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大数据时代的管理决策 - byelenin.github.io · a random variable, so CEF is also a random...
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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 大数据时代的管理决策 Lecture 2 : Econometrics, Machine Learning and Causal Inference Zhaopeng Qu Business School,Nanjing University March. 21, 2020 Zhaopeng Qu (Nanjing University) 大数据时代的管理决策 March. 21, 2020 1 / 53
Transcript of 大数据时代的管理决策 - byelenin.github.io · a random variable, so CEF is also a random...
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大数据时代的管理决策Lecture 2 : Econometrics, Machine Learning and Causal Inference
Zhaopeng Qu
Business School,Nanjing University
March. 21, 2020
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Outlines
1 Review to the last lecture
2 The Purpose of Econometrics and Machine Learning
3 Causal Inference in Social Science
4 Experimental Design as an Benchmark
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Review to the last lecture
Review to the last lecture
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Review to the last lecture
Introduction: Two Missions for Data Science
My View: In general, a series of scientific methods tosearching for economic logics from data.It could include two jobs
Making a causal inference,such asTesting economic theories.Estimating causal effects.Using data to give policy recommendations.
Forecasting or predicting future valuesMore and more prevalence in
other social science such as political science, sociology,law and education studies etcand business practice, like the hottest one: Data Science.
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Review to the last lecture
Conditional Expectation Function
Conditional ExpectationConditional on X, Y’s Conditional Expectation is
E(Y|X) =
{∑yfY|X(y|x) discrete Y∫
yfY|X(y|x)dy continuous Y
Conditional Expectation Function(CEF) is a function of x, since X isa random variable, so CEF is also a random variable.Intuition：期望就是求平均值，而条件期望就是“分组取平均”或“在... 条件下的均值”。
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Review to the last lecture
Properties of Conditional Expectation
1 E[c(X) | X] = c(X) for any function c(X).Thus if we know X, thenwe also know c(X).
eg. E[(X2 + 2X3) | X] =X2 + 2X3
if X and Y are independent r.v.s, then
E[Y | X = x] = E[Y]
if X and Y independent conditional on Z, thus X ⊥ Y | Z ,
E[Y | X = x,Z = z] = E[Y | Z = z]
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The Purpose of Econometrics and Machine Learning
The Purpose of Econometrics and Machine Learning
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The Purpose of Econometrics and Machine Learning
The Purposes of Econometrics(Machine Learning)
To prove or disprove a theory(a relations)“The objective of science is the discovery of the relations”—Lord Kelvin
In most cases,we often want to explore the relationship betweentwo variables in one study.
eg. education and wageThen, in simplicity, there are two relationships between twovariables.
Correlation(相关）V.S. Causality（因果）
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The Purpose of Econometrics and Machine Learning
A Classical Example: Hemline Index（裙边指数）
George Taylor, an economist in the United States, made up thephrase it in the 1920s. The phrase is derived from the idea thathemlines on skirts are shorter or longer depending on theeconomy.
Before 1930s, fashion women favored middle skirts most.In 1929, long skirts became popular. While the Dow Jones IndustrialIndex(DJII) plunged from about 400 to 200 and to 40 two years later.In 1960s, DJII rushed to 1000. At the same time, short skirts showedup.In 1970s, DJII fell to 590 and women began to wear long skirts again.In 1990s, mini skirt debuted, DJII rushed to 10000.In 2000s, bikini became a nice choice for girls, DJII was high up to13000.
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The Purpose of Econometrics and Machine Learning
Hemline Index:1920s-2010s
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The Purpose of Econometrics and Machine Learning
The Core of Empirical Studies: Causality v.s. Forecasting
Questions you would like to ask
1 What was the real relationship between two variables? TheAmerican economy depended on how long the skirts or the viceverse?
In other words, is the length of skirts the reason(at least oneof) why economy are good or bad?
