The Impact of Privatized Education on the Level of Labour Productivity
Jaewon Kim - Statistics for International Relations Research II
1. Introduction
The aim of this research is to explore the potential causal relationship between the privatization of education and labor productivity.In recent years, many countries have embarked on the application of market-based privatization approaches to different levels of education. Mounting budget deficits of the government, deteriorating quality of services, and out-of-date curriculum are among the core reasons why a huge portion of responsibilities to education service delivery that have long been recognized as public goods were shifted onto the private sector. The theoretical rationale behind the privatization of education is that market-oriented forces can better serve as a tool to increase the quality of the education while lowering the cost through extensive competition among providers, ensure more flexibility in contracting of competent teacher, and above all, to reduce the burden of education cost and expectations (Fennell, 2012; Steiner-Khamsi & Draxler, 2018).
However such trend has also stimulated considerable controversy as the private sector is inherently ‘profit-seeking’ and ‘efficiency-seeking.’ Many scholars and practitioners point out that such different nature of the private sector would rather hamper the universal access to education or damage the quality of education in a long run. Compared to sectors such as transportation, roads, or energy that have widely enjoyed the engagement of the private sector, the education sector, therefore, is relatively a late adopter of privatization schemes, due in large part to the widely-held perception that the provision and management of education services ought to be the responsibility of the public sector as it is a public good (Draxler, 2013).
Against this backdrop, this research attempts to examine whether the privatization of education contributes to the improvement of labour productivity. Among different levels of education from pre-primary to tertiary, this research will specifically focus on secondary education due to the fact that it is generally considered to play a fundamental role in preparing pupils directly for the labour market as it is when the pupils start receiving ‘vocational education’. This study will examine whether there is any meaningful causal relationship between the level of the private sector engagement in education and labour productivity by testing the hypothesis ‘The increased level of private sector engagement in the delivery of secondary education services increases overall labour productivity.’
2. Data
To test the hypothesis, the first model will use a ‘School enrollment, secondary, private (% of total secondary)’ data set prepared by the World Bank as the independent variable. It shows the ratio of pupils enrolled in institutions that are operated by a private sector body, not a public authority, from 1998 to 2019.A high ratio would consequently mean that the private sector (e.g. NGOs, firms, religious bodies, or local communities)is strongly engaged in the delivery of education services. An ‘output per worker (GDP constant 2011 international $ in PPP)’ data set prepared by ILO will be the dependent variable. Labour productivity in this data set refers to the total volume of output (GDP) produced per one-unit of labour during a time frame of 2010-2019. The usage of this data set is expected to allow me to assess the level of GDP-to-labour input as well as growth rates over the given time frame, which would help me identify the degree of efficiency as well as quality of labour in the production process in each sample country.
lpdata <- read.csv("ILO_labour_productivity.csv", header = TRUE)
pedata <- read.csv("WB_private education.csv", header = TRUE)
Both are time series data sets that contain a total of 3 variables - country, year, and value. However we can see that there is difference in the number of observations as the number of countries covered are different: labour productivity data has 1890 observations of a total of 189 countries while private education data has 1780 observations of a total of 178 countries. Some countries covered in the private education data are missing in the labour productivity data, and vice versa. For example, the private education data developed by the World Bank contains a number of territories that are not recognized as a country under the UN system, such as Gibraltar, a British overseas territory and headland or West Bank and Gaza area. However it only includes countries who have data for at least one year during the given time span. Therefore I will tailor the extra variables of the World Bank data and ILO data to combine two data frames vertically in the later stage.
Three control variables that are assumed to be related (either closely or loosely) to labour productivity will be also added: mean weekly working hour (mwwhour), consumer price for health service (healthconpri), and average cost for educational services (educost). All three data sets are those imported from ILO. A data set of ‘weekly working hour’ presents the mean values of weekly working hours of all employees, while the remaining two data sets of consumer price for health service and average cost for educational services present the values of consumer price index (CPI).
working_hr <- read.csv("mean_weekly_working_hour.csv", header = TRUE)
conpri_health <- read.csv("consumer_price_health.csv", header = TRUE)
edu_price <- read.csv("education_service_aveprice.csv", header = TRUE)
All three of them have 3 variables: country, year, value, and they all cover maximum 10 years of data between 2010 and 2019. However, the volume of observations vary (2079 for mwwhour; 1717 for healthconpri; and 1676 for educost) according to the availability of country data.
3. Visualization of the distribution of the variable
(1-1) The distribution of the dependent variable by year
library(arsenal)
require(knitr)
## Loading required package: knitr
require(survival)
## Loading required package: survival
str(lpdata)
## 'data.frame': 1890 obs. of 3 variables:
## $ Country: chr "Afghanistan" "Afghanistan" "Afghanistan" "Afghanistan" ...
## $ Year : int 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 ...
## $ Value : int 9573 9219 9910 9943 9697 9365 9178 9048 8871 8794 ...
lpdata_table <- tableby(Year ~ Value, data = lpdata)
summary(lpdata_table, title = "Labour Productivity Data - Summary Statistics, by year")
##
##
## Table: Labour Productivity Data - Summary Statistics, by year
##
## | | 2010 (N=189) | 2011 (N=189) | 2012 (N=189) | 2013 (N=189) | 2014 (N=189) | 2015 (N=189) | 2016 (N=189) | 2017 (N=189) | 2018 (N=189) | 2019 (N=189) | Total (N=1890) | p value|
## |:---------------------------|:---------------------:|:---------------------:|:---------------------:|:---------------------:|:---------------------:|:---------------------:|:---------------------:|:---------------------:|:---------------------:|:---------------------:|:---------------------:|-------:|
## |**Value** | | | | | | | | | | | | 1.000|
## | Mean (SD) | 44040.635 (41188.903) | 44590.513 (42246.687) | 44929.180 (42127.220) | 45270.444 (42554.979) | 45461.772 (42289.946) | 45506.132 (41560.604) | 45841.190 (41852.116) | 46372.979 (42421.424) | 46816.640 (42865.544) | 47013.016 (42849.813) | 45584.250 (42107.871) | |
## | Range | 1534.000 - 240632.000 | 1535.000 - 242518.000 | 1510.000 - 245190.000 | 1492.000 - 265200.000 | 1478.000 - 253445.000 | 1480.000 - 240693.000 | 1472.000 - 249868.000 | 1441.000 - 244315.000 | 1430.000 - 244196.000 | 1419.000 - 241729.000 | 1419.000 - 265200.000 | |
(1-2) The distribution of the dependent variable by country
lpdata_table_2 <- tableby(Country ~ Value, data = lpdata)
summary(lpdata_table_2, title = "Labour Productivity Data - Summary Statistics, by country")
##
##
## Table: Labour Productivity Data - Summary Statistics, by country
##
## | | Afghanistan (N=10) | Albania (N=10) | Algeria (N=10) | Angola (N=10) | Argentina (N=10) | Armenia (N=10) | Australia (N=10) | Austria (N=10) | Azerbaijan (N=10) | Bahamas (N=10) | Bahrain (N=10) | Bangladesh (N=10) | Barbados (N=10) | Belarus (N=10) | Belgium (N=10) | Belize (N=10) | Benin (N=10) | Bhutan (N=10) | Bolivia (N=10) | Bosnia and Herzegovina (N=10) | Botswana (N=10) | Brazil (N=10) | Brunei Darussalam (N=10) | Bulgaria (N=10) | Burkina Faso (N=10) | Burundi (N=10) | C?te d'Ivoire (N=10) | Cambodia (N=10) | Cameroon (N=10) | Canada (N=10) | Cape Verde (N=10) | Central African Republic (N=10) | Chad (N=10) | Channel Islands (N=10) | Chile (N=10) | China (N=10) | Colombia (N=10) | Comoros (N=10) | Congo (N=10) | Congo, Democratic Republic of the (N=10) | Costa Rica (N=10) | Croatia (N=10) | Cuba (N=10) | Cyprus (N=10) | Czechia (N=10) | Denmark (N=10) | Djibouti (N=10) | Dominican Republic (N=10) | Ecuador (N=10) | Egypt (N=10) | El Salvador (N=10) | Equatorial Guinea (N=10) | Eritrea (N=10) | Estonia (N=10) | Eswatini (N=10) | Ethiopia (N=10) | Fiji (N=10) | Finland (N=10) | France (N=10) | French Polynesia (N=10) | Gabon (N=10) | Gambia (N=10) | Georgia (N=10) | Germany (N=10) | Ghana (N=10) | Greece (N=10) | Guam (N=10) | Guatemala (N=10) | Guinea (N=10) | Guinea-Bissau (N=10) | Guyana (N=10) | Haiti (N=10) | Honduras (N=10) | Hong Kong, China (N=10) | Hungary (N=10) | Iceland (N=10) | India (N=10) | Indonesia (N=10) | Iran, Islamic Republic of (N=10) | Iraq (N=10) | Ireland (N=10) | Israel (N=10) | Italy (N=10) | Jamaica (N=10) | Japan (N=10) | Jordan (N=10) | Kazakhstan (N=10) | Kenya (N=10) | Korea, Democratic People's Republic of (N=10) | Korea, Republic of (N=10) | Kuwait (N=10) | Kyrgyzstan (N=10) | Lao People's Democratic Republic (N=10) | Latvia (N=10) | Lebanon (N=10) | Lesotho (N=10) | Liberia (N=10) | Libya (N=10) | Lithuania (N=10) | Luxembourg (N=10) | Macau, China (N=10) | Madagascar (N=10) | Malawi (N=10) | Malaysia (N=10) | Maldives (N=10) | Mali (N=10) | Malta (N=10) | Mauritania (N=10) | Mauritius (N=10) | Mexico (N=10) | Moldova, Republic of (N=10) | Mongolia (N=10) | Montenegro (N=10) | Morocco (N=10) | Mozambique (N=10) | Myanmar (N=10) | Namibia (N=10) | Nepal (N=10) | Netherlands (N=10) | New Caledonia (N=10) | New Zealand (N=10) | Nicaragua (N=10) | Niger (N=10) | Nigeria (N=10) | North Macedonia (N=10) | Norway (N=10) | Occupied Palestinian Territory (N=10) | Oman (N=10) | Pakistan (N=10) | Panama (N=10) | Papua New Guinea (N=10) | Paraguay (N=10) | Peru (N=10) | Philippines (N=10) | Poland (N=10) | Portugal (N=10) | Puerto Rico (N=10) | Qatar (N=10) | Romania (N=10) | Russian Federation (N=10) | Rwanda (N=10) | Saint Lucia (N=10) | Saint Vincent and the Grenadines (N=10) | Samoa (N=10) | Sao Tome and Principe (N=10) | Saudi Arabia (N=10) | Senegal (N=10) | Serbia (N=10) | Sierra Leone (N=10) | Singapore (N=10) | Slovakia (N=10) | Slovenia (N=10) | Solomon Islands (N=10) | Somalia (N=10) | South Africa (N=10) | South Sudan (N=10) | Spain (N=10) | Sri Lanka (N=10) | Sudan (N=10) | Suriname (N=10) | Sweden (N=10) | Switzerland (N=10) | Syrian Arab Republic (N=10) | Taiwan, China (N=10) | Tajikistan (N=10) | Tanzania, United Republic of (N=10) | Thailand (N=10) | Timor-Leste (N=10) | Togo (N=10) | Tonga (N=10) | Trinidad and Tobago (N=10) | Tunisia (N=10) | Turkey (N=10) | Turkmenistan (N=10) | Uganda (N=10) | Ukraine (N=10) | United Arab Emirates (N=10) | United Kingdom (N=10) | United States (N=10) | United States Virgin Islands (N=10) | Uruguay (N=10) | Uzbekistan (N=10) | Vanuatu (N=10) | Venezuela, Bolivarian Republic of (N=10) | Viet Nam (N=10) | Western Sahara (N=10) | Yemen (N=10) | Zambia (N=10) | Zimbabwe (N=10) | Total (N=1890) | p value|
## |:---------------------------|:-------------------:|:---------------------:|:---------------------:|:---------------------:|:---------------------:|:---------------------:|:---------------------:|:-----------------------:|:---------------------:|:---------------------:|:---------------------:|:--------------------:|:---------------------:|:---------------------:|:-----------------------:|:---------------------:|:-------------------:|:---------------------:|:---------------------:|:-----------------------------:|:---------------------:|:---------------------:|:------------------------:|:---------------------:|:-------------------:|:-------------------:|:---------------------:|:-------------------:|:-------------------:|:---------------------:|:---------------------:|:-------------------------------:|:-------------------:|:----------------------:|:---------------------:|:---------------------:|:---------------------:|:---------------------:|:--------------------:|:----------------------------------------:|:---------------------:|:---------------------:|:---------------------:|:---------------------:|:---------------------:|:-----------------------:|:--------------------:|:-------------------------:|:---------------------:|:---------------------:|:---------------------:|:------------------------:|:-------------------:|:---------------------:|:---------------------:|:-------------------:|:---------------------:|:----------------------:|:-----------------------:|:-----------------------:|:---------------------:|:-------------------:|:---------------------:|:----------------------:|:--------------------:|:---------------------:|:----------------------:|:---------------------:|:-------------------:|:--------------------:|:---------------------:|:-------------------:|:---------------------:|:-----------------------:|:---------------------:|:----------------------:|:---------------------:|:---------------------:|:--------------------------------:|:---------------------:|:-----------------------:|:---------------------:|:-----------------------:|:---------------------:|:---------------------:|:---------------------:|:---------------------:|:-------------------:|:---------------------------------------------:|:-------------------------:|:----------------------:|:---------------------:|:---------------------------------------:|:---------------------:|:---------------------:|:-------------------:|:-------------------:|:---------------------:|:---------------------:|:-----------------------:|:-----------------------:|:-------------------:|:-------------------:|:---------------------:|:---------------------:|:-------------------:|:----------------------:|:---------------------:|:---------------------:|:---------------------:|:---------------------------:|:---------------------:|:---------------------:|:---------------------:|:-------------------:|:--------------------:|:---------------------:|:-------------------:|:-----------------------:|:-----------------------:|:---------------------:|:---------------------:|:-------------------:|:---------------------:|:----------------------:|:-----------------------:|:-------------------------------------:|:---------------------:|:---------------------:|:---------------------:|:-----------------------:|:---------------------:|:---------------------:|:---------------------:|:---------------------:|:---------------------:|:-----------------------:|:-----------------------:|:---------------------:|:-------------------------:|:-------------------:|:---------------------:|:---------------------------------------:|:---------------------:|:----------------------------:|:-----------------------:|:---------------------:|:---------------------:|:-------------------:|:-----------------------:|:---------------------:|:---------------------:|:----------------------:|:-------------------:|:---------------------:|:-------------------:|:---------------------:|:---------------------:|:---------------------:|:---------------------:|:-----------------------:|:-----------------------:|:---------------------------:|:---------------------:|:--------------------:|:-----------------------------------:|:---------------------:|:-------------------:|:-------------------:|:---------------------:|:--------------------------:|:---------------------:|:---------------------:|:---------------------:|:-------------------:|:---------------------:|:---------------------------:|:---------------------:|:-----------------------:|:-----------------------------------:|:---------------------:|:---------------------:|:-------------------:|:----------------------------------------:|:--------------------:|:---------------------:|:--------------------:|:-------------------:|:-------------------:|:---------------------:|-------:|
## |**Value** | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | < 0.001|
## | Mean (SD) | 9359.800 (409.767) | 31149.300 (1807.674) | 41751.200 (2049.561) | 20087.400 (1496.409) | 56680.200 (1899.561) | 30620.400 (4954.162) | 95269.800 (3529.443) | 109305.300 (1911.516) | 30068.000 (797.536) | 72694.600 (4674.283) | 81722.900 (3536.810) | 9491.000 (1240.419) | 32197.400 (301.566) | 36578.100 (1018.088) | 120154.300 (2234.551) | 17926.100 (1031.117) | 7477.800 (427.736) | 21529.800 (1839.159) | 16923.600 (1553.025) | 42641.600 (1953.918) | 44468.300 (1253.839) | 33498.800 (670.081) | 139504.600 (7527.023) | 46287.500 (2425.957) | 5603.000 (463.809) | 1945.500 (123.978) | 13983.900 (2165.098) | 6244.900 (989.442) | 8102.100 (408.304) | 91709.600 (2340.117) | 17638.100 (562.342) | 2574.300 (465.785) | 4716.100 (329.496) | 99632.700 (4065.382) | 50566.800 (1502.980) | 22150.900 (4551.050) | 29086.700 (1264.697) | 12060.400 (105.097) | 9859.500 (473.323) | 3047.300 (286.037) | 41019.200 (2648.200) | 65195.900 (2231.562) | 32205.600 (1875.759) | 58245.300 (1333.154) | 74505.500 (3296.985) | 111191.800 (3707.176) | 11930.900 (1553.228) | 36418.200 (2751.243) | 25427.500 (1271.958) | 38081.500 (3300.784) | 19893.500 (821.929) | 81477.500 (19929.435) | 3363.700 (289.594) | 65120.200 (3631.592) | 34511.200 (554.051) | 3820.100 (656.239) | 30480.600 (4098.078) | 102079.600 (2196.284) | 107105.400 (3048.820) | 78378.700 (2733.572) | 58494.200 (1898.454) | 7170.000 (356.961) | 25338.500 (3242.980) | 102478.200 (2217.853) | 11653.200 (1169.703) | 86100.800 (1938.579) | 100326.600 (3141.186) | 19941.600 (533.342) | 6631.900 (686.898) | 4597.800 (192.511) | 25081.500 (2284.967) | 4587.100 (100.669) | 12930.500 (247.228) | 111177.600 (5670.623) | 64789.800 (2278.646) | 90664.900 (6745.689) | 15609.200 (2759.765) | 21523.700 (2135.827) | 46277.800 (2625.652) | 45007.300 (2688.477) | 151458.000 (25626.265) | 90668.100 (3288.615) | 110329.100 (1756.229) | 22488.400 (1019.681) | 77339.600 (1011.766) | 46531.700 (1247.565) | 48885.900 (4637.063) | 9076.700 (415.110) | 3099.700 (87.979) | 75100.600 (3727.882) | 101992.500 (10692.671) | 12081.100 (1447.326) | 12397.300 (1751.755) | 56993.000 (4241.074) | 52465.600 (4852.991) | 7782.100 (391.886) | 3573.900 (206.147) | 50145.100 (14979.567) | 66282.900 (4963.387) | 240620.100 (5323.347) | 222396.300 (25455.741) | 3145.800 (71.738) | 2543.900 (43.337) | 53041.300 (3880.721) | 36540.300 (2541.821) | 6269.700 (408.060) | 88027.600 (10017.010) | 20565.300 (548.391) | 45163.600 (3542.535) | 45337.200 (862.676) | 21728.100 (2713.828) | 25779.700 (3896.292) | 52702.100 (1493.241) | 22750.900 (2045.054) | 2847.600 (263.887) | 8974.400 (1721.896) | 32745.600 (1471.076) | 5296.300 (500.248) | 106911.500 (3052.767) | 115686.300 (2424.126) | 77362.800 (2724.652) | 12539.100 (580.275) | 3046.000 (282.385) | 17760.100 (1420.669) | 43285.800 (487.479) | 120820.400 (3018.868) | 26748.200 (710.554) | 61284.600 (8464.270) | 13182.700 (869.023) | 60564.800 (6075.044) | 13374.500 (1426.162) | 25050.800 (1535.376) | 21821.400 (1510.875) | 17944.000 (2513.695) | 62406.300 (4738.862) | 70615.700 (1156.234) | 119226.900 (2531.834) | 130025.300 (4546.875) | 55501.900 (6970.748) | 52747.800 (2313.555) | 3731.000 (433.268) | 32063.000 (968.601) | 28846.900 (396.818) | 24598.700 (1265.057) | 12769.300 (767.219) | 125558.000 (4739.288) | 12288.800 (1039.129) | 34875.900 (1383.014) | 5139.100 (626.473) | 148445.400 (8328.323) | 64797.400 (2474.990) | 75999.800 (3682.700) | 4630.200 (162.787) | 1479.100 (40.534) | 44426.100 (724.253) | 5362.800 (835.670) | 95101.200 (1872.262) | 29645.400 (3673.821) | 17524.100 (556.187) | 49739.700 (2727.299) | 104597.600 (3875.188) | 120116.500 (2008.969) | 14843.200 (4873.076) | 91608.000 (4754.108) | 11399.800 (1755.713) | 4955.100 (475.438) | 28804.100 (3106.600) | 8185.800 (352.699) | 4250.600 (366.544) | 19423.500 (1611.412) | 59071.700 (2007.947) | 34456.800 (1149.159) | 74061.000 (5835.638) | 31790.500 (6150.547) | 5654.800 (153.149) | 27801.400 (1234.782) | 89519.600 (8185.854) | 90900.600 (1395.549) | 122450.300 (2739.975) | 99258.100 (10218.263) | 42719.200 (3232.592) | 14111.000 (2080.878) | 7457.800 (119.772) | 63608.600 (17495.907) | 10912.800 (1663.980) | 17264.800 (452.308) | 13311.500 (4061.056) | 9354.500 (308.728) | 6294.500 (569.730) | 45584.250 (42107.871) | |
## | Range | 8794.000 - 9943.000 | 27399.000 - 33439.000 | 38950.000 - 43699.000 | 17297.000 - 21705.000 | 52790.000 - 58957.000 | 25297.000 - 40102.000 | 89581.000 - 99210.000 | 106515.000 - 112371.000 | 29124.000 - 31231.000 | 67086.000 - 78538.000 | 76456.000 - 86323.000 | 7709.000 - 11534.000 | 31445.000 - 32495.000 | 34587.000 - 37874.000 | 116249.000 - 122800.000 | 16332.000 - 19317.000 | 6851.000 - 8229.000 | 18025.000 - 23723.000 | 14384.000 - 18491.000 | 39350.000 - 45032.000 | 42048.000 - 45924.000 | 32677.000 - 34525.000 | 129057.000 - 150120.000 | 41866.000 - 49625.000 | 4783.000 - 6243.000 | 1763.000 - 2110.000 | 11101.000 - 17286.000 | 4818.000 - 7774.000 | 7522.000 - 8612.000 | 87797.000 - 94634.000 | 16941.000 - 18867.000 | 2141.000 - 3376.000 | 4290.000 - 5154.000 | 93378.000 - 104611.000 | 47690.000 - 52153.000 | 15687.000 - 29363.000 | 26947.000 - 31182.000 | 11887.000 - 12259.000 | 8993.000 - 10454.000 | 2525.000 - 3335.000 | 37234.000 - 44074.000 | 60813.000 - 68355.000 | 28996.000 - 34638.000 | 55560.000 - 59721.000 | 70703.000 - 80539.000 | 105854.000 - 116692.000 | 9882.000 - 14559.000 | 33283.000 - 40628.000 | 24012.000 - 27674.000 | 34212.000 - 43931.000 | 18808.000 - 21131.000 | 51613.000 - 105037.000 | 3003.000 - 4051.000 | 61153.000 - 72479.000 | 33789.000 - 35497.000 | 2882.000 - 4790.000 | 25197.000 - 35502.000 | 99852.000 - 105600.000 | 102274.000 - 111772.000 | 75466.000 - 83209.000 | 55421.000 - 60495.000 | 6825.000 - 8056.000 | 20717.000 - 31066.000 | 99349.000 - 105427.000 | 9258.000 - 13290.000 | 83401.000 - 88737.000 | 96508.000 - 104874.000 | 18467.000 - 20380.000 | 5779.000 - 7704.000 | 4360.000 - 4909.000 | 21370.000 - 28543.000 | 4368.000 - 4706.000 | 12638.000 - 13445.000 | 103893.000 - 119741.000 | 62705.000 - 70088.000 | 84788.000 - 103296.000 | 11945.000 - 19693.000 | 18360.000 - 24425.000 | 41360.000 - 49423.000 | 40381.000 - 48324.000 | 124610.000 - 187658.000 | 86383.000 - 96573.000 | 108643.000 - 113700.000 | 20752.000 - 23592.000 | 75611.000 - 78759.000 | 45339.000 - 48684.000 | 41390.000 - 56446.000 | 8580.000 - 9848.000 | 2899.000 - 3192.000 | 70117.000 - 81060.000 | 88471.000 - 115511.000 | 10138.000 - 14264.000 | 9843.000 - 14887.000 | 50838.000 - 64221.000 | 44309.000 - 60334.000 | 6995.000 - 8304.000 | 3260.000 - 3910.000 | 30085.000 - 80453.000 | 59615.000 - 75717.000 | 231570.000 - 249868.000 | 194060.000 - 265200.000 | 3058.000 - 3267.000 | 2475.000 - 2600.000 | 48813.000 - 59364.000 | 34120.000 - 41621.000 | 5743.000 - 6869.000 | 77607.000 - 103313.000 | 19534.000 - 21204.000 | 40034.000 - 51105.000 | 43960.000 - 46390.000 | 18570.000 - 26506.000 | 18584.000 - 29905.000 | 50494.000 - 54911.000 | 19698.000 - 25322.000 | 2374.000 - 3078.000 | 6689.000 - 11548.000 | 31092.000 - 35211.000 | 4529.000 - 6055.000 | 103118.000 - 110932.000 | 110049.000 - 118487.000 | 73912.000 - 82100.000 | 11648.000 - 13422.000 | 2574.000 - 3385.000 | 15288.000 - 19134.000 | 42419.000 - 44047.000 | 117219.000 - 124972.000 | 25920.000 - 28082.000 | 52740.000 - 78622.000 | 12245.000 - 14556.000 | 49249.000 - 67184.000 | 11587.000 - 14858.000 | 22207.000 - 26774.000 | 18832.000 - 23344.000 | 14955.000 - 21832.000 | 55547.000 - 71046.000 | 68574.000 - 72660.000 | 115354.000 - 122964.000 | 123661.000 - 138639.000 | 46495.000 - 66848.000 | 48634.000 - 56659.000 | 3084.000 - 4468.000 | 30883.000 - 33876.000 | 28229.000 - 29420.000 | 23147.000 - 26257.000 | 11737.000 - 13640.000 | 119151.000 - 133454.000 | 11154.000 - 13910.000 | 33139.000 - 36958.000 | 4267.000 - 6278.000 | 136243.000 - 160348.000 | 61033.000 - 68993.000 | 71054.000 - 82608.000 | 4184.000 - 4750.000 | 1419.000 - 1535.000 | 43508.000 - 45455.000 | 4286.000 - 6365.000 | 91652.000 - 97280.000 | 23511.000 - 34990.000 | 16375.000 - 18329.000 | 46471.000 - 52974.000 | 100470.000 - 110270.000 | 117860.000 - 123736.000 | 11576.000 - 24648.000 | 85368.000 - 99189.000 | 9158.000 - 14501.000 | 4206.000 - 5623.000 | 24542.000 - 33502.000 | 7704.000 - 8632.000 | 3701.000 - 4771.000 | 17118.000 - 21350.000 | 56463.000 - 60916.000 | 32486.000 - 36031.000 | 64341.000 - 81694.000 | 21669.000 - 40307.000 | 5340.000 - 5923.000 | 25419.000 - 29280.000 | 77311.000 - 98205.000 | 88575.000 - 92646.000 | 118879.000 - 127046.000 | 92961.000 - 122431.000 | 37451.000 - 46795.000 | 11089.000 - 17181.000 | 7268.000 - 7674.000 | 28945.000 - 79334.000 | 8833.000 - 13817.000 | 16473.000 - 17826.000 | 8678.000 - 18921.000 | 8880.000 - 9734.000 | 4984.000 - 6891.000 | 1419.000 - 265200.000 | |
(1-3) Changes in the distribution of the dependent variable between 2010 and 2019, by country
library(CGPfunctions)
library(magrittr)
##
## Attaching package: 'magrittr'
## The following object is masked from 'package:arsenal':
##
## set_attr
library(dplyr)
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
library(ggplot2)
lp_slope <- lpdata %>%
filter(Year %in% c(2010, 2015, 2019) &
Country %in% c("Afghanistan", "Argentina", "Australia", "Austria", "Bahamas", "Bangladesh", "Belgium", "Bhutan", "Bolivia", "Brazil", "Brunei Darussalam", "Cambodia", "Canada", "Chad", "Chile", "China", "Chroatia", "Djibouti", "Egypt", "Ethiopia", "France", "Gabon", "Germany", "Guatemala", "Honduras", "Hungary", "India", "Iraq", "Japan", "Korea, Republic of", "Luxembourg", "Macau, China", "Malaysia", "Mexico", "Myanmar", "Nepal", "Netherlands", "Pakistan", "Philippines", "Russian Federation", "Singapore", "South Africa", "Sri Lanka", "Switzerand", "Turkey", "Uganda", "United States", "Yemen", "Zimbabwe" )) %>%
mutate(Year = factor(Year),
Value = round(Value))
newggslopegraph(lp_slope, Year, Value, Country) +labs(title="Change in labour productivity, by country, from 2010 to 2019", check_overlap = T)
##
## Converting 'Year' to an ordered factor
## Warning: ggrepel: 2 unlabeled data points (too many overlaps). Consider
## increasing max.overlaps
## Warning: ggrepel: 2 unlabeled data points (too many overlaps). Consider
## increasing max.overlaps
Table 1-1 above suggests that there was an overall 6.75% increase in the level of labour productivity between 2010 and 2019 across the globe. Figure 1-3 shows that labour productivity has generally increased in most of the countries at a gradual pace.
(2-1) The distribution of the independent variable by year
str(pedata)
## 'data.frame': 1780 obs. of 3 variables:
## $ Country: chr "Aruba" "Aruba" "Aruba" "Aruba" ...
## $ Year : int 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 ...
## $ Value : num 91.8 91.6 92.4 NA NA ...
pedata_table <- tableby(Year ~ Value, data = pedata)
summary(pedata_table, title = "Private Education Data")
##
##
## Table: Private Education Data
##
## | | 2010 (N=178) | 2011 (N=178) | 2012 (N=178) | 2013 (N=178) | 2014 (N=178) | 2015 (N=178) | 2016 (N=178) | 2017 (N=178) | 2018 (N=178) | 2019 (N=178) | Total (N=1780) | p value|
## |:---------------------------|:---------------:|:---------------:|:---------------:|:---------------:|:---------------:|:---------------:|:---------------:|:---------------:|:---------------:|:---------------:|:---------------:|-------:|
## |**Value** | | | | | | | | | | | | 0.994|
## | N-Miss | 55 | 47 | 54 | 54 | 47 | 45 | 48 | 54 | 56 | 119 | 579 | |
## | Mean (SD) | 19.039 (19.558) | 18.531 (18.821) | 18.929 (19.579) | 19.410 (19.361) | 19.426 (18.624) | 19.667 (19.183) | 18.752 (18.339) | 19.386 (19.633) | 18.499 (18.132) | 22.024 (21.684) | 19.219 (19.109) | |
## | Range | 0.077 - 95.356 | 0.271 - 95.347 | 0.000 - 95.516 | 0.014 - 95.543 | 0.041 - 95.742 | 0.037 - 95.952 | 0.054 - 95.919 | 0.000 - 96.062 | 0.089 - 95.986 | 0.146 - 96.253 | 0.000 - 96.253 | |
(2-2) The distribution of the independent variable by country
pedata_table_2 <- tableby(Country ~ Value, data = pedata)
summary(pedata_table_2, title = "Private Education Data")
##
##
## Table: Private Education Data
##
## | | Afghanistan (N=10) | Albania (N=10) | Algeria (N=10) | American Samoa (N=10) | Andorra (N=10) | Angola (N=10) | Antigua and Barbuda (N=10) | Argentina (N=10) | Aruba (N=10) | Australia (N=10) | Austria (N=10) | Azerbaijan (N=10) | Bahamas, The (N=10) | Bahrain (N=10) | Bangladesh (N=10) | Barbados (N=10) | Belarus (N=10) | Belgium (N=10) | Belize (N=10) | Benin (N=10) | Bermuda (N=10) | Bhutan (N=10) | Bolivia (N=10) | Bosnia and Herzegovina (N=10) | Botswana (N=10) | Brazil (N=10) | British Virgin Islands (N=10) | Brunei Darussalam (N=10) | Bulgaria (N=10) | Burkina Faso (N=10) | Burundi (N=10) | Cabo Verde (N=10) | Cambodia (N=10) | Cameroon (N=10) | Canada (N=10) | Cayman Islands (N=10) | Central African Republic (N=10) | Chad (N=10) | Chile (N=10) | China (N=10) | Colombia (N=10) | Comoros (N=10) | Congo, Dem. Rep. (N=10) | Congo, Rep. (N=10) | Costa Rica (N=10) | Cote d'Ivoire (N=10) | Croatia (N=10) | Cyprus (N=10) | Czech Republic (N=10) | Denmark (N=10) | Djibouti (N=10) | Dominica (N=10) | Dominican Republic (N=10) | Ecuador (N=10) | Egypt, Arab Rep. (N=10) | El Salvador (N=10) | Eritrea (N=10) | Estonia (N=10) | Ethiopia (N=10) | Fiji (N=10) | Finland (N=10) | France (N=10) | Georgia (N=10) | Germany (N=10) | Ghana (N=10) | Gibraltar (N=10) | Greece (N=10) | Grenada (N=10) | Guatemala (N=10) | Guinea (N=10) | Guyana (N=10) | Honduras (N=10) | Hong Kong SAR, China (N=10) | Hungary (N=10) | Iceland (N=10) | India (N=10) | Indonesia (N=10) | Iran, Islamic Rep. (N=10) | Ireland (N=10) | Israel (N=10) | Italy (N=10) | Jamaica (N=10) | Japan (N=10) | Jordan (N=10) | Kazakhstan (N=10) | Kenya (N=10) | Korea, Rep. (N=10) | Kuwait (N=10) | Kyrgyz Republic (N=10) | Lao PDR (N=10) | Latvia (N=10) | Lebanon (N=10) | Lesotho (N=10) | Liberia (N=10) | Libya (N=10) | Liechtenstein (N=10) | Lithuania (N=10) | Luxembourg (N=10) | Macao SAR, China (N=10) | Madagascar (N=10) | Malawi (N=10) | Malaysia (N=10) | Maldives (N=10) | Mali (N=10) | Malta (N=10) | Marshall Islands (N=10) | Mauritania (N=10) | Mauritius (N=10) | Mexico (N=10) | Moldova (N=10) | Monaco (N=10) | Mongolia (N=10) | Morocco (N=10) | Mozambique (N=10) | Myanmar (N=10) | Namibia (N=10) | Nepal (N=10) | Netherlands (N=10) | New Zealand (N=10) | Nicaragua (N=10) | Niger (N=10) | Nigeria (N=10) | North Macedonia (N=10) | Norway (N=10) | Oman (N=10) | Pakistan (N=10) | Palau (N=10) | Panama (N=10) | Paraguay (N=10) | Peru (N=10) | Philippines (N=10) | Poland (N=10) | Portugal (N=10) | Puerto Rico (N=10) | Qatar (N=10) | Romania (N=10) | Russian Federation (N=10) | Rwanda (N=10) | Samoa (N=10) | Saudi Arabia (N=10) | Senegal (N=10) | Serbia (N=10) | Seychelles (N=10) | Sierra Leone (N=10) | Singapore (N=10) | Slovak Republic (N=10) | Slovenia (N=10) | Solomon Islands (N=10) | South Africa (N=10) | Spain (N=10) | Sri Lanka (N=10) | St. Lucia (N=10) | Sudan (N=10) | Suriname (N=10) | Sweden (N=10) | Switzerland (N=10) | Syrian Arab Republic (N=10) | Tajikistan (N=10) | Tanzania (N=10) | Thailand (N=10) | Timor-Leste (N=10) | Togo (N=10) | Tonga (N=10) | Tunisia (N=10) | Turkey (N=10) | Turks and Caicos Islands (N=10) | Tuvalu (N=10) | Uganda (N=10) | Ukraine (N=10) | United Arab Emirates (N=10) | United Kingdom (N=10) | United States (N=10) | Uruguay (N=10) | Uzbekistan (N=10) | Venezuela, RB (N=10) | West Bank and Gaza (N=10) | Yemen, Rep. (N=10) | Zimbabwe (N=10) | Total (N=1780) | p value|
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## |**Value** | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
## | N-Miss | 3 | 3 | 8 | 4 | 1 | 7 | 3 | 2 | 7 | 6 | 1 | 8 | 1 | 0 | 2 | 2 | 1 | 1 | 2 | 5 | 4 | 1 | 1 | 0 | 10 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 10 | 4 | 1 | 6 | 8 | 2 | 1 | 0 | 1 | 6 | 6 | 10 | 0 | 4 | 1 | 1 | 2 | 1 | 1 | 6 | 0 | 1 | 5 | 1 | 3 | 1 | 7 | 10 | 1 | 1 | 3 | 1 | 1 | 7 | 1 | 4 | 0 | 8 | 7 | 1 | 0 | 2 | 1 | 4 | 1 | 3 | 2 | 1 | 1 | 1 | 1 | 2 | 0 | 10 | 1 | 5 | 4 | 1 | 1 | 0 | 4 | 8 | 10 | 2 | 1 | 1 | 0 | 2 | 4 | 0 | 8 | 4 | 1 | 8 | 1 | 0 | 1 | 0 | 0 | 9 | 7 | 3 | 6 | 10 | 10 | 4 | 1 | 9 | 4 | 3 | 3 | 1 | 2 | 0 | 10 | 4 | 6 | 1 | 6 | 1 | 1 | 2 | 0 | 1 | 2 | 0 | 5 | 5 | 8 | 0 | 0 | 4 | 7 | 1 | 1 | 7 | 3 | 1 | 6 | 0 | 4 | 3 | 1 | 2 | 6 | 8 | 6 | 0 | 0 | 8 | 5 | 4 | 3 | 8 | 7 | 10 | 0 | 8 | 2 | 1 | 2 | 2 | 2 | 0 | 6 | 9 | 579 | |
## | Mean (SD) | 2.788 (1.134) | 7.758 (1.183) | 0.174 (0.137) | 2.263 (0.322) | 2.631 (0.367) | 14.344 (6.173) | 18.131 (0.825) | 26.151 (0.516) | 91.909 (0.424) | 43.726 (6.028) | 10.028 (0.364) | 12.588 (0.428) | 26.708 (4.131) | 24.260 (1.682) | 93.616 (2.461) | 6.326 (0.633) | 0.477 (0.039) | 58.376 (0.422) | 64.342 (3.059) | 16.167 (2.276) | 43.726 (0.868) | 11.124 (0.807) | 12.180 (0.477) | 2.067 (0.451) | NA | 13.822 (0.581) | 17.477 (0.932) | 15.549 (0.963) | 3.082 (1.826) | 40.556 (0.983) | 8.315 (0.840) | 10.281 (2.662) | NA | 27.138 (1.069) | 7.586 (0.452) | 30.090 (2.950) | 22.813 (1.020) | 18.890 (4.880) | 60.612 (1.383) | 11.192 (1.261) | 20.655 (0.345) | 51.868 (2.385) | 16.603 (1.440) | NA | 9.096 (0.523) | 51.299 (0.628) | 2.026 (0.372) | 17.855 (0.423) | 9.148 (0.598) | 14.083 (0.903) | 9.869 (0.882) | 30.629 (2.235) | 19.226 (1.306) | 29.092 (3.036) | 7.564 (0.538) | 16.775 (0.589) | 6.074 (1.234) | 3.636 (0.263) | 10.760 (3.909) | NA | 12.726 (2.777) | 25.731 (0.446) | 10.376 (0.405) | 9.121 (0.391) | 16.210 (0.590) | 7.393 (2.979) | 4.439 (0.219) | 62.999 (1.021) | 62.425 (1.013) | 32.776 (9.227) | 7.625 (1.264) | 26.624 (1.761) | 18.452 (1.686) | 18.926 (4.413) | 13.738 (0.946) | 50.311 (1.312) | 41.804 (0.712) | 12.432 (1.045) | 0.585 (0.211) | 11.599 (0.493) | 7.281 (0.673) | 2.946 (1.355) | 19.792 (0.557) | 19.945 (1.387) | 5.176 (0.396) | NA | 31.279 (0.281) | 34.357 (1.821) | 2.893 (0.110) | 2.969 (0.234) | 2.360 (0.950) | 60.237 (1.180) | 1.380 (0.619) | 59.174 (1.140) | NA | 3.702 (0.911) | 2.294 (0.905) | 18.195 (0.356) | 95.768 (0.314) | 40.326 (2.779) | 8.120 (1.680) | 8.522 (2.340) | 4.980 (0.296) | 37.523 (4.863) | 34.909 (2.688) | 19.410 (1.943) | 26.544 (1.673) | 57.712 (0.988) | 13.339 (0.244) | 1.518 (0.263) | 27.273 (4.752) | 7.205 (NA) | 10.331 (0.391) | 11.443 (1.566) | 4.052 (1.916) | NA | NA | 5.294 (1.602) | 10.862 (3.288) | 21.834 (NA) | 17.672 (1.896) | 21.011 (2.203) | 0.980 (0.476) | 7.387 (0.435) | 10.760 (2.027) | 32.765 (1.887) | NA | 16.292 (0.158) | 21.507 (0.345) | 28.005 (2.204) | 20.165 (3.090) | 8.926 (3.432) | 16.831 (0.535) | 24.641 (1.680) | 44.365 (3.705) | 1.375 (0.304) | 1.122 (0.205) | 16.404 (4.094) | 32.542 (1.069) | 12.290 (0.637) | 22.118 (1.615) | 0.592 (0.180) | 10.194 (2.259) | 8.874 (1.448) | 4.791 (0.496) | 10.725 (0.756) | 2.644 (1.164) | 31.609 (2.154) | 4.256 (0.458) | 28.230 (1.222) | 7.043 (0.412) | 3.352 (0.302) | 16.341 (2.905) | 0.869 (0.134) | 17.778 (1.527) | 10.984 (1.709) | 3.905 (0.245) | 1.160 (0.126) | 18.660 (0.424) | 12.992 (2.841) | 24.673 (0.930) | 25.141 (2.645) | 67.265 (2.356) | 6.337 (1.248) | 5.078 (2.055) | 18.675 (5.404) | 18.168 (10.304) | NA | 0.436 (0.096) | 64.991 (2.031) | 56.658 (20.254) | 8.426 (0.397) | 12.424 (0.626) | 0.056 (0.046) | 30.763 (2.079) | 6.605 (0.643) | 3.960 (0.411) | 77.410 (NA) | 19.219 (19.109) | |
## | Range | 1.274 - 4.458 | 6.144 - 9.463 | 0.077 - 0.271 | 1.706 - 2.645 | 2.045 - 3.058 | 10.584 - 21.468 | 16.712 - 19.505 | 25.366 - 26.830 | 91.570 - 92.384 | 40.457 - 52.759 | 9.488 - 10.542 | 12.285 - 12.891 | 17.744 - 31.064 | 21.249 - 26.118 | 87.602 - 95.115 | 5.316 - 7.301 | 0.421 - 0.559 | 57.616 - 58.765 | 60.622 - 70.352 | 12.972 - 18.682 | 42.829 - 45.247 | 10.052 - 12.503 | 11.499 - 12.754 | 1.457 - 2.748 | NA | 12.878 - 14.981 | 15.913 - 18.830 | 13.523 - 16.813 | 1.030 - 5.374 | 38.777 - 41.857 | 6.859 - 9.252 | 7.444 - 13.711 | NA | 25.442 - 28.260 | 6.985 - 8.352 | 27.726 - 34.379 | 22.091 - 23.534 | 14.821 - 26.280 | 57.909 - 61.913 | 9.830 - 13.650 | 20.214 - 21.185 | 49.653 - 55.012 | 14.957 - 18.470 | NA | 7.938 - 9.656 | 50.566 - 52.069 | 1.469 - 2.354 | 17.244 - 18.646 | 8.170 - 10.064 | 12.914 - 15.639 | 8.867 - 11.617 | 28.702 - 33.580 | 17.805 - 21.580 | 25.978 - 33.388 | 6.978 - 8.370 | 16.135 - 18.007 | 4.554 - 7.471 | 3.314 - 4.165 | 6.620 - 14.387 | NA | 8.310 - 14.859 | 25.205 - 26.169 | 9.945 - 11.070 | 8.480 - 9.632 | 15.403 - 17.184 | 4.381 - 10.338 | 4.205 - 4.811 | 61.594 - 64.453 | 60.309 - 63.445 | 26.251 - 39.300 | 6.235 - 8.706 | 24.483 - 30.192 | 16.470 - 21.012 | 12.864 - 22.444 | 12.290 - 14.970 | 47.995 - 51.888 | 40.913 - 43.356 | 10.527 - 13.556 | 0.213 - 0.747 | 10.517 - 12.096 | 6.761 - 8.520 | 1.784 - 5.150 | 19.132 - 20.706 | 18.583 - 21.727 | 4.671 - 5.718 | NA | 30.752 - 31.669 | 31.516 - 36.371 | 2.720 - 3.006 | 2.690 - 3.312 | 1.151 - 3.750 | 58.117 - 62.203 | 0.850 - 2.559 | 58.368 - 59.981 | NA | 2.508 - 5.064 | 1.096 - 3.461 | 17.717 - 18.804 | 95.347 - 96.253 | 35.995 - 43.098 | 5.919 - 10.232 | 4.487 - 11.253 | 4.770 - 5.189 | 31.260 - 43.767 | 28.945 - 37.980 | 18.036 - 20.784 | 24.565 - 29.360 | 56.587 - 59.596 | 13.068 - 13.790 | 1.250 - 2.027 | 21.741 - 32.582 | 7.205 - 7.205 | 9.940 - 10.722 | 9.477 - 13.329 | 1.268 - 5.580 | NA | NA | 3.320 - 7.177 | 9.082 - 19.485 | 21.834 - 21.834 | 14.816 - 19.393 | 18.699 - 24.182 | 0.000 - 1.510 | 6.904 - 8.165 | 6.975 - 13.068 | 30.878 - 35.830 | NA | 16.111 - 16.472 | 21.007 - 21.802 | 24.099 - 30.050 | 18.079 - 24.730 | 4.148 - 11.467 | 16.075 - 17.575 | 21.278 - 27.205 | 38.603 - 49.181 | 1.067 - 1.838 | 0.763 - 1.306 | 11.335 - 24.246 | 30.904 - 33.827 | 11.464 - 13.036 | 20.976 - 23.260 | 0.413 - 0.948 | 6.738 - 12.897 | 6.971 - 10.790 | 4.228 - 5.166 | 9.621 - 11.885 | 1.485 - 4.192 | 29.846 - 34.010 | 3.679 - 5.038 | 26.944 - 30.233 | 6.441 - 7.329 | 2.828 - 3.746 | 13.254 - 20.347 | 0.778 - 1.157 | 16.291 - 20.967 | 7.370 - 12.080 | 3.596 - 4.191 | 1.071 - 1.249 | 18.047 - 19.016 | 10.481 - 16.784 | 23.338 - 26.490 | 23.271 - 27.011 | 64.221 - 69.297 | 4.766 - 7.467 | 3.039 - 7.816 | 14.854 - 22.496 | 6.661 - 26.540 | NA | 0.368 - 0.647 | 63.555 - 66.427 | 29.316 - 74.760 | 7.911 - 8.953 | 11.423 - 13.002 | 0.000 - 0.146 | 28.299 - 33.311 | 5.450 - 7.286 | 3.468 - 4.453 | 77.410 - 77.410 | 0.000 - 96.253 | |
(2-3) Changes in the distribution of the independent variable between 2010 and 2018, by country (The figure presents the year 2018 instead of 2019 as many countries miss the latest data for the year)
pe_slope <- pedata %>%
filter(Year %in% c(2010, 2015, 2018) &
Country %in% c("Andorra", "Austria", "Bangladesh", "Brundi", "Belgium", "Bulgaria", "Bolivia", "Brazil", "Brunei Darussalam", "Swizerland", "Cyprus", "Czech Republic", "Denmark", "Ecuador", "Eritrea", "Djibouti", "Spain", "Estonia", "France", "Finland", "Germany", "United Kingdom", "Iceland", "Hungary", "Indonesia", "Italy", "Japan", "Korea, Republic of", "Luxembourg", "Lao PDR", "Lebanon", "Lithuania", "Macao SAR, China", "Mexico", "Malaysia", "New Zealand", "Poland", "West Bank and Gaza", "Qatar", "Romania", "Slobak Republic", "Venezuela, RB", "Uganda", "United States", "Yemen", "Zimbabwe" )) %>%
mutate(Year = factor(Year),
Value = round(Value))
newggslopegraph(pe_slope, Year, Value, Country) +labs(title="Change in the share of private secondary education, by country, from 2010 to 2019", check_overlap = T)
##
## Converting 'Year' to an ordered factor
Table 2-1 illustrates that the overall share of private secondary education has continuously remained at slightly below 20%, except the year 2019 when it marked above 22%. It is interesting to observe from Figure 2-3 that around 96% of the secondary education service has been provided by the private sector in Macao, China while it take s up only 1% in Bulgaria and Romania, implying that each country’s approaches to application of the privatization schemes in education enormously vary. Another interesting phenomenon is a stark increase in the share of private sector provision of secondary education from 29% to 75% over the last ten years in the UK.
4. Relationships between the independent variable and dependent variable
Before plotting the relationship between the independent Variable (lp_gdp) and dependent variable (pe_share), and further creating and analzing regression models, all 5 separate data sets introduced in the previous section has to be merged into one. Also the dependent variable will be lagged in an attempt to provide more robust estimates of the effects of the independent variable by overcoming omitted variable bias and accounting for autocorrelation. *After trying several different lag combinations, 3-year lag structure was selected based on Akaike (AIC) and Bayesian (BIC) information criteria.
##merging two main data sets: the main independent variable and dependent variable
dataset_merged1 <- merge(lpdata, pedata, by=c("Country","Year"))
dataset_merged1 <- dataset_merged1 %>%
rename(
lp_gdp = Value.x,
pe_share = Value.y
)
##lagging the dependent variable
library(Hmisc)
## Loading required package: lattice
## Loading required package: Formula
##
## Attaching package: 'Hmisc'
## The following objects are masked from 'package:dplyr':
##
## src, summarize
## The following object is masked from 'package:arsenal':
##
## %nin%
## The following objects are masked from 'package:base':
##
## format.pval, units
dataset_merged1$lp_gdp_lagged <- Lag(dataset_merged1$lp_gdp, -3)
lagged_lpgdp_data <- dplyr::select(dataset_merged1, Country, Year, pe_share, lp_gdp, lp_gdp_lagged)
head(lagged_lpgdp_data, addrownums = FALSE)
## Country Year pe_share lp_gdp lp_gdp_lagged
## 1 Afghanistan 2010 NA 9573 9943
## 2 Afghanistan 2011 1.27354 9219 9697
## 3 Afghanistan 2012 1.94761 9910 9365
## 4 Afghanistan 2013 NA 9943 9178
## 5 Afghanistan 2014 1.97750 9697 9048
## 6 Afghanistan 2015 2.72148 9365 8871
##further merging the data sets for control variables
dataset_merged2 <- merge(lagged_lpgdp_data, working_hr, by=c("Country","Year"))
dataset_merged2 <- dataset_merged2 %>%
rename(
mwwhour = Value
)
dataset_merged3 <- merge(dataset_merged2, conpri_health, by=c("Country","Year"))
dataset_merged3 <- dataset_merged3 %>%
rename(
healthconpri = Value
)
dataset_merged4 <- merge(dataset_merged3, edu_price, by=c("Country","Year"))
dataset_merged4 <- dataset_merged4 %>%
rename(
educost = Value
)
##filtering years that are lagged
library(dplyr)
data_filtered <- filter(dataset_merged4, Year >=2010 & Year < 2017)
After merging and filtering, countries that are covered in all 5 separate data sets between 2010 and 2016 are left. Through this we obtain a total of 764 observations with 8 variables.
Using this tailored data set, relationship between the independent variables and the dependent variable were plotted below.
plot(lm(data_filtered$lp_gdp_lagged ~ data_filtered$pe_share))
The
5.Regression results for models
First, three regression models (pooled OLS, fixed-effects and random-effects) that do not include control variables were prepared below. While using pooled OLS is often considered problematic in a panel context as it ignores all individually specific effects, it is worth trying to test it here.
ols1 <- lm(lp_gdp_lagged ~ pe_share, data_filtered)
library(sjPlot)
## #refugeeswelcome
tab_model(ols1, digits = 3)
| lp\_gdp\_lagged | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 62060.589 | 56877.492 – 67243.686 | <0.001 |
| pe\_share | -268.902 | -466.435 – -71.369 | 0.008 |
| Observations | 591 | ||
| R2 / R2 adjusted | 0.012 / 0.010 | ||
library(lme4)
## Loading required package: Matrix
fe1 <- lm(lp_gdp_lagged ~ pe_share + factor(Country), data = data_filtered)
tab_model(fe1, digits = 3)
| lp\_gdp\_lagged | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 8610.536 | 4528.714 – 12692.358 | <0.001 |
| pe\_share | 108.538 | -12.435 – 229.510 | 0.079 |
| Country | 23028.371 | 17853.127 – 28203.615 | <0.001 |
| Country | 9992.285 | 4068.616 – 15915.955 | 0.001 |
| Country | 41297.864 | 32664.483 – 49931.245 | <0.001 |
| Country | 86073.461 | 78161.640 – 93985.282 | <0.001 |
| Country | 100307.993 | 95367.721 – 105248.265 | <0.001 |
| Country | 71696.659 | 66216.419 – 77176.899 | <0.001 |
| Country | -8819.769 | -20998.941 – 3359.403 | 0.155 |
| Country | 22832.774 | 17670.906 – 27994.641 | <0.001 |
| Country | 28194.445 | 23324.007 – 33064.883 | <0.001 |
| Country | 106331.599 | 98034.816 – 114628.381 | <0.001 |
| Country | 2183.220 | -6651.399 – 11017.839 | 0.627 |
| Country | -2569.466 | -7967.415 – 2828.484 | 0.350 |
| Country | 13112.243 | 7866.012 – 18358.474 | <0.001 |
| Country | 7800.386 | 2799.494 – 12801.277 | 0.002 |
| Country | 34883.295 | 30019.176 – 39747.414 | <0.001 |
| Country | 124750.196 | 119535.750 – 129964.642 | <0.001 |
| Country | 38460.515 | 33597.511 – 43323.520 | <0.001 |
| Country | -6742.397 | -14577.661 – 1092.867 | 0.092 |
| Country | -7650.669 | -12569.249 – -2732.090 | 0.002 |
| Country | -3138.646 | -9093.953 – 2816.660 | 0.301 |
| Country | 85154.478 | 78691.926 – 91617.029 | <0.001 |
| Country | -5992.857 | -12607.696 – 621.983 | 0.076 |
| Country | 36251.206 | 27760.446 – 44741.966 | <0.001 |
| Country | 18901.259 | 13573.724 – 24228.794 | <0.001 |
| Country | -2055.745 | -10668.812 – 6557.323 | 0.639 |
| Country | 32467.603 | 27538.577 – 37396.629 | <0.001 |
| Country | 57392.310 | 52528.455 – 62256.166 | <0.001 |
| Country | 47546.141 | 42355.844 – 52736.439 | <0.001 |
| Country | 102857.259 | 97815.685 – 107898.833 | <0.001 |
| Country | 3888.911 | -1550.888 – 9328.709 | 0.161 |
| Country | 26968.502 | 21686.794 – 32250.210 | <0.001 |
| Country | 13665.942 | 7790.274 – 19541.610 | <0.001 |
| Country | 9820.990 | 4666.951 – 14975.028 | <0.001 |
| Country | 57464.203 | 52599.932 – 62328.474 | <0.001 |
| Country | -5879.042 | -11714.890 – -43.195 | 0.048 |
| Country | 92806.116 | 87811.072 – 97801.160 | <0.001 |
| Country | 97143.207 | 91530.068 – 102756.345 | <0.001 |
| Country | 18753.605 | 13290.767 – 24216.442 | <0.001 |
| Country | 93811.169 | 88889.145 – 98733.192 | <0.001 |
| Country | 2046.318 | -3361.476 – 7454.111 | 0.458 |
| Country | 76643.067 | 71775.471 – 81510.664 | <0.001 |
| Country | 4816.604 | -3919.750 – 13552.958 | 0.279 |
| Country | -5336.918 | -12727.212 – 2053.375 | 0.157 |
| Country | 1316.588 | -4365.626 – 6998.803 | 0.649 |
| Country | 53496.843 | 48190.244 – 58803.443 | <0.001 |
| Country | 82933.025 | 77897.094 – 87968.957 | <0.001 |
| Country | 152939.726 | 147950.715 – 157928.736 | <0.001 |
| Country | 82285.659 | 77308.394 – 87262.924 | <0.001 |
| Country | 100003.821 | 95107.839 – 104899.804 | <0.001 |
| Country | 12233.977 | 5800.028 – 18667.925 | <0.001 |
| Country | 67140.714 | 61867.139 – 72414.288 | <0.001 |
| Country | 35411.070 | 29901.884 – 40920.255 | <0.001 |
| Country | 41988.056 | 37114.380 – 46861.733 | <0.001 |
| Country | 84601.653 | 78187.135 – 91016.171 | <0.001 |
| Country | 50039.958 | 45176.237 – 54903.679 | <0.001 |
| Country | 34898.183 | 26362.051 – 43434.314 | <0.001 |
| Country | -781.296 | -5766.959 – 4204.367 | 0.758 |
| Country | -11573.187 | -20956.579 – -2189.794 | 0.016 |
| Country | 59693.503 | 54829.760 – 64557.246 | <0.001 |
| Country | 231069.001 | 225863.239 – 236274.762 | <0.001 |
| Country | -9658.019 | -16412.514 – -2903.524 | 0.005 |
| Country | -6899.473 | -12319.588 – -1479.358 | 0.013 |
| Country | 45184.497 | 40276.454 – 50092.540 | <0.001 |
| Country | -6179.716 | -12735.367 – 375.936 | 0.065 |
| Country | 79678.129 | 73462.055 – 85894.204 | <0.001 |
| Country | 9328.416 | 3652.024 – 15004.808 | 0.001 |
| Country | 31839.686 | 23576.618 – 40102.755 | <0.001 |
| Country | 35671.256 | 30639.913 – 40702.599 | <0.001 |
| Country | 15744.474 | 7588.970 – 23899.978 | <0.001 |
| Country | -6831.258 | -11917.421 – -1745.095 | 0.009 |
| Country | 2147.052 | -4286.095 – 8580.198 | 0.512 |
| Country | 99690.187 | 94303.417 – 105076.957 | <0.001 |
| Country | 68666.828 | 63692.402 – 73641.255 | <0.001 |
| Country | 1456.702 | -7003.196 – 9916.600 | 0.735 |
| Country | -7332.067 | -12811.038 – -1853.096 | 0.009 |
| Country | 7683.371 | 2339.970 – 13026.772 | 0.005 |
| Country | 34763.359 | 29613.049 – 39913.669 | <0.001 |
| Country | 112792.837 | 107896.431 – 117689.243 | <0.001 |
| Country | 46128.923 | 40912.861 – 51344.984 | <0.001 |
| Country | 1380.769 | -4701.592 – 7463.130 | 0.656 |
| Country | 53529.362 | 48282.284 – 58776.440 | <0.001 |
| Country | 14384.918 | 8541.811 – 20228.026 | <0.001 |
| Country | 10974.429 | 5113.384 – 16835.474 | <0.001 |
| Country | 10503.638 | 4435.298 – 16571.978 | 0.001 |
| Country | 54946.474 | 50037.366 – 59855.582 | <0.001 |
| Country | 60753.153 | 55605.629 – 65900.677 | <0.001 |
| Country | 114440.267 | 107569.264 – 121311.269 | <0.001 |
| Country | 45308.218 | 40321.175 – 50295.261 | <0.001 |
| Country | -6638.629 | -11845.494 – -1431.764 | 0.013 |
| Country | 12883.875 | 6597.962 – 19169.788 | <0.001 |
| Country | 110441.418 | 103891.828 – 116991.009 | <0.001 |
| Country | 555.820 | -7876.283 – 8987.923 | 0.897 |
| Country | 25674.042 | 20803.803 – 30544.280 | <0.001 |
| Country | -4268.633 | -9464.901 – 927.635 | 0.107 |
| Country | 68659.701 | 63796.377 – 73523.025 | <0.001 |
| Country | 35186.456 | 30037.174 – 40335.737 | <0.001 |
| Country | 84504.715 | 78776.871 – 90232.560 | <0.001 |
| Country | 6420.349 | -236.480 – 13077.178 | 0.059 |
| Country | 95645.244 | 90452.980 – 100837.508 | <0.001 |
| Country | 110991.737 | 105917.251 – 116066.222 | <0.001 |
| Country | -3106.091 | -8872.075 – 2659.892 | 0.290 |
| Country | -6941.307 | -15450.405 – 1567.792 | 0.110 |
| Country | 25794.207 | 20791.820 – 30796.593 | <0.001 |
| Country | 69720.939 | 64571.527 – 74870.350 | <0.001 |
| Country | 82384.588 | 71175.828 – 93593.348 | <0.001 |
| Country | 77307.130 | 69651.981 – 84962.279 | <0.001 |
| Country | 114231.963 | 109322.538 – 119141.389 | <0.001 |
| Country | 34875.039 | 29746.454 – 40003.624 | <0.001 |
| Country | -10463.463 | -22624.252 – 1697.325 | 0.092 |
| Observations | 591 | ||
| R2 / R2 adjusted | 0.995 / 0.993 | ||
library(stargazer)
##
## Please cite as:
## Hlavac, Marek (2018). stargazer: Well-Formatted Regression and Summary Statistics Tables.
## R package version 5.2.2. https://CRAN.R-project.org/package=stargazer
stargazer(ols1, fe1, type="text", title = "Regression Results for Models without Control Variables", column.labels = c("Pooled OLS", "Fixed-Effects"), dep.var.labels=c("Labour Productivity"), align=TRUE)
##
## Regression Results for Models without Control Variables
## =======================================================================================
## Dependent variable:
## -------------------------------------------------
## Labour Productivity
## Pooled OLS Fixed-Effects
## (1) (2)
## ---------------------------------------------------------------------------------------
## pe_share -268.902*** 108.538*
## (100.577) (61.566)
##
## factor(Country)Albania 23,028.370***
## (2,633.821)
##
## factor(Country)Angola 9,992.285***
## (3,014.715)
##
## factor(Country)Argentina 41,297.860***
## (4,393.760)
##
## factor(Country)Australia 86,073.460***
## (4,026.539)
##
## factor(Country)Austria 100,308.000***
## (2,514.238)
##
## factor(Country)Bahrain 71,696.660***
## (2,789.042)
##
## factor(Country)Bangladesh -8,819.769
## (6,198.309)
##
## factor(Country)Barbados 22,832.770***
## (2,627.014)
##
## factor(Country)Belarus 28,194.440***
## (2,478.697)
##
## factor(Country)Belgium 106,331.600***
## (4,222.456)
##
## factor(Country)Belize 2,183.220
## (4,496.176)
##
## factor(Country)Benin -2,569.466
## (2,747.162)
##
## factor(Country)Bhutan 13,112.240***
## (2,669.949)
##
## factor(Country)Bolivia 7,800.386***
## (2,545.089)
##
## factor(Country)Bosnia and Herzegovina 34,883.290***
## (2,475.481)
##
## factor(Country)Brunei Darussalam 124,750.200***
## (2,653.772)
##
## factor(Country)Bulgaria 38,460.510***
## (2,474.914)
##
## factor(Country)Burkina Faso -6,742.397*
## (3,987.577)
##
## factor(Country)Burundi -7,650.669***
## (2,503.198)
##
## factor(Country)Cameroon -3,138.646
## (3,030.816)
##
## factor(Country)Canada 85,154.480***
## (3,288.967)
##
## factor(Country)Chad -5,992.857*
## (3,366.470)
##
## factor(Country)Chile 36,251.210***
## (4,321.177)
##
## factor(Country)Colombia 18,901.260***
## (2,711.326)
##
## factor(Country)Comoros -2,055.745
## (4,383.422)
##
## factor(Country)Costa Rica 32,467.600***
## (2,508.514)
##
## factor(Country)Croatia 57,392.310***
## (2,475.347)
##
## factor(Country)Cyprus 47,546.140***
## (2,641.482)
##
## factor(Country)Denmark 102,857.300***
## (2,565.793)
##
## factor(Country)Djibouti 3,888.911
## (2,768.460)
##
## factor(Country)Dominican Republic 26,968.500***
## (2,688.004)
##
## factor(Country)Ecuador 13,665.940***
## (2,990.286)
##
## factor(Country)El Salvador 9,820.990***
## (2,623.029)
##
## factor(Country)Estonia 57,464.200***
## (2,475.559)
##
## factor(Country)Ethiopia -5,879.042**
## (2,970.020)
##
## factor(Country)Finland 92,806.120***
## (2,542.112)
##
## factor(Country)France 97,143.210***
## (2,856.677)
##
## factor(Country)Georgia 18,753.600***
## (2,780.186)
##
## factor(Country)Germany 93,811.170***
## (2,504.950)
##
## factor(Country)Ghana 2,046.318
## (2,752.172)
##
## factor(Country)Greece 76,643.070***
## (2,477.251)
##
## factor(Country)Guatemala 4,816.604
## (4,446.166)
##
## factor(Country)Guinea -5,336.918
## (3,761.120)
##
## factor(Country)Honduras 1,316.588
## (2,891.832)
##
## factor(Country)Hungary 53,496.840***
## (2,700.672)
##
## factor(Country)Iceland 82,933.020***
## (2,562.921)
##
## factor(Country)Ireland 152,939.700***
## (2,539.042)
##
## factor(Country)Israel 82,285.660***
## (2,533.064)
##
## factor(Country)Italy 100,003.800***
## (2,491.698)
##
## factor(Country)Jamaica 12,233.980***
## (3,274.410)
##
## factor(Country)Japan 67,140.710***
## (2,683.864)
##
## factor(Country)Jordan 35,411.070***
## (2,803.773)
##
## factor(Country)Kazakhstan 41,988.060***
## (2,480.345)
##
## factor(Country)Kuwait 84,601.650***
## (3,264.521)
##
## factor(Country)Latvia 50,039.960***
## (2,475.279)
##
## factor(Country)Lebanon 34,898.180***
## (4,344.267)
##
## factor(Country)Lesotho -781.296
## (2,537.338)
##
## factor(Country)Liberia -11,573.190**
## (4,775.462)
##
## factor(Country)Lithuania 59,693.500***
## (2,475.290)
##
## factor(Country)Luxembourg 231,069.000***
## (2,649.352)
##
## factor(Country)Madagascar -9,658.019***
## (3,437.545)
##
## factor(Country)Malawi -6,899.473**
## (2,758.443)
##
## factor(Country)Malaysia 45,184.500***
## (2,497.836)
##
## factor(Country)Mali -6,179.716*
## (3,336.348)
##
## factor(Country)Malta 79,678.130***
## (3,163.528)
##
## factor(Country)Mauritania 9,328.416***
## (2,888.869)
##
## factor(Country)Mauritius 31,839.690***
## (4,205.298)
##
## factor(Country)Mexico 35,671.260***
## (2,560.586)
##
## factor(Country)Mongolia 15,744.470***
## (4,150.556)
##
## factor(Country)Mozambique -6,831.258***
## (2,588.485)
##
## factor(Country)Myanmar 2,147.052
## (3,274.002)
##
## factor(Country)Netherlands 99,690.190***
## (2,741.472)
##
## factor(Country)New Zealand 68,666.830***
## (2,531.620)
##
## factor(Country)Nicaragua 1,456.702
## (4,305.470)
##
## factor(Country)Niger -7,332.067***
## (2,788.396)
##
## factor(Country)Nigeria 7,683.371***
## (2,719.401)
##
## factor(Country)North Macedonia 34,763.360***
## (2,621.132)
##
## factor(Country)Norway 112,792.800***
## (2,491.913)
##
## factor(Country)Oman 46,128.920***
## (2,654.594)
##
## factor(Country)Pakistan 1,380.769
## (3,095.477)
##
## factor(Country)Panama 53,529.360***
## (2,670.379)
##
## factor(Country)Paraguay 14,384.920***
## (2,973.715)
##
## factor(Country)Peru 10,974.430***
## (2,982.844)
##
## factor(Country)Philippines 10,503.640***
## (3,088.342)
##
## factor(Country)Poland 54,946.470***
## (2,498.377)
##
## factor(Country)Portugal 60,753.150***
## (2,619.714)
##
## factor(Country)Qatar 114,440.300***
## (3,496.838)
##
## factor(Country)Russian Federation 45,308.220***
## (2,538.041)
##
## factor(Country)Rwanda -6,638.629**
## (2,649.914)
##
## factor(Country)Samoa 12,883.880***
## (3,199.071)
##
## factor(Country)Saudi Arabia 110,441.400***
## (3,333.263)
##
## factor(Country)Senegal 555.820
## (4,291.324)
##
## factor(Country)Serbia 25,674.040***
## (2,478.596)
##
## factor(Country)Sierra Leone -4,268.633
## (2,644.521)
##
## factor(Country)Slovenia 68,659.700***
## (2,475.077)
##
## factor(Country)South Africa 35,186.460***
## (2,620.608)
##
## factor(Country)Spain 84,504.710***
## (2,915.054)
##
## factor(Country)Sudan 6,420.349*
## (3,387.840)
##
## factor(Country)Sweden 95,645.240***
## (2,642.483)
##
## factor(Country)Switzerland 110,991.700***
## (2,582.543)
##
## factor(Country)Timor-Leste -3,106.091
## (2,934.465)
##
## factor(Country)Togo -6,941.307
## (4,330.510)
##
## factor(Country)Tunisia 25,794.210***
## (2,545.849)
##
## factor(Country)Turkey 69,720.940***
## (2,620.674)
##
## factor(Country)United Arab Emirates 82,384.590***
## (5,704.440)
##
## factor(Country)United Kingdom 77,307.130***
## (3,895.912)
##
## factor(Country)United States 114,232.000***
## (2,498.539)
##
## factor(Country)Uruguay 34,875.040***
## (2,610.075)
##
## factor(Country)Zimbabwe -10,463.460*
## (6,188.953)
##
## Constant 62,060.590*** 8,610.536***
## (2,639.052) (2,077.349)
##
## ---------------------------------------------------------------------------------------
## Observations 591 591
## R2 0.012 0.995
## Adjusted R2 0.010 0.993
## Residual Std. Error 43,964.570 (df = 589) 3,586.478 (df = 480)
## F Statistic 7.148*** (df = 1; 589) 810.024*** (df = 110; 480)
## =======================================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01
<Pooled OLS, Fixed-Effects, and Random-Effects>
library(plm)
##
## Attaching package: 'plm'
## The following objects are masked from 'package:dplyr':
##
## between, lag, lead
pooledols1 <- plm(lp_gdp_lagged ~ pe_share, data=data_filtered, model = "pooling", index = c("Country", "Year"))
fixeff1 <- plm(lp_gdp_lagged ~ pe_share, data=data_filtered, model = "within", index = c("Country", "Year"))
randeff1 <- plm(lp_gdp_lagged ~ pe_share, data=data_filtered, model = "random", index = c("Country", "Year"))
library(stargazer)
stargazer(pooledols1, fixeff1, randeff1, type="text", title = "Regression Results for Models without Control Variables", column.labels = c("Pooled OLS", "Fixed-Effects", "Random-Effects") ,dep.var.labels=c("Labour Productivity"), align=TRUE)
##
## Regression Results for Models without Control Variables
## =======================================================================
## Dependent variable:
## ----------------------------------------------------------
## Labour Productivity
## Pooled OLS Fixed-Effects Random-Effects
## (1) (2) (3)
## -----------------------------------------------------------------------
## pe_share -268.902*** 108.538* 82.469
## (100.577) (61.566) (59.395)
##
## Constant 62,060.590*** 49,722.330***
## (2,639.052) (4,380.876)
##
## -----------------------------------------------------------------------
## Observations 591 591 591
## R2 0.012 0.006 0.0001
## Adjusted R2 0.010 -0.221 -0.002
## F Statistic 7.148*** (df = 1; 589) 3.108* (df = 1; 480) 1.928
## =======================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01
The first regression results for models without control variables do not allow us to observe any statistically significant correlation between the share of private education and the level of productivity. Pooled OLS model shows that the share of private education (pe-share) is statistically significant at 95% confidence level, while it is statistically significant at 90% confidence level for the Fixed=Effects Model. However, the fact that: i) R-square value and adjusted R-square value are extremely low and even negative for the Fixed-Effects model and the Random-effects model; and ii) the overall significance of the model presented by F-statistic is low, suggests that the models hardly explains the variation in the dependent variable. These results let us conclude that none of the above models without control variable are a good fit.
It is followed by three additional regression models with three control variables included.
ols2 <- lm(lp_gdp_lagged ~ pe_share + mwwhour + healthconpri + educost, data_filtered)
tab_model(ols2, digits = 3)
| lp\_gdp\_lagged | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 58105.628 | 48943.016 – 67268.240 | <0.001 |
| pe\_share | 42.417 | -190.712 – 275.546 | 0.721 |
| mwwhour | 0.005 | 0.000 – 0.009 | 0.033 |
| healthconpri | 2497.464 | 1041.250 – 3953.677 | 0.001 |
| educost | -5307.204 | -7392.403 – -3222.004 | <0.001 |
| Observations | 577 | ||
| R2 / R2 adjusted | 0.072 / 0.065 | ||
library(lme4)
fe2 <- lm(lp_gdp_lagged ~ pe_share + mwwhour + healthconpri + educost + factor(Country), data = data_filtered)
tab_model(fe2, digits = 3)
| lp\_gdp\_lagged | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 5363.991 | -866.914 – 11594.897 | 0.091 |
| pe\_share | 34.048 | -86.172 – 154.269 | 0.578 |
| mwwhour | 0.008 | -0.001 – 0.017 | 0.072 |
| healthconpri | 120.235 | -685.591 – 926.061 | 0.769 |
| educost | 798.586 | -101.767 – 1698.938 | 0.082 |
| Country | 24923.508 | 19050.324 – 30796.691 | <0.001 |
| Country | 9050.157 | 2774.905 – 15325.408 | 0.005 |
| Country | 37757.624 | 28598.115 – 46917.132 | <0.001 |
| Country | 85252.000 | 77123.113 – 93380.887 | <0.001 |
| Country | 101494.692 | 96407.363 – 106582.021 | <0.001 |
| Country | 71637.800 | 63522.695 – 79752.906 | <0.001 |
| Country | 25639.561 | 19614.191 – 31664.930 | <0.001 |
| Country | 28670.630 | 23368.055 – 33973.205 | <0.001 |
| Country | 111591.049 | 103026.494 – 120155.604 | <0.001 |
| Country | 6984.313 | -2887.241 – 16855.868 | 0.165 |
| Country | -3694.976 | -10928.874 – 3538.922 | 0.316 |
| Country | 15204.084 | 9300.053 – 21108.114 | <0.001 |
| Country | 6269.437 | -769.412 – 13308.285 | 0.081 |
| Country | 36752.177 | 31477.410 – 42026.944 | <0.001 |
| Country | 125003.698 | 116687.784 – 133319.611 | <0.001 |
| Country | 39712.307 | 34634.523 – 44790.091 | <0.001 |
| Country | -4467.078 | -12765.905 – 3831.748 | 0.291 |
| Country | -6090.063 | -11927.671 – -252.456 | 0.041 |
| Country | -3855.513 | -10119.434 – 2408.407 | 0.227 |
| Country | 81723.430 | 74259.879 – 89186.982 | <0.001 |
| Country | -4227.747 | -11424.448 – 2968.954 | 0.249 |
| Country | 35280.181 | 25332.544 – 45227.818 | <0.001 |
| Country | 12061.573 | 2985.644 – 21137.501 | 0.009 |
| Country | 1307.206 | -9298.245 – 11912.658 | 0.809 |
| Country | 30291.526 | 22987.974 – 37595.078 | <0.001 |
| Country | 59160.412 | 53686.265 – 64634.558 | <0.001 |
| Country | 48329.069 | 42001.171 – 54656.968 | <0.001 |
| Country | 105366.537 | 99666.942 – 111066.132 | <0.001 |
| Country | 6240.934 | -547.193 – 13029.061 | 0.071 |
| Country | 27260.504 | 21336.198 – 33184.810 | <0.001 |
| Country | 11963.369 | 5081.364 – 18845.375 | 0.001 |
| Country | 10155.828 | 4207.354 – 16104.302 | 0.001 |
| Country | 59056.646 | 53542.502 – 64570.790 | <0.001 |
| Country | -12113.382 | -22425.862 – -1800.902 | 0.021 |
| Country | 95249.037 | 89989.372 – 100508.702 | <0.001 |
| Country | 92982.512 | 84343.982 – 101621.041 | <0.001 |
| Country | 17010.528 | 9698.172 – 24322.885 | <0.001 |
| Country | 84992.167 | 74080.181 – 95904.154 | <0.001 |
| Country | -432.662 | -7309.873 – 6444.548 | 0.902 |
| Country | 75651.036 | 70179.955 – 81122.116 | <0.001 |
| Country | 7127.486 | -2123.631 – 16378.603 | 0.131 |
| Country | -2438.663 | -11164.637 – 6287.312 | 0.583 |
| Country | 2636.800 | -3964.005 – 9237.605 | 0.433 |
| Country | 55056.927 | 49548.340 – 60565.514 | <0.001 |
| Country | 85811.427 | 79982.899 – 91639.954 | <0.001 |
| Country | 153339.779 | 147441.949 – 159237.610 | <0.001 |
| Country | 80474.245 | 73187.541 – 87760.949 | <0.001 |
| Country | 95276.348 | 88468.938 – 102083.759 | <0.001 |
| Country | 13084.784 | 6031.233 – 20138.336 | <0.001 |
| Country | 47915.096 | 27785.833 – 68044.360 | <0.001 |
| Country | 34800.036 | 26643.485 – 42956.587 | <0.001 |
| Country | 40488.283 | 34933.592 – 46042.974 | <0.001 |
| Country | 87118.571 | 79064.644 – 95172.497 | <0.001 |
| Country | 51235.513 | 45885.768 – 56585.258 | <0.001 |
| Country | 35502.174 | 25205.511 – 45798.837 | <0.001 |
| Country | -256.599 | -7022.146 – 6508.948 | 0.941 |
| Country | -7614.036 | -17711.874 – 2483.801 | 0.139 |
| Country | 60504.725 | 55136.404 – 65873.046 | <0.001 |
| Country | 234259.643 | 227886.463 – 240632.823 | <0.001 |
| Country | -9960.912 | -17914.893 – -2006.931 | 0.014 |
| Country | -8762.485 | -16369.562 – -1155.407 | 0.024 |
| Country | 43008.415 | 36732.810 – 49284.020 | <0.001 |
| Country | -3903.092 | -11032.904 – 3226.720 | 0.283 |
| Country | 12900.892 | 6159.624 – 19642.159 | <0.001 |
| Country | 35827.248 | 26235.714 – 45418.781 | <0.001 |
| Country | 18501.382 | 1401.827 – 35600.937 | 0.034 |
| Country | 14926.591 | 5584.830 – 24268.351 | 0.002 |
| Country | -6726.619 | -12842.055 – -611.184 | 0.031 |
| Country | -6140.434 | -16789.028 – 4508.161 | 0.258 |
| Country | 100247.249 | 94331.716 – 106162.782 | <0.001 |
| Country | 70035.752 | 64581.806 – 75489.698 | <0.001 |
| Country | 965.703 | -8468.747 – 10400.153 | 0.841 |
| Country | -6449.584 | -12477.480 – -421.688 | 0.036 |
| Country | -8889.916 | -26578.390 – 8798.557 | 0.324 |
| Country | 36532.197 | 30760.801 – 42303.593 | <0.001 |
| Country | 115220.973 | 109764.704 – 120677.242 | <0.001 |
| Country | 48148.965 | 41589.316 – 54708.615 | <0.001 |
| Country | -19606.527 | -42924.280 – 3711.227 | 0.099 |
| Country | 55126.405 | 48928.981 – 61323.829 | <0.001 |
| Country | 14513.414 | 7535.571 – 21491.257 | <0.001 |
| Country | 3715.834 | -6535.198 – 13966.866 | 0.477 |
| Country | -1593.513 | -15165.932 – 11978.906 | 0.818 |
| Country | 51855.841 | 46131.650 – 57580.031 | <0.001 |
| Country | 61371.602 | 55950.428 – 66792.775 | <0.001 |
| Country | 115370.890 | 105803.077 – 124938.702 | <0.001 |
| Country | 24999.519 | 3047.750 – 46951.287 | 0.026 |
| Country | -5440.572 | -12487.044 – 1605.901 | 0.130 |
| Country | 16910.687 | 8574.265 – 25247.110 | <0.001 |
| Country | 106514.372 | 98404.783 – 114623.961 | <0.001 |
| Country | 1848.066 | -6976.455 – 10672.586 | 0.681 |
| Country | 26346.679 | 21329.200 – 31364.159 | <0.001 |
| Country | -4800.947 | -11969.068 – 2367.173 | 0.189 |
| Country | 70163.112 | 64833.683 – 75492.541 | <0.001 |
| Country | 31475.993 | 24459.787 – 38492.198 | <0.001 |
| Country | 82748.569 | 76120.941 – 89376.198 | <0.001 |
| Country | 6166.548 | -1543.996 – 13877.091 | 0.117 |
| Country | 98078.354 | 92636.571 – 103520.138 | <0.001 |
| Country | 111389.004 | 102297.785 – 120480.224 | <0.001 |
| Country | -126.318 | -7936.917 – 7684.280 | 0.975 |
| Country | -4674.483 | -13514.625 – 4165.659 | 0.299 |
| Country | 25174.206 | 19537.983 – 30810.429 | <0.001 |
| Country | 61291.532 | 51303.173 – 71279.892 | <0.001 |
| Country | 81522.286 | 67938.454 – 95106.117 | <0.001 |
| Country | 73884.430 | 63628.256 – 84140.604 | <0.001 |
| Country | 71578.300 | 26716.567 – 116440.033 | 0.002 |
| Country | 35179.165 | 29111.689 – 41246.640 | <0.001 |
| Country | -5116.328 | -18169.033 – 7936.377 | 0.442 |
| Observations | 577 | ||
| R2 / R2 adjusted | 0.995 / 0.994 | ||
stargazer(ols2, fe2, type="text", title = "Regression Results for Models without Control Variables", column.labels = c("Pooled OLS", "Fixed-Effects"), dep.var.labels=c("Labour Productivity"), align=TRUE)
##
## Regression Results for Models without Control Variables
## ========================================================================================
## Dependent variable:
## --------------------------------------------------
## Labour Productivity
## Pooled OLS Fixed-Effects
## (1) (2)
## ----------------------------------------------------------------------------------------
## pe_share 42.417 34.048
## (118.694) (61.178)
##
## mwwhour 0.005** 0.008*
## (0.002) (0.004)
##
## healthconpri 2,497.464*** 120.235
## (741.408) (410.073)
##
## educost -5,307.204*** 798.586*
## (1,061.646) (458.176)
##
## factor(Country)Albania 24,923.510***
## (2,988.778)
##
## factor(Country)Angola 9,050.157***
## (3,193.384)
##
## factor(Country)Argentina 37,757.620***
## (4,661.141)
##
## factor(Country)Australia 85,252.000***
## (4,136.672)
##
## factor(Country)Austria 101,494.700***
## (2,588.868)
##
## factor(Country)Bahrain 71,637.800***
## (4,129.659)
##
## factor(Country)Barbados 25,639.560***
## (3,066.223)
##
## factor(Country)Belarus 28,670.630***
## (2,698.403)
##
## factor(Country)Belgium 111,591.000***
## (4,358.378)
##
## factor(Country)Belize 6,984.313
## (5,023.491)
##
## factor(Country)Benin -3,694.976
## (3,681.226)
##
## factor(Country)Bhutan 15,204.080***
## (3,004.475)
##
## factor(Country)Bolivia 6,269.437*
## (3,581.968)
##
## factor(Country)Bosnia and Herzegovina 36,752.180***
## (2,684.252)
##
## factor(Country)Brunei Darussalam 125,003.700***
## (4,231.848)
##
## factor(Country)Bulgaria 39,712.310***
## (2,584.011)
##
## factor(Country)Burkina Faso -4,467.078
## (4,223.152)
##
## factor(Country)Burundi -6,090.063**
## (2,970.673)
##
## factor(Country)Cameroon -3,855.513
## (3,187.618)
##
## factor(Country)Canada 81,723.430***
## (3,798.093)
##
## factor(Country)Chad -4,227.747
## (3,662.297)
##
## factor(Country)Chile 35,280.180***
## (5,062.208)
##
## factor(Country)Colombia 12,061.570***
## (4,618.608)
##
## factor(Country)Comoros 1,307.206
## (5,396.960)
##
## factor(Country)Costa Rica 30,291.530***
## (3,716.671)
##
## factor(Country)Croatia 59,160.410***
## (2,785.713)
##
## factor(Country)Cyprus 48,329.070***
## (3,220.176)
##
## factor(Country)Denmark 105,366.500***
## (2,900.441)
##
## factor(Country)Djibouti 6,240.934*
## (3,454.379)
##
## factor(Country)Dominican Republic 27,260.500***
## (3,014.793)
##
## factor(Country)Ecuador 11,963.370***
## (3,502.153)
##
## factor(Country)El Salvador 10,155.830***
## (3,027.092)
##
## factor(Country)Estonia 59,056.650***
## (2,806.068)
##
## factor(Country)Ethiopia -12,113.380**
## (5,247.871)
##
## factor(Country)Finland 95,249.040***
## (2,676.567)
##
## factor(Country)France 92,982.510***
## (4,396.022)
##
## factor(Country)Georgia 17,010.530***
## (3,721.152)
##
## factor(Country)Germany 84,992.170***
## (5,552.951)
##
## factor(Country)Ghana -432.662
## (3,499.712)
##
## factor(Country)Greece 75,651.040***
## (2,784.153)
##
## factor(Country)Guatemala 7,127.486
## (4,707.759)
##
## factor(Country)Guinea -2,438.663
## (4,440.522)
##
## factor(Country)Honduras 2,636.800
## (3,359.054)
##
## factor(Country)Hungary 55,056.930***
## (2,803.240)
##
## factor(Country)Iceland 85,811.430***
## (2,966.053)
##
## factor(Country)Ireland 153,339.800***
## (3,001.320)
##
## factor(Country)Israel 80,474.240***
## (3,708.098)
##
## factor(Country)Italy 95,276.350***
## (3,464.192)
##
## factor(Country)Jamaica 13,084.780***
## (3,589.450)
##
## factor(Country)Japan 47,915.100***
## (10,243.490)
##
## factor(Country)Jordan 34,800.040***
## (4,150.750)
##
## factor(Country)Kazakhstan 40,488.280***
## (2,826.702)
##
## factor(Country)Kuwait 87,118.570***
## (4,098.526)
##
## factor(Country)Latvia 51,235.510***
## (2,722.408)
##
## factor(Country)Lebanon 35,502.170***
## (5,239.822)
##
## factor(Country)Lesotho -256.599
## (3,442.889)
##
## factor(Country)Liberia -7,614.036
## (5,138.643)
##
## factor(Country)Lithuania 60,504.720***
## (2,731.861)
##
## factor(Country)Luxembourg 234,259.600***
## (3,243.218)
##
## factor(Country)Madagascar -9,960.912**
## (4,047.665)
##
## factor(Country)Malawi -8,762.485**
## (3,871.131)
##
## factor(Country)Malaysia 43,008.420***
## (3,193.564)
##
## factor(Country)Mali -3,903.092
## (3,628.258)
##
## factor(Country)Mauritania 12,900.890***
## (3,430.533)
##
## factor(Country)Mauritius 35,827.250***
## (4,880.992)
##
## factor(Country)Mexico 18,501.380**
## (8,701.715)
##
## factor(Country)Mongolia 14,926.590***
## (4,753.886)
##
## factor(Country)Mozambique -6,726.619**
## (3,112.056)
##
## factor(Country)Myanmar -6,140.434
## (5,418.915)
##
## factor(Country)Netherlands 100,247.200***
## (3,010.329)
##
## factor(Country)New Zealand 70,035.750***
## (2,775.434)
##
## factor(Country)Nicaragua 965.703
## (4,801.055)
##
## factor(Country)Niger -6,449.584**
## (3,067.508)
##
## factor(Country)Nigeria -8,889.916
## (9,001.407)
##
## factor(Country)North Macedonia 36,532.200***
## (2,936.979)
##
## factor(Country)Norway 115,221.000***
## (2,776.616)
##
## factor(Country)Oman 48,148.960***
## (3,338.110)
##
## factor(Country)Pakistan -19,606.530*
## (11,866.070)
##
## factor(Country)Panama 55,126.400***
## (3,153.779)
##
## factor(Country)Paraguay 14,513.410***
## (3,550.923)
##
## factor(Country)Peru 3,715.834
## (5,216.601)
##
## factor(Country)Philippines -1,593.513
## (6,906.807)
##
## factor(Country)Poland 51,855.840***
## (2,912.957)
##
## factor(Country)Portugal 61,371.600***
## (2,758.756)
##
## factor(Country)Qatar 115,370.900***
## (4,868.921)
##
## factor(Country)Russian Federation 24,999.520**
## (11,170.940)
##
## factor(Country)Rwanda -5,440.572
## (3,585.847)
##
## factor(Country)Samoa 16,910.690***
## (4,242.284)
##
## factor(Country)Saudi Arabia 106,514.400***
## (4,126.852)
##
## factor(Country)Senegal 1,848.066
## (4,490.670)
##
## factor(Country)Serbia 26,346.680***
## (2,553.322)
##
## factor(Country)Sierra Leone -4,800.947
## (3,647.752)
##
## factor(Country)Slovenia 70,163.110***
## (2,712.069)
##
## factor(Country)South Africa 31,475.990***
## (3,570.445)
##
## factor(Country)Spain 82,748.570***
## (3,372.704)
##
## factor(Country)Sudan 6,166.548
## (3,923.783)
##
## factor(Country)Sweden 98,078.350***
## (2,769.245)
##
## factor(Country)Switzerland 111,389.000***
## (4,626.390)
##
## factor(Country)Timor-Leste -126.318
## (3,974.700)
##
## factor(Country)Togo -4,674.483
## (4,498.620)
##
## factor(Country)Tunisia 25,174.210***
## (2,868.192)
##
## factor(Country)Turkey 61,291.530***
## (5,082.931)
##
## factor(Country)United Arab Emirates 81,522.290***
## (6,912.615)
##
## factor(Country)United Kingdom 73,884.430***
## (5,219.218)
##
## factor(Country)United States 71,578.300***
## (22,829.480)
##
## factor(Country)Uruguay 35,179.170***
## (3,087.650)
##
## factor(Country)Zimbabwe -5,116.328
## (6,642.332)
##
## Constant 58,105.630*** 5,363.991*
## (4,664.996) (3,170.817)
##
## ----------------------------------------------------------------------------------------
## Observations 577 577
## R2 0.072 0.995
## Adjusted R2 0.065 0.994
## Residual Std. Error 42,763.310 (df = 572) 3,466.238 (df = 465)
## F Statistic 11.076*** (df = 4; 572) 840.889*** (df = 111; 465)
## ========================================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01
<Pooled OLS, Fixed-Effects, and Random-Effects>
pooledols2 <- plm(lp_gdp_lagged ~ pe_share + mwwhour + healthconpri + educost, data=data_filtered, model = "pooling", index = c("Country", "Year"))
fixeff2 <- plm(lp_gdp_lagged ~ pe_share + mwwhour + healthconpri + educost, data=data_filtered, model = "within", index = c("Country", "Year"))
randeff2 <- plm(lp_gdp_lagged ~ pe_share + mwwhour + healthconpri + educost, data=data_filtered, model = "random", index = c("Country", "Year"))
stargazer(pooledols2, fixeff2, randeff2, type="text", title = "Regression Results for Models with Control Variables", column.labels = c("Pooled OLS", "Fixed-Effects", "Random-Effects") ,dep.var.labels=c("Labour Productivity"), align=TRUE)
##
## Regression Results for Models with Control Variables
## ========================================================================
## Dependent variable:
## -----------------------------------------------------------
## Labour Productivity
## Pooled OLS Fixed-Effects Random-Effects
## (1) (2) (3)
## ------------------------------------------------------------------------
## pe_share 42.417 34.048 19.193
## (118.694) (61.178) (59.086)
##
## mwwhour 0.005** 0.008* 0.007**
## (0.002) (0.004) (0.003)
##
## healthconpri 2,497.464*** 120.235 294.378
## (741.408) (410.073) (398.051)
##
## educost -5,307.204*** 798.586* 610.373
## (1,061.646) (458.176) (449.341)
##
## Constant 58,105.630*** 45,259.910***
## (4,664.996) (4,797.314)
##
## ------------------------------------------------------------------------
## Observations 577 577 577
## R2 0.072 0.018 0.005
## Adjusted R2 0.065 -0.217 -0.002
## F Statistic 11.076*** (df = 4; 572) 2.090* (df = 4; 465) 8.155*
## ========================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01
Above all, after including control variables, the most notable problem detected is that the coefficient for the independent variable of interest “pe_share” changes drastically for all three models of Pooled OLS, Fixed-Effects, and Random-Effects. Also none of the above models show any statistically significant sign of correlations between the independent variable of main interest and dependent variable, while mean weekly working hours (mwwhour), consumer price for health services (healthconpri), and cost for educational services (educost) are statistically significant at 95% and 99% confidence level for Pooled OLS, and mean weekly working hours (mwwhour) is statistically significant at 90% and 95% confidence level, respectively, for Fixed-Effects model and Random-Effects model. Consistently low R-square value and adjusted R-square value across the regression models as well as F-statistic value also lead us to confirm that there is no statistically significant correlation that we can observed to prove the hypothesis in these models.
6.Robustness Check
Bera, Sosa-Escudero and Yoon locally robust test helps us test residual serial correlation against AR(1) residuals in a pooled OLS model. It is useful in that it helps us detect “the right direction of the departure from the null” (Croissant and Millo, 2018). The result below presents the p-value being much lower than 0,05, which leads us to adopt the alternative hypothesis that errors have either serial correlation or random effect.
pbsytest(pooledols1)
##
## Bera, Sosa-Escudero and Yoon locally robust test - unbalanced panel
##
## data: formula
## chisq = 23.233, df = 1, p-value = 1.435e-06
## alternative hypothesis: AR(1) errors sub random effects
pbsytest(pooledols2)
##
## Bera, Sosa-Escudero and Yoon locally robust test - unbalanced panel
##
## data: formula
## chisq = 28.556, df = 1, p-value = 9.103e-08
## alternative hypothesis: AR(1) errors sub random effects
On the other hand, Croissant and Millo (2018) points out that the “locally corrected” tests are relatively inferior in terms of statistical properties compared to the tests that are not corrected if the latter tests are correctly specified.If there Their argument is that a better test in the case when there is no serial correlation could be the likelihood-based Lagrange Multiplier Test refined by Honda. Therefore we run LM Test to supplement the above locally robust test and to identify the autocorrelation in the residuals, and the result shows that the p-values for both Pooled OLS models are much less than 0.05, which allows us to adopt the alternative hypothesis that there are significant individual/time effects.
plmtest(pooledols1)
##
## Lagrange Multiplier Test - (Honda) for unbalanced panels
##
## data: lp_gdp_lagged ~ pe_share
## normal = 38.844, p-value < 2.2e-16
## alternative hypothesis: significant effects
plmtest(pooledols2)
##
## Lagrange Multiplier Test - (Honda) for unbalanced panels
##
## data: lp_gdp_lagged ~ pe_share + mwwhour + healthconpri + educost
## normal = 37.44, p-value < 2.2e-16
## alternative hypothesis: significant effects
Therefore, the results from the two tests allow us to conclude that the Pooled OLS models are not relevant to be applied for this data.
Lastly, to determine whether the Fixed-Effects model or the Random-Effects model is proper for this data, we run the Hausman test. The null hypothesis for this test is that the preferred model is random effects. The results for both models below show the p-values being higher than 0.05, which leads us to stick to the null hypothesis. However, as we observed in the previous section, either the Fixed-Effects model or the Random-Effects model does not present any statistical significance, meaning that even if the Hausman test leads us to choose the Random-Effects model, it does not give us much implications.
phtest(fixeff1,randeff1)
##
## Hausman Test
##
## data: lp_gdp_lagged ~ pe_share
## chisq = 2.5871, df = 1, p-value = 0.1077
## alternative hypothesis: one model is inconsistent
phtest(fixeff2,randeff2)
##
## Hausman Test
##
## data: lp_gdp_lagged ~ pe_share + mwwhour + healthconpri + educost
## chisq = 5.1683, df = 4, p-value = 0.2705
## alternative hypothesis: one model is inconsistent
7.Conclusion
Based on the regression models and tests we have conducted, it seems that the data we used does not allow us to either accept or reject the hypothesis that ‘the increased level of private sector engagement in the delivery of secondary education services increases overall labour productivity.’ While it may require further analysis based on better sets of data, what we could learn or assume at least from this statistical test is that: i) the impact of the secondary level of education may not be directly related to the level of labour productivity of employees but rather the privatization of higher education or vocational training might give us better insights, ii) we might be able to obtain some meaningful results if we test with the data set for the privatization of education that distinguishes the private ownership of education services, such as private firms, NGOs, or religious groups, and iii) more detailed analysis of the time taken for the educational attainment to have statistically significant impact on individual’s labour productivity, or simply lag structures, would help researchers who study the relationship between education and labour at various levels aggregate or utilize relevant data more effectively.
8.Reference
Croissant and Millo (2018). Panel Data Econometrics with R, ISBN-13:978-1-118-94918-4.
Draxler, A. (2013). International PPPs in Education: New Potential or Privatizing Public Goods’ in S. Robertson, K. Mundy, A. Verger and F. Menashy (eds.) Public Private Partnerships in Education: New Actors and Modes of Governance in a Globalizing World (Cheltenham: Edward Elgar).
Fennell, S. (2012). Why girls’ education rather than gender equality? The strange political economy of PPPs in Pakistan. In: Robertson S, Mundy K (Eds) Public-private partnerships in education: new actors and modes of governance in a globalizing world. Cheltenham: Edward Elgar Publishing.
Steiner-Khamsi, G. & Draxler, A., eds. (2018). The state, business, and education: Public-private partnerships revisited. Cheltenham, UK: E. Elgar. Open-access book.
