Income,Technological Advances and the Convergence Hypothesis in the Asia-Pacific
Introduction
Methodology
Development accounting
(Absolute) Beta convergence
Data
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns; sns.set_theme(color_codes=True)
import plotly.express as px
import plotly.graph_objects as go
#chart_studio.tools.set_credentials_file(username='econdata777', api_key='ADDhere')
import statsmodels.api as sm
import statsmodels.formula.api as smf
!pip install stargazer
from stargazer.stargazer import Stargazer, LineLocation
#from spreg import OLS
#from spreg import MoranRes
#from spreg import ML_Lag
#from spreg import ML_Error
import warnings
#warnings.filterwarnings('ignore')
WARNING: The directory '/home/jovyan/.cache/pip' or its parent directory is not owned or is not writable by the current user. The cache has been disabled. Check the permissions and owner of that directory. If executing pip with sudo, you should use sudo's -H flag.
Collecting stargazer
Downloading stargazer-0.0.5-py3-none-any.whl (9.7 kB)
Installing collected packages: stargazer
Successfully installed stargazer-0.0.5
WARNING: You are using pip version 21.2.3; however, version 22.2.2 is available.
You should consider upgrading via the '/home/jovyan/venv/bin/python -m pip install --upgrade pip' command.
df00 = pd.read_csv("/work/data/PWT100+countryIDs.csv")
df00
countryIDint64
1 - 183
CountryCodeobject
PRT1.1%
PSE1.1%
181 others97.8%
0
1
ALB
1
1
ALB
2
1
ALB
3
1
ALB
4
1
ALB
5
1
ALB
6
1
ALB
7
1
ALB
8
1
ALB
9
1
ALB
df00.columns
df00.dtypes
# Import dataset descriptions
df00_def = pd.read_csv("/work/data/PWT100+countryIDs-descriptions.csv")
df00_def
Variable_nameobject
countryID1.6%
CountryCode1.6%
61 others96.8%
Varariable_labelobject
Numeric country ID based on the alphabetical order of PWT1001.6%
56 others88.9%
Missing9.5%
20
hc
Human capital index, see note hc
21
ccon
Real consumption of households and government, at current PPPs (in mil. 2017US$)
22
cda
Real domestic absorption, see note cda
23
cgdpe
Expenditure-side real GDP at current PPPs (in mil. 2017US$)
24
cgdpo
Output-side real GDP at current PPPs (in mil. 2017US$)
25
cn
Capital stock at current PPPs (in mil. 2017US$)
26
ck
Capital services levels at current PPPs (USA=1)
27
ctfp
TFP level at current PPPs (USA=1)
28
cwtfp
Welfare-relevant TFP levels at current PPPs (USA=1)
29
rgdpna
Real GDP at constant 2017 national prices (in mil. 2017US$)
# Generate log of real GDP per worker (labor productivity)
df00['ln_lp'] = np.log(df00['rgdpo']/df00['emp'])
# Generate log of the adjusted ratio of physical capital to output
df00['ln_k'] = np.log(df00['cn']/df00['cgdpo'])
# Generate log of human capital per worker = human capital index
df00['ln_h'] = df00['hc']
# Generate log of aggregate efficiency = normalized total factor productivity
df00['ln_A'] = df00['cwtfp']
# Subset the sample
df0 = df00[['CountryCode', 'CountryName', 'year', 'SubRegion_PWT100', 'SubContinent', 'Continent',
'incomegroup', 'nonoil', 'intermediate', 'OECD', 'pop', 'ln_lp', 'ln_k', 'ln_h', 'ln_A']]
# Select time period (1980~2019)
# [The np.range function doesn't include the termination parameter (enter n+1 to include n)]
df1 = df0[df0['year'].isin(np.arange(1980, 2020))]
