Difference-in-Differences with Spatial Spillovers

Kyle Butts^1
1University of Colorado: Boulder

Paper | Five-minute Summary

Abstract

Empirical work often uses treatment assigned following geographic boundaries. When the effects of treatment cross over borders, classical difference-in-differences estimation produces biased estimates for the average treatment effect. In this paper, I introduce a potential outcomes framework to model spillover effects and decompose the estimate's bias in two parts: (1) the control group no longer identifies the counterfactual trend because their outcomes are affected by treatment and (2) changes in treated units' outcomes reflect the effect of their own treatment status and the effect from the treatment status of ``close'' units. I propose estimation strategies that can remove both sources of bias and semi-parametrically estimate the spillover effects themselves including in settings with staggered treatment timing. To highlight the importance of spillover effects, I revisit analyses of three place-based interventions.

Replication

Figure 1: Comparison of Single vs. Multiple Rings Estimation of Spillover Effects

• code/rings-example/rings_example.R

Figure 2: TVA Effective Sample and Spillover Variables

• code/tva/tva-data-build.do
• code/tva/analysis.R

Table 1: Effects of Tennessee Valley Authority on Decadel Growth

• code/tva/tva-data-build.do
• code/tva/analysis.R

Table B1: Effects of Opportunity Zones on Annual Home Price Growth

• code/OZ/replication.R
• code/OZ/spillovers.R

Figure C1: Total and Spillover Effects of Community Health Centers

• code/CHC/analysis.R

Code Layout

.
├── code/
│   ├── main.R                          # Main script to run all analyses
│   ├── rings-example/                  # Figure 1: Single vs. Multiple Rings
│   │   └── rings_example.R             # Generates comparison figures
│   ├── TVA/                            # Table 1: Tennessee Valley Authority
│   │   ├── analysis.R                  # Main analysis and Figure 2
│   │   ├── analysis_1930_base.R        # Alternative baseline (1930)
│   │   ├── tva-data-build.do           # Stata data preparation
│   │   ├── helpers.R                   # Helper functions
│   │   ├── helper-conley.R             # Conley standard errors
│   │   ├── helper-conley.cpp           # C++ implementation
│   │   └── pretrends.R                 # Pretrend analysis
│   ├── CHC/                            # Figure C1: Community Health Centers
│   │   └── analysis.R                  # Event study analysis
│   ├── OZ/                             # Table B1: Opportunity Zones
│   │   ├── replication.R               # Replicate CGW (2023)
│   │   └── spillovers.R                # Add spillover controls
│   └── simulations/                    # Monte Carlo simulations
│       ├── misspecified_exposure_mapping.R
│       ├── helper-sim_function.R
│       ├── helper-sim_function_misspecification.R
│       └── prepare_county_data.R
├── out/
│   ├── figures/                        # Generated figures
│   │   ├── rings-example/              # Figure 1 outputs
│   │   ├── tva/                        # Figure 2 outputs
│   │   ├── chc/                        # Figure C1 outputs
│   │   └── example/                    # Additional examples
│   └── tables/                         # Generated tables
│       ├── tva_long.tex                # Table 1 (long differences)
│       ├── tva_short.tex               # Table 1 (short differences)
│       ├── tva_long_1930.tex           # Alternative baseline
│       ├── tva_replication.tex         # Replication table
│       ├── tva_replication_short.tex   # Short replication
│       └── OZ_replication.tex          # Table B1
└── data/                               # Data files (not tracked in git)

Scripts and Outputs

Script	Purpose	Outputs
code/rings-example/rings_example.R	Figure 1: Single vs. Multiple Rings estimation comparison	rings_pt_everywhere.pdf, rings_pt_on_avg.pdf, rings_v_within_pt_everywhere.pdf, rings_v_within_pt_on_avg.pdf, within_pt_everywhere.pdf, within_pt_on_avg.pdf
code/TVA/analysis.R	Figure 2 & Table 1: TVA analysis with spillover controls	tva-sample.pdf, tva_long.tex, tva_short.tex
code/TVA/analysis_1930_base.R	Alternative TVA analysis with 1930 baseline	tva_long_1930.tex, tva_short_1930.tex
code/CHC/analysis.R	Figure C1: CHC event study with spillovers	chc-es_original.pdf, chc-es_combined.pdf
code/OZ/replication.R	Table B1: Replicate CGW (2023)	OZ_replication.tex
code/OZ/spillovers.R	Add spillover controls to OZ analysis	Same as above
code/simulations/misspecified_exposure_mapping.R	Misspecification simulations	misspecification.tex, misspecification_mspe.tex, misspecification_mspe_percent.tex

Running the Code

Execute all analyses:

source("code/main.R")

Or use the render system for individual files:

source("logbook/render_file.R")
render_file(here("code/TVA/analysis.R"))

Citation

@article{butts2023difference,
  title={Difference-in-Differences Estimation with Spatial Spillovers},
  author={Butts, Kyle},
  journal={arXiv preprint arXiv:2105.03737},
  year={2023}
}