Econ 104 Project Part 2
Anvita Chinthada 106287217| Kexin (Asteria) Xue 306293123| Khun Sint Nay Chi Tin Tun 206230876
2025-03-03
#Panel Data
#Load Packages
install.packages("plm", repos = "https://cran.rstudio.com/")##
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## /var/folders/t5/ftzmv8gs4cjdl7zs60z01hqw0000gn/T//RtmphVciTe/downloaded_packageslibrary(plm)
library(AER)## Loading required package: car## Loading required package: carData## Loading required package: lmtest## Loading required package: zoo##
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## Hlavac, Marek (2022). stargazer: Well-Formatted Regression and Summary Statistics Tables.
## R package version 5.2.3. https://CRAN.R-project.org/package=stargazerlibrary(coefplot)
library(fixest)##
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## coefplot#Load Panel Data Set
file_list <- list.files(path = "/Users/asteriaxue/Documents/UCLA/R Studio /archive(2)", pattern = "*.csv", full.names = TRUE)
all_columns <- unique(unlist(lapply(file_list, function(x) colnames(read.csv(x)))))
df_list <- lapply(file_list, function(file) {
data <- read.csv(file)
data[setdiff(all_columns, colnames(data))] <- NA
data[, all_columns]
})
df <- do.call(rbind, df_list)
head(df)## NULLindicators <<- read.csv("/Users/asteriaxue/Documents/UCLA/R Studio /archive (2)/indicators.csv")
attach(indicators)
head(indicators)## Country Year GDP..in.billion.USD. Inflation.Rate.... Unemployment.Rate....
## 1 USA 2010 15000 1.64 9.63
## 2 USA 2011 15500 3.16 8.94
## 3 USA 2012 16000 2.07 8.10
## 4 USA 2013 16500 1.50 7.70
## 5 USA 2014 17000 1.62 7.25
## 6 USA 2015 17500 0.12 5.32
## Economic.Growth....
## 1 2.55
## 2 1.53
## 3 2.28
## 4 1.84
## 5 2.53
## 6 3.08# Rename columns
colnames(indicators)[colnames(indicators) == "GDP..in.billion.USD."] <- "GDP"
colnames(indicators)[colnames(indicators) == "Inflation.Rate...."] <- "inflation"
colnames(indicators)[colnames(indicators) == "Unemployment.Rate...."] <- "unemployment"
colnames(indicators)[colnames(indicators) == "Economic.Growth...."] <- "growth"
indicators.panel <- pdata.frame(indicators, c("Country", "Year"))
head(indicators)## Country Year GDP inflation unemployment growth
## 1 USA 2010 15000 1.64 9.63 2.55
## 2 USA 2011 15500 3.16 8.94 1.53
## 3 USA 2012 16000 2.07 8.10 2.28
## 4 USA 2013 16500 1.50 7.70 1.84
## 5 USA 2014 17000 1.62 7.25 2.53
## 6 USA 2015 17500 0.12 5.32 3.08(1) Brief Explaination of The Data Set & Economical Intuition
Data Set
Economic Intuition
(2) Descriptive Analysis of Variables
Histogram and Fitted Distribution
Distribution across Countries (Inflation Rate)
ggplot(indicators, aes(x = inflation)) +
geom_histogram(aes(y = ..density..), bins = 30, fill = "#81D8D0", color = "black", alpha = 0.7) +
facet_wrap(~ Country, scales = "free_y") +
stat_function(fun = dnorm,
args = list(mean = mean(indicators$inflation, na.rm = TRUE),
sd = sd(indicators$inflation, na.rm = TRUE)),
color = "pink", lwd = 1) +
labs(title = "Distribution of Inflation Rate Across Countries", x = "Inflation Rate", y = "Density") +
theme_minimal()
Distribution across Countries (Inflation Rate): Most countries show a right skewed distribution except for Turkey and Indonesia. However this is because all graphs have a range up to the maximum value of inflation for the whole data set. That means that most countries actually have a normal distribution but Turkey and Indonesia have a skewed distribution.
Distribution across Countries (Unemployment Rate)
ggplot(indicators, aes(x = unemployment)) +
geom_histogram(aes(y = ..density..), bins = 30, fill = "#81D8D0", color = "black", alpha = 0.7) +
facet_wrap(~ Country, scales = "free_y") +
stat_function(fun = dnorm,
args = list(mean = mean(indicators$unemployment, na.rm = TRUE),
sd = sd(indicators$unemployment, na.rm = TRUE)),
color = "pink", lwd = 1) +
labs(title = "Distribution of Unemployment Rate Across Countries", x = "Unemployment Rate", y = "Density") +
theme_minimal()
Distribution across Countries (Unemployment Rate): Most countries show a right skewed distribution except for Turkey and Indonesia. However this is because all graphs have a range up to the maximum value of Unemployment for the whole data set. That means that most countries actually have a normal distribution but Turkey and Indonesia have a skewed distribution.
Distribution across Countries (GDP)
ggplot(indicators, aes(x = GDP)) +
geom_histogram(aes(y = ..density..), bins = 30, fill = "#81D8D0", color = "black", alpha = 0.7) + facet_wrap(~ Country, ncol = 2)+
facet_wrap(~ Country, scales = "free_y") +
stat_function(fun = dnorm,
args = list(mean = mean(indicators$GDP, na.rm = TRUE),
sd = sd(indicators$GDP, na.rm = TRUE)),
color = "pink", lwd = 1) +
labs(title = "Distribution of GDP in billions of USD Across Countries", x = "GDP in Billions of USD", y = "Density") +
theme_minimal()
Distribution across Countries (GDP): Most countries seem to have similar GDP distributions, The United States and China however had clearly higher values of GDP than the other countries.
Distribution across Countries (Economic Growth)
indicators$growth <- as.numeric(as.character(indicators$growth))
ggplot(indicators, aes(x = growth)) +
geom_histogram(aes(y = ..density..), bins = 30, fill = "#81D8D0", color = "black", alpha = 0.7) +
facet_wrap(~ Country, scales = "free_y") +
stat_function(fun = dnorm,
args = list(mean = mean(indicators$growth, na.rm = TRUE),
sd = sd(indicators$growth, na.rm = TRUE)),
color = "pink", lwd = 1) +
labs(title = "Distribution of Economic Growth Across Countries", x = "Economic Growth", y = "Density") +
theme_minimal()
Distribution across Countries (Economic Growth): Most countries seem to have a left skewed distribution of Economic Growth, meaning that for the most part, countries throughout the time period have had positive economic growth and few values of negative economic growth.
