. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction to Econometrics Lecture 1: Review of Probability Theory & Introduction to Causal Inference Zhaopeng Qu Business School,Nanjing University Sep. 18, 2020 Zhaopeng Qu (Nanjing University) Introduction to Econometrics Sep. 18, 2020 1 / 100
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Introduction to EconometricsLecture 1: Review of Probability Theory & Introduction to
A Short Review of Probability Theory Probabilities, the Sample Space and Random Variables
Probabilities and the Sample Space
Random Phenomena, Outcomes and ProbabilitiesThe mutually exclusive potential results of a random process are calledthe outcomes(结果).The probability of an outcome is the proportion of the time that theoutcome occurs in the long run.
The Sample Space and Random Event(样本空间与随机事件)The set of all possible outcomes is called the sample space.An event is a subset of the sample space, that is, an event is a set ofone or more outcomes.
A Short Review of Probability Theory Probabilities, the Sample Space and Random Variables
Probabilities and the Sample Space
Random Phenomena, Outcomes and ProbabilitiesThe mutually exclusive potential results of a random process are calledthe outcomes(结果).The probability of an outcome is the proportion of the time that theoutcome occurs in the long run.
The Sample Space and Random Event(样本空间与随机事件)The set of all possible outcomes is called the sample space.An event is a subset of the sample space, that is, an event is a set ofone or more outcomes.
A Short Review of Probability Theory Probabilities, the Sample Space and Random Variables
Probabilities and the Sample Space
Random Phenomena, Outcomes and ProbabilitiesThe mutually exclusive potential results of a random process are calledthe outcomes(结果).The probability of an outcome is the proportion of the time that theoutcome occurs in the long run.
The Sample Space and Random Event(样本空间与随机事件)The set of all possible outcomes is called the sample space.An event is a subset of the sample space, that is, an event is a set ofone or more outcomes.
A Short Review of Probability Theory Probabilities, the Sample Space and Random Variables
Probabilities and the Sample Space
Random Phenomena, Outcomes and ProbabilitiesThe mutually exclusive potential results of a random process are calledthe outcomes(结果).The probability of an outcome is the proportion of the time that theoutcome occurs in the long run.
The Sample Space and Random Event(样本空间与随机事件)The set of all possible outcomes is called the sample space.An event is a subset of the sample space, that is, an event is a set ofone or more outcomes.
A Short Review of Probability Theory Probabilities, the Sample Space and Random Variables
Probabilities and the Sample Space
Random Phenomena, Outcomes and ProbabilitiesThe mutually exclusive potential results of a random process are calledthe outcomes(结果).The probability of an outcome is the proportion of the time that theoutcome occurs in the long run.
The Sample Space and Random Event(样本空间与随机事件)The set of all possible outcomes is called the sample space.An event is a subset of the sample space, that is, an event is a set ofone or more outcomes.
A Short Review of Probability Theory Probabilities, the Sample Space and Random Variables
Probabilities and the Sample Space
Random Phenomena, Outcomes and ProbabilitiesThe mutually exclusive potential results of a random process are calledthe outcomes(结果).The probability of an outcome is the proportion of the time that theoutcome occurs in the long run.
The Sample Space and Random Event(样本空间与随机事件)The set of all possible outcomes is called the sample space.An event is a subset of the sample space, that is, an event is a set ofone or more outcomes.
