SYNTHETIC CONTROL METHODS FOR COMPARATIVE CASE STUDIES: ESTIMATING THE EFFECT OF CALIFORNIA’S TOBACCO CONTROL PROGRAM Program 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

Universidad del Rosario (Institute)

Program Evaluation

October 2009

2 / 18

One Slide Presentation

Motivation California’s Background

Universidad del Rosario (Institute)

Program Evaluation

October 2009

2 / 18

One Slide Presentation

Motivation California’s Background Methodology

Universidad del Rosario (Institute)

Program Evaluation

October 2009

2 / 18

One Slide Presentation

Motivation California’s Background Methodology Implementation

Universidad del Rosario (Institute)

Program Evaluation

October 2009

2 / 18

One Slide Presentation

Motivation California’s Background Methodology Implementation Data and Sample

Universidad del Rosario (Institute)

Program Evaluation

October 2009

2 / 18

One Slide Presentation

Motivation California’s Background Methodology Implementation Data and Sample Estimation Steps

Universidad del Rosario (Institute)

Program Evaluation

October 2009

2 / 18

One Slide Presentation

Motivation California’s Background Methodology Implementation Data and Sample Estimation Steps Tables and Figures

Universidad del Rosario (Institute)

Program Evaluation

October 2009

2 / 18

Motivation

Justify the synthetic control approach

Universidad del Rosario (Institute)

Program Evaluation

October 2009

3 / 18

Motivation

Justify the synthetic control approach Study the e¤ects of California’s Proposition 99.

Universidad del Rosario (Institute)

Program Evaluation

October 2009

3 / 18

California’s Background

Washington 1893. Moral and Health Proposition 99. 1988 Earmarked: $100 million State, $20 million research

Universidad del Rosario (Institute)

Program Evaluation

October 2009

4 / 18

Methodology 1

Objective: Construct a Synthetic variable Framework: j + 1 Regions: 1 exposed to treatment and j controls T0 Number of pre-intervention periods and 1 T0 T YitN is the outcome that would be observed by region i in time t with no treatment YitI is outcome that would be observed by region i in time t with treatment

Universidad del Rosario (Institute)

Program Evaluation

October 2009

5 / 18

Methodology 2

A1: Intervention has no e¤ect on the outcome before the treatment period, so YitN = YitI

Universidad del Rosario (Institute)

Program Evaluation

October 2009

6 / 18

Methodology 2

A1: Intervention has no e¤ect on the outcome before the treatment period, so YitN = YitI After the treatment period YitI

Universidad del Rosario (Institute)

YitN = αit

Program Evaluation

October 2009

6 / 18

Methodology 2

A1: Intervention has no e¤ect on the outcome before the treatment period, so YitN = YitI After the treatment period YitI

YitN = αit

Dit is an indicator if i is exposed to the treatment

Universidad del Rosario (Institute)

Program Evaluation

October 2009

6 / 18

Methodology 2

A1: Intervention has no e¤ect on the outcome before the treatment period, so YitN = YitI After the treatment period YitI

YitN = αit

Dit is an indicator if i is exposed to the treatment Therefore we can write Yit = YitN + αit Dit

Universidad del Rosario (Institute)

Program Evaluation

October 2009

6 / 18

Methodology procedure

The aim is to estimate each αit for all t > T0 Hence Y1tI is observed, we need to estimate Y1tN to get α1t = Y1t

Universidad del Rosario (Institute)

Program Evaluation

N T1t

(1)

October 2009

7 / 18

Methodology procedure

The aim is to estimate each αit for all t > T0 Hence Y1tI is observed, we need to estimate Y1tN to get α1t = Y1t

N T1t

(1)

A2: YitN = δt + θ t Zi + λt µi + εit

Universidad del Rosario (Institute)

Program Evaluation

October 2009

7 / 18

Methodology procedure

The aim is to estimate each αit for all t > T0 Hence Y1tI is observed, we need to estimate Y1tN to get α1t = Y1t

N T1t

(1)

A2: YitN = δt + θ t Zi + λt µi + εit Covariates are Zi

Universidad del Rosario (Institute)

Program Evaluation

October 2009

7 / 18

Methodology procedure

The aim is to estimate each αit for all t > T0 Hence Y1tI is observed, we need to estimate Y1tN to get α1t = Y1t

N T1t

(1)

A2: YitN = δt + θ t Zi + λt µi + εit Covariates are Zi Unknown common factor is λt

Universidad del Rosario (Institute)

Program Evaluation

October 2009

7 / 18

Methodology procedure

The aim is to estimate each αit for all t > T0 Hence Y1tI is observed, we need to estimate Y1tN to get α1t = Y1t

