Financial Econometrics Chapter 8.Difference-in-difference Model 2 Jin Ling School of Finance,Zhongnan University of Economics and Law
Financial Econometrics Chapter 8. Difference-in-difference Model 2 Jin Ling School of Finance, Zhongnan University of Economics and Law 1
The DID Model The model specification: 因果效应 D】 yD.o Yoo T=0 T-1 2
• The model specification: 2 The DID Model
The DID Model 。The base model: Yit a+BTreati Postt +B2Treati+B3Postt+Eit Treat;is a dummy variable that equals 1 for treatment group,and is 0 otherwise. Postt is a dummy variable that equals I for period after treatment,and is 0 otherwise. 因果效应 Y Y T-0 7-l 3
• The base model: 𝑌𝑖,𝑡 = 𝛼 + 𝛽1𝑇𝑟𝑒𝑎𝑡𝑖 ∗ 𝑃𝑜𝑠𝑡𝑡 + 𝛽2𝑇𝑟𝑒𝑎𝑡𝑖 + 𝛽3𝑃𝑜𝑠𝑡𝑡 + 𝜀𝑖,𝑡 • 𝑇𝑟𝑒𝑎𝑡𝑖 is a dummy variable that equals 1 for treatment group, and is 0 otherwise. • 𝑃𝑜𝑠𝑡𝑡 is a dummy variable that equals 1 for period after treatment, and is 0 otherwise. 3 The DID Model
The DID Model ·The Parallel Trend Assumption(共同趋势假定或平行趋势假定)： (X E[Yis -YouI D.=1,X] =E[YIR I D:=1,X ]-E[Yo D;=1,X.] E[Y&D:=1,X2]-(E[Yo-1 D:=1,X2 +E[Ym-Ya-1|D,=0,X]} E[Yoit-You-1X D;=1]E[Yo-Yo-1Xi,D=0] 或写为： E[△Yoa|X。,D,=1]=E[△Yai Xa,D:=0]
• The Parallel Trend Assumption (共同趋势假定或平行趋势假定）: 4 The DID Model
The DID Model 。Another form: ECYo X ,D;=1]-E[YoXi,D;=0] =E[Yo-1X,D;=1]-E[YoiXD;=0] 或写为： B,(x)=B-1(x） 其中， B,(x)=E[Yoa|X。=x;D,=1]-E[Yoa{X。=x,D,=0]
• Another form: 5 The DID Model
The DID Model The problem in the applications for base DID model: The treatment period is different for different groups. The treatment group is not precise. The Parallel Trend Assumption is hard to satisfy. 6
• The problem in the applications for base DID model: • The treatment period is different for different groups. • The treatment group is not precise. • The Parallel Trend Assumption is hard to satisfy. 6 The DID Model
Outline ·Staggered DID Model DID Model without strict treatment group Difference-in-Difference-in-Difference Model
• Staggered DID Model • DID Model without strict treatment group • Difference-in-Difference-in-Difference Model 7 Outline
Staggered DID Model The prevalence of staggered DID model in all DID model: Use of DiD and Staggered DiD in Finance and Accounting:2000-2019. (1) (2) (3) DiD Staggered DiD Staggered All ( Journal of Finance 52 30 57.6% Journal of Financial Economics 163 85 52.1% Review of Financial Studies 138 75 54.3% Review of Finance 27 14 51.8% Journal of Financial and Quantitative Analysis 51 32 62.7% Finance 431 236 54.7% Journal of Accounting Research 52 24 46.1% Journal of Accounting and Economics 6 38 60.3% The Accounting Review 110 63 572% Review of Accounting Studies 47 28 59.5% Contemporary Accounting Research 4 43.9% Accounting 313 171 54.6% Finance and Accounting 744 407 54.7% 9
• The prevalence of staggered DID model in all DID model: 8 Staggered DID Model
Staggered DID Model The characteristic for treatment: A single treatment period;Static treatment effects. Yit a+BTreati Postt B2Treati+B3Postt+it A single treatment period;Dynamic treatment effects. Yit a+BTreatCit B2Treati+B3Postt +it Staggered timing of treatment;Static treatment effects.The model? Short-selling;Capital market liberalization. 9
• The characteristic for treatment: • A single treatment period; Static treatment effects. 𝑌𝑖,𝑡 = 𝛼 + 𝛽1𝑇𝑟𝑒𝑎𝑡𝑖 ∗ 𝑃𝑜𝑠𝑡𝑡 + 𝛽2𝑇𝑟𝑒𝑎𝑡𝑖 + 𝛽3𝑃𝑜𝑠𝑡𝑡 + 𝜀𝑖,𝑡 • A single treatment period; Dynamic treatment effects. 𝑌𝑖,𝑡 = 𝛼 + 𝛽1𝑇𝑟𝑒𝑎𝑡𝐶𝑖,𝑡 + 𝛽2𝑇𝑟𝑒𝑎𝑡𝑖 + 𝛽3𝑃𝑜𝑠𝑡𝑡 + 𝜀𝑖,𝑡 • Staggered timing of treatment; Static treatment effects. The model? • Short-selling; Capital market liberalization. 9 Staggered DID Model
Staggered DID Model The model specification: Yit a BiTreatit +8i+8t+8it Why we control for 6;(Individual-fixed effect)and ot(Time-fixed effect) If we control for Treati and Postt,what will happen? Is the staggered DID model more convincing?The Parallel Trend Assumption is more likely to satisfy? 10
• The model specification: 𝑌𝑖,𝑡 = 𝛼 + 𝛽1𝑇𝑟𝑒𝑎𝑡𝑖,𝑡 + 𝛿𝑖 + 𝛿𝑡 + 𝜀𝑖,𝑡 • Why we control for 𝛿𝑖 (Individual-fixed effect) and 𝛿𝑡 (Time-fixed effect) • If we control for 𝑇𝑟𝑒𝑎𝑡𝑖 and 𝑃𝑜𝑠𝑡𝑡 , what will happen? • Is the staggered DID model more convincing? The Parallel Trend Assumption is more likely to satisfy? 10 Staggered DID Model