2 Now the economy seems extremely bad. But if we could shortenthe length of skirts, could the economy boom again?
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The Purpose of Econometrics and Machine Learning
The Core of Empirical Studies: Explaining v.s. Forecasting
1 The first case is a typical “explanatory”question: Trying tofind the reason behind the phenomenon or calculate the effect ofa counterfactual intervention.
2 The second case is a typical“predictive” question: Tryingcalculating the effect of a hypothetical intervention.
Having a good prediction does work sometimes but does NOTmean understanding causality.While In most cases, if we could find real reasons to behind thephenomena, we could safely to predict the phenomenon by aproper intervention.
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The Purpose of Econometrics and Machine Learning
The Core of Empirical Studies: Causality v.s. Forecasting
Questions you would like to ask
1 What was the real relationship between two variables? TheAmerican economy depended on how long the skirts or the viceverse?
In other words, is the length of skirts the reason(at least oneof) why economy are good or bad?
2 Now the economy seems extremely bad. But if we could shortenthe length of skirts, could the economy boom again?
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The Purpose of Econometrics and Machine Learning
Machine Learning is mostly about prediction
Some Big Data researchers think causality is not important anymore in our times..“Look at correlations. Look at the ’what’ rather than the
’why’, because that is often good enough.”-ViktorMayer-Schonberger(2013)
Machine learning is a set of data-driven algorithms that usedata to predict or classify some variable Y as a function of othervariables X.
There are many machine learning algorithm. The bestmethods vary with the particular data applicationMachine learning is mostly about prediction.
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The Purpose of Econometrics and Machine Learning
Econometrics is mostly about causal inference
Most empirical economists think that correlation only tell us thesuperficial, even false relationship while causal relationship canprovide solid evidence to make interference to the realrelationship.
Today, empirical economists care more about the causalrelationship of their interests than ever before.“the most interesting and challenging research in social
science is about cause and effect”——Angrist andLavy(2008)
The biggest difference between machine learning andeconometrics(or causal inference)
Different goals: Causal inference v.s Prediction
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The Purpose of Econometrics and Machine Learning
Econometrics and Machine Learning
By a perspective of methodology, they share some commonstatistical methods.Machine learning use a lot of classical statistical method andseveral advanced econometric method(semi and non parametricalmethods)
Supervised learning: regression and classification,K-nearstneighbors(matching)Unsupervised learning: cluster analysis, principal components analysis.
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The Purpose of Econometrics and Machine Learning
Our Roadmap
Causal Inference and Random Controlled TrailOLS RegressionLogistical RegressionIntroduction to ML
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The Purpose of Econometrics and Machine Learning
An Amazing Journey
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Causal Inference in Social Science
Causal Inference in Social Science
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Causal Inference in Social Science
The Central Question of Causality(I)
A simple example: Do hospitals make people healthier? (Q:Dependent variable and Independent variable?)A naive solution: compare the health status of those who havebeen to the hospital to the health of those who have not.Two key questions are documented by the questionnaires（问卷）from The National Health Interview Survey(NHIS)
1“During the past 12 months, was the respondent a patient ina hospital overnight?”
2“Would you say your health in general is excellent, verygood, good ,fair and poor”and scale it from the number“1”to “5”respectively.
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Causal Inference in Social Science
The Central Question of Causality(II)Hospital v.s. No Hospital
Group Sample Size Mean Health Status Std.DevHospital 7774 2.79 0.014
No Hospital 90049 2.07 0.003
In favor of the non-hospitalized, WHY?Hospitals not only cure but also hurt people.
1 hospitals are full of other sick people who might infect us2 dangerous machines and chemicals that might hurt us.
More important : people having worse health tends to visithospitals.
This simple case exhibits that it is not easy to answer an causalquestion, so let us formalize an model to show where the problemis.
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Causal Inference in Social Science
The Central Question of Causality(III)
So A right way to answer a causal questions is construct acounterfactual world, thus “What If ....then”, Such asAn example: How much wage premium you can get from collegeattendance(上大学使工资增加多少？）
For any worker, we want to compareWage if he have a college degree (上了大学后的工资）Wage if he had not a college degree （假设没上大学，工作后的工资）
Then make a difference. This is the right answer to ourquestion.