A Short Review of Probability Theory Probabilities, the Sample Space and Random Variables
Random VariablesRandom Variables(R.V.)A random variable (r.v.) is a function that maps from the sample space ofan experiment to the real line or X : Ω R
A random variable is a numerical summary of a random outcome.They are numeric representation of uncertain events.(thus we can usemath!)Notation: R.V.s are usually denoted by upper case letters (e.g. X),particular realizations are denoted by the corresponding lowercaseletters (e.g. x = 3)
ExampleTossing a coin 5 times
but not a random variable because it‘s not numeric.X(ω) = number of heads in the five tosses. X(HTHTT) = 2
A Short Review of Probability Theory Probabilities, the Sample Space and Random Variables
Random VariablesRandom Variables(R.V.)A random variable (r.v.) is a function that maps from the sample space ofan experiment to the real line or X : Ω R
A random variable is a numerical summary of a random outcome.They are numeric representation of uncertain events.(thus we can usemath!)Notation: R.V.s are usually denoted by upper case letters (e.g. X),particular realizations are denoted by the corresponding lowercaseletters (e.g. x = 3)
ExampleTossing a coin 5 times
but not a random variable because it‘s not numeric.X(ω) = number of heads in the five tosses. X(HTHTT) = 2
A Short Review of Probability Theory Probabilities, the Sample Space and Random Variables
Random VariablesRandom Variables(R.V.)A random variable (r.v.) is a function that maps from the sample space ofan experiment to the real line or X : Ω R
A random variable is a numerical summary of a random outcome.They are numeric representation of uncertain events.(thus we can usemath!)Notation: R.V.s are usually denoted by upper case letters (e.g. X),particular realizations are denoted by the corresponding lowercaseletters (e.g. x = 3)
ExampleTossing a coin 5 times
but not a random variable because it‘s not numeric.X(ω) = number of heads in the five tosses. X(HTHTT) = 2
A Short Review of Probability Theory Probabilities, the Sample Space and Random Variables
Random VariablesRandom Variables(R.V.)A random variable (r.v.) is a function that maps from the sample space ofan experiment to the real line or X : Ω R
A random variable is a numerical summary of a random outcome.They are numeric representation of uncertain events.(thus we can usemath!)Notation: R.V.s are usually denoted by upper case letters (e.g. X),particular realizations are denoted by the corresponding lowercaseletters (e.g. x = 3)
ExampleTossing a coin 5 times
but not a random variable because it‘s not numeric.X(ω) = number of heads in the five tosses. X(HTHTT) = 2
A Short Review of Probability Theory Probabilities, the Sample Space and Random Variables
Random VariablesRandom Variables(R.V.)A random variable (r.v.) is a function that maps from the sample space ofan experiment to the real line or X : Ω R
A random variable is a numerical summary of a random outcome.They are numeric representation of uncertain events.(thus we can usemath!)Notation: R.V.s are usually denoted by upper case letters (e.g. X),particular realizations are denoted by the corresponding lowercaseletters (e.g. x = 3)
ExampleTossing a coin 5 times
but not a random variable because it‘s not numeric.X(ω) = number of heads in the five tosses. X(HTHTT) = 2
A Short Review of Probability Theory Probabilities, the Sample Space and Random Variables
Random VariablesRandom Variables(R.V.)A random variable (r.v.) is a function that maps from the sample space ofan experiment to the real line or X : Ω R
A random variable is a numerical summary of a random outcome.They are numeric representation of uncertain events.(thus we can usemath!)Notation: R.V.s are usually denoted by upper case letters (e.g. X),particular realizations are denoted by the corresponding lowercaseletters (e.g. x = 3)
ExampleTossing a coin 5 times
but not a random variable because it‘s not numeric.X(ω) = number of heads in the five tosses. X(HTHTT) = 2
A Short Review of Probability Theory Probabilities, the Sample Space and Random Variables
Probability DistributionsUncertainty over the value of ω. We’ll use probability to formalizethis uncertainty.The probability distribution of a r.v. gives the probability of all of thepossible values of the r.v.
PX(X = x) = P (ω ∈ Ω : X(ω) = x)
ExampleTossing two coins: let X be the number of heads.ω P(ω) X(ω)
A Short Review of Probability Theory Probabilities, the Sample Space and Random Variables
Probability DistributionsUncertainty over the value of ω. We’ll use probability to formalizethis uncertainty.The probability distribution of a r.v. gives the probability of all of thepossible values of the r.v.
PX(X = x) = P (ω ∈ Ω : X(ω) = x)
ExampleTossing two coins: let X be the number of heads.ω P(ω) X(ω)
A Short Review of Probability Theory Probabilities, the Sample Space and Random Variables
Probability DistributionsUncertainty over the value of ω. We’ll use probability to formalizethis uncertainty.The probability distribution of a r.v. gives the probability of all of thepossible values of the r.v.
PX(X = x) = P (ω ∈ Ω : X(ω) = x)
ExampleTossing two coins: let X be the number of heads.ω P(ω) X(ω)
A Short Review of Probability Theory Probabilities, the Sample Space and Random Variables
Distributional Functions of R.V.
It is cumbersome to derive the probabilities of X each time we needthem, so it is helpful to have a function that can give us theprobability of values or sets of values of X.
DefinitionThe cumulative distribution function or c.d.f of a r.v. X, denotedFX(x), is defined by
FX(x) ≡ PX(X ≤ x)
The c.d.f tells us the probability of a r.v. being less than some givenvalue.
A Short Review of Probability Theory Probabilities, the Sample Space and Random Variables
Distributional Functions of R.V.