Distribution across Time (Inflation Rate)
ggplot(indicators, aes(x = inflation)) +
geom_histogram(aes(y = ..density..), bins = 30, fill = "lightblue", color = "black", alpha = 0.7) +
facet_wrap(~ Year, scales = "free_y") +
stat_function(fun = dnorm,
args = list(mean = mean(indicators$inflation, na.rm = TRUE),
sd = sd(indicators$inflation, na.rm = TRUE)),
color = "pink", lwd = 1) +
labs(title = "Distribution of Inflation Rate Across Time (Year)", x = "Inflation Rate", y = "Density") +
theme_minimal()
Distribution across Time (Inflation Rate) shows that in most years inflation is skewed to the right (low inflation). It is apparent though that some years have very high values (could be coming from one specfiic country).
Distribution across Time (Unemployment Rate)
ggplot(indicators, aes(x = unemployment)) +
geom_histogram(aes(y = ..density..), bins = 30, fill = "#81D8D0", color = "black", alpha = 0.7) +
facet_wrap(~ Year, scales = "free_y") +
stat_function(fun = dnorm,
args = list(mean = mean(indicators$unemployment, na.rm = TRUE),
sd = sd(indicators$unemployment, na.rm = TRUE)),
color = "pink", lwd = 1) +
labs(title = "Distribution of Unemployment Rate Across Time (Year)", x = "Unemployment Rate", y = "Density") +
theme_minimal()
Distribution across Time (Unemployment Rate) shows that unemployment in all years is low (right skewed). It is aparent that high unemployment values are seen in 2021, 2022, and 2023. However these distributions could be misleading if all ranges are being taken from only one observation, therefore the years could have normal distributions with 2021-2023 having skewed distributions.
Distribution across Time (GDP)
ggplot(indicators, aes(x = GDP)) +
geom_histogram(aes(y = ..density..), bins = 30, fill = "#81D8D0", color = "black", alpha = 0.7) +
facet_wrap(~ Year, scales = "free_y") +
stat_function(fun = dnorm,
args = list(mean = mean(indicators$GDP, na.rm = TRUE),
sd = sd(indicators$GDP, na.rm = TRUE)),
color = "pink", lwd = 1) +
labs(title = "Distribution of GDP in billions of USD Across Time (Year)", x = "Unemployment Rate", y = "Density") +
theme_minimal()
Distribution across Time (GDP) looks similar across time. This is because each countries is contributing to a certain value on the histogram and that country will continue to rise slowly in GDP. Every year however there are values that are moving down significantly faster than others meaning that a few countries are growing faster than others in this time period.
Distribution across Time (Economics Growth)
ggplot(indicators, aes(x = growth)) +
geom_histogram(aes(y = ..density..), bins = 30, fill = "#81D8D0", color = "black", alpha = 0.7) +
facet_wrap(~ Year, scales = "free_y") +
stat_function(fun = dnorm,
args = list(mean = mean(indicators$growth, na.rm = TRUE),
sd = sd(indicators$growth, na.rm = TRUE)),
color = "pink", lwd = 1) +
labs(title = "Distribution of Economic Growth Across Time (Year)", x = "Unemployment Rate", y = "Density") +
theme_minimal()
Distribution across Time (Economics Growth) mostly looks normal with a few years being more left skewed. It is clear that over the years countries have mostly positive economic growth.
## Correlation Plots
install.packages("corrplot") ##
## The downloaded binary packages are in
## /var/folders/t5/ftzmv8gs4cjdl7zs60z01hqw0000gn/T//RtmphVciTe/downloaded_packageslibrary(corrplot)## corrplot 0.95 loadedindicators_subset <- indicators[, c("GDP", "inflation", "unemployment", "growth")]
correlation_matrix <- cor(indicators_subset, use = "complete.obs")
corrplot(correlation_matrix, method = "circle", type = "upper", col = colorRampPalette(c("#81D8D0", "white", "pink"))(200), addCoef.col = "black", tl.col = "black", tl.srt = 45)
Correlation Plots show the correlations between each variable. The significant negative correlations exist between GDP vs inflation (-0.18), GDP vs Unemployment (-0.12) and GDP vs Economic growth (-0.14), which are all weak correlations. The positive correlations exist between Inflation vs Unemployment (0.26), Inflation vs Economic Growth (0.37) and Unemployment vs Economic Growth (0.13). Which are weak, moderate, and strong correlations, respectively.
attach(indicators)## The following objects are masked from indicators (pos = 4):
##
## Country, Year## The following object is masked from package:lmtest:
##
## unemployment## Box plot
boxplot(inflation, ylab="Inflation Rate")
Box plot for inflation rate is highly skewed. Interquartile range is very small which means that most of the values are clustered near lower inflation rates. However there are outliers that are significantly higher than the majority of values which exceed 800%
boxplot(unemployment, ylab="Unemployment Rate")
Box plot for unemployment rate is highly skewed. Interquartile range is very small, which means that most of the values are clustered near lower unemployment rates. In this box plot however the median line (black line) is seen, indicating a better distribution compared to inflation rates. There are outliers that are significantly higher than the majority of values which exceed 80%
boxplot(GDP, ylab="GDP")
Box plot for GDP is highly skewed. Interquartile range is small which means that most of the values are clustered near lower GDP (in billion). However there are outliers that are significantly higher than the majority of values which exceed 15000 in billion of dollars). These values must be GDP across the time period for China and the United States.
boxplot(growth, ylab="Economics Growth")
###Box plot for Economic growth shows the median line above 0, meaning that most countries have positive economic growth values across this time period. There are a few outliers which are negative (could mean either one country has those values, or a certain year had those negative values). The interquartile range is centered, showing that most countries in this data set experience moderate growth.
#Scatterplots (ALL)
# OVER TIME
## Scatter plot for inflation over time
ggplot(indicators, aes(x = Year, y = inflation, color = Country)) +
geom_point(size = 1) +
labs(title = "Inflation Over Time", x = "Year", y = "Inflation") +
theme_minimal()
Scatterplot for inflation over time shows that most values are very low (between 0-25%), however Turkey seems to have extremely high inflation rates scattered across 2010-2015 with the highest being 857%. Indonesia also has extremely high inflation rates wit the highest being 550%.
## Scatterplot for GDP (in billions) over time
ggplot(indicators, aes(x = Year, y = GDP, color = Country)) +
geom_point(size = 1) +
labs(title = "GDP Over Time", x = "Year", y = "GDP") +
theme_minimal()
Scatterplot for GDP (in billions) over time shows that all countries slowly grow their GDP over time (very subtle). Major upward trends are shown in countries are the US, China. The countries with higher GDP’s in general (already starting at high GDP in 2011) are US, China, Japan, and Germany.
