Dynamics of Minimum Wage, Inflation and Unemployment: VAR and Granger Causality Tests

VAR and Granger Causality for Human Resource Management

Field: Human Resource ManagementLevel: Master's thesis (S2)Method: VAR and Granger Causality

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The goal is to test causal direction and impulse responses among wages, inflation and unemployment; the data are synthetic and for illustration only. VAR (Vector Autoregression) models several stationary time series that influence one another, and Granger causality tests, impulse responses and variance decompositions reveal the direction and size of the dynamic effects. It suits theses studying two-way links among macro, financial, health or environmental variables measured monthly or quarterly.

Dynamics of Minimum Wage, Inflation and Unemployment: VAR and Granger Causality Tests: result sheet

Project info

Field of studyHuman Resource Management
LevelMaster's thesis (S2)
Method typeTime Series
Estimated build time± 5 working days
Toolsvars::VARselect, vars::VAR, vars::serial.test, vars::causality, vars::irf, vars::fevd, car::linearHypothesis, ggplot2
PriceUS$22 - US$147

Research goal

The goal is to test causal direction and impulse responses among wages, inflation and unemployment; the data are synthetic and for illustration only.

Variables

Role	Variable	Unit
Main	Minimum wage	IDR thousand
Supporting 1	Inflation rate	%
Supporting 2	Unemployment rate	%

Example result

1Lag order (AIC)
<0.001p-value Inflation rate -> Y
0.01p-value Unemployment -> Y
0.465Max root modulus
0.187Portmanteau p-value
48.134Inflation rate FEVD (%)

The AIC-selected VAR(1) model is stable (maximum root modulus 0.465). Inflation rate Granger-causes Minimum wage (p < 0.001), and the effect of Unemployment rate is significant (p = 0.010). At horizon 10, shocks to Inflation rate explain 48.1% of the forecast error variance of Minimum wage.

Computed from illustrative synthetic data, not from a real study.

About VAR and Granger Causality

VAR (Vector Autoregression) models several stationary time series that influence one another, and Granger causality tests, impulse responses and variance decompositions reveal the direction and size of the dynamic effects. It suits theses studying two-way links among macro, financial, health or environmental variables measured monthly or quarterly.

Steps

1Prepare three time series covering the same periods and make sure they are stationary (run unit root tests if needed)
2Choose the optimal lag length with vars::VARselect using AIC
3Estimate the VAR model and check stability (root moduli below 1)
4Test residual autocorrelation with the Portmanteau test (serial.test)
5Test Granger causality from X1 and X2 to Y with a Wald test on the Y equation
6Compute impulse response functions with bootstrap bands and the variance decomposition (FEVD)
7Interpret the direction of effects, how long shocks last and each variable's contribution

Assumptions to check

All series are stationary (otherwise difference them or use a VECM)
Residuals are free of autocorrelation and behave as white noise
The model is stable: all roots of the characteristic polynomial lie inside the unit circle
Variable ordering affects orthogonal IRFs (Cholesky decomposition)

Reading and reporting the results

Report the selected lag length, the stability check and the Portmanteau test as diagnostics. A Granger p-value below 0.05 means the lags of that variable help forecast Y; the IRF shows the direction and duration of the response, and the FEVD gives the share of Y's forecast error variance explained by each shock.

Example R code

A short starting script with this project's variable names. The delivered version is adapted to your data and fully commented.

Show code

# Contoh kode R: VAR and Granger Causality
suppressPackageStartupMessages({
  library(ggplot2)
  library(patchwork)
  library(vars)
  library(car)
})
set.seed(42)
# ---- Gaya grafik ----
pal <- c("#1f6feb", "#e8590c", "#2f9e44", "#ae3ec9", "#f59f00")
warna <- list(bg = "#f4f6fa", panel = "#ffffff", teks = "#1f2933", redup = "#5f6b78", grid = "#e3e8ee", bar = "#1d3557")
tata <- 1
theme_set(theme_minimal(base_size = 11) + theme(legend.position = "bottom"))

