📊 Econometric Analysis: Trade, FDI, Growth, and Industrial Value Added
Wesal Megahed
2025-09-14
Introduction
This report investigates the relationship between trade openness (OT), foreign direct investment (FDI), per capita GDP (PGDP), savings (S), and globalization (GL) with industrial value added (AI).
We simulate a dataset for the period 1990–2020, perform econometric analyses, and visualize the relationships. The goal is to explore short-run and long-run dynamics, including correlation, stationarity, regression, cointegration, diagnostics, and robustness checks.
Objectives
- Simulate data representing key economic
indicators.
- Perform correlation analysis and visualize variable
relationships.
- Test for unit roots using the Augmented
Dickey-Fuller (ADF) test.
- Estimate regression models linking AI to OT, PGDP,
S, FDI, and GL.
- Run diagnostic tests for heteroskedasticity,
autocorrelation, and structural breaks.
- Conduct cointegration analysis (Johansen test) to
assess long-run equilibrium.
- Check robustness with control variables and Chow
tests.
- Visualize results using time-series plots, correlation heatmaps, regression plots, and animated graphs.
Data Simulation
library(tidyverse)
library(tseries)
library(urca)
library(vars)
library(GGally)
library(stargazer)
library(lmtest)
library(strucchange)
library(psych)
set.seed(123)
year <- 1990:2020
n <- length(year)
OT <- 50 + 0.5*(1:n) + rnorm(n, 0, 5)
PGDP <- 2000 + 50*(1:n) + rnorm(n, 0, 200)
S <- 15 + rnorm(n, 0, 2)
FDI <- runif(n, 1, 10) + 0.2*(1:n)
GL <- seq(40, 70, length.out = n) + rnorm(n, 0, 3)
AI <- 100 + 0.3*OT + 0.002*PGDP + 0.5*FDI + rnorm(n, 0, 20)
data <- data.frame(year, AI, OT, PGDP, S, FDI, GL)
head(data)## year AI OT PGDP S FDI GL
## 1 1990 127.7265 47.69762 1990.986 14.33359 3.585295 39.30921
## 2 1991 100.8852 49.84911 2279.025 12.96285 6.481314 45.19228
## 3 1992 112.2394 59.29354 2325.627 12.85642 9.818694 47.29096
## 4 1993 120.1130 52.35254 2364.316 15.60706 9.916870 44.45680
## 5 1994 107.9039 53.14644 2387.728 15.89642 4.467500 43.20278
## 6 1995 134.6547 61.57532 2410.784 15.10601 5.093345 45.45483cor_matrix <- cor(data[, c("OT","PGDP","S","FDI","GL","AI")])
round(cor_matrix, 2)## OT PGDP S FDI GL AI
## OT 1.00 0.60 0.08 0.44 0.66 0.33
## PGDP 0.60 1.00 0.30 0.34 0.90 0.28
## S 0.08 0.30 1.00 0.15 0.22 0.27
## FDI 0.44 0.34 0.15 1.00 0.40 0.16
## GL 0.66 0.90 0.22 0.40 1.00 0.18
## AI 0.33 0.28 0.27 0.16 0.18 1.00GGally::ggpairs(data[, c("OT","PGDP","S","FDI","GL","AI")],
title = "Scatterplot Matrix for Key Variables")## Warning in geom_point(): All aesthetics have length 1, but the data has 36 rows.
