Replication Lab: Minimum Wages and Employment

Overview

In this replication lab, you will reproduce the central findings from one of the most famous natural experiments in economics:

Card, David, and Alan B. Krueger. 1994. "Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania." American Economic Review 84(4): 772–793.

On April 1, 1992, New Jersey raised its minimum wage from $4.25 to $5.05 per hour, while neighboring Pennsylvania kept its minimum at $4.25. Card and Krueger surveyed fast-food restaurants in both states before and after the increase, using Pennsylvania as a control group for New Jersey.

Why this paper matters: It challenged the textbook prediction that minimum wage increases necessarily reduce employment, contributed to the modern "credibility revolution" in empirical economics, and remains one of the most replicated (and debated) studies in the field.

What you will do:

• Learn why simulation is used when original microdata are unavailable and how matching summary statistics enables pedagogical replication
• Simulate data matching the published summary statistics from Table 3
• Construct the canonical 2x2 DiD table
• Estimate DiD by hand and via regression
• Test the parallel trends assumption
• Compare your results to the published findings

Step 1: Simulate the Fast-Food Employment Data

The original study surveyed 410 fast-food restaurants: 331 in New Jersey and 79 in Pennsylvania. Each restaurant was surveyed before (February/March 1992) and after (November/December 1992) the minimum wage increase.

1library(estimatr)
2library(modelsummary)
3
4set.seed(1994)
5n_nj <- 331; n_pa <- 79; n <- n_nj + n_pa
6
7nj <- c(rep(1, n_nj), rep(0, n_pa))
8chain <- sample(c("bk","kfc","wendys","roys"), n, replace = TRUE,
9              prob = c(0.41, 0.20, 0.24, 0.15))
10co_owned <- rbinom(n, 1, 0.22)
11
12fte_before <- pmax(ifelse(nj == 1, rnorm(n, 20.44, 9.0),
13                                  rnorm(n, 23.33, 11.4)), 0)
14fte_after <- pmax(ifelse(nj == 1, fte_before + rnorm(n, 0.59, 7.0),
15                                 fte_before + rnorm(n, -2.16, 7.0)), 0)
16
17df <- data.frame(
18restaurant_id = rep(1:n, 2),
19nj = rep(nj, 2),
20after = c(rep(0, n), rep(1, n)),
21fte = c(fte_before, fte_after),
22chain_bk = rep(as.integer(chain == "bk"), 2),
23chain_kfc = rep(as.integer(chain == "kfc"), 2),
24chain_wendys = rep(as.integer(chain == "wendys"), 2),
25co_owned = rep(co_owned, 2)
26)
27
28cat("Panel:", nrow(df), "obs (", n, "restaurants x 2 periods)\n")

Expected output:

Panel dataset: 820 obs (410 restaurants x 2 periods)
NJ restaurants: 331, PA restaurants: 79

Summary statistics:

Sample data (first 5 rows):

Step 2: Construct the 2x2 DiD Table

The heart of the Card-Krueger analysis is a simple 2x2 table of mean employment.

1# 2x2 DiD table
2tab <- tapply(df$fte, list(State = ifelse(df$nj, "NJ", "PA"),
3                          Period = ifelse(df$after, "After", "Before")), mean)
4cat("=== 2x2 DiD Table ===\n")
5print(round(tab, 2))
6
7# DiD by hand
8did_manual <- (tab["NJ","After"] - tab["NJ","Before"]) -
9            (tab["PA","After"] - tab["PA","Before"])
10cat("\nDiD estimate:", round(did_manual, 2), "\n")
11cat("Published: 2.76 (SE=1.36)\n")

Expected output — 2x2 DiD table:

DiD estimate (by hand): 2.75
Published DiD estimate: 2.76 (SE = 1.36)

Interpretation: NJ employment increased by 2.75 FTEs relative to PA
after the minimum wage increase.

The DiD estimate is positive, indicating that the minimum wage increase did not reduce employment — in fact, NJ employment rose relative to PA. Values will vary slightly from the published 2.76 due to simulation randomness, but the qualitative finding is the same.

Step 3: DiD via Regression

The regression version of DiD is more flexible and allows easy addition of controls.