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Causal Inference in Social Science
Difficulty in Identification
Others are the same asMilitary serviceMigrationRoad buildingJob trainingParty membershipPublic policiesOthers...
Difficulty: only one state can be observed
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Causal Inference in Social Science
Formalization: Rubin Causal Model
Treatment : Di is a dummy that indicate whether individual ireceive treatment or not
Di =
{1 if individual i received the treatment0 otherwise
Examples:Go to college or notHave health insurance or notJoin a training program or notMake an online-advertisement or not....
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Causal Inference in Social Science
Formalization: Treatment
Treatment : Di can be a multiple valued(continues) variable
Di = s
Examples:Schooling yearsNumber of ChildrenNumber of advertisementsMoney Supply
For simplicity, we assume treatment variable Di is just a dummy.
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Causal Inference in Social Science
Formalization: Potential Outcomes
A potential outcome is the outcome that would be realized if theindividual received a specific value of the treatment.
Annual earnings if attending to collegeAnnual earnings if not attending to college
For each individual, we has two potential outcomes,Y1i and Y0i,one for each value of the treatment
Y1i : Potential outcome for an individual i with treatment.Y0i : Potential outcome for an individual i with treatment.
Potential Outcomes ={
Y1i if Di = 1
Y0i if Di = 0
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Causal Inference in Social Science
Stable Unit Treatment Value Assumption (SUTVA)
Observed outcomes are realized as
Yi = Y1iDi + Y0i(1− Di)
Implies that potential outcomes for an individual i are unaffectedby the treatment status of other individual jIndividual j ’ s potential outcomes are only affected by his/herown treatment.Rules out possible treatment effect from other individuals(spillover effect/externality)
ContagionDisplacement
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Causal Inference in Social Science
Causal effect for an Individual
To know the difference between Y1i and Y0i, which can be saidto be the causal effect of going to college for individual i. (Doyou agree with it?)
DefinitionCausal inference is the process of estimating a comparison ofcounterfactuals under different treatment conditions on the same setof units. It also call Individual Treatment Effect(ICE)
δi = Y1i − Y0i
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Causal Inference in Social Science
Formalization: Estimate ICE
Due to unobserved counterfactual outcome, we need to makestrong assumptions to estimate ICE.
Rule out that the ICE differs across individuals (“heterogeneity effect”)
Knowing individual effect is not our final goal. As a socialscientist, we would like more to know the Average effect as asocial pattern.So it make us focus on the average wage for a group of people.
How can we get the average wage premium for collegeattendance?
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Causal Inference in Social Science
Conditional Expectation:
Expectation: We usually use E[Yi] (the expectation of avariable Yi) to denote population average of Yi
Suppose we have a population with N individuals
E[Yi] =1
NΣNi=1Yi
Conditional Expectation:The average wage for those who attend college: E[Yi|Di = 1]The average wage for those who did not attend college: E[Yi|Di = 0]
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Causal Inference in Social Science
Average Causal Effects
Average Treatment Effect (ATE)
αATE = E[δi] = E[Y1i − Y0i]
It is average of ICEs over the population.
Average treatment effect on the treated(ATT)
αATT = E[δi|Di = 1] = E[Y1i − Y0i|Di = 1]
Average of ICEs over the treated population
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Causal Inference in Social Science
Fundamental Problem of Causal Inference
We can never directly observe causal effects (ICE, ATE or ATT)Because we can never observe both potential outcomes (Y0i,Y1i)for any individual.We need to compare potential outcomes, but we only haveobserved outcomesSo by this view, causal inference is a missing data problem.
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Causal Inference in Social Science
Fundamental Problem of Causal Inference
Imagine a population with 4 people
i Yi1 Y0i Yi Di Yi1 − Y0i
Tom 3 ? 3 1 ?Jerry 2 ? 2 1 ?