# ---- Data sintetis: tiga deret bulanan dari proses VAR(2) yang stasioner ----
nt <- 120
# matriks koefisien lag 1 dan lag 2; diulang sampai prosesnya stabil (semua akar < 0.9)
repeat {
  A1 <- diag(runif(3, 0.3, 0.55))
  A1[1, 2] <- runif(1, 0.25, 0.45)                              # X1 -> Y
  A1[1, 3] <- runif(1, 0.1, 0.35) * sample(c(-1, 1), 1)        # X2 -> Y
  A1[2, 3] <- runif(1, -0.15, 0.15)
  A1[3, 2] <- runif(1, -0.1, 0.2)
  A2 <- diag(runif(3, -0.15, 0.15))
  A2[1, 2] <- runif(1, 0.05, 0.2)
  komp <- rbind(cbind(A1, A2), cbind(diag(3), matrix(0, 3, 3)))  # matriks pendamping (companion)
  if (max(Mod(eigen(komp)$values)) < 0.9) break
}
z <- matrix(0, nt + 50, 3)
for (i in 3:(nt + 50)) z[i, ] <- A1 %*% z[i - 1, ] + A2 %*% z[i - 2, ] + rnorm(3, 0, c(0.6, 1, 1))
z <- scale(z[-(1:50), ])                                        # buang periode pemanasan (burn-in)
d <- data.frame(periode = seq(as.Date("2015-01-01"), by = "month", length.out = nt),
                minimum_wage = round(pmax(100 + 15 * z[, 1], 0), 3),
                inflation_rate = round(pmax(50 + 10 * z[, 2], 0), 3),
                unemployment_rate = round(pmax(30 + 6 * z[, 3], 0), 3))
write.csv(d, "data_contoh.csv", row.names = FALSE)

# ---- Analisis: Vector Autoregression (VAR) ----
dv <- d[, c("minimum_wage", "inflation_rate", "unemployment_rate")]
sel <- VARselect(dv, lag.max = 6, type = "const")               # pemilihan panjang lag
print(sel$selection)
p_lag <- max(1, as.integer(sel$selection[["AIC(n)"]]))
fit <- do.call(VAR, list(y = dv, p = p_lag, type = "const"))  # do.call: nilai lag tersimpan di objek
print(summary(fit))

# ---- Diagnostik: stabilitas dan autokorelasi residual ----
akar <- roots(fit)                                              # modulus akar; < 1 berarti VAR stabil
st <- serial.test(fit, lags.pt = 12, type = "PT.asymptotic")    # uji Portmanteau
print(akar); print(st)

# ---- Kausalitas Granger ----
# uji Wald pada persamaan minimum_wage: apakah semua lag X1 (atau X2) bersama-sama nol?
eq_y <- fit$varresult$minimum_wage
gr_x1 <- car::linearHypothesis(eq_y, paste0("inflation_rate.l", 1:p_lag, " = 0"))
gr_x2 <- car::linearHypothesis(eq_y, paste0("unemployment_rate.l", 1:p_lag, " = 0"))
p_x1 <- gr_x1[2, "Pr(>F)"]; p_x2 <- gr_x2[2, "Pr(>F)"]
print(gr_x1); print(gr_x2)
print(causality(fit, cause = "inflation_rate")$Granger)                 # versi blok (X1 -> semua variabel lain)

# ---- Impulse response function (IRF) dan dekomposisi varians (FEVD) ----
ir <- irf(fit, impulse = c("inflation_rate", "unemployment_rate"), response = "minimum_wage", n.ahead = 10,
          ortho = TRUE, boot = TRUE, runs = 200)
fv <- fevd(fit, n.ahead = 10)
print(round(fv$minimum_wage, 3))


# ---- Grafik ----
nm3 <- make.unique(c("minimum_wage", "inflation_rate", "unemployment_rate"), sep = " ")
dl <- data.frame(periode = rep(d$periode, 3), nilai = c(d$minimum_wage, d$inflation_rate, d$unemployment_rate),
                 seri = factor(rep(nm3, each = nt), levels = nm3))
p1 <- ggplot(dl, aes(periode, nilai, colour = seri)) +
  geom_line(linewidth = 0.7, show.legend = FALSE) +
  facet_wrap(~seri, ncol = if (tata == 1) 1 else 3, scales = "free_y") +
  scale_colour_manual(values = pal[1:3]) +
  labs(title = "The three series", x = NULL, y = NULL)
kej <- c("inflation_rate", "unemployment_rate")
lab_s <- make.unique(c("Shock: inflation_rate", "Shock: unemployment_rate"), sep = " ")
di <- do.call(rbind, lapply(1:2, function(i) data.frame(
  h = 0:10, irf = ir$irf[[kej[i]]][, 1], lo = ir$Lower[[kej[i]]][, 1], hi = ir$Upper[[kej[i]]][, 1],
  guncangan = lab_s[i])))
di$guncangan <- factor(di$guncangan, levels = lab_s)
p2 <- ggplot(di, aes(h, irf)) +
  geom_hline(yintercept = 0, colour = warna$redup) +
  geom_ribbon(aes(ymin = lo, ymax = hi, fill = guncangan), alpha = 0.22, show.legend = FALSE) +
  geom_line(aes(colour = guncangan), linewidth = 1, show.legend = FALSE) +
  facet_wrap(~guncangan, ncol = 2) +
  scale_colour_manual(values = pal[2:3]) + scale_fill_manual(values = pal[2:3]) +
  scale_x_continuous(breaks = seq(0, 10, 2)) +
  labs(title = "Orthogonal IRF of minimum_wage (95% bootstrap)", x = "Horizon", y = "Response")
nm_s <- make.unique(c("minimum_wage", "inflation_rate", "unemployment_rate"), sep = " ")
dfv <- data.frame(h = rep(1:10, 3), porsi = 100 * c(fv$minimum_wage),
                  sumber = factor(rep(nm_s, each = 10), levels = nm_s))
p3 <- ggplot(dfv, aes(factor(h), porsi, fill = sumber)) +
  geom_col(width = 0.75, colour = warna$panel, linewidth = 0.3) +
  scale_fill_manual(values = pal[1:3], name = "Shock") +
  labs(title = "FEVD of minimum_wage", x = "Horizon", y = "Share of variance (%)")
p_hasil <- if (tata == 1) p1 | (p2 / p3) else p1 / (p2 | p3)