### Scatterplot for Economic Growth over time
ggplot(indicators, aes(x = Year, y = growth, color = Country)) +
geom_point(size = 1) +
labs(title = "Economic Growth Over Time", x = "Year", y = "Economic Growth") +
theme_minimal()
Scatterplot for Economic Growth over time shows that most countries have an Economig Growth percentage above 0%. Economic growth was negative for all countries in 2020 (COVID-19). Lowest economic growth (-14%) in Saudi Arabia in 2015. The highest economic growth in Turkey (13%) in 2019.
# Across Countries
## Scatter Plot for inflation across countries
ggplot(indicators, aes(x = Country, y = inflation, color = Year)) +
geom_point(size = 1) +
labs(title = "Inflation Across Country", x = "Country", y = "Inflation") +
theme_minimal()+ scale_x_discrete(guide = guide_axis(n.dodge = 2)) + theme(axis.text.x = element_text(size = 8)) + theme(axis.text.x = element_text(angle = 45, vjust = 0.5, hjust = 1))
Scatter Plot for inflation across countries shows that Indonesia and Turkey are the countries that had the most variation and high values of inflation in the time period.
## Scatter plot for GDP across countries
ggplot(indicators, aes(x = Country, y = GDP, color = Year)) +
geom_point(size = 1) +
labs(title = "GDP Across Country", x = "Country", y = "GDP") +
theme_minimal()+ scale_x_discrete(guide = guide_axis(n.dodge = 2)) + theme(axis.text.x = element_text(size = 8)) + theme(axis.text.x = element_text(angle = 45, vjust = 0.5, hjust = 1))
Scatter plot for GDP across countries shows that GDP grows hgiher over time for all countries. All countrues start at different places and it is apparent that the United Sates and China have significantly higher GDP than the rest.
## Scatterplot for Unemployment Rate across countries
ggplot(indicators, aes(x = Country, y = unemployment, color = Year)) +
geom_point(size = 1) +
labs(title = "Unemployment Across Country", x = "Country", y = "Unemployment") +
theme_minimal()+ scale_x_discrete(guide = guide_axis(n.dodge = 2)) + theme(axis.text.x = element_text(size = 8)) + theme(axis.text.x = element_text(angle = 45, vjust = 0.5, hjust = 1))
Scatterplot for Unemployment Rate across countries shows that unemployment rate for most countries has stayed below 10% hwoever some countries have passed that. These countries include Brazil, France, Italy, Bangladesh, and Turkey. Turkey specfically has had extremely high unempyloyment rate.
## Scatter Plot fot Economic Growth across countries
ggplot(indicators, aes(x = Country, y = growth, color = Year)) +
geom_point(size = 1) +
labs(title = "Economic Growth Across Country", x = "Country", y = "Economic Growth") +
theme_minimal()+ scale_x_discrete(guide = guide_axis(n.dodge = 2)) + theme(axis.text.x = element_text(size = 8)) + theme(axis.text.x = element_text(angle = 45, vjust = 0.5, hjust = 1))
Scatter Plot fot Economic Growth across countries show that in the time period most countrues have had postive economic growth. However all countries have had their negative valued economic growth for atleast a year.
``` r
# Five Number Summaries:
summary_inflation <- indicators %>%
group_by(Year) %>%
summarise(
Min = min(inflation, na.rm = TRUE),
Q1 = quantile(inflation, 0.25, na.rm = TRUE),
Median = median(inflation, na.rm = TRUE),
Q3 = quantile(inflation, 0.75, na.rm = TRUE),
Max = max(inflation, na.rm = TRUE))
print(summary_inflation)## # A tibble: 16 × 6
## Year Min Q1 Median Q3 Max
## <int> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 2010 -0.72 1.67 3.3 6.16 12.0
## 2 2011 0 3.08 4 6.3 226
## 3 2012 0.02 2 2.8 7.3 384
## 4 2013 0.2 1.35 2.5 7.1 592
## 5 2014 -0.2 1.56 2.5 6.7 767
## 6 2015 0 0.5 1.5 5.95 857
## 7 2016 -0.5 0.8 1.8 5.4 853
## 8 2017 0.6 1.7 2.7 3.9 315
## 9 2018 0.3 1.9 2.44 3.82 853
## 10 2019 0.3 1.35 1.9 4.85 119
## 11 2020 -1.2 0.55 1.25 5.45 717
## 12 2021 -0.1 1.75 3.1 5.4 186
## 13 2022 0.5 5.05 5.79 8 500
## 14 2023 0 4.03 5.4 6.1 400
## 15 2024 1.2 3.1 3.9 5.55 500
## 16 2025 0 2.65 2.9 4.95 550summary_GDP <- indicators %>%
group_by(Year) %>%
summarise(
Min = min(GDP, na.rm = TRUE),
Q1 = quantile(GDP, 0.25, na.rm = TRUE),
Median = median(GDP, na.rm = TRUE),
Q3 = quantile(GDP, 0.75, na.rm = TRUE),
Max = max(GDP, na.rm = TRUE))
print(summary_GDP)## # A tibble: 16 × 6