Scarlett ? 1 1 0 ?Nicole ? 1 1 0 ?
What is Individual causal effect (ICE) of attending college forTom? for Nicole?
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Causal Inference in Social Science
Individual Causal Effect
Suppose we can observe counterfactual outcomes
i Yi1 Y0i Yi Di Yi1 − Y0i
Tom 3 2 3 1 1Jerry 2 1 2 1 1
Scarlett 1 1 1 0 0Nicole 1 1 1 0 0
The ICE for TomδTom = 3− 2 = 11
The ICE for NicoleδNicole = 1− 1 = 0
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Causal Inference in Social Science
Average Treatment Effect(ATE)
Missing data problem also arises when we estimate ATE
i Yi1 Y0i Yi Di Yi1 − Y0i
Tom 3 ? 3 1 ?Jerry 2 ? 2 1 ?
Scarlett ? 1 1 0 ?Nicole ? 1 1 0 ?E[Y1i] ?E[Y0i] ?
E[Y1i − Y0i] ?
What is the effect of attending college on average wage ofpopulation(ATE)
αATE = E[δi] = E[Y1i − Y0i]
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Causal Inference in Social Science
Average Treatment Effect(ATE)Missing data problem also arises when we estimate ATE
i Yi1 Y0i Yi Di Yi1 − Y0i
Tom 3 2 3 1 1Jerry 2 1 2 1 1
Scarlett 1 1 1 0 0Nicole 1 1 1 0 0E[Y1i]
3+2+1+14 = 1.75
E[Y0i]2+1+1+1
4 = 1.25
E[Y1i − Y0i] 0.5
What is the effect of attending college on average wage of thepopulation(ATE)
αATE = E[δi] = E[Y1i − Y0i] =1 + 1 + 0 + 0
4= 0.5
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Causal Inference in Social Science
Average Treatment Effect on the Treated(ATT)
Missing data problem arises when we estimate ATT
i Yi1 Y0i Yi Di Yi1 − Y0i
Tom 3 ? 3 1 ?Jerry 2 ? 2 1 ?
Scarlett ? 1 1 0 ?Nicole ? 1 1 0 ?
E[Y1i|Di = 1] ?E[Y0i|Di = 1] ?
E[Y1i − Y0i|Di = 1] ?
What is the effect of attending college on average wage for thosewho attend college(ATT)
αATE = E[δi] = E[Y1i − Y0i|Di = 1]
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Causal Inference in Social Science
Average Treatment Effect on the Treated(ATT)Missing data problem also arises when we estimate ATE
i Yi1 Y0i Yi Di Yi1 − Y0i
Tom 3 2 3 1 1Jerry 2 1 2 1 1
Scarlett 1 1 1 0 0Nicole 1 1 1 0 0
E[Y1i|Di = 1] 3+22 = 2.5
E[Y0i|Di = 1] 2+12 = 1.5
E[Y1i − Y0i|Di = 1] 1
The effect of attending college on average wage for those whoattend college(ATT)
αATE = E[Y1i − Y0i|Di = 1] =1 + 1
2= 1
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Causal Inference in Social Science
Observed Association and Selection Bias
Causality is defined by potential outcomes, not by realized(observed) outcomes.In fact, we can not observe all potential outcomes .Therefore, wecan not estimate the above causal effects without furtherassumptions.By using observed data, we can only establish association(correlation), which is the observed difference in averageoutcome between those getting treatment and those not gettingtreatment.
αcorr = E[Y1i|Di = 1]− E[Y0i|Di = 0]
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Causal Inference in Social Science
College vs Non-College Wage Differentials:
Comparing the average wage in labor market who went to collegeand did not go.
College vs Non-College Wage Differentials:
=E[Y1i|Di = 1]− E[Y0i|Di = 0]
={E[Y1i|Di = 1]−E[Y0i|Di = 1]}+ {E[Y0i|Di = 1]− E[Y0i|Di = 0]}
Question 1: Which one defines the causal effect of collegeattendance?