It is cumbersome to derive the probabilities of X each time we needthem, so it is helpful to have a function that can give us theprobability of values or sets of values of X.
DefinitionThe cumulative distribution function or c.d.f of a r.v. X, denotedFX(x), is defined by
FX(x) ≡ PX(X ≤ x)
The c.d.f tells us the probability of a r.v. being less than some givenvalue.
A Short Review of Probability Theory Probabilities, the Sample Space and Random Variables
Distributional Functions of R.V.
It is cumbersome to derive the probabilities of X each time we needthem, so it is helpful to have a function that can give us theprobability of values or sets of values of X.
DefinitionThe cumulative distribution function or c.d.f of a r.v. X, denotedFX(x), is defined by
FX(x) ≡ PX(X ≤ x)
The c.d.f tells us the probability of a r.v. being less than some givenvalue.
A Short Review of Probability Theory Probabilities, the Sample Space and Random Variables
Probability Distribution of a Continuous R.V.
Probability density functionThe probability density function or p.d.f., for a continuous random variableX is the function that satisfies for any interval, B
A Short Review of Probability Theory Probabilities, the Sample Space and Random Variables
Probability Distribution of a Continuous R.V.Cumulative probability distributionjust as it is for a discrete random variable, except using p.d.f to calculatethe probability of x,
A Short Review of Probability Theory Expected Values, Mean, and Variance
Properties of Distributions
Probability distributions describe the uncertainty about r.v.s. Thecdf/pmf/pdf give us all the information about the distribution ofsome r.v., but we are quite often interested in some feature of thedistribution rather than the entire distribution.
What is the difference between these two density curves? How mightwe summarize this difference?
There are two simple indictors:1 Central tendency: where the center of the distribution is.
Mean/expectation (均值或期望)2 Spread: how spread out the distribution is around the center.
A Short Review of Probability Theory Expected Values, Mean, and Variance
Properties of Distributions
Probability distributions describe the uncertainty about r.v.s. Thecdf/pmf/pdf give us all the information about the distribution ofsome r.v., but we are quite often interested in some feature of thedistribution rather than the entire distribution.
What is the difference between these two density curves? How mightwe summarize this difference?
There are two simple indictors:1 Central tendency: where the center of the distribution is.
Mean/expectation (均值或期望)2 Spread: how spread out the distribution is around the center.
A Short Review of Probability Theory Expected Values, Mean, and Variance
Properties of Distributions
Probability distributions describe the uncertainty about r.v.s. Thecdf/pmf/pdf give us all the information about the distribution ofsome r.v., but we are quite often interested in some feature of thedistribution rather than the entire distribution.
What is the difference between these two density curves? How mightwe summarize this difference?
There are two simple indictors:1 Central tendency: where the center of the distribution is.
Mean/expectation (均值或期望)2 Spread: how spread out the distribution is around the center.
A Short Review of Probability Theory Expected Values, Mean, and Variance
Properties of Distributions
Probability distributions describe the uncertainty about r.v.s. Thecdf/pmf/pdf give us all the information about the distribution ofsome r.v., but we are quite often interested in some feature of thedistribution rather than the entire distribution.
What is the difference between these two density curves? How mightwe summarize this difference?
There are two simple indictors:1 Central tendency: where the center of the distribution is.
Mean/expectation (均值或期望)2 Spread: how spread out the distribution is around the center.
A Short Review of Probability Theory Expected Values, Mean, and Variance
Properties of Distributions
Probability distributions describe the uncertainty about r.v.s. Thecdf/pmf/pdf give us all the information about the distribution ofsome r.v., but we are quite often interested in some feature of thedistribution rather than the entire distribution.
What is the difference between these two density curves? How mightwe summarize this difference?
There are two simple indictors:1 Central tendency: where the center of the distribution is.
Mean/expectation (均值或期望)2 Spread: how spread out the distribution is around the center.
A Short Review of Probability Theory Expected Values, Mean, and Variance
Properties of Distributions
Probability distributions describe the uncertainty about r.v.s. Thecdf/pmf/pdf give us all the information about the distribution ofsome r.v., but we are quite often interested in some feature of thedistribution rather than the entire distribution.
What is the difference between these two density curves? How mightwe summarize this difference?
There are two simple indictors:1 Central tendency: where the center of the distribution is.
Mean/expectation (均值或期望)2 Spread: how spread out the distribution is around the center.
