Exercise 2 (20 minutes)

You practice: instrumental variables — does arrest deter repeat domestic violence? The Minneapolis experiment. When you're done, assist some of the others …

The Minneapolis Domestic Violence Experiment (Sherman & Berk 1984) randomly told officers how to respond to a domestic-violence call — but officers didn't always comply. Copy the starter:

pacman::p_load(tidyverse, estimatr, modelsummary, masteringmetrics)
data("mdve", package = "masteringmetrics") # ships with the package

1. T_RANDOM is the randomly assigned strategy, T_FINAL what the officer actually did (1 = arrest; 2 & 3 = the lenient "coddle"; 4 = other → NA). Recode both into two-category factors (Arrest as reference), then cross-tabulate. How many officers complied with their randomly assigned strategy?

R solution -> don't peek too early ;) !

mdve <- mdve %>%
  mutate(
    T_RANDOM = case_when(T_RANDOM %in% c(2, 3) ~ "Coddle!",
                         T_RANDOM == 1 ~ "Arrest!", TRUE ~ NA_character_) %>%
      fct_relevel("Arrest!"),
    T_FINAL  = case_when(T_FINAL %in% c(2, 3) ~ "Coddled",
                         T_FINAL == 1 ~ "Arrested", TRUE ~ NA_character_) %>%
      fct_relevel("Arrested"))

mdve %>% select(T_RANDOM, T_FINAL) %>% table()
#          T_FINAL
# T_RANDOM  Arrested Coddled
#   Arrest!       91       1
#   Coddle!       45     177
91 + 177 # compliers: arranged-and-arrested + coddle-and-coddled
# [1] 268

2. Was the randomly assigned strategy balanced across the subject's race (S_RACE)? Recode race, then make a balance table across T_RANDOM. No — the absolute frequencies differ a lotYes, and every single group is perfectly balancedBroadly balanced across groups, though 'Indian' looks a bit off

R solution -> don't peek too early ;) !

mdve <- mdve %>%
  mutate(S_RACE = case_when(S_RACE == 1 ~ "White", S_RACE == 2 ~ "Black",
                            S_RACE == 3 ~ "Indian", S_RACE == 4 ~ "Asian",
                            S_RACE == 5 ~ "Hispanic", TRUE ~ "Other"))

mdve %>% select(T_RANDOM, S_RACE) %>%
  datasummary_balance(~ T_RANDOM, data = .,
                      title = "Subject's race by *assigned* strategy")

Subject's race by *assigned* strategy

		Arrest! (N=93)		Coddle! (N=237)
		N	Pct.	N	Pct.
S_RACE	Asian	0	0.0	2	0.8
	Black	34	36.6	83	35.0
	Hispanic	1	1.1	7	3.0
	Indian	19	20.4	32	13.5
	Other	1	1.1	4	1.7
	White	38	40.9	109	46.0

3. Now balance race across what officers actually did (T_FINAL). What changed? Still perfectly balancedNow the groups look imbalanced — actual treatment is not randomWhite subjects were treated more harshly than assigned

R solution -> don't peek too early ;) !

mdve %>% select(T_FINAL, S_RACE) %>%
  datasummary_balance(~ T_FINAL, data = .,
                      title = "Subject's race by *actual* strategy")

Subject's race by *actual* strategy

		Arrested (N=136)		Coddled (N=178)
		N	Pct.	N	Pct.
S_RACE	Asian	0	0.0	2	1.1
	Black	49	36.0	62	34.8
	Hispanic	2	1.5	4	2.2
	Indian	24	17.6	24	13.5
	Other	1	0.7	3	1.7
	White	60	44.1	83	46.6

4. First stage. Regress actual coddling (1 = coddled) on the assigned strategy. How much more likely was an officer to coddle when randomly told to, rather than arrest? — in IV language this is the first stagereduced formLATE estimate.

R solution -> don't peek too early ;) !

mdve <- mdve %>%
  mutate(T_FINAL_01 = if_else(T_FINAL == "Coddled", 1, 0))

first_stage <- lm_robust(T_FINAL_01 ~ T_RANDOM, data = mdve)
modelsummary(list("Coddled (0/1)" = first_stage), stars = TRUE,
             coef_rename = c("T_RANDOMCoddle!" = "Randomly told to coddle"),
             gof_map = c("nobs", "r.squared"))

	Coddled (0/1)
+ p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001
(Intercept)	0.011
	(0.011)
Randomly told to coddle	0.786***
	(0.029)
Num.Obs.	314
R2	0.522

5. Sherman & Berk report that being randomly told to coddle raised the probability of a repeat assault by 0.114, versus being told to arrest (regardless of what the officer did). In IV language this is the reduced formfirst stageLATE estimate.

6. Put it together. The IV estimate of the local average causal effect of coddling (vs. arresting) on repeat assault is reduced form ÷ first stage: (two digits).

R solution

0.114 / 0.79 # reduced form / first stage = LATE
# [1] 0.14

So, for compliers, coddling rather than arresting raised the probability of a repeat assault by about 0.14 — evidence that arrest did deter. (Careful: it is a LATE, for the officers whose behaviour the random instruction actually changed.)

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Discuss with your neighbour: which of the three IV requirements is hardest to defend here — that the random instruction affects repeat violence only through what the officer actually did (the exclusion restriction)? Could being told to arrest change an officer's demeanour in other ways?