Zhaopeng Qu (Nanjing University) 大数据时代的管理决策 March. 21, 2020 40 / 53
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Causal Inference in Social Science
Formalization: Rubin Causal Model
Selection Bias(SB) implies the potential outcomes oftreatment and control groups are different even if both groupsreceive the same treatment
E[Y0i|Di = 1]− E[Y0i|Di = 0]
Question 2: Selection Bias is positive or negative in the case?This means two groups could be quite different in otherdimensions: other things are not equal.Observed association is neither necessary nor sufficient forcausality.
Zhaopeng Qu (Nanjing University) 大数据时代的管理决策 March. 21, 2020 41 / 53
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Causal Inference in Social Science
Observed Association:College vs Non-College WageDifferentials:
Missing data problem also arises when we estimate ATE
i Yi1 Y0i Yi Di Yi1 − Y0i
Tom 3 ? 3 1 ?Jerry 2 ? 2 1 ?
Scarlett ? 1 1 0 ?Nicole ? 1 1 0 ?
E[Y1i|Di = 1] 3+22 = 2.5
E[Y0i|Di = 0] 1+12 = 1
E[Y1i|Di = 1]− E[Y0i|Di = 0] 1.5
The Observed Association of attending college on average wage
αcorr = 2.5− 1 = 1.5
Zhaopeng Qu (Nanjing University) 大数据时代的管理决策 March. 21, 2020 42 / 53
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Causal Inference in Social Science
Observed Association and Selection Bias
But we are interested in causal effect, here is ATT
αATT = E[δi|Di = 1] = E[Y1i − Y0i|Di = 1] = 1
So the selection bias
E[Y0i|Di = 1]− E[Y0i|Di = 0] = 0.5
The Selection Bias is positive: Those who attend college couldbe more intelligent so they can earn more even if they did notattend college.
Zhaopeng Qu (Nanjing University) 大数据时代的管理决策 March. 21, 2020 43 / 53
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Causal Inference in Social Science
Causal Effect and Identification Strategy
Many Many Other examplesthe effect of job training program on worker’s earningsthe effect of class size on students performance....
Identification strategy tells us what we can learn about a causaleffect from the available data.The main goal of identification strategy is to eliminate theselection bias.Identification depends on assumptions, not on estimationstrategies.“What’s your identification strategy?”= what are theassumptions that allow you to claim you’ve estimated a causaleffect?
Zhaopeng Qu (Nanjing University) 大数据时代的管理决策 March. 21, 2020 44 / 53
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Experimental Design as an Benchmark
Experimental Design as an Benchmark
Zhaopeng Qu (Nanjing University) 大数据时代的管理决策 March. 21, 2020 45 / 53
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Experimental Design as an Benchmark
Randomized Controlled Trial
A randomized controlled trial (RCT) is a form of investigation inwhich units of observation (e.g. individuals, households, schools,states) are randomly assigned to treatment and control groups.RCT has two features that can help us hold “other things equal”and then eliminates selection bias
Random assign treatment:Randomly assign treatment (such as a coin flip) ensures that everyobservation has the same probability of being assigned to the treatmentgroup.Therefore, the probability of receiving treatment is unrelated to anyother confounding factors.
Sufficient large sampleLarge sample size can ensure that the group differences in individualcharacteristics wash out
Zhaopeng Qu (Nanjing University) 大数据时代的管理决策 March. 21, 2020 46 / 53
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Experimental Design as an Benchmark
How to Solves the Selection Problem
Random assignment of treatment Di can eliminates selectionbias. It means that the treated group is a random sample fromthe population.Being a random sample, we know that those included in thesample are the same, on average, as those not included in thesample on any measure.Mathematically ,it makes Di independent of potentialoutcomes, thus
Di ⊥ (Y0i,Y1i)
Independence: Two variables are said to be independent ifknowing the outcome of one provides no useful information aboutthe outcome of the other.
Knowing outcome of Di(0, 1) does not help us understand whatpotential outcomes of (Y0i,Y1i) will be
Zhaopeng Qu (Nanjing University) 大数据时代的管理决策 March. 21, 2020 47 / 53
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Experimental Design as an Benchmark
Random Assignment Solves the Selection Problem
So we haveE[Y0i|Di = 1] = E[Y0i|Di = 0]
Thus the Selection Bias equals to ZERO.Then ATT equals Observed Association because the
E[Y1i|Di = 1]− E[Y0i|Di = 0] = E[Y1i|Di = 1]− E[Y0i|Di = 1]
=E[Y1i − Y0i|Di = 1]
No matter what assumptions we make about the distribution ofY , we can always estimate it with the difference in means.
Zhaopeng Qu (Nanjing University) 大数据时代的管理决策 March. 21, 2020 48 / 53
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Experimental Design as an Benchmark
Our Benchmark: Randomized Experimental Methods
Think of causal effects in terms of comparing counterfactuals orpotential outcomes. However, we can never observe bothcounterfactuals —fundamental problem of causal inference.To construct the counterfactuals, we could use two broadcategories of empirical strategies.
Random Controlled Trials/Experiments:it can eliminates selection bias which is the mostimportant bias arises in empirical research. If we couldobserve the counterfactual directly, then there is noevaluation problem, just simply difference.
Zhaopeng Qu (Nanjing University) 大数据时代的管理决策 March. 21, 2020 49 / 53
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Experimental Design as an Benchmark
Our Benchmark: Randomized Experimental Methods
We can generate the data of our interest by controllingexperiments just as physical scientists or biologists do. But tooobviously, we face more difficult and controversy situation thanthose in any other sciences.The various approaches using naturally-occurring data providealternative methods of constructing the proper counterfactual
EconometricsCongratulation! We are working and studying in a more tough andintractable area than others including most science knowledge.
We should take the randomized experimental methods as ourbenchmark when we do empirical research whatever the methodswe apply.
Zhaopeng Qu (Nanjing University) 大数据时代的管理决策 March. 21, 2020 50 / 53
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Experimental Design as an Benchmark
Program Evaluation Econometrics(项目评估计量经济学）
Question: How to do empirical research scientifically when wecan not do experiments? It means that we always have selectionbias in our data, or in term of “endogeneity”.Answer: Build a reasonable counterfactual world by naturallyoccurring data to find a proper control group is the core ofeconometrical methods.Here you Furious Seven Weapons in Applied Econometrics(七种盖世武器）
1 Random Controlled Trials(RCT)2 OLS(回归）3 Matching（匹配）4 Decomposition（分解）5 Instrumental Variable（工具变量）6 Regression Discontinuity（断点回归）7 Differences in Differences（双差分) and Synthetic Control （合成控制法）
Zhaopeng Qu (Nanjing University) 大数据时代的管理决策 March. 21, 2020 51 / 53
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Experimental Design as an Benchmark
Program Evaluation Econometrics(项目评估计量经济学）
Question: How to do empirical research scientifically when wecan not do experiments? It means that we always have selectionbias in our data, or in term of “endogeneity”.
Answer: Build a reasonable counterfactual world by naturallyoccurring data to find a proper control group is the core ofeconometrical methods.Here you Furious Seven Weapons in AppliedEconometrics(七种盖世武器）
1 Random Controlled Trials(RCT)2 OLS(回归）3 Matching（匹配）4 Decomposition（分解）5 Instrumental Variable（工具变量）6 Regression Discontinuity（断点回归）7 Differences in Differences（双差分) and Synthetic Control （合成控制法）
Zhaopeng Qu (Nanjing University) 大数据时代的管理决策 March. 21, 2020 52 / 53
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Experimental Design as an Benchmark
Q & A
Question?
Zhaopeng Qu (Nanjing University) 大数据时代的管理决策 March. 21, 2020 53 / 53