A Short Review of Probability Theory Expected Values, Mean, and Variance
Properties of Distributions
Probability distributions describe the uncertainty about r.v.s. Thecdf/pmf/pdf give us all the information about the distribution ofsome r.v., but we are quite often interested in some feature of thedistribution rather than the entire distribution.
What is the difference between these two density curves? How mightwe summarize this difference?
There are two simple indictors:1 Central tendency: where the center of the distribution is.
Mean/expectation (均值或期望)2 Spread: how spread out the distribution is around the center.
A Short Review of Probability Theory Expected Values, Mean, and Variance
The Expected Value of a Random Variable
The expected value of a random variable X, denoted E(X) or µx, isthe long-run average value of the random variable over many repeatedtrials or occurrences. it is a natural measure of central tendency.For a discrete r.v., X ∈ x1, x2, ..., xk
µX = E[X] =k∑
j=1
xjpj
it is computed as a weighted average of the value of r.v., where theweights are the probability of each value occurring.For a continuous r.v., X, use the integral
A Short Review of Probability Theory Expected Values, Mean, and Variance
The Expected Value of a Random Variable
The expected value of a random variable X, denoted E(X) or µx, isthe long-run average value of the random variable over many repeatedtrials or occurrences. it is a natural measure of central tendency.For a discrete r.v., X ∈ x1, x2, ..., xk
µX = E[X] =k∑
j=1
xjpj
it is computed as a weighted average of the value of r.v., where theweights are the probability of each value occurring.For a continuous r.v., X, use the integral
A Short Review of Probability Theory Expected Values, Mean, and Variance
The Expected Value of a Random Variable
The expected value of a random variable X, denoted E(X) or µx, isthe long-run average value of the random variable over many repeatedtrials or occurrences. it is a natural measure of central tendency.For a discrete r.v., X ∈ x1, x2, ..., xk
µX = E[X] =k∑
j=1
xjpj
it is computed as a weighted average of the value of r.v., where theweights are the probability of each value occurring.For a continuous r.v., X, use the integral
A Short Review of Probability Theory Multiple Random Variables
Why multiple random variables?
We are going to want to know what the relationships are betweenvariables.“The objective of science is the discovery of the relations”—Lord KelvinIn most cases,we often want to explore the relationship between twovariables in one study.
A Short Review of Probability Theory Multiple Random Variables
Why multiple random variables?
We are going to want to know what the relationships are betweenvariables.“The objective of science is the discovery of the relations”—Lord KelvinIn most cases,we often want to explore the relationship between twovariables in one study.
A Short Review of Probability Theory Multiple Random Variables
Why multiple random variables?
We are going to want to know what the relationships are betweenvariables.“The objective of science is the discovery of the relations”—Lord KelvinIn most cases,we often want to explore the relationship between twovariables in one study.
A Short Review of Probability Theory Multiple Random Variables
Joint Probability Distribution
Consider two discrete random variables X and Y with a jointprobability distribution,Then the joint probability mass function of (X,Y) describes theprobability of any pair of values:
A Short Review of Probability Theory Multiple Random Variables
Joint Probability Distribution
Consider two discrete random variables X and Y with a jointprobability distribution,Then the joint probability mass function of (X,Y) describes theprobability of any pair of values:
A Short Review of Probability Theory Multiple Random Variables
Joint Probability Density Function
Consider two continuous random variables X and Y with a jointprobability distribution, then the joint probability density functionof (X,Y) is a function, denoted as fX,Y(x, y) such that:
1 fX,Y(x, y) ≥ 02
∫ +∞−∞
∫ +∞−∞ fX,Y(x, y) dxdy = 1
3 P(a < X < b, c < Y < d) =∫ d
c∫ b
a fX,Y(x, y) dxdy, thus the probabilityin the a, b, c, darea.
A Short Review of Probability Theory Multiple Random Variables
Joint Probability Density Function
Consider two continuous random variables X and Y with a jointprobability distribution, then the joint probability density functionof (X,Y) is a function, denoted as fX,Y(x, y) such that:
1 fX,Y(x, y) ≥ 02
∫ +∞−∞
∫ +∞−∞ fX,Y(x, y) dxdy = 1
3 P(a < X < b, c < Y < d) =∫ d
c∫ b
a fX,Y(x, y) dxdy, thus the probabilityin the a, b, c, darea.