# Eliminate missing values
df2 = df1.dropna(axis=0, how='any', thresh=None, subset=None, inplace=False)
# Focus on countries in East Asia & Pacific
df = df2[df2["SubRegion_PWT100"].isin(['East Asia & Pacific'],)]
# Reset data index
df = df.reset_index(drop=True)
df
CountryCodeobject
AUS6.3%
CHN6.3%
14 others87.5%
CountryNameobject
Australia6.3%
China6.3%
14 others87.5%
630
THA
Thailand
631
THA
Thailand
632
THA
Thailand
633
THA
Thailand
634
THA
Thailand
635
THA
Thailand
636
THA
Thailand
637
THA
Thailand
638
THA
Thailand
639
THA
Thailand
df.columns
# Save the final-studied data to the local path
df.to_csv("/work/data/AS&P.csv")
Descriptive statistics
df.describe().round(2)
yearfloat64
nonoilfloat64
count
640
640
mean
1999.5
0.62
std
11.55
0.48
min
1980
0
25%
1989.75
0
50%
1999.5
1
75%
2009.25
1
max
2019
1
df.query("year == 1980").describe().round(2)
yearfloat64
nonoilfloat64
count
16
16
mean
1980
0.62
std
0
0.5
min
1980
0
25%
1980
0
50%
1980
1
75%
1980
1
max
1980
1
df.query("year == 2019").describe().round(2)
yearfloat64
nonoilfloat64
count
16
16
mean
2019
0.62
std
0
0.5
min
2019
0
25%
2019
0
50%
2019
1
75%
2019
1
max
2019
1
Exploratory data analysis
Labor productivity:
px.line(df,
x='year',
y='ln_lp',
color='CountryName',
hover_name = 'CountryName',
hover_data= [ 'pop', 'ln_lp'],
labels=dict(ln_lp = 'Log of labor productivity',
pop = 'Population',
CountryName = 'Country'),
)
px.line(df,
x='year',
y='ln_lp',
color='CountryName',
hover_name = 'CountryName',
facet_col= 'incomegroup', facet_col_wrap=2, width=900, height=600,
labels=dict(ln_lp = 'Log of labor productivity',
incomegroup = 'Income group',
CountryName = 'Country'),
title='Labor productivity across income groups'
)
TFP
px.line(df,
x='year',
y='ln_A',
color='CountryName',
hover_name = 'CountryName',
hover_data= [ 'pop', 'ln_A'],
labels=dict(ln_A = 'TFP in logs',
pop = 'Population',
CountryName = 'Country'),
)
px.line(df,
x='year',
y='ln_A',
color='CountryName',
hover_name = 'CountryName',
facet_col= 'incomegroup', facet_col_wrap=2, width=900, height=600,
labels=dict(ln_A = 'TFP in logs',
incomegroup = 'Income group',
CountryName = 'Country'),
title='Total factor productivity across income groups'
)
Regression analysis
Global relationship: Labor productivity & TFP
px.scatter(df,
x = 'ln_A',
y = 'ln_lp',
color = 'incomegroup',
hover_name = 'CountryName',
range_x = [0.1,1.4],
range_y = [7,14],
trendline = 'ols',
trendline_scope = 'overall',
labels=dict(ln_A = 'TFP in logs',
ln_lp = 'Log of labor productivity',
incomegroup = 'Income group'),
animation_frame = 'year'
)
x = df['ln_A']
y = df['ln_lp']
# ingredients of the OLS formula:
x_bar = np.mean(x)
y_bar = np.mean(y)
var_x = np.var(x, ddof = 1)
cov_xy = np.cov(x, y)[1,0]
y = df['ln_lp']
x0 = df['ln_A']
x0 = sm.add_constant(x0)
ols = sm.OLS(y, x0).fit()
print(ols.summary())
OLS Regression Results
==============================================================================
Dep. Variable: ln_lp R-squared: 0.466
Model: OLS Adj. R-squared: 0.466
Method: Least Squares F-statistic: 557.7
Date: Sun, 14 Aug 2022 Prob (F-statistic): 4.37e-89
Time: 13:15:25 Log-Likelihood: -709.16
No. Observations: 640 AIC: 1422.
Df Residuals: 638 BIC: 1431.
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const 8.3449 0.088 94.837 0.000 8.172 8.518
ln_A 3.1547 0.134 23.616 0.000 2.892 3.417
==============================================================================
Omnibus: 20.301 Durbin-Watson: 0.175
Prob(Omnibus): 0.000 Jarque-Bera (JB): 15.150
Skew: -0.275 Prob(JB): 0.000513
Kurtosis: 2.485 Cond. No. 6.45
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
/home/jovyan/venv/lib/python3.9/site-packages/statsmodels/tsa/tsatools.py:142: FutureWarning:
In a future version of pandas all arguments of concat except for the argument 'objs' will be keyword-only
mod1 = smf.ols(formula='ln_lp ~ ln_A', data=df).fit()
Stargazer([mod1])
Relationship by income groups
px.scatter(df,
x = 'ln_A',
y = 'ln_lp',
color = 'incomegroup',
hover_name = 'CountryName',
range_x = [0.1,1.4],
range_y = [7,14],
trendline = 'ols',
labels=dict(ln_A = 'TFP in logs',
ln_lp = 'Log of labor productivity',
incomegroup = 'Income group'),
animation_frame = 'year'
)
hi = df.query('incomegroup=="High income"')
y = hi['ln_lp']
x1 = hi['ln_A']
x1 = sm.add_constant(x1)
ols_hi = sm.OLS(y, x1).fit()
print(ols_hi.summary())
OLS Regression Results
==============================================================================
Dep. Variable: ln_lp R-squared: 0.000
Model: OLS Adj. R-squared: -0.003
Method: Least Squares F-statistic: 0.004212
Date: Sun, 14 Aug 2022 Prob (F-statistic): 0.948
Time: 13:15:26 Log-Likelihood: -183.90
No. Observations: 320 AIC: 371.8
Df Residuals: 318 BIC: 379.3
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const 11.1295 0.120 92.954 0.000 10.894 11.365
ln_A -0.0097 0.149 -0.065 0.948 -0.303 0.284
==============================================================================
Omnibus: 17.944 Durbin-Watson: 0.186
Prob(Omnibus): 0.000 Jarque-Bera (JB): 27.503
Skew: -0.388 Prob(JB): 1.07e-06
Kurtosis: 4.208 Cond. No. 10.1
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
/home/jovyan/venv/lib/python3.9/site-packages/statsmodels/tsa/tsatools.py:142: FutureWarning:
In a future version of pandas all arguments of concat except for the argument 'objs' will be keyword-only
upmid = df.query('incomegroup=="Upper middle income"')
y = upmid['ln_lp']
x2 = upmid['ln_A']
x2 = sm.add_constant(x2)
ols_upmid = sm.OLS(y, x2).fit()
print(ols_upmid.summary())
OLS Regression Results
==============================================================================
Dep. Variable: ln_lp R-squared: 0.178
Model: OLS Adj. R-squared: 0.173
Method: Least Squares F-statistic: 34.21
Date: Sun, 14 Aug 2022 Prob (F-statistic): 2.76e-08
Time: 13:15:26 Log-Likelihood: -148.11
No. Observations: 160 AIC: 300.2
Df Residuals: 158 BIC: 306.4
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const 8.7853 0.178 49.285 0.000 8.433 9.137
ln_A 2.0748 0.355 5.849 0.000 1.374 2.775
==============================================================================
Omnibus: 8.851 Durbin-Watson: 0.085
Prob(Omnibus): 0.012 Jarque-Bera (JB): 5.992
Skew: -0.335 Prob(JB): 0.0500
Kurtosis: 2.329 Cond. No. 9.04
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
/home/jovyan/venv/lib/python3.9/site-packages/statsmodels/tsa/tsatools.py:142: FutureWarning:
In a future version of pandas all arguments of concat except for the argument 'objs' will be keyword-only
lowmid = df.query('incomegroup=="Lower middle income"')
y = lowmid['ln_lp']
x3 = lowmid['ln_A']
x3 = sm.add_constant(x3)
ols_lowmid = sm.OLS(y, x3).fit()
print(ols_lowmid.summary())
OLS Regression Results
==============================================================================
Dep. Variable: ln_lp R-squared: 0.007
Model: OLS Adj. R-squared: 0.001
Method: Least Squares F-statistic: 1.141
Date: Sun, 14 Aug 2022 Prob (F-statistic): 0.287
Time: 13:15:26 Log-Likelihood: -146.50
No. Observations: 160 AIC: 297.0
Df Residuals: 158 BIC: 303.2
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const 8.9459 0.238 37.628 0.000 8.476 9.416
ln_A 0.5770 0.540 1.068 0.287 -0.490 1.644
==============================================================================
Omnibus: 5.104 Durbin-Watson: 0.152
Prob(Omnibus): 0.078 Jarque-Bera (JB): 5.112
Skew: -0.436 Prob(JB): 0.0776
Kurtosis: 2.920 Cond. No. 13.3
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
/home/jovyan/venv/lib/python3.9/site-packages/statsmodels/tsa/tsatools.py:142: FutureWarning:
In a future version of pandas all arguments of concat except for the argument 'objs' will be keyword-only
mod = smf.ols(formula='ln_lp ~ ln_A', data=df).fit()
mod_hi = smf.ols(formula='ln_lp ~ ln_A', data=hi).fit()
mod_upmid = smf.ols(formula='ln_lp ~ ln_A ', data=upmid).fit()
mod_lowmid = smf.ols(formula='ln_lp ~ ln_A', data=lowmid).fit()
Stargazer([mod, mod_hi, mod_upmid, mod_lowmid])
Relationship with controls
y = df['ln_lp']
x = df[['ln_A', 'ln_k', 'ln_h']]
x = sm.add_constant(x)
ols = sm.OLS(y, x).fit()
print(ols.summary())
OLS Regression Results
==============================================================================
Dep. Variable: ln_lp R-squared: 0.856
Model: OLS Adj. R-squared: 0.855
Method: Least Squares F-statistic: 1257.
Date: Sun, 14 Aug 2022 Prob (F-statistic): 8.56e-267
Time: 13:15:26 Log-Likelihood: -290.73
No. Observations: 640 AIC: 589.5
Df Residuals: 636 BIC: 607.3
Df Model: 3
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const 5.8509 0.076 77.056 0.000 5.702 6.000
ln_A 2.8735 0.080 36.114 0.000 2.717 3.030
ln_k 0.7399 0.056 13.138 0.000 0.629 0.850
ln_h 0.6949 0.039 17.810 0.000 0.618 0.771
==============================================================================
Omnibus: 90.798 Durbin-Watson: 0.123
Prob(Omnibus): 0.000 Jarque-Bera (JB): 248.209
Skew: 0.713 Prob(JB): 1.26e-54
Kurtosis: 5.697 Cond. No. 19.9
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
/home/jovyan/venv/lib/python3.9/site-packages/statsmodels/tsa/tsatools.py:142: FutureWarning:
In a future version of pandas all arguments of concat except for the argument 'objs' will be keyword-only
mod1 = smf.ols(formula='ln_lp ~ ln_A', data=df).fit()
mod2 = smf.ols(formula='ln_lp ~ ln_A + ln_k ', data=df).fit()
mod3 = smf.ols(formula='ln_lp ~ ln_A + ln_h ', data=df).fit()
mod4 = smf.ols(formula='ln_lp ~ ln_A + ln_k + ln_h ', data=df).fit()
Stargazer([mod1, mod2, mod3, mod4])
# For TFP: Pivot panel data from long form to wide form
df_wide_A = df.pivot_table(index=['CountryName'], columns=['year'], values='ln_A')
# Reset data index
df_wide_A = df_wide_A.reset_index(drop=False)
df_wide_A
# Generate the respective growth rates of labor productivity & TFP (1980~2019)
df_wide_lp['growth_lp'] = (df_wide_lp[2019] - df_wide_lp[1980]).round(4)
df_wide_A['growth_A'] = (df_wide_A[2019] - df_wide_A[1980]).round(4)
df_wide_lp.columns
df_wide_lp.to_csv("/work/data/AS&P-LPConv.csv")
df_wide_A.to_csv("/work/data/AS&P-AConv.csv")
df_wide_lp.describe().round(2)
1980float64
1981float64
count
16
16
mean
9.71
9.72
std
1
0.99
min
7.61
7.74
25%
9.05
9.07
50%
9.92
9.9
75%
10.55
10.59
max
10.96
10.99
df_wide_A.describe().round(2)
1980float64
1981float64
count
16
16
mean
0.71
0.71
std
0.26
0.26
min
0.37
0.35
25%
0.5
0.5
50%
0.69
0.66
75%
0.89
0.9
max
1.2
1.2
px.scatter(
df_wide_lp,
x=1980,
y="growth_lp",
hover_name="CountryName",
#color="",
trendline="ols",
trendline_scope="overall",
marginal_x="rug",
marginal_y="rug",
labels={"1980": "Log labour productivity in 1980",
"growth_lp": "Growth rate from 1980 to 2019"}
)
y = df_wide_lp['growth_lp']
x = df_wide_lp[1980]
x_withconst = sm.add_constant(x)
ols = sm.OLS(y, x_withconst).fit()
print(ols.summary())
OLS Regression Results
==============================================================================
Dep. Variable: growth_lp R-squared: 0.528
Model: OLS Adj. R-squared: 0.494
Method: Least Squares F-statistic: 15.65
Date: Sun, 14 Aug 2022 Prob (F-statistic): 0.00143
Time: 13:15:27 Log-Likelihood: -4.2473
No. Observations: 16 AIC: 12.49
Df Residuals: 14 BIC: 14.04
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const 4.5199 0.852 5.305 0.000 2.692 6.347
1980 -0.3455 0.087 -3.956 0.001 -0.533 -0.158
==============================================================================
Omnibus: 0.206 Durbin-Watson: 2.287
Prob(Omnibus): 0.902 Jarque-Bera (JB): 0.224
Skew: 0.207 Prob(JB): 0.894
Kurtosis: 2.593 Cond. No. 99.6
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
/home/jovyan/venv/lib/python3.9/site-packages/statsmodels/tsa/tsatools.py:142: FutureWarning:
In a future version of pandas all arguments of concat except for the argument 'objs' will be keyword-only
/opt/conda/lib/python3.9/site-packages/scipy/stats/stats.py:1603: UserWarning:
kurtosistest only valid for n>=20 ... continuing anyway, n=16
px.scatter(
df_wide_A,
x=1980,
y="growth_A",
hover_name="CountryName",
#color="",
trendline="ols",
trendline_scope="overall",
marginal_x="rug",
marginal_y="rug",
labels={"1980": "Log TFP in 1980 in 1980",
"growth_A": "Growth rate from 2009 to 2019"}
)
y = df_wide_A['growth_A']
x = df_wide_A[1980]
x_withconst = sm.add_constant(x)
OLS = sm.OLS(y, x_withconst).fit()
print(OLS.summary())
OLS Regression Results
==============================================================================
Dep. Variable: growth_A R-squared: 0.698
Model: OLS Adj. R-squared: 0.677
Method: Least Squares F-statistic: 32.43
Date: Sun, 14 Aug 2022 Prob (F-statistic): 5.53e-05
Time: 13:15:27 Log-Likelihood: 15.058
No. Observations: 16 AIC: -26.12
Df Residuals: 14 BIC: -24.57
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const 0.2659 0.076 3.511 0.003 0.103 0.428
1980 -0.5692 0.100 -5.695 0.000 -0.784 -0.355
==============================================================================
Omnibus: 0.020 Durbin-Watson: 2.924
Prob(Omnibus): 0.990 Jarque-Bera (JB): 0.117
Skew: 0.018 Prob(JB): 0.943
Kurtosis: 2.583 Cond. No. 6.07
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
/home/jovyan/venv/lib/python3.9/site-packages/statsmodels/tsa/tsatools.py:142: FutureWarning:
In a future version of pandas all arguments of concat except for the argument 'objs' will be keyword-only
/opt/conda/lib/python3.9/site-packages/scipy/stats/stats.py:1603: UserWarning:
kurtosistest only valid for n>=20 ... continuing anyway, n=16