Example: Regulatory Shock -- Dieselgate VW-Group vs Peers

Abstract

This worked example uses the bundled dieselgate dataset to demonstrate a two-group event study that isolates an idiosyncratic shock from an industry-wide one. Volkswagen and Porsche (the directly-exposed VW Group) are compared against peer automakers BMW and Mercedes-Benz (Other). By contrasting the cumulative average abnormal return (CAAR) across groups around the September 2015 emissions disclosure, we ask whether the scandal caused abnormal losses beyond the German auto sector as a whole.

For the market model, see Return Models; for the cross-sectional and sign tests, see Test Statistics.

Research question

Did the VW emissions announcement cause significantly more negative cumulative abnormal returns for the VW corporate family (VOW.DE, PAH3.DE) than for the industry-peer group (BMW.DE, MBG.DE)? We test, separately for each group,

H_0:\ \mathbb{E}[CAAR] = 0,

and then compare the two groups’ CAR distributions directly.

Data

The dieselgate dataset ships in data/ and needs no network access. Like the other bundled datasets it is a named list – firm (all four automakers’ daily adjusted prices, stacked), index (the benchmark), a four-row request carrying the per-firm event windows and the crucial group assignment, and a meta provenance block. See the provenance notes in ?dieselgate.

library(EventStudy)
data("dieselgate", package = "EventStudy")

dplyr::glimpse(dieselgate$firm)
#> Rows: 1,440
#> Columns: 3
#> $ symbol   <chr> "VOW.DE", "VOW.DE", "VOW.DE", "VOW.DE", "VOW.DE", "VOW.DE", "…
#> $ date     <chr> "02.06.2014", "03.06.2014", "04.06.2014", "05.06.2014", "06.0…
#> $ adjusted <dbl> 112.5, 112.4, 109.5, 111.6, 111.9, 112.4, 111.7, 111.7, 112.5…

# The group column drives the two-group comparison.
dplyr::count(dieselgate$request, group)
#> # A tibble: 2 × 2
#>   group        n
#>   <chr>    <int>
#> 1 Other        2
#> 2 VW Group     2

Setup and pipeline

We build the task from the three tibbles and fit a market model, attaching the cross-sectional t-test (CSectTTest) and the SignTest as multi-event statistics. Both aggregate the firm-level abnormal returns within each group.

task <- EventStudyTask$new(
  dieselgate$firm,
  dieselgate$index,
  dieselgate$request
)

params <- ParameterSet$new(
  return_model = MarketModel$new(),
  multi_event_statistics = MultiEventStatisticsSet$new(
    tests = list(CSectTTest$new(), SignTest$new())
  )
)

result <- run_event_study(task, params)

See ParameterSet, MultiEventStatisticsSet, CSectTTest, and SignTest.

Results table

The per-group CAAR at the end of the event window is the headline result. We pull it from the tidy AAR/CAAR output, and summarise the raw per-firm CARs by group with car_by_group().

caar_tbl <- EventStudy::tidy.EventStudyTask(result, type = "aar")

caar_tbl |>
  dplyr::group_by(group) |>
  dplyr::slice_tail(n = 1) |>
  dplyr::ungroup() |>
  dplyr::select(group, term, caar, caar_statistic, caar_p.value) |>
  knitr::kable(
    digits  = 4,
    caption = "CAAR by group at the end of the event window: VW-Group vs Peers"
  )

CAAR by group at the end of the event window: VW-Group vs Peers
group	term	caar	caar_statistic	caar_p.value
Other	10	0.0132	0.3377	0.7927
VW Group	10	-0.3858	-12.6016	0.0504


# Group-level CAR summary and a between-group difference test.
grp <- car_by_group(result)
knitr::kable(grp$summary, digits = 4,
             caption = "Per-firm CAR summary by group")

Per-firm CAR summary by group
group	n	mean_car	sd_car	median_car	min_car	max_car
Other	2	0.0132	0.0555	0.0132	-0.0260	0.0525
VW Group	2	-0.3858	0.0433	-0.3858	-0.4164	-0.3551

Plot

gg <- plot_event_study(
  result,
  type  = "aar",
  group = "VW Group",
  title = "VW Group: cumulative average abnormal return with 95% band"
)
plotly::ggplotly(gg)

Interpretation

vw_caar  <- result$aar_caar_tbl$CSectT[[
  which(result$aar_caar_tbl$group == "VW Group")]]
oth_caar <- result$aar_caar_tbl$CSectT[[
  which(result$aar_caar_tbl$group == "Other")]]

vw_end   <- round(utils::tail(vw_caar$caar,   1L), 4)
vw_t     <- round(utils::tail(vw_caar$caar_t, 1L), 2)
oth_end  <- round(utils::tail(oth_caar$caar,  1L), 4)
oth_t    <- round(utils::tail(oth_caar$caar_t, 1L), 2)

By the end of the window the VW Group CAAR is -0.3858 (cross-sectional t = -12.6), while the Other group’s CAAR is 0.0132 (t = 0.34). The contrast is the whole story: VW Group firms crater while peer automakers barely move. Because the peer group – exposed to the same macro and sector conditions – shows no comparable drop, the shock is idiosyncratic to the VW corporate family rather than an industry-wide contagion. The SignTest corroborates the direction non-parametrically: with every VW-group firm posting negative CARs, the sign statistic points the same way as the parametric test, which matters when a two-firm group makes the normality assumption of the t-test fragile (Brown and Warner 1985). This two-group design is the standard technique for separating firm-specific from sector-wide regulatory shocks.

Diagnostics note

With only a handful of firms per group, groupwise residual autocorrelation and non-normality materially affect the standard errors. Check the estimation-window fit with es_diagnostics() before trusting the parametric p-values.

Session info

#> R version 4.6.1 (2026-06-24)
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#>  [1] LC_CTYPE=C.UTF-8       LC_NUMERIC=C           LC_TIME=C.UTF-8       
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#> [1] stats     graphics  grDevices utils     datasets  methods   base     
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#> [1] EventStudy_0.62.0
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#> [46] xfun_0.60            tibble_3.3.1         tidyselect_1.2.1    
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#> [52] rmarkdown_2.32       labeling_0.4.3       compiler_4.6.1      
#> [55] S7_0.2.2             distributional_0.8.1

Brown, Stephen J., and Jerold B. Warner. 1985. “Using Daily Stock Returns: The Case of Event Studies.” Journal of Financial Economics 14 (1): 3–31.