## ℹ Please consider using `annotate()` or provide this layer with data containing
## a single row.
adf_results <- list(
AI = adf.test(data$AI, k = 1),
OT = adf.test(data$OT, k = 1),
PGDP = adf.test(data$PGDP, k = 1),
S = adf.test(data$S, k = 1),
FDI = adf.test(data$FDI, k = 1),
GL = adf.test(data$GL, k = 1)
)## Warning in adf.test(data$OT, k = 1): p-value smaller than printed p-value## Warning in adf.test(data$S, k = 1): p-value smaller than printed p-value## Warning in adf.test(data$FDI, k = 1): p-value smaller than printed p-value## Warning in adf.test(data$GL, k = 1): p-value smaller than printed p-valuelapply(adf_results, function(x) data.frame(Test=x$statistic, Pval=x$p.value))## $AI
## Test Pval
## Dickey-Fuller -3.943974 0.02413138
##
## $OT
## Test Pval
## Dickey-Fuller -4.92252 0.01
##
## $PGDP
## Test Pval
## Dickey-Fuller -3.799713 0.03384465
##
## $S
## Test Pval
## Dickey-Fuller -5.107193 0.01
##
## $FDI
## Test Pval
## Dickey-Fuller -4.47167 0.01
##
## $GL
## Test Pval
## Dickey-Fuller -4.387605 0.01model <- lm(AI ~ OT + PGDP + S + FDI + GL, data = data)
summary(model)##
## Call:
## lm(formula = AI ~ OT + PGDP + S + FDI + GL, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -42.65 -11.95 -2.43 12.84 42.04
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.08693 53.76064 0.095 0.925
## OT 1.54441 0.96611 1.599 0.122
## PGDP 0.02505 0.02058 1.217 0.235
## S 2.89208 2.55583 1.132 0.269
## FDI 0.15432 1.87269 0.082 0.935
## GL -1.55855 1.14668 -1.359 0.186
##
## Residual standard error: 22.78 on 25 degrees of freedom
## Multiple R-squared: 0.2237, Adjusted R-squared: 0.06841
## F-statistic: 1.441 on 5 and 25 DF, p-value: 0.2445stargazer(model, type = "text")##
## ===============================================
## Dependent variable:
## ---------------------------
## AI
## -----------------------------------------------
## OT 1.544
## (0.966)
##
## PGDP 0.025
## (0.021)
##
## S 2.892
## (2.556)
##
## FDI 0.154
## (1.873)
##
## GL -1.559
## (1.147)
##
## Constant 5.087
## (53.761)
##
## -----------------------------------------------
## Observations 31
## R2 0.224
## Adjusted R2 0.068
## Residual Std. Error 22.783 (df = 25)
## F Statistic 1.441 (df = 5; 25)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01A multiple linear regression model explains AI (Industrial Value Added) using OT, PGDP, S, FDI, and GL.
Key results:
None of the predictors are statistically significant at 5%.
R² = 0.22 (low explanatory power).
Interpretation: In the simulated dataset, relationships are weak, which is expected because we used random components.
lmtest::bptest(model) # Heteroskedasticity##
## studentized Breusch-Pagan test
##
## data: model
## BP = 7.8807, df = 5, p-value = 0.1629lmtest::dwtest(model) # Autocorrelation (Durbin-Watson)##
## Durbin-Watson test
##
## data: model
## DW = 2.4313, p-value = 0.8556
## alternative hypothesis: true autocorrelation is greater than 0lmtest::bgtest(model, order=1)##
## Breusch-Godfrey test for serial correlation of order up to 1
##
## data: model
## LM test = 3.1066, df = 1, p-value = 0.07798Breusch-Pagan test → no heteroskedasticity (p = 0.16).
Durbin-Watson → no evidence of autocorrelation.
Breusch-Godfrey → weak sign of serial correlation (p ≈ 0.07).
✅ Model residuals look fairly well-behaved.