1df$nj_after <- df$nj * df$after
2
3# Model 1: Basic DiD
4m1 <- lm_robust(fte ~ nj + after + nj_after, data = df,
5              clusters = restaurant_id, se_type = "CR2")
6
7# Model 2: With controls
8m2 <- lm_robust(fte ~ nj + after + nj_after + chain_bk + chain_kfc +
9               chain_wendys + co_owned, data = df,
10               clusters = restaurant_id, se_type = "CR2")
11
12modelsummary(list("Basic DiD" = m1, "+ Controls" = m2),
13           coef_map = c("nj_after" = "NJ x After (DiD)"),
14           stars = c('*' = 0.1, '**' = 0.05, '***' = 0.01))

Expected output — DiD regression results:

Full regression output (Basic DiD):

Adding chain and ownership controls changes the DiD estimate by less than 0.1 FTE, indicating that the NJ/PA comparison is well-balanced on observables. The standard errors with restaurant-level clustering are somewhat smaller than the published conventional SEs.

Step 4: Assess the Parallel Trends Assumption

The key identifying assumption of DiD is that NJ and PA employment would have followed parallel trends in the absence of the minimum wage increase. We cannot test this directly, but we can check pre-treatment trends if we had multiple pre-periods.

1# Simulate pre-treatment periods for trend check
2set.seed(42)
3periods <- c(-3, -2, -1, 0)
4common_trend <- c(0, -0.5, -1.0, 0)
5
6trend_list <- list()
7for (t in seq_along(periods)) {
8fte_t <- fte_before + common_trend[t] + rnorm(n, 0, 2)
9if (periods[t] == 0) fte_t[nj == 1] <- fte_t[nj == 1] + 2.76
10trend_list[[t]] <- data.frame(restaurant_id = 1:n, period = periods[t],
11                               nj = nj, fte = pmax(fte_t, 0))
12}
13trend_df <- do.call(rbind, trend_list)
14
15# Pre-treatment gap check
16cat("=== Pre-Treatment Trends ===\n")
17for (t in periods[-length(periods)]) {
18nj_m <- mean(trend_df$fte[trend_df$nj == 1 & trend_df$period == t])
19pa_m <- mean(trend_df$fte[trend_df$nj == 0 & trend_df$period == t])
20cat("Period", t, ": NJ=", round(nj_m, 2), " PA=", round(pa_m, 2),
21    " Gap=", round(nj_m - pa_m, 2), "\n")
22}

Expected output — pre-treatment trends check:

The NJ--PA gap is roughly constant across the three pre-treatment periods (around -2.89), supporting the parallel trends assumption. The level difference (NJ has lower FTE than PA) is not a concern for DiD — what matters is that the change over time is similar in both groups. At period 0 (the treatment period), the gap narrows as NJ receives the treatment effect of +2.76.

Step 5: Compare with Published Results

cat("=== Comparison with Published Table 3 ===\n")
cat("Published DiD: 2.76 (SE=1.36)\n")
cat("Our DiD:", round(did_manual, 2), "\n")
cat("Qualitative conclusion: No negative employment effect.\n")

Expected output — published vs. replicated comparison:

The point estimates closely match the published values because the simulation targets the same means. Small differences arise from sampling variability. The qualitative conclusion is confirmed: the minimum wage increase in New Jersey did not reduce fast-food employment relative to Pennsylvania.

Summary

Our replication confirms the central finding of Card and Krueger (1994):

1. No negative employment effect. The DiD estimate is positive: employment in NJ fast-food restaurants increased (or at least did not decrease) relative to PA after the minimum wage increase.

2. Robustness to controls. Adding chain and ownership controls does not substantially change the DiD estimate, consistent with the quasi-random nature of the NJ/PA comparison.

3. The parallel trends assumption is crucial. The entire causal interpretation rests on the assumption that NJ and PA employment would have evolved similarly absent the policy change. Pre-trend checks are suggestive but cannot definitively validate this assumption.

4. Ongoing debate. Neumark and Wascher (2000) challenged these results using payroll data rather than survey data, finding negative employment effects. The debate highlights how data sources and measurement choices can affect conclusions.

Extension Exercises

1. Continuous treatment intensity. Instead of a binary NJ indicator, use the "gap" variable (the wage increase needed to reach the new minimum) as a continuous treatment measure. Restaurants already paying above $5.05 should show no effect.

2. Triple difference. Use high-wage restaurants (already above $5.05) within NJ as an additional control group. Estimate a DDD model.

3. Placebo test. Apply the same DiD design to a period before the minimum wage increase. If you find a "treatment effect" in a period with no treatment, it suggests the parallel trends assumption may be violated.

4. Synthetic control. Construct a synthetic PA from other states' fast-food employment data and compare with the DiD estimate.

5. Inference with few clusters. Implement wild cluster bootstrap or randomization inference to address the two-cluster problem.