.61 |
| Austria | 0.67 | 0.44 |
| Singapore | 1.00 | 0.61 |
| Italy | 0.33 | 0.67 |
| UK | 0.78 | 0.64 |
| Japan | 0.67 | 0.78 |
| Belgium | 0.78 | 0.53 |
| Trinidad | 1.00 | 0.53 |
| Netherlands | 0.44 | 0.47 |
| Finland | 0.44 | 0.50 |
| Denmark | 0.44 | 0.42 |
| West Germany | 0.67 | 0.78 |
| France | 0.33 | 0.19 |
| Sweden | 0.44 | 0.36 |
| Norway | 0.44 | 0.78 |
| Switzerland | 0.89 | 0.50 |
| Canada | 0.22 | 0.56 |
| USA | 0.56 | 0.72 |
| All countries | 0.62 | 0.62 |
Notes
The Stata code that I run returns the same values as R. However:
- Austria should have values 0.67 and 0.47. I got 0.67 and 0.44.
- France should have values 0.33 and 0.22. I got 0.33 and 0.19.
- Switzerland should have values 0.89 and 0.47. I got 0.89 and 0.50.
Exercise 3
Allowing all factors in each country to have different productivities, now run the program compute_pi.do to compute factor productivities \(\pi_k^i\) as Trefler (1993). Note that there are 9 factors in the original data set, but these are now aggregated to just 4 factors, which are labor (endowment 1), capital (endowment 2), cropland (endowment 3) and pasture (endowment 4). Using the results in pi_.log or alternatively in the data files pi_1.dta, pi_2.dta, pi_3.dta, pi_4.dta to answer the following:
- Which factor has the most negative productivities estimated?
- What is the correlation between the estimated labor productivity and the productivities of other factors? What is the correlation between each factor productivity and GDP per-capita (which you can find in the file
trefler.dta)?
Feenstra’s code
* This program is to compute pai, the factor productivity *
capture log close
* log using c:\Empirical_Exercise\Chapter_2\pi.log,replace *
log using "Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-2\pi.log", replace
set mem 30m
* use c:\Empirical_Exercise\Chapter_2\trefler, clear *
use "Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-2\trefler", clear
* number of country in the dataset *
egen C=max(indexc)
egen F=max(indexf)
* Calculate the world level of Yw, Bw and Vw *
egen Yww=sum(Y)
gen Yw=Yww/F
egen Bww=sum(B)
gen Bw=Bww/F
egen Vfw=sum(V), by(indexf)
* Calculate country share Sc *
gen Sc=(Y-B)/(Yw-Bw)
* Calculate epsilon(fc) and sigma^2(f) according to eq.2 in Trefler (1995)
gen Efc=AT-(V-Sc*Vfw)
* Construct the average epsilon for a given factor *
egen total=sum(Efc),by(indexf)
gen ave=total/C
* Construct sigma^2 and the weight *
egen tot=sum((Efc-ave)^2), by(indexf)
gen sigma2f=tot/(C-1)
codebook sigma2f
gen sigmaf=sqrt(sigma2f)
gen weight=sigmaf*sqrt(Sc)
* Using the weight, convert all the data *
gen trAT=AT/(sigmaf*sqrt(Sc))
gen trV=V/(sigmaf*sqrt(Sc))
gen trY=Y/sqrt(Sc)
gen trB=B/sqrt(Sc)
gen trVfw=Vfw/sigmaf
gen AThat=trV-Sc*trVfw
gen AThat2=(V-Sc*Vfw)/weight
* Construct Aggregate Labor Endowment *
preserve
keep if indexf==7 |indexf==8 | indexf==9