johansen_test <- ca.jo(data[,c("AI","OT","PGDP","S","FDI","GL")],
type="trace", ecdet="const", K=2)
summary(johansen_test)##
## ######################
## # Johansen-Procedure #
## ######################
##
## Test type: trace statistic , without linear trend and constant in cointegration
##
## Eigenvalues (lambda):
## [1] 8.561622e-01 7.744786e-01 5.646242e-01 3.588287e-01 2.986216e-01
## [6] 2.217681e-01 1.221245e-15
##
## Values of teststatistic and critical values of test:
##
## test 10pct 5pct 1pct
## r <= 5 | 7.27 7.52 9.24 12.97
## r <= 4 | 17.56 17.85 19.96 24.60
## r <= 3 | 30.45 32.00 34.91 41.07
## r <= 2 | 54.56 49.65 53.12 60.16
## r <= 1 | 97.75 71.86 76.07 84.45
## r = 0 | 153.99 97.18 102.14 111.01
##
## Eigenvectors, normalised to first column:
## (These are the cointegration relations)
##
## AI.l2 OT.l2 PGDP.l2 S.l2 FDI.l2
## AI.l2 1.000000000 1.0000000 1.000000000 1.000000 1.00000000
## OT.l2 -0.148659574 0.3615621 -5.050394606 1042.895471 -4.54034816
## PGDP.l2 0.006632476 -0.1322558 -0.002890405 -9.902398 0.08946461
## S.l2 -11.568660669 3.4986042 9.599767909 1321.622866 13.07789214
## FDI.l2 -5.402675095 -0.3225803 -8.540152975 -2374.577167 37.62872907
## GL.l2 0.186279587 6.2257913 1.488810156 234.196088 -6.81334447
## constant 84.537301856 -167.8259281 19.408833893 -41232.829791 -213.16538192
## GL.l2 constant
## AI.l2 1.00000000 1.00000000
## OT.l2 12.65562857 0.73737058
## PGDP.l2 0.09109959 0.07481978
## S.l2 13.01092055 -6.26496117
## FDI.l2 0.40365394 -9.81380633
## GL.l2 -10.47823363 7.70058750
## constant -747.26540762 -617.65811891
##
## Weights W:
## (This is the loading matrix)
##
## AI.l2 OT.l2 PGDP.l2 S.l2 FDI.l2
## AI.d -1.39125237 -0.32060932 -0.36129503 1.392100e-04 0.010609998
## OT.d -0.02189632 -0.11328973 0.06391529 -5.131351e-05 0.007360513
## PGDP.d 2.32608915 4.85603489 -2.69867587 1.290151e-02 0.351818557
## S.d 0.04805255 -0.02476208 -0.04851825 -2.949498e-05 -0.006748419
## FDI.d -0.03898077 -0.02502523 0.03176905 1.755338e-04 -0.010192811
## GL.d 0.06910920 -0.09383745 0.01832506 1.060221e-04 0.011471450
## GL.l2 constant
## AI.d -0.0633530916 2.819205e-15
## OT.d -0.0279638327 5.903653e-16
## PGDP.d -0.7704138611 -4.032766e-14
## S.d -0.0007571062 -1.532588e-16
## FDI.d -0.0000980359 7.778162e-17
## GL.d 0.0084302998 4.247617e-16Johansen test evaluates long-run equilibrium relationships.
Output: Trace statistics exceed critical values at multiple ranks → suggests at least one cointegration relationship among variables.
Meaning: despite short-run noise, variables move together in the long run.
data %>%
pivot_longer(-year, names_to="Variable", values_to="Value") %>%
ggplot(aes(year, Value, color=Variable)) +
geom_line(size=1.2) +
facet_wrap(~Variable, scales="free_y") +
theme_minimal()## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
library(reshape2)## Warning: package 'reshape2' was built under R version 4.2.3##
## Attaching package: 'reshape2'## The following object is masked from 'package:tidyr':
##
## smithscor_melt <- melt(round(cor(data[, -1]), 2))
ggplot(cor_melt, aes(Var1, Var2, fill=value)) +
geom_tile(color="white") +
geom_text(aes(label=value)) +
scale_fill_gradient2(low="blue", mid="white", high="red", midpoint=0)
library(broom)## Warning: package 'broom' was built under R version 4.2.3tidy_model <- tidy(model, conf.int=TRUE)
ggplot(tidy_model, aes(estimate, term)) +
geom_point(size=3, color="steelblue") +
geom_errorbarh(aes(xmin=conf.low, xmax=conf.high), height=0.2) +
theme_minimal() +
labs(title="Regression Coefficients with 95% CI")
ggpairs(data[, c("OT","PGDP","S","FDI","GL","AI")])## Warning in geom_point(): All aesthetics have length 1, but the data has 36 rows.
## ℹ Please consider using `annotate()` or provide this layer with data containing
## a single row.