A Short Review of Probability Theory Multiple Random Variables
Joint Probability Density Function
Consider two continuous random variables X and Y with a jointprobability distribution, then the joint probability density functionof (X,Y) is a function, denoted as fX,Y(x, y) such that:
1 fX,Y(x, y) ≥ 02
∫ +∞−∞
∫ +∞−∞ fX,Y(x, y) dxdy = 1
3 P(a < X < b, c < Y < d) =∫ d
c∫ b
a fX,Y(x, y) dxdy, thus the probabilityin the a, b, c, darea.
A Short Review of Probability Theory Multiple Random Variables
Joint Probability Density Function
Consider two continuous random variables X and Y with a jointprobability distribution, then the joint probability density functionof (X,Y) is a function, denoted as fX,Y(x, y) such that:
1 fX,Y(x, y) ≥ 02
∫ +∞−∞
∫ +∞−∞ fX,Y(x, y) dxdy = 1
3 P(a < X < b, c < Y < d) =∫ d
c∫ b
a fX,Y(x, y) dxdy, thus the probabilityin the a, b, c, darea.
A Short Review of Probability Theory Properties of Joint Distributions
Independence
Independence
Two r.v.s X and Y are independent, which we denote it as X ⊥ Y, if for allsets A and B
P(X ∈ A,Y ∈ B) = P(X ∈ A)P(Y ∈ B)
Intuition: knowing the value of X gives us no information about thevalue of Y.IfX and Y are independent, then
Joint p.d.f is the product of marginal p.d.f, thus fX,Y(x, y) = fX(x)fY(y)Joint c.d.f is the product of marginal c.d.f, thus fX,Y(x, y) = fX(x)fY(y)functions of independent r.v.s are independent, thus h(X) ⊥ g(Y) forany functions h(·) and g(·).
A Short Review of Probability Theory Properties of Joint Distributions
Independence
Independence
Two r.v.s X and Y are independent, which we denote it as X ⊥ Y, if for allsets A and B
P(X ∈ A,Y ∈ B) = P(X ∈ A)P(Y ∈ B)
Intuition: knowing the value of X gives us no information about thevalue of Y.IfX and Y are independent, then
Joint p.d.f is the product of marginal p.d.f, thus fX,Y(x, y) = fX(x)fY(y)Joint c.d.f is the product of marginal c.d.f, thus fX,Y(x, y) = fX(x)fY(y)functions of independent r.v.s are independent, thus h(X) ⊥ g(Y) forany functions h(·) and g(·).
A Short Review of Probability Theory Properties of Joint Distributions
Independence
Independence
Two r.v.s X and Y are independent, which we denote it as X ⊥ Y, if for allsets A and B
P(X ∈ A,Y ∈ B) = P(X ∈ A)P(Y ∈ B)
Intuition: knowing the value of X gives us no information about thevalue of Y.IfX and Y are independent, then
Joint p.d.f is the product of marginal p.d.f, thus fX,Y(x, y) = fX(x)fY(y)Joint c.d.f is the product of marginal c.d.f, thus fX,Y(x, y) = fX(x)fY(y)functions of independent r.v.s are independent, thus h(X) ⊥ g(Y) forany functions h(·) and g(·).
A Short Review of Probability Theory Properties of Joint Distributions
Independence
Independence
Two r.v.s X and Y are independent, which we denote it as X ⊥ Y, if for allsets A and B
P(X ∈ A,Y ∈ B) = P(X ∈ A)P(Y ∈ B)
Intuition: knowing the value of X gives us no information about thevalue of Y.IfX and Y are independent, then
Joint p.d.f is the product of marginal p.d.f, thus fX,Y(x, y) = fX(x)fY(y)Joint c.d.f is the product of marginal c.d.f, thus fX,Y(x, y) = fX(x)fY(y)functions of independent r.v.s are independent, thus h(X) ⊥ g(Y) forany functions h(·) and g(·).
A Short Review of Probability Theory Properties of Joint Distributions
Independence
Independence
Two r.v.s X and Y are independent, which we denote it as X ⊥ Y, if for allsets A and B
P(X ∈ A,Y ∈ B) = P(X ∈ A)P(Y ∈ B)
Intuition: knowing the value of X gives us no information about thevalue of Y.IfX and Y are independent, then
Joint p.d.f is the product of marginal p.d.f, thus fX,Y(x, y) = fX(x)fY(y)Joint c.d.f is the product of marginal c.d.f, thus fX,Y(x, y) = fX(x)fY(y)functions of independent r.v.s are independent, thus h(X) ⊥ g(Y) forany functions h(·) and g(·).
