Machine Learning and Applied Econometrics

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Wendy Long
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1 Machine Learning and Applied Econometrics Double Machine Learning for Treatment and Causal Effects Machine Learning and Econometrics 1

2 Double Machine Learning for Treatment and Causal Effects This presentation is in part based on: Alexandre Belloni, Victor Chernozhukov, and Christian Hansen, High-Dimensional Methods and Inference on Structural and Treatment Effects, Journal of Economic Perspectives 28:2 (29-50), Spring Victor Chernozhukov, Denis Chetverikov, Mert Demirer, Esther Duflo, Christian Hansen, and Whitney Newey, Double Machine Learning for Treatment and Causal Parameters, CEMMAP Working Paper, Machine Learning and Econometrics 2

3 The Model Treatment Effects Y f ( D, Z) u, E( u Z, D) 0 D h( Z) v, E( v Z) 0 D is the target variable of interest or the treatment variable (typically, D=0 or 1) Z is the set of exogenous covariates or control variables (instruments, confounders), may be high-dimensional. Partial Linear Model: f ( D, Z) D g( Z) Machine Learning and Econometrics 3

4 Treatment Effects Average Treatment Effect (ATE) E f (1, Z) f (0, Z) Average Treatment Effect for the Treated (ATT) E f (1, Z) f (0, Z) D 1 Machine Learning and Econometrics 4

5 Treatment Effects Based on Partial Linear Model, ATE = Frisch-Waugh-Lovel Theorem: uˆ Y ˆ D gˆ( Z) u Y g( Z) v D h( Z) Machine Learning : OLS: u v ˆ g( Z) and h( Z) This estimate is biased and inefficient! Machine Learning and Econometrics 5

6 Treatment Effects Based on Partial Linear Model, ATE = Sample Splitting {1,,N} = Set of all observations I 1 = main sample = set of observation numbers, of size n, is used to estimate θ; e.g., n=n/2. I 2 = auxilliary sample = set of observations, of size πn = N n, is used to estimate g; I 1 and I 2 form a random partition of the set {1,...,N} Cross Fitting on {I 1,I 2 } and {I 2,I 1 } Machine Learning and Econometrics 6

7 Treatment Effects Cross Fitting on {I 1,I 0 } and {I 0,I 1 } Machine Learning: g ( Z) and h ( Z) on ( I, I ) g ( Z) and h ( Z) on ( I, I ) OLS: 2 ( I1, I2) ( I2, I1) is N consistent and approximately centered normal (Chernozhukov, et.al., 2017) Machine Learning and Econometrics 7

8 Example: Wine Sales in Vancouver BC Price Elasticity Estimation Total Weekly Sales of Imported and Domestic Table Wine in Vancouver, BC, Canada from week ending April 4, 2009 to week ending May 28, 2011 (372,228 sales) Irregularly-spaced time series Data Source: American Association of Wine Economists Machine Learning and Econometrics 8

9 Example: Wine Sales in Vancouver BC Price Elasticity Estimation 372,228 observations of 17 variables in an Excel spreadsheet: SKU #, Product Long Name, Store Category Major Name, Store Category Sub Name, Store Category Minor Name, Current Display Price, Bottled Location Code, Bottle Location Desc, Domestic/Import Indicator, VQA Indicator, Product Sweetness Code, Product Sweetness Desc, Alcohol Percent, Julian Week No, Week Ending Date, Total Weekly Selling Unit, Total Weekly Volume Litre Machine Learning and Econometrics 9

10 Example: Wine Sales in Vancouver BC Price Elasticity Estimation Y = log of quantity (total weekly selling unit in bottles) D = log of price (current display price in Canadian $) Z = { What = Store Category Minor Name (Red/White), Where = Store Category Sub Name (Countries), Loc = Bottled Location Code, Alc = Alcohol Percent, Age = Julian Week No, } = Price Elasticity Y D g( Z) u, E( u Z, D) 0 D m( Z) v, E( v Z) 0 Machine Learning and Econometrics 10

Uniform Post Selection Inference for LAD Regression and Other Z-estimation problems. ArXiv: Alexandre Belloni (Duke) + Kengo Kato (Tokyo)

Uniform Post Selection Inference for LAD Regression and Other Z-estimation problems. ArXiv: 1304.0282 Victor MIT, Economics + Center for Statistics Co-authors: Alexandre Belloni (Duke) + Kengo Kato (Tokyo)