print(p_hasil)

The project file you can download

The original project file is available. It is not just the picture above: you get the working R project. It can be downloaded after payment, and we send it by WhatsApp or email.

ZIP: analisis.R + data_contoh.csv + BACA-DULU.txt

What is inside the ZIP

The complete analysis script (analisis.R), commented step by step, ready to run in RStudio.
A sample dataset (data_contoh.csv) so the script runs straight away.
A short guide (BACA-DULU.txt): which packages to install, how to run it and how to swap in your own data.

Packages and prices

Choose how much help you need. Each higher package includes everything in the lower ones. Prices exclude 11% VAT.

Package 1

Code and Explanation

US$22

excl. 11% VAT

Duration: 5 working days

Output: R files + result figures

Deliverables

Fully commented R code (.R) for VAR and Granger Causality
Example data and step-by-step run instructions
Ready-to-use result figures and metrics table
Short explanation of the method, its assumptions and how to read the results

Choose Package 1

Package 2 · most chosen

Your Data Analysis + Interpretation

US$66

excl. 11% VAT

Duration: 9 working days

Output: Code + analysis + interpretation notes

Includes all of Package 1, plus

Adapting the code to your own research dataset (CSV or Excel)
Assumption checks, result validation and data cleaning
Tables and figures formatted for your manuscript
Interpretation notes for the methods and discussion sections, for you to write up in your own words

Choose Package 2

Package 3

Full Guidance

US$147

excl. 11% VAT

Duration: 14-17 working days

Output: Code + analysis + guidance until ready to present

Includes all of Packages 1 & 2, plus

Comparison against one alternative method with the reasoning for the choice
Two 60-minute online coaching sessions so you fully understand the code and results
Revisions following your supervisor feedback (up to 3 rounds)
Practice Q&A to prepare for your seminar and defence
Full documentation (README, R package list (sessionInfo)) so the results can be reproduced

Choose Package 3

Payment: 50% down payment before work starts, balance after the deliverables are handed over
Tax: Prices exclude 11% VAT
Data and academic integrity: Results are computed from your own research data; you write and stand behind your manuscript, we help with the analysis and your understanding of it
Revisions: Up to 2 revisions are included in the price (Package 3: 3 rounds)

Frequently asked questions

Do I get the real project file?

Yes. The original project file is a ZIP containing the complete analisis.R script, a data_contoh.csv sample dataset and a BACA-DULU.txt guide. It can be downloaded after payment, and we send it by WhatsApp or email. For your own data (Package 2 and 3) the script is adapted to your dataset.

Is this suitable for a Master's thesis (S2)?

Yes. VAR and Granger Causality is commonly used at this level in Human Resource Management. We adapt the analysis to your research question, your own data and your supervisor's requirements.

Is the result sheet real data?

No. The sheet is computed from illustrative synthetic data so you can see the kind of output R Studio gives. For your order we run the same method on your own data.

Will I understand the code?

That is the point of the packages. Every script is commented, and Package 3 includes two coaching sessions plus practice questions so you can explain the method and the results at your seminar and defence.

How is the price decided?

Each project has three packages: Package 1 (code and explanation) US$22, Package 2 (your data analysis and interpretation) US$66 and Package 3 (full guidance) US$147, excluding 11% VAT. Larger datasets, extra methods or tight deadlines adjust the quote after a short consultation.

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