A Short Review of Probability Theory Properties of Joint Distributions
Independence
Independence
Two r.v.s X and Y are independent, which we denote it as X ⊥ Y, if for allsets A and B
P(X ∈ A,Y ∈ B) = P(X ∈ A)P(Y ∈ B)
Intuition: knowing the value of X gives us no information about thevalue of Y.IfX and Y are independent, then
Joint p.d.f is the product of marginal p.d.f, thus fX,Y(x, y) = fX(x)fY(y)Joint c.d.f is the product of marginal c.d.f, thus fX,Y(x, y) = fX(x)fY(y)functions of independent r.v.s are independent, thus h(X) ⊥ g(Y) forany functions h(·) and g(·).
A Short Review of Probability Theory Conditional Distributions
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 is arandom 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”。
A Short Review of Probability Theory Conditional Distributions
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 is arandom 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”。
A Short Review of Probability Theory Conditional Distributions
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 is arandom 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”。
A Short Review of Probability Theory Famous Distributions
Families of distributions
There are several important families of distributions:The p.m.f./p.d.f. within the family has the same form, with parametersthat might vary across the family.The parameters determine the shape of the distribution
Statistical modeling in a nutshell: to study probability distributionfunction.
Assume the data, X1,X2, ...,Xn, are independent draws from a commondistribution fθ(x) within a family of distributions (normal, poisson, etc)Use a function of the observed data to estimate the value of theθ : θ(X1,X2, ...,Xn)
A Short Review of Probability Theory Famous Distributions
Families of distributions
There are several important families of distributions:The p.m.f./p.d.f. within the family has the same form, with parametersthat might vary across the family.The parameters determine the shape of the distribution
Statistical modeling in a nutshell: to study probability distributionfunction.
Assume the data, X1,X2, ...,Xn, are independent draws from a commondistribution fθ(x) within a family of distributions (normal, poisson, etc)Use a function of the observed data to estimate the value of theθ : θ(X1,X2, ...,Xn)
A Short Review of Probability Theory Famous Distributions
Families of distributions
There are several important families of distributions:The p.m.f./p.d.f. within the family has the same form, with parametersthat might vary across the family.The parameters determine the shape of the distribution
Statistical modeling in a nutshell: to study probability distributionfunction.
Assume the data, X1,X2, ...,Xn, are independent draws from a commondistribution fθ(x) within a family of distributions (normal, poisson, etc)Use a function of the observed data to estimate the value of theθ : θ(X1,X2, ...,Xn)
A Short Review of Probability Theory Famous Distributions
Families of distributions
There are several important families of distributions:The p.m.f./p.d.f. within the family has the same form, with parametersthat might vary across the family.The parameters determine the shape of the distribution
Statistical modeling in a nutshell: to study probability distributionfunction.
Assume the data, X1,X2, ...,Xn, are independent draws from a commondistribution fθ(x) within a family of distributions (normal, poisson, etc)Use a function of the observed data to estimate the value of theθ : θ(X1,X2, ...,Xn)
A Short Review of Probability Theory Famous Distributions
Families of distributions
There are several important families of distributions:The p.m.f./p.d.f. within the family has the same form, with parametersthat might vary across the family.The parameters determine the shape of the distribution
Statistical modeling in a nutshell: to study probability distributionfunction.
Assume the data, X1,X2, ...,Xn, are independent draws from a commondistribution fθ(x) within a family of distributions (normal, poisson, etc)Use a function of the observed data to estimate the value of theθ : θ(X1,X2, ...,Xn)
A Short Review of Probability Theory Famous Distributions
Families of distributions
There are several important families of distributions:The p.m.f./p.d.f. within the family has the same form, with parametersthat might vary across the family.The parameters determine the shape of the distribution
Statistical modeling in a nutshell: to study probability distributionfunction.
Assume the data, X1,X2, ...,Xn, are independent draws from a commondistribution fθ(x) within a family of distributions (normal, poisson, etc)Use a function of the observed data to estimate the value of theθ : θ(X1,X2, ...,Xn)
A Short Review of Probability Theory Famous Distributions
The Chi-Square DistributionLet Zi(i = 1, 2, ...,m) be independent random variables, eachdistributed as standard normal. Then a new random variable can bedefined as the sum of the squares of Zi :
X =
m∑i=1
Z2i
Then X has a chi-squared distribution with m degrees of freedomThe form of the distribution varies with the number of degrees offreedom, i.e. the number of standard normal random variables Ziincluded in X.The distