September 14, 2020

Motivation


  • Many studies about effect of quarantines on COVID-19 spread:
    Some (+), some (0).
  • Differences in populations?
  • How appropriate is the counterfactual?
  • How about heterogeneity?

This paper

  • Objective: What was the effect of lockdowns on new COVID-19 cases by income level in Santiago?

  • Contributions:

    • Use of small-area lockdowns.
    • Heterogeneity in effect by groups of interest.
    • Mediation analysis for potential mechanisms,

  • Quick preview of results:

    • Positive effectiveness of lockdowns on high-income areas; null effect for lower-income municipalities.
    • Effect partially mediated by mobility and testing differences.

Context of Lockdowns
in the Metropolitan Region

“Dynamic” Lockdowns in the Metropolitan Region



  • Early lockdowns in East side (high-income) + Santiago and Independencia (lower-income): Heterogeneity in types of municipalities.
  • Later lockdowns in other lower-income areas.
  • Quarantines were not fully determined by COVID spread.

Augmented Synthetic Control Method

An (Augmented) Synthetic Control Method Approach

  • Let \(Y_{it}(z)\) be the potential outcome under treatment \(z\) for unit \(i\) in period \(t\):
    • E.g. \(W_i\) is a treatment indicator, where unit \(i\) is treated for all periods \(T_0<T\).
  • Under traditional Synthetic Control Method (SCM) (Abadie & Gardeazabal, 2003), the counterfactual for \(Y_{1T}\) is: \[\hat{Y}_{1T}(0) = \sum_{W_i=0}\gamma_iY_{iT}\]

An (Augmented) Synthetic Control Method Approach

  • Under Augmented Synthetic Control Method (ASCM) (Ben-Michael et al., 2020) there is a correction for poor fit: \[\hat{Y}^{aug}_{1T}(0) = \sum_{W_i=0}\gamma_iY_{iT}+\color{#2ca3c1}{(\hat{m}_{iT}(\mathbf{X_i})-\sum_{W_i=0}\gamma_i\hat{m}_{iT}(\mathbf{X_i}))}\]
    • \(m_{iT}\): Estimator for \(Y_{iT}(0)\)
    • Extrapolation for ``bias correction’’.
    • If ridge regression is used \(\rightarrow\) penalization for extrapolation

Identification Strategy

  • For estimating a causal effect:
    1. Assignment of treatment is random conditional on donor pool, obs. covariates, and pre-treatment trends.

Identification Strategy

  • For estimating a causal effect:
    1. Assignment of treatment is random conditional on donor pool, obs. covariates, and pre-treatment trends.

      \(\rightarrow\) Pre-intervention trend did not fully determine quarantine assignment.

Identification Strategy

  • For estimating a causal effect:
    1. Assignment of treatment is random conditional on donor pool, obs. covariates, and pre-treatment trends.

      \(\rightarrow\) Pre-intervention trend did not fully determine quarantine assignment.

    2. SUTVA (e.g. no spillovers)

Identification Strategy

  • For estimating a causal effect:
    1. Assignment of treatment is random conditional on donor pool, obs. covariates, and pre-treatment trends.

      \(\rightarrow\) Pre-intervention trend did not fully determine quarantine assignment.

    2. SUTVA (e.g. no spillovers)

      \(\rightarrow\) Take out buffer municipalities from donor pool.

Identification Strategy

  • For estimating a causal effect:
    1. Assignment of treatment is random conditional on donor pool, obs. covariates, and pre-treatment trends.

      \(\rightarrow\) Pre-intervention trend did not fully determine quarantine assignment.

    2. SUTVA (e.g. no spillovers)

      \(\rightarrow\) Take out buffer municipalities from donor pool.

    3. Intervention had no effect prior to \(t=0\)

Identification Strategy

  • For estimating a causal effect:
    1. Assignment of treatment is random conditional on donor pool, obs. covariates, and pre-treatment trends.

      \(\rightarrow\) Pre-intervention trend did not fully determine quarantine assignment.

    2. SUTVA (e.g. no spillovers)

      \(\rightarrow\) Take out buffer municipalities from donor pool.

    3. Intervention had no effect prior to \(t=0\)

      \(\rightarrow\) Use date of announcement as \(t=0\).

Results on Spread of COVID-19

Some Parameters

  • Time period: March 15th to May 4th.
  • Donor pool: municipalities > 70.000 hab.
  • Obs. covariates: Population density, income per capita, poverty rate, total cases.
  • Types of municipalities:
    • High-income Q: Las Condes, Lo Barnechea, Nunoa, Providencia, Vitacura.
    • Low-income Q: (1) Santiago, Independencia, (2) Puente Alto, El Bosque, San Bernardo, Quinta Normal, PAC.
    • Donor Pool: All other municipalities \(\not\in\) Q

Effect on New Cases: Average Treatment Effect of the Treated


  • Decreasing trend in number of new cases over time.

Effect on New Cases: High-Income


  • Negative effect on new cases \(t\geq 12\)

Effect on New Cases: Low-Income (All)


  • Null effect, but shorter post-treatment period

Effect on New Cases: Low-Income (1st Wave)


  • Null effect for same period as high-income.

Potential Mechanisms

Why differential effects?

  • Differential costs of staying at home \(\rightarrow\) Mobility:
    • Savings constraints
    • Inability to work from home
  • Information asymmetry by income level \(\rightarrow\) Testing:
    • Delay in testing results \(\rightarrow\) difficulty in tracing

Differences in mobility: Subway validations

Low income Q similar to No Q

High income Q larger drop in mobility

High income Q larger drop in mobility

Differences in mobility: ASCM using Mobility Index

Differences in testing: Private sector more lax about testing

Differences in testing: Time to diagnosis

Conclusions

Conclusions


  • Policies have heterogeneous effects
  • Analyze mechanisms and identify bottlenecks.
  • Bundles of policies can help reduce differences.
  • Importance of timely data.

Heterogeneity in Policy Effectiveness against
COVID-19 Spread in Chile