Empirics, Tables and Figures

[rafaelchduran]

March 26, 2021

• [X] why do I lose half of the observations (from 24000 to 13000)? --because we only have homicides for certain years. Then, the control group is municipalities with low homicide levels and not no homicides! --another reason (the good one) is that the variable reform had an error. --I fixed this in the dofiles
• [ ] revise pretreatment covariates -- Revised Zeldow and Hatfield (2019) --confounders are those that threaten the parallel trends assumption when not accounted for --1. for time-invariant covariates, the parallel trends are violated if there are two conditions of the control X: 1. the mean of X varies by treatment group and 2. the relationship of X to the outcome varies over time --2. for time-invariant covariates, X is a confounder if its distribution evolves differentially between the treated and comparison groups, regardless of whether the effect on the outcome is constant --a confounder is a variable with a time-varying effect on the outcome or a time-varying difference between groups --so confounder always has a time-varying effect --so how to add the controls following Zeldow and Hatfield (2019):
  1. if confounder x is time-invariant: x*time
  2. if confounder x is time-variant: in this case if we include it directly (add x) or its interaction with time in regression, we risk conditioning on post-treatment covariates that may be affected by treatment (Rosenbaum 1984). This is because the time-varying covariate can act as both a confounder and as a mediator. However, if we fail to account for the covariate, we face parallel trend violations. One way is through g-methods such as inverse probability weighting following Stuart et al. 2014, and Han et al. 2017. Matching in a DiD can yield unwanted results: in some settings, it reduces bias [Stuart et al. 2014, Ryan et al. 2015], while in others, matching induces regression to the mean and create bias [O'Neill et al. 2016, Daw & Hatfield 2018]. Moreover, if confounding arises because of differential evolution of the covariate in the two groups, matching only on pre-treatment values will be insufficient to address the confounding. Thus, we would wish to match on pre and post-treatment values but may fell to posttreatment bias (Rosenbaum 1984).

-On Abraham and Sun (2021) and the introduction of covariates (see page 16): cohort weights can be estimated controlling for covariates in the main specification. However, the interpretation of the DiD per cohort mu_g is a bit different. Depending on how covariates are controlled in main regression, we may need an additional assumption for identification that the counterfactual trends are linear in the time-varying covariates X_i,t. This is left for future work.

• [ ] I can update inegi defunciones por homicidio for 2019 and then consider the municipal elections of 2019

[rafaelchduran]

On Models

• [X] run reform effect on homicides with log pop and defunciones per level -- eststo: xi: areg logdefunciones reform i.year logpop, a(inegi) vce(cluster estado)
• cannot include state-year linear time trends since they are correlated with the treatment