gen en=2
replace en=3 if indexf==8
replace en=4 if indexf==9
keep country factor AT V en indexc Sc
* save c:\Empirical_Exercise\Chapter_2\indexf_189,replace *
save "Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-2\indexf_189", replace
restore
preserve
drop if indexf==7 |indexf==8 | indexf==9
egen v_l=sum(V), by(country)
egen AT_l=sum(AT), by(country)
drop V AT factor
rename v_l V
rename AT_l AT
gen en=1
collapse (mean)AT V en indexc Sc, by(country)
gen str5 factor="Labor"
* save c:\Empirical_Exercise\Chapter_2\indexf_L,replace *
save "Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-2\indexf_L", replace
restore
* use c:\Empirical_Exercise\Chapter_2\indexf_189,clear *
use "Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-2\indexf_189", clear
* append using c:\Empirical_Exercise\Chapter_2\indexf_L *
append using "Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-2\indexf_L"
sort indexc en
* save c:\Empirical_Exercise\Chapter_2\pi,replace *
save "Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-2\pi", replace
************************************
* Compute Pi: factor productivity *
************************************
* use c:\Empirical_Exercise\Chapter_2\pi, clear *
use "Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-2\pi", clear
gen p_0=1
gen p_1=1
local i=1
while `i'<=4{
preserve
keep if en==`i'
local j=1
while `j'<51{
replace p_0=p_1
gen Vp=p_0*V
egen Vpw=sum(Vp)
replace p_1=(AT+Sc*Vpw)/V
replace p_1=1 if country=="USA"
drop Vp Vpw
local j=`j'+1
}
keep en country indexc p_1
* save c:\Empirical_Exercise\Chapter_2\pi_`i',replace *
save "Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-2\pi_`i'", replace
restore
local i=`i'+1
}
local i=1
while `i'<=4{
* use c:\Empirical_Exercise\Chapter_2\pi_`i',clear *
use "Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-2\pi_`i'", clear
sort en indexc
by en: list en indexc country p_1
local i=`i'+1
}
log close
exitMy code
trefler <- readRDS(fout) %>%
# Number of country in the dataset
mutate(
c = max(indexc),
f = max(indexf)
) %>%
# Calculate the world level of Yw, Bw and Vw
mutate(
yww = sum(y),
yw = yww / f,
bww = sum(b),
bw = bww / f
) %>%
group_by(indexf) %>%
mutate(
vfw = sum(v),
vw = sum(delta * v)
) %>%
ungroup() %>%
# Calculate country share Sc
mutate(
sc = (y - b) / (yw - bw)
) %>%
# Calculate epsilon(fc) and sigma^2(f) according to eq.2 in Trefler (1995)
mutate(
efc = delta * at - (delta * v - sc * vw)
) %>%
# Construct the average epsilon for a given factor
group_by(indexf) %>%
mutate(ave = sum(efc) / c) %>%
# Construct sigma^2 and the weight
mutate(
sigma2f = sum((efc - ave)^2) / (c - 1),
sigmaf = sqrt(sigma2f),
weight = sigmaf * sqrt(sc)
) %>%
ungroup() %>%
# Using the weight, convert all the data
mutate(
trat = delta * at / weight,
athat2 = (delta * v - (sc * vw)) / weight
)
# No need to save changes and restore
trefler2 <- trefler %>%
