synthetic control methods for comparative case

SYNTHETIC CONTROL METHODS FORCOMPARATIVE CASE STUDIES: ESTIMATING THEEFFECT OF CALIFORNIA�S TOBACCO CONTROL

PROGRAMProgram Evaluation Presentation

Alberto Abadie Alexis Diamond Jens Hainmueller

Andrés Castañeda

October 2009

Universidad del Rosario (Institute) Program Evaluation October 2009 1 / 18

One Slide Presentation

Motivation

California�s Background

Methodology

Implementation

Data and Sample

Estimation Steps

Tables and Figures

Motivation

Methodology

Implementation

Data and Sample

Estimation Steps

Tables and Figures

Motivation

Methodology

Implementation

Data and Sample

Estimation Steps

Tables and Figures

Motivation

Methodology

Implementation

Data and Sample

Estimation Steps

Tables and Figures

Motivation

Methodology

Implementation

Data and Sample

Estimation Steps

Tables and Figures

Motivation

Methodology

Implementation

Data and Sample

Estimation Steps

Tables and Figures

Motivation

Methodology

Implementation

Data and Sample

Estimation Steps

Tables and Figures

Motivation

Justify the synthetic control approach

Study the e¤ects of California�s Proposition 99.

Motivation

Justify the synthetic control approach

Study the e¤ects of California�s Proposition 99.

Washington 1893. Moral and Health

Proposition 99. 1988

Earmarked: $100 million State, $20 million research

Methodology1

Objective: Construct a Synthetic variable

Framework:

j + 1 Regions: 1 exposed to treatment and j controlsT0 Number of pre-intervention periods and 1 � T0 � TY Nit is the outcome that would be observed by region i in time t withno treatmentY Iit is outcome that would be observed by region i in time t withtreatment

Methodology2

A1: Intervention has no e¤ect on the outcome before the treatmentperiod, so Y Nit = Y

After the treatment period Y Iit � Y Nit = αit

Dit is an indicator if i is exposed to the treatment

Therefore we can write Yit = Y Nit + αitDit

Methodology2

Methodologyprocedure

The aim is to estimate each αit for all t > T0Hence Y I1t is observed, we need to estimate Y

N1t to get

α1t = Y1t � TN1t (1)

A2: Y Nit = δt + θtZi + λtµi + εit

Covariates are ZiUnknown common factor is λt

Varying factor loadings µiIf λt is constant we get dif in dif

N1t to get

α1t = Y1t � TN1t (1)

N1t to get

α1t = Y1t � TN1t (1)

Covariates are Zi

Unknown common factor is λt

N1t to get

α1t = Y1t � TN1t (1)

N1t to get

α1t = Y1t � TN1t (1)

Varying factor loadings µi

If λt is constant we get dif in dif

N1t to get

α1t = Y1t � TN1t (1)

MethodologyProcedure 2

Consider W = (w2, ...,wj+1)0 such that wj � 0 and ∑j+1

j=2 wj = 1

A3: we can chose�w �2 , ...,w

�j+1

�0such that

∑j=2w �j Y

Nj = Y N1 (2)

∑j=2w �j Z

Nj = ZN1 (3)

This suggest that equation (1) would be

α̂1t = Y1t �j+1

∑j=2w �j Y

Nj (4)

j=2 wj = 1

�j+1

�0such that

∑j=2w �j Y

Nj = Y N1 (2)

∑j=2w �j Z

Nj = ZN1 (3)

α̂1t = Y1t �j+1

∑j=2w �j Y

Nj (4)

j=2 wj = 1

�j+1

�0such that

∑j=2w �j Y

Nj = Y N1 (2)

∑j=2w �j Z

Nj = ZN1 (3)

α̂1t = Y1t �j+1

∑j=2w �j Y

Nj (4)

j=2 wj = 1

�j+1

�0such that

∑j=2w �j Y

Nj = Y N1 (2)

∑j=2w �j Z

Nj = ZN1 (3)

α̂1t = Y1t �j+1

∑j=2w �j Y

Nj (4)

Implementation

Let X1 be a vector of characteristics for the exposed region

And X0 is a matrix that contains the same variables for the untreatedregions

The idea is obtain the vector W � that minimize jjX1 � X0W �jj

In particular jjX1 � X0W jjv =q(X1 � X0W )0 V (X1 � X0W )

Implementation

Let X1 be a vector of characteristics for the exposed region

And X0 is a matrix that contains the same variables for the untreatedregions

The idea is obtain the vector W � that minimize jjX1 � X0W �jj

In particular jjX1 � X0W jjv =q(X1 � X0W )0 V (X1 � X0W )

Data and Sample1

Variable of interest: Annual per capita cigarette consumption at thestate level

Panel data for the period 1970 �2000

Proposition 99 (P.99) was passed in 1988

Synthetic California is meant to reproduce the consumption ofcigarettes that would have been observed without the treatment in1988

Discarding:

Large-scale tobacco controlTaxes by 50 cents

Data and Sample2

Average retail price of cigarettes

Per capital personal income (logged)

The percentage of population age 15 �24

Per capita beer consumption

Three year lagged smoking consumption (1975, 1980 and 1988)eamer�font themes�de�ne the use of fonts in a presentation

Estimation Steps

1 Using the techniques described above the synthetic California (SC) isconstructed

SC is the mirror of the predictors of cigarette consumption in Californiabefore the treatment

2 The e¤ect of P.99 is estimated as the di¤erence in cigaretteconsumption between California and SC after P.99 was passed

3 A series of placebo studies are performed

Before Results

Trend in per capital sales: California Vs United States

Trend in per capital sales: California Vs SyntheticCalifornia

Per capital sales gap: California Vs 38 Control States

Per capital sales gap: California Vs 19 Control States withmean square prediction error less than two timesCalifornia�s

Final Remarks

Cigarettes sales in California were about 26 packs lower than whatthey would have been in the absence of P.99

The Methods are consistent regardless of the number of availablecomparison units.

The probability of obtaining a post/pre-P.99 MSPE ratio as large asCalifornia�s is 0.026

synthetic control methods for comparative case

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