N T1t

(1)

A2: YitN = δt + θ t Zi + λt µi + εit Covariates are Zi Unknown common factor is λt Varying factor loadings µi

Universidad del Rosario (Institute)

Program Evaluation

October 2009

7 / 18

Methodology procedure

The aim is to estimate each αit for all t > T0 Hence Y1tI is observed, we need to estimate Y1tN to get α1t = Y1t

N T1t

(1)

A2: YitN = δt + θ t Zi + λt µi + εit Covariates are Zi Unknown common factor is λt Varying factor loadings µi If λt is constant we get dif in dif

Universidad del Rosario (Institute)

Program Evaluation

October 2009

7 / 18

Methodology Procedure 2

Consider W = (w2 , ..., wj +1 )0 such that wj

Universidad del Rosario (Institute)

Program Evaluation

1 0 and ∑jj + = 2 wj = 1

October 2009

8 / 18

Methodology Procedure 2

Consider W = (w2 , ..., wj +1 )0 such that wj A3: we can chose w2 , ..., wj +1

Universidad del Rosario (Institute)

0

1 0 and ∑jj + = 2 wj = 1

such that

Program Evaluation

October 2009

8 / 18

Methodology Procedure 2

Consider W = (w2 , ..., wj +1 )0 such that wj A3: we can chose w2 , ..., wj +1

0

1 0 and ∑jj + = 2 wj = 1

such that

j +1

∑ wj YjN

= Y1N

(2)

= Z1N

(3)

j =2

j +1

∑ wj ZjN

j =2

Universidad del Rosario (Institute)

Program Evaluation

October 2009

8 / 18

Methodology Procedure 2

Consider W = (w2 , ..., wj +1 )0 such that wj A3: we can chose w2 , ..., wj +1

0

1 0 and ∑jj + = 2 wj = 1

such that

j +1

∑ wj YjN

= Y1N

(2)

= Z1N

(3)

j =2

j +1

∑ wj ZjN

j =2

This suggest that equation (1) would be j +1

αˆ 1t = Y1t

∑ wj YjN

(4)

j =2

Universidad del Rosario (Institute)

Program Evaluation

October 2009

8 / 18

Implementation

Let X1 be a vector of characteristics for the exposed region And X0 is a matrix that contains the same variables for the untreated regions The idea is obtain the vector W that minimize jjX1

Universidad del Rosario (Institute)

Program Evaluation

X0 W jj

October 2009

9 / 18

Implementation

Let X1 be a vector of characteristics for the exposed region And X0 is a matrix that contains the same variables for the untreated regions The idea is obtain the vector W that minimize jjX1 X0 W jj q In particular jjX1 X0 W jjv = (X1 X0 W )0 V (X1 X0 W )

Universidad del Rosario (Institute)

Program Evaluation

October 2009

9 / 18

Data and Sample 1

Variable of interest: Annual per capita cigarette consumption at the state level Panel data for the period 1970 – 2000 Proposition 99 (P.99) was passed in 1988 Synthetic California is meant to reproduce the consumption of cigarettes that would have been observed without the treatment in 1988 Discarding: Large-scale tobacco control Taxes by 50 cents

Universidad del Rosario (Institute)

Program Evaluation

October 2009

10 / 18

Data and Sample 2

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

Universidad del Rosario (Institute)

Program Evaluation

October 2009

11 / 18

Estimation Steps

1

Using the techniques described above the synthetic California (SC) is constructed SC is the mirror of the predictors of cigarette consumption in California before the treatment

2

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

3

A series of placebo studies are performed

Universidad del Rosario (Institute)

Program Evaluation

October 2009

12 / 18

Before Results

Universidad del Rosario (Institute)

Program Evaluation

October 2009

13 / 18

Trend in per capital sales: California Vs United States

Universidad del Rosario (Institute)

Program Evaluation

October 2009

14 / 18

Trend in per capital sales: California Vs Synthetic California

Universidad del Rosario (Institute)

Program Evaluation

October 2009

15 / 18

Per capital sales gap: California Vs 38 Control States

Universidad del Rosario (Institute)

Program Evaluation

October 2009

16 / 18

Per capital sales gap: California Vs 19 Control States with mean square prediction error less than two times California’s

Universidad del Rosario (Institute)

Program Evaluation

October 2009

17 / 18

Final Remarks

Cigarettes sales in California were about 26 packs lower than what they would have been in the absence of P.99 The Methods are consistent regardless of the number of available comparison units. The probability of obtaining a post/pre-P.99 MSPE ratio as large as California’s is 0.026

Universidad del Rosario (Institute)

Program Evaluation

October 2009

18 / 18