# Construct Aggregate Labor Endowment
filter(indexf %in% 7:9) %>%
mutate(
en = case_when(
indexf == 7 ~ 2,
indexf == 8 ~ 3,
indexf == 9 ~ 4
)
) %>%
select(country, factor, indexf, at, v, en, indexc, sc)
trefler3 <- trefler %>%
filter(!(indexf %in% 7:9)) %>%
group_by(country) %>%
# No need to create v_l and at_l to then rename and then collapse
summarise(
v = sum(v),
at = sum(at),
sc = mean(sc),
indexc = mean(indexc)
) %>%
mutate(
en = 1,
factor = "Labor"
)
trefler3 <- trefler2 %>%
select(-indexf) %>%
bind_rows(trefler3) %>%
arrange(indexc, en)
# Compute Pi: factor productivity
# No need to save intermediate outputs, we proceed with iteration
trefler4 <- map_df(
trefler3 %>%
distinct(en) %>%
pull(),
function(x) {
d <- trefler3 %>%
filter(en == x) %>%
mutate(p0 = 1, p1 = 1)
iter <- 50
for (i in seq_len(iter)) {
d <- d %>%
mutate(
p0 = p1,
vp = p0 * v,
vpw = sum(vp),
p1 = ifelse(country == "USA", 1, (at + sc * vpw) / v)
) %>%
select(-vp, -vpw)
}
# Tidy alternative to the for loop
# d <- accumulate(seq_len(iter), .init = d, ~ .x %>%
# mutate(
# p0 = p1,
# p1 = ifelse(country == "USA", 1, (at + sc * sum(p1 * v)) / v)
# )) %>%
# .[[iter + 1]]
d %>%
select(country, indexc, en, p1)
}
)Extra step: formatting the tables
trefler4 %>%
arrange(country, en) %>%
kable()| country | indexc | en | p1 |
|---|---|---|---|
| Austria | 17 | 1 | 0.5694186 |
| Austria | 17 | 2 | 0.5421980 |
| Austria | 17 | 3 | 1.1596592 |
| Austria | 17 | 4 | 1.9753040 |
| Bangladesh | 1 | 1 | 0.0165219 |
| Bangladesh | 1 | 2 | 0.9119021 |
| Bangladesh | 1 | 3 | 0.0230836 |
| Bangladesh | 1 | 4 | 1.2561775 |
| Belgium | 22 | 1 | 0.7233988 |
| Belgium | 22 | 2 | 0.6457500 |
| Belgium | 22 | 3 | 0.4575561 |
| Belgium | 22 | 4 | 6.8868596 |
| Canada | 32 | 1 | 0.7799865 |
| Canada | 32 | 2 | 0.7359194 |
| Canada | 32 | 3 | 0.4738445 |
| Canada | 32 | 4 | 0.9541137 |
| Colombia | 6 | 1 | 0.1940833 |
| Colombia | 6 | 2 | 0.4856291 |
| Colombia | 6 | 3 | 0.5963939 |
| Colombia | 6 | 4 | 0.1271541 |
| Denmark | 26 | 1 | 0.7061784 |
| Denmark | 26 | 2 | 0.7035640 |
| Denmark | 26 | 3 | 1.7598990 |
| Denmark | 26 | 4 | 28.7283398 |
| Finland | 25 | 1 | 0.6969619 |
| Finland | 25 | 2 | 0.6453199 |
| Finland | 25 | 3 | 0.6789600 |
| Finland | 25 | 4 | 22.2966445 |
| France | 28 | 1 | 0.7356650 |
| France | 28 | 2 | 0.6150762 |
| France | 28 | 3 | 1.5589519 |
| France | 28 | 4 | 3.1663974 |
| Greece | 11 | 1 | 0.3140718 |
| Greece | 11 | 2 | 0.4401574 |
| Greece | 11 | 3 | 0.6072472 |
| Greece | 11 | 4 | 0.5059134 |
| Hong Kong | 15 | 1 | 0.3781684 |
| Hong Kong | 15 | 2 | 0.5150965 |
| Hong Kong | 15 | 3 | -229.0729738 |
| Hong Kong | 15 | 4 | -879.5376414 |
| Indonesia | 3 | 1 | 0.0432824 |
| Indonesia | 3 | 2 | 0.2506530 |
| Indonesia | 3 | 3 | 0.1641388 |
| Indonesia | 3 | 4 | 0.4576649 |
| Ireland | 12 | 1 | 0.4166084 |
| Ireland | 12 | 2 | 0.4783923 |