## Year Min Q1 Median Q3 Max
## <int> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 2010 105 740 1500 2312. 15000
## 2 2011 1 682 1600 2554. 15500
## 3 2012 1 478 1700 2532. 16000
## 4 2013 1 526. 1750 2600 16500
## 5 2014 1 530 1800 2700 17000
## 6 2015 1 471 1750 2800 17500
## 7 2016 1 471 1800 2900 18000
## 8 2017 1 480 1850 3000 18500
## 9 2018 1 505 1900 3100 19000
## 10 2019 1 506. 1950 3200 19500
## 11 2020 1 491 2000 3558. 20000
## 12 2021 1 509 2050 3750 20500
## 13 2022 1 528 2100 4050 21000
## 14 2023 1 543 2150 4150 21500
## 15 2024 1 553 2200 4250 22000
## 16 2025 1 573 2300 4350 22500summary_Unemployment <- indicators %>%
group_by(Year) %>%
summarise(
Min = min(unemployment, na.rm = TRUE),
Q1 = quantile(unemployment, 0.25, na.rm = TRUE),
Median = median(unemployment, na.rm = TRUE),
Q3 = quantile(unemployment, 0.75, na.rm = TRUE),
Max = max(unemployment, na.rm = TRUE))
print(summary_Unemployment)## # A tibble: 16 × 6
## Year Min Q1 Median Q3 Max
## <int> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 2010 3.2 5.05 7.1 8.95 11.9
## 2 2011 3.1 4.85 6.5 8.6 10.5
## 3 2012 3 4.55 6 7.95 10.7
## 4 2013 2.9 4.85 6.4 7.55 12.2
## 5 2014 2.8 4.75 6 7.72 12.7
## 6 2015 3.1 4.6 5.6 7.25 11.9
## 7 2016 3.3 4.25 5 7.7 11.7
## 8 2017 3 4.1 5 7.9 12.7
## 9 2018 2.4 3.85 4.8 7.45 20.3
## 10 2019 2.4 3.7 4.5 7.2 11.9
## 11 2020 1.7 4.5 6.2 9.45 14.6
## 12 2021 1.6 4.3 5.2 8.05 36.1
## 13 2022 2.4 4.5 5.5 7 85.5
## 14 2023 2.3 4.4 5 6.7 65
## 15 2024 2.2 3.75 5 6.35 33
## 16 2025 2.1 3.55 5 6 15summary_economicgrowth <- indicators %>%
group_by(Year) %>%
summarise(
Min = min(growth, na.rm = TRUE),
Q1 = quantile(growth, 0.25, na.rm = TRUE),
Median = median(growth, na.rm = TRUE),
Q3 = quantile(growth, 0.75, na.rm = TRUE),
Max = max(growth, na.rm = TRUE))
print(summary_economicgrowth)## # A tibble: 16 × 6
## Year Min Q1 Median Q3 Max
## <int> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 2010 1.7 2.75 4.2 6.7 10.3
## 2 2011 -0.1 2.02 3.6 6.5 10.5
## 3 2012 -2.8 1.91 3.4 6.2 8.4
## 4 2013 -1.8 1.95 2.9 5.9 10
## 5 2014 -0.4 1.52 3.3 6.25 10
## 6 2015 -14 1.15 3.08 5.6 10.3
## 7 2016 -3.6 1.1 2.69 5.5 10.9
## 8 2017 0 1.8 2.9 5.7 10.8
## 9 2018 0 1.6 2.7 5.4 11.1
## 10 2019 0 1.3 2 4.8 13.7
## 11 2020 -9.8 -5.45 -3.42 -0.25 13.2
## 12 2021 0 4.15 5.7 6.95 12
## 13 2022 -2 2.50 3.2 5.95 10
## 14 2023 -0.5 1.75 2 4.8 9
## 15 2024 0 2.05 2.3 4.35 8
## 16 2025 0 2.5 2.6 4.15 7.9# Across Countries:
summary_inflation2 <- indicators %>%
group_by(Country) %>%
summarise(
Min = min(inflation, na.rm = TRUE),
Q1 = quantile(inflation, 0.25, na.rm = TRUE),
Median = median(inflation, na.rm = TRUE),
Q3 = quantile(inflation, 0.75, na.rm = TRUE),
Max = max(inflation, na.rm = TRUE))
print(summary_inflation2)## # A tibble: 19 × 6
## Country Min Q1 Median Q3 Max
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Australia 0.9 1.8 2.3 2.92 6.1
## 2 Bangladesh 5 5.5 5.5 7.12 8.8
## 3 Brazil 3.2 3.74 5.82 6.35 10.1
## 4 Canada 0.7 1.48 1.9 2.97 6.8
## 5 China 0.9 1.95 2.3 2.65 5.4
## 6 France 0.1 0.8 1.55 2.42 6.1
## 7 Germany 0.3 1.05 1.85 3.55 7.1
## 8 India 3.4 4.97 5.4 6.93 12.0
## 9 Indonesia 3.8 38.5 102. 350. 550
## 10 Italy -0.2 0.175 1.6 3.08 8.7
## 11 Japan -0.72 0.015 0.45 0.95 2.4
## 12 Malaysia -1.2 1.67 2.1 3.05 3.8
## 13 Pakistan 3.8 6.22 9.8 12.7 25
## 14 Russia 2.9 4.68 5.85 7.62 15.5
## 15 Saudi Arabia 5.4 5.4 5.4 5.4 5.4
## 16 South Korea 0.4 1.23 1.95 2.82 5
## 17 Turkey 0 31.6 442 730. 857
## 18 UK 0 1.5 2.65 3.45 6
## 19 USA 0.12 1.59 2.1 3.6 8summary_GDP2 <- indicators %>%
group_by(Country) %>%
summarise(
Min = min(GDP, na.rm = TRUE),
Q1 = quantile(GDP, 0.25, na.rm = TRUE),
Median = median(GDP, na.rm = TRUE),
Q3 = quantile(GDP, 0.75, na.rm = TRUE),
Max = max(GDP, na.rm = TRUE))
print(summary_GDP2)## # A tibble: 19 × 6
## Country Min Q1 Median Q3 Max
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Australia 1300 1488. 1675 1862. 2050
## 2 Bangladesh 105 142. 180 212. 250
## 3 Brazil 1800 2175 2275 2465 2600
## 4 Canada 1500 1688. 1875 2062. 2250
## 5 China 6700 7825 8950 10500 12000
## 6 France 2400 2775 3150 3525 3900
## 7 Germany 3300 3675 4050 4425 4800
## 8 India 1500 1875 2250 2625 3000
## 9 Indonesia 1 1 1 1 846
## 10 Italy 1848 2129. 2730 4125 5200
## 11 Japan 5500 5875 6250 6625 7000
## 12 Malaysia 236 296 325 382. 480
## 13 Pakistan 164 243 287 323 500
## 14 Russia 1500 1688. 1750 1925 2300
## 15 Saudi Arabia 434 646 646 646 746
## 16 South Korea 1000 1188. 1375 1562. 1750
## 17 Turkey 1 1 2.5 4.25 774
## 18 UK 2200 2575 2950 3325 3700
## 19 USA 15000 16875 18750 20625 22500summary_Unemployment2 <- indicators %>%
group_by(Country) %>%
summarise(
Min = min(unemployment, na.rm = TRUE),
Q1 = quantile(unemployment, 0.25, na.rm = TRUE),
Median = median(unemployment, na.rm = TRUE),
Q3 = quantile(unemployment, 0.75, na.rm = TRUE),
Max = max(unemployment, na.rm = TRUE))
print(summary_Unemployment2)## # A tibble: 19 × 6
## Country Min Q1 Median Q3 Max
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Australia 4.6 5 5.35 5.72 7
## 2 Bangladesh 4.5 4.5 4.5 4.5 4.5
## 3 Brazil 5.3 6.52 8.5 11.6 13.5
## 4 Canada 5.4 5.88 6.85 7.25 9.5
## 5 China 3.7 4 4.1 5.03 5.4
## 6 France 6.9 8.02 9.45 10 10.5
## 7 Germany 3 3.58 4.25 5.2 6.8
## 8 India 5 5.48 5.9 7.35 9.6
## 9 Indonesia 1.6 3.42 3.95 6.4 8.4
## 10 Italy 6.5 8.33 9.8 11.3 12.7
## 11 Japan 2.1 2.4 2.9 4.18 5.1
## 12 Malaysia 2.8 3.1 3.3 4.08 4.6
## 13 Pakistan 5 5 5 5.5 6.5
## 14 Russia 4.5 5.2 5.6 5.95 7.5
## 15 Saudi Arabia 10.5 10.5 10.5 10.5 10.5
## 16 South Korea 3 3.2 3.45 3.7 4
## 17 Turkey 6.2 8.43 11.9 23.5 85.5
## 18 UK 3.3 3.77 4.45 6.35 8
## 19 USA 3.7 4.45 5.36 7.8 9.63summary_economicgrowth2 <- indicators %>%
group_by(Country) %>%
summarise(
Min = min(growth, na.rm = TRUE),
Q1 = quantile(growth, 0.25, na.rm = TRUE),
Median = median(growth, na.rm = TRUE),
Q3 = quantile(growth, 0.75, na.rm = TRUE),
Max = max(growth, na.rm = TRUE))
print(summary_economicgrowth2)## # A tibble: 19 × 6
## Country Min Q1 Median Q3 Max
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Australia -2.1 2.45 2.85 3 4.4
## 2 Bangladesh 5.2 6.45 7 7.55 8.2
## 3 Brazil -3.9 0.875 1.96 2.52 7.53
## 4 Canada -5.3 1.78 2.1 2.7 4.6
## 5 China 2.3 4.05 6.8 7.72 10.3
## 6 France -7.8 0.875 1.4 2.15 7
## 7 Germany -4.9 2.5 3.1 3.6 4
## 8 India -7.3 6.18 6.9 7.45 9.3
## 9 Indonesia 4.5 5.45 5.9 6.2 7.1
## 10 Italy -8.9 0.125 0.95 1.63 6.6
## 11 Japan -4.8 0.95 1.35 1.8 4.2
## 12 Malaysia -5.6 4.45 4.9 5.67 8.7
## 13 Pakistan -0.5 3.27 3.9 5.4 6
## 14 Russia -3.7 -0.275 1.4 2.58 4.3
## 15 Saudi Arabia -14 0 0 4.78 10.5
## 16 South Korea -1 2.25 2.75 3.15 6.2
## 17 Turkey 7 9.15 9.95 11.0 13.7
## 18 UK -9.8 1.37 1.85 2.58 7.4
## 19 USA -3.42 2.32 2.58 2.9 5.92##Data Visualization of Log difference ## Visualizing Predictors vs Inflation by Countries
### Visualize log(inflation) vs log(unemployment) by countries
ggplot(indicators, aes(x=log(inflation), y=log(unemployment), colour = factor(Country))) +
geom_point() + xlab("log(Inflation)") +
ylab("log(Unemployment)") +
scale_color_discrete(name="Countries")
Visualize log(inflation) vs log(unemployment) by countries-does not show a strong correlation between variables.
### Visualize log(inflation) vs log(GDP) by countries
ggplot(indicators, aes(x=log(inflation), y=log(GDP), colour = factor(Country))) +
geom_point() + xlab("log(Inflation)") +
ylab("log(GDP)") +
scale_color_discrete(name="Countries")
Visualize log(inflation) vs log(GDP) by countries- does not show stringent relationship between variables. If a relationship were to be stated it would be a very weak negative correlation.
### Visualize log(inflation) vs log(growth) by countries
ggplot(indicators, aes(x=log(inflation), y=log(growth), colour = factor(Country))) +
geom_point() + xlab("log(Inflation)") +
ylab("log(Growth)") +
scale_color_discrete(name="Countries")
Visualize log(inflation) vs log(growth) by countries shows a slight positive correlation.
### Visualize log(inflation) vs log(unemployment) by year
ggplot(indicators, aes(x=log(inflation), y=log(unemployment), colour = factor(Year))) +
geom_point() + xlab("log(Inflation)") +
ylab("log(Unemployment)") +
scale_color_discrete(name="Year")
Visualize log(inflation) vs log(unemployment) by year does not show a strong relationship.
### Visualize log(inflation) vs log(GDP) by year
ggplot(indicators, aes(x=log(inflation), y=log(GDP), colour = factor(Year))) +
geom_point() + xlab("log(Inflation)") +
ylab("log(GDP)") +
scale_color_discrete(name="Year")
Visualize log(inflation) vs log(GDP) by year shows a slight negative correlation.
### Visualize log(inflation) vs log(growth) by year
ggplot(indicators, aes(x=log(inflation), y=log(growth), colour = factor(Year))) +
geom_point() + xlab("log(Inflation)") +
ylab("log(Growth)") +
scale_color_discrete(name="Year")
Visualize log(inflation) vs log(growth) by year shows a positive correlation.
(3) Pooled, Fixed Effects, and Random Effects
attach(indicators)## The following objects are masked from indicators (pos = 3):
##
## Country, GDP, growth, inflation, unemployment, Year## The following objects are masked from indicators (pos = 5):
##
## Country, Year## The following object is masked from package:lmtest:
##
## unemploymentPooled Model
library(plm)
library(AER)
indicators.panel.1 <- pdata.frame(indicators, index=c("Country", "Year"))
head(indicators.panel.1)## Country Year GDP inflation unemployment growth
## Australia-2010 Australia 2010 1300 2.8 5.2 2.9
## Australia-2011 Australia 2011 1350 3.0 5.0 3.1
## Australia-2012 Australia 2012 1400 2.0 5.1 3.3
## Australia-2013 Australia 2013 1450 2.5 5.6 2.5
## Australia-2014 Australia 2014 1500 2.5 5.8 2.9
## Australia-2015 Australia 2015 1550 1.5 6.2 3.0dim(indicators.panel.1)## [1] 304 6indicators.panel.1 <- subset(indicators.panel.1,
inflation > 0 &
GDP > 0 &
unemployment > 0 &
growth > 0)
pooled_model <- plm(log(inflation) ~log(GDP)+log(unemployment)+log(growth), model="pooling", data=indicators.panel.1)
summary(pooled_model)## Pooling Model
##
## Call:
## plm(formula = log(inflation) ~ log(GDP) + log(unemployment) +
## log(growth), data = indicators.panel.1, model = "pooling")
##
## Unbalanced Panel: n = 19, T = 5-16, N = 259
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -4.13513 -0.59341 0.10170 0.65212 2.23533
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## (Intercept) 3.305377 0.361732 9.1376 < 2.2e-16 ***
## log(GDP) -0.471904 0.027331 -17.2664 < 2.2e-16 ***
## log(unemployment) 0.564432 0.133658 4.2230 3.358e-05 ***
## log(growth) 0.339132 0.089806 3.7763 0.0001981 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 717.61
## Residual Sum of Squares: 239.1
## R-Squared: 0.66682
## Adj. R-Squared: 0.6629
## F-statistic: 170.114 on 3 and 255 DF, p-value: < 2.22e-16coeftest(pooled_model, vcov=vcovHC(pooled_model,
type="HC0",cluster="group"))##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.305377 0.571738 5.7813 2.159e-08 ***
## log(GDP) -0.471904 0.051959 -9.0823 < 2.2e-16 ***
## log(unemployment) 0.564432 0.265011 2.1298 0.03414 *
## log(growth) 0.339132 0.159140 2.1310 0.03404 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Fixed Effects Model
library(plm)
library(AER)
indicators.panel <- subset(indicators.panel,
inflation > 0 &
GDP > 0 &
unemployment > 0 &
growth > 0)
indicators.panel <- pdata.frame(indicators.panel, index = c("Country", "Year"))
indicators.panel <- indicators.panel %>%
filter(!is.infinite(log(GDP)) & !is.infinite(log(unemployment)) &
!is.infinite(log(growth)) & !is.infinite(log(inflation))) %>%
na.omit()
# Fixed Effect:
fixed_effects_model_individual <- plm(log(inflation) ~log(GDP)+log(unemployment)+log(growth), data = indicators.panel, model = "within", effect = "individual")
summary(fixed_effects_model_individual)## Oneway (individual) effect Within Model
##
## Call:
## plm(formula = log(inflation) ~ log(GDP) + log(unemployment) +
## log(growth), data = indicators.panel, effect = "individual",
## model = "within")
##
## Unbalanced Panel: n = 19, T = 5-16, N = 259
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -3.338241 -0.289432 0.010049 0.430274 1.808224
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## log(GDP) -0.457344 0.072235 -6.3313 1.207e-09 ***
## log(unemployment) -0.296021 0.189312 -1.5637 0.1192
## log(growth) 0.148903 0.111340 1.3374 0.1824
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 180.63
## Residual Sum of Squares: 150
## R-Squared: 0.16957
## Adj. R-Squared: 0.095989
## F-statistic: 16.1316 on 3 and 237 DF, p-value: 1.4169e-09fixed_effects_model_time <- plm(log(inflation) ~log(GDP)+log(unemployment)+log(growth), data = indicators.panel, model = "within", effect = "time")
summary(fixed_effects_model_time)## Oneway (time) effect Within Model
##
## Call:
## plm(formula = log(inflation) ~ log(GDP) + log(unemployment) +
## log(growth), data = indicators.panel, effect = "time", model = "within")
##
## Unbalanced Panel: n = 19, T = 5-16, N = 259
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -3.9261041 -0.4602518 0.0046608 0.5650221 2.5065397
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## log(GDP) -0.485010 0.025082 -19.3368 < 2.2e-16 ***
## log(unemployment) 0.614846 0.122931 5.0016 1.099e-06 ***
## log(growth) 0.335060 0.084183 3.9801 9.128e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 663.55
## Residual Sum of Squares: 178.83
## R-Squared: 0.7305
## Adj. R-Squared: 0.71028
## F-statistic: 216.841 on 3 and 240 DF, p-value: < 2.22e-16fixed_effects_model_full <- plm(log(inflation) ~log(GDP)+log(unemployment)+log(growth), data = indicators.panel, model = "within", effect = "twoways")
summary(fixed_effects_model_full)## Twoways effects Within Model
##
## Call:
## plm(formula = log(inflation) ~ log(GDP) + log(unemployment) +
## log(growth), data = indicators.panel, effect = "twoways",
## model = "within")
##
## Unbalanced Panel: n = 19, T = 5-16, N = 259
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -3.076123 -0.254986 0.051086 0.324675 1.462256
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## log(GDP) -0.572290 0.059778 -9.5735 <2e-16 ***
## log(unemployment) -0.240381 0.161034 -1.4927 0.1369
## log(growth) 0.044232 0.099582 0.4442 0.6573
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 130.79
## Residual Sum of Squares: 89.594
## R-Squared: 0.31499
## Adj. R-Squared: 0.20391
## F-statistic: 34.0278 on 3 and 222 DF, p-value: < 2.22e-16Random Effects Model
random_effects_model <- plm(log(inflation) ~log(GDP)+log(unemployment)+log(growth), data = indicators.panel, model = "random")
summary(random_effects_model)## Oneway (individual) effect Random Effect Model
## (Swamy-Arora's transformation)
##
## Call:
## plm(formula = log(inflation) ~ log(GDP) + log(unemployment) +
## log(growth), data = indicators.panel, model = "random")
##
## Unbalanced Panel: n = 19, T = 5-16, N = 259
##
## Effects:
## var std.dev share
## idiosyncratic 0.6329 0.7955 0.691
## individual 0.2831 0.5321 0.309
## theta:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.4442 0.6170 0.6399 0.6274 0.6399 0.6499
##
## Residuals:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -3.8158 -0.3041 -0.0054 -0.0005 0.4604 1.6995
##
## Coefficients:
## Estimate Std. Error z-value Pr(>|z|)
## (Intercept) 4.6001878 0.4829250 9.5257 < 2e-16 ***
## log(GDP) -0.4978827 0.0459727 -10.8300 < 2e-16 ***
## log(unemployment) -0.0066999 0.1662149 -0.0403 0.96785
## log(growth) 0.2166982 0.1016131 2.1326 0.03296 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 255.59
## Residual Sum of Squares: 166.38
## R-Squared: 0.34903
## Adj. R-Squared: 0.34137
## Chisq: 137.25 on 3 DF, p-value: < 2.22e-16Comparison with Hausman Test
random_effects_model <- plm(log(inflation) ~log(GDP)+log(unemployment)+log(growth), data = indicators.panel, model = "random")## Testing both effects jointly
phtest(fixed_effects_model_full, pooled_model)##
## Hausman Test
##
## data: log(inflation) ~ log(GDP) + log(unemployment) + log(growth)
## chisq = 142.9, df = 3, p-value < 2.2e-16
## alternative hypothesis: one model is inconsistentThe p-value is very small, indicating that we reject the null hypothesis. This suggests that the fixed effects model (with individual country effects) is preferred over the pooled model.
## Only individual (country) effect
phtest(fixed_effects_model_individual,pooled_model)##
## Hausman Test
##
## data: log(inflation) ~ log(GDP) + log(unemployment) + log(growth)
## chisq = 48.066, df = 3, p-value = 2.062e-10
## alternative hypothesis: one model is inconsistentThe p-value is large (greater than 0.05), which means we fail to reject the null hypothesis. This suggests that the pooled model is consistent with the data and that the fixed effects model with only time effects doesn’t improve the model significantly.
## Only time effect
phtest(fixed_effects_model_time,pooled_model)##
## Hausman Test
##
## data: log(inflation) ~ log(GDP) + log(unemployment) + log(growth)
## chisq = 2.6949, df = 3, p-value = 0.4411
## alternative hypothesis: one model is inconsistentThe p-value is large (greater than 0.05), which means we fail to reject the null hypothesis. This suggests that the pooled model is consistent with the data and that the fixed effects model with only time effects doesn’t improve the model significantly.
## FE vs RE
phtest(fixed_effects_model_full, random_effects_model)##
## Hausman Test
##
## data: log(inflation) ~ log(GDP) + log(unemployment) + log(growth)
## chisq = 102.53, df = 3, p-value < 2.2e-16
## alternative hypothesis: one model is inconsistentBased on the small p-value, it is suggested that the Random Effects model is biased and thus, we reject the null-hypothesis and conclude that the Fixed Effects model is a better fit.
## Pooled vs RE
phtest(random_effects_model, pooled_model)##
## Hausman Test
##
## data: log(inflation) ~ log(GDP) + log(unemployment) + log(growth)
## chisq = 39.961, df = 3, p-value = 1.086e-08
## alternative hypothesis: one model is inconsistentAgain, based on the small p-value, we reject the null hypothesis, and conclude that the Random Effects model is a better fit than the Pooled.
#Comparison with pFtest
## Testing both effects jointly
pFtest(fixed_effects_model_full, pooled_model)##
## F test for twoways effects
##
## data: log(inflation) ~ log(GDP) + log(unemployment) + log(growth)
## F = 11.226, df1 = 33, df2 = 222, p-value < 2.2e-16
## alternative hypothesis: significant effectsThe very small p-value indicates that we reject the null hypothesis, suggesting that both individual (country) and time effects are significant. Therefore, the fixed effects model with both country and time effects is preferred over the pooled model
## Only individual (country) effect
pFtest(fixed_effects_model_individual,pooled_model)##
## F test for individual effects
##
## data: log(inflation) ~ log(GDP) + log(unemployment) + log(growth)
## F = 7.8213, df1 = 18, df2 = 237, p-value = 5.484e-16
## alternative hypothesis: significant effectsThe small p-value suggests rejecting the null hypothesis, indicating that the individual (country) effects are significant. Therefore, the fixed effects model with individual (country) effects is preferred over the pooled model.
## Only time effect
pFtest(fixed_effects_model_time,pooled_model)##
## F test for time effects
##
## data: log(inflation) ~ log(GDP) + log(unemployment) + log(growth)
## F = 5.3921, df1 = 15, df2 = 240, p-value = 2.377e-09
## alternative hypothesis: significant effectsThe small p-value indicates rejecting the null hypothesis, meaning that the time effects are significant. This suggests that the fixed effects model with only time effects is preferred over the pooled model.
PLM test for Random Effects Model
plmtest(random_effects_model, type= 'bp')##
## Lagrange Multiplier Test - (Breusch-Pagan)
##
## data: log(inflation) ~ log(GDP) + log(unemployment) + log(growth)
## chisq = 109.66, df = 1, p-value < 2.2e-16
## alternative hypothesis: significant effectsThe Breusch-Pagan test strongly suggests that the random effects model is appropriate for the data, as there are significant random effects present. The very small p-value indicates that we reject the null hypothesis, which suggests that there are no random effects in the model. The alternative hypothesis, which posits that random effects are significant, is supported by the data. Therefore, this test suggests that the random effects model is appropriate and that the data exhibits significant random effects.
Heterogeneity Plots
Across Time
##data cleanup
indicators <- indicators %>%
mutate(inflation = ifelse(inflation <= 0, NA, inflation + 0.0001))
cators_clean <- indicators %>%
filter(!is.na(inflation) & !is.infinite(inflation) & !is.nan(inflation))
indicators <- indicators %>%
filter(inflation > 0 & unemployment > 0 & GDP > 0 & growth > 0)
indicators$Country <- as.factor(indicators$Country)
indicators <- indicators %>%
filter(!is.na(Country) & !is.infinite(Country))
scatterplot(log(inflation)~Year, data = indicators, main = "Heterogeneity of Inflation across Time")
In the plot of log(inflation) over the years, we can observe the dashed line dipping slightly downwards after 2015, hinting at a decline in inflation. However, we can see it increasing again in an upward incline around 2017. We can also see that it is around 2015 to 2017 that inflation was unstable by the wide confidence interval. There are also many outliers observed above suggesting that there were occasional extreme spikes in inflation. These extreme values contribute to heterogeneity.
scatterplot(log(unemployment)~Year, data = indicators, main = "Heterogeneity of Unemployment across Time")
For Unemployment, the dots are more clustered compared to those of Inflation, suggesting that it is more stable. The confidence interval is much narrower here too. However, by the dashed line, we can see that unemployment has been having a steady decline without increasing back up like inflation.
scatterplot(log(GDP)~Year, data = indicators, main = "Heterogeneity of GDP across Time")
For GDP, we can observe a steady increase in GDP over the years by the upward inclining line. The confidence interval is much wider here, suggesting a more unstable trend in GDP.
scatterplot(log(growth)~Year, data = indicators, main = "Heterogeneity of Economics Growth across Time")
For Economic Growth, there is a decrease observed in 2016 and an increase in 2017 before decreasing again in 2021 and into a steady and slight decline. There are also a handful of outliers that might suggest that unstable trend.
Across Country
scatterplot(log(inflation)~Country, data = indicators, main = "Heterogeneity of Inflation across Country")
## [1] "125" "27" "17" "131" "132" "32" "238" "239" "106" "150" "217" "226"
## [13] "6"In the plot for inflation across countries, we can see that countries like Italy have a wider range and appear to have larger variations. There are also counties that have outliers like Germany, suggesting extreme inflation spikes, and again, contributing to heterogeneity. And from the median, we can see that some are lower inflation instability in countries like Canada.
scatterplot(log(unemployment)~Country, data = indicators, main = "Heterogeneity of Unemployment across Country")
## [1] "248" "109" "102" "228"For unemployment across countries, Pakistan seems to have several outliers. This contributes to heterogeneity. Countries like Turkey show a long whisker, with a left skewed distribution, suggesting spikes in unemployment.
scatterplot(log(GDP)~Country, data = indicators, main = "Heterogeneity of GDP across Country")
## [1] "201" "202" "111" "112" "217"For GDP, Turkey can be observed to have low GDP value and a wider range than other countries, suggesting a more unstable GDP trend. There are also outliers present and countries like Pakistan have extreme value, contributing to heterogeneity.
scatterplot(log(growth)~Country, data = indicators, main = "Heterogeneity of Economics Growth across Country")
## [1] "125" "123" "130" "136" "180" "34" "240" "241" "141" "229" "226" "227"
## [13] "75" "82" "2" "4" "11"For Economic Growth, there are a lot of extreme outliers spotted in countries like Germany and Turkey. And some countries like Italy have wider ranges too, suggesting that economic growth tends to be volatile.
Comparison of Coefficients: Fixed Effect vs Random Effect
fixed_effects_coef <- coef(fixed_effects_model_full)
random_effects_coef <- coef(random_effects_model)
fixed_effects_data <- data.frame(
predictor = names(fixed_effects_coef),
coefficient = fixed_effects_coef,
model = "Fixed Effects")
random_effects_data <- data.frame(
predictor = names(random_effects_coef),
coefficient = random_effects_coef,
model = "Random Effects")
coef_data <- rbind(fixed_effects_data, random_effects_data)
ggplot(coef_data, aes(x = reorder(predictor, coefficient), y = coefficient, fill = model)) +
geom_bar(stat = "identity", position = "dodge", width = 0.5) + # Dodge for side-by-side bars
coord_flip() + # Flip the axes for better readability
xlab("Predictor") +
ylab("Coefficient Estimate") +
theme_minimal() +
scale_fill_manual(values = c("Fixed Effects" = "steelblue", "Random Effects" = "orange")) +
ggtitle("Comparison of Coefficients: Fixed Effects vs. Random Effects") +
theme(legend.position = "top")
We can observe a significant difference on the coefficient bars of Fixed Effects and Random Effects, suggesting that the Random Effects assumption is violated here. This matches with the result we got from the Hausman Test, where we rejected the null hypothesis based on the small p-value observed, meaning that the Fixed Effect model is a better fit.
Full Effect Coefficient Plot
extract_coefficients <- function(model) {
coef_summary <- summary(model)$coefficients # Extract coefficients
data.frame(
predictor = rownames(coef_summary), # Ensure all predictors are included
coefficient = coef_summary[, 1] # Extract coefficient estimates
)
}
fixed_effects_data_full <- extract_coefficients(fixed_effects_model_full)
fixed_effects_data_time <- extract_coefficients(fixed_effects_model_time)
fixed_effects_data_individual <- extract_coefficients(fixed_effects_model_individual)
# Plot for Fixed Effects Full Model
ggplot(fixed_effects_data_full, aes(x = reorder(predictor, coefficient), y = coefficient)) +
geom_bar(stat = "identity", fill = "steelblue") +
coord_flip() +
xlab("Predictor") +
ylab("Coefficient Estimate") +
theme_minimal() +
ggtitle("Fixed Effects Full Model Coefficients")
The plot shows a strongly negative coefficient for log(GDP), indicating that higher GDP is associated with lower values of the dependent variable. The coefficient for log(unemployment) is also negative but smaller in magnitude. Meanwhile, the coefficient for log(growth) is positive, though relatively small. This suggests that GDP has the most significant impact on the inflation in this fixed effects model, while unemployment and growth have comparatively weaker effects.
# Plot for Fixed Effects Time Model
ggplot(fixed_effects_data_time, aes(x = reorder(predictor, coefficient), y = coefficient)) +
geom_bar(stat = "identity", fill = "darkgreen") +
coord_flip() +
xlab("Predictor") +
ylab("Coefficient Estimate") +
theme_minimal() +
ggtitle("Fixed Effects Time Model Coefficients")
In this plot, the log(GDP) coefficient remains negative, though with a smaller magnitude compared to the full model. The coefficient for log(unemployment) is positive and larger, suggesting a stronger influence of unemployment in this model. The log(growth) coefficient is also positive but smaller than the unemployment coefficient indicating that in the time-fixed effects model, unemployment plays a larger role than in the full model, possibly due to time-dependent variations in its influence.
# Plot for Fixed Effects Individual Model
ggplot(fixed_effects_data_individual, aes(x = reorder(predictor, coefficient), y = coefficient)) +
geom_bar(stat = "identity", fill = "purple") +
coord_flip() +
xlab("Predictor") +
ylab("Coefficient Estimate") +
theme_minimal() +
ggtitle("Fixed Effects Individual Model Coefficients")
###The log(GDP) coefficient remains negative, similar in magnitude to the full model. The coefficient for log(unemployment) is also negative and slightly stronger than in the full model. The log(growth) coefficient remains positive and is comparable in magnitude to the other models. This suggests that the individual fixed effects model emphasizes the strong negative impact of both GDP and unemployment on the dependent variable.
Random Effect Coefficient Plot
ggplot(random_effects_data, aes(x = reorder(predictor, coefficient), y = coefficient)) +
geom_bar(stat = "identity", fill = "orange") +
coord_flip() + # Flips the axes for better readability
xlab("Predictor") +
ylab("Coefficient Estimate") +
theme_minimal() +
ggtitle("Random Effects Model Coefficients")
There is a very large intercept, suggesting substantial unobserved heterogeneity in the data. The log(GDP) coefficient is negative but small and the log(unemployment) coefficient is almost zero, indicating little impact in this model. The log(growth) coefficient is small but remains positive. The large intercept may imply significant unexplained variance that is not fully accounted for by the predictors.
Coefficient Comparison: FE vs RE
library(ggplot2)
ce <- function(model.obj) {
summ.model <- summary(get(model.obj))$coefficients
extract <- data.frame(Estimate = summ.model[,1],
SE = summ.model[,2],
vars = row.names(summ.model),
model = model.obj)
return(extract)
}
coefs <- do.call(rbind, sapply(
c("fixed_effects_model_full", "random_effects_model"),
ce,
simplify = FALSE
))
names(coefs)[2] <- "se"
gg_coef <- ggplot(coefs, aes(vars, Estimate)) +
geom_hline(yintercept = 0, lty = 1, lwd = 0.5, colour = "red") +
geom_errorbar(aes(ymin = Estimate - se, ymax = Estimate + se, colour = vars),
lwd = 1, width = 0) +
geom_point(size = 3, aes(colour = vars)) +
facet_grid(model ~ ., scales = "free") +
coord_flip() +
guides(colour = FALSE) +
labs(x = "Coefficient", y = "Value") +
ggtitle("Model Coefficients")
print(gg_coef)