| Ireland | 12 | 3 | 1.4803708 |
| Ireland | 12 | 4 | 0.6129137 |
| Israel | 14 | 1 | 0.6131932 |
| Israel | 14 | 2 | 0.5049116 |
| Israel | 14 | 3 | 2.5171947 |
| Israel | 14 | 4 | 2.1567210 |
| Italy | 19 | 1 | 0.5907437 |
| Italy | 19 | 2 | 0.5122213 |
| Italy | 19 | 3 | 0.6419316 |
| Italy | 19 | 4 | 3.1452732 |
| Japan | 21 | 1 | 0.6049210 |
| Japan | 21 | 2 | 0.6502130 |
| Japan | 21 | 3 | 4.2923043 |
| Japan | 21 | 4 | 100.5984017 |
| Netherlands | 24 | 1 | 0.7933355 |
| Netherlands | 24 | 2 | 0.7513015 |
| Netherlands | 24 | 3 | 9.0914542 |
| Netherlands | 24 | 4 | 13.0978390 |
| New Zealand | 16 | 1 | 0.5850298 |
| New Zealand | 16 | 2 | 0.6197254 |
| New Zealand | 16 | 3 | 7.5203295 |
| New Zealand | 16 | 4 | 0.3673216 |
| Norway | 30 | 1 | 0.7816517 |
| Norway | 30 | 2 | 0.6199874 |
| Norway | 30 | 3 | 1.8129219 |
| Norway | 30 | 4 | 34.5985787 |
| Pakistan | 2 | 1 | 0.0394124 |
| Pakistan | 2 | 2 | 0.4867497 |
| Pakistan | 2 | 3 | 0.0975686 |
| Pakistan | 2 | 4 | 0.4731917 |
| Panama | 7 | 1 | 0.2279774 |
| Panama | 7 | 2 | 0.3224079 |
| Panama | 7 | 3 | 0.5834955 |
| Panama | 7 | 4 | 0.2973391 |
| Portugal | 9 | 1 | 0.1759864 |
| Portugal | 9 | 2 | 0.2971070 |
| Portugal | 9 | 3 | -0.3833130 |
| Portugal | 9 | 4 | 1.6397757 |
| Singapore | 18 | 1 | 0.4873306 |
| Singapore | 18 | 2 | 0.3209652 |
| Singapore | 18 | 3 | -25.4922493 |
| Singapore | 18 | 4 | 795.1006524 |
| Spain | 13 | 1 | 0.4172726 |
| Spain | 13 | 2 | 0.5194890 |
| Spain | 13 | 3 | 0.2365766 |
| Spain | 13 | 4 | 1.0176692 |
| Sri Lanka | 4 | 1 | 0.0344433 |
| Sri Lanka | 4 | 2 | 0.1259789 |
| Sri Lanka | 4 | 3 | 0.2300838 |
| Sri Lanka | 4 | 4 | 0.7949096 |
| Sweden | 29 | 1 | 0.7270576 |
| Sweden | 29 | 2 | 0.9445322 |
| Sweden | 29 | 3 | 0.9073509 |
| Sweden | 29 | 4 | 7.6468612 |
| Switzerland | 31 | 1 | 0.9317447 |
| Switzerland | 31 | 2 | 0.6079722 |
| Switzerland | 31 | 3 | 3.7425295 |
| Switzerland | 31 | 4 | 3.3350218 |
| Thailand | 5 | 1 | 0.0489020 |
| Thailand | 5 | 2 | 0.3929541 |
| Thailand | 5 | 3 | 0.3002516 |
| Thailand | 5 | 4 | 16.9392348 |
| Trinidad | 23 | 1 | 0.4483440 |
| Trinidad | 23 | 2 | 0.4193396 |
| Trinidad | 23 | 3 | -0.9042060 |
| Trinidad | 23 | 4 | 4.6219780 |
| UK | 20 | 1 | 0.6332355 |
| UK | 20 | 2 | 0.8159872 |
| UK | 20 | 3 | 1.4765402 |
| UK | 20 | 4 | 2.2422499 |
| USA | 33 | 1 | 1.0000000 |
| USA | 33 | 2 | 1.0000000 |
| USA | 33 | 3 | 1.0000000 |
| USA | 33 | 4 | 1.0000000 |
| Uruguay | 10 | 1 | 0.2029693 |
| Uruguay | 10 | 2 | 0.4060566 |
| Uruguay | 10 | 3 | 0.5709917 |
| Uruguay | 10 | 4 | 0.0984165 |
| West Germany | 27 | 1 | 0.7691833 |
| West Germany | 27 | 2 | 0.6629313 |
| West Germany | 27 | 3 | 1.0541740 |
| West Germany | 27 | 4 | 6.8647780 |
| Yugoslavia | 8 | 1 | 0.1997569 |
| Yugoslavia | 8 | 2 | 0.2985477 |
| Yugoslavia | 8 | 3 | 0.3189656 |
| Yugoslavia | 8 | 4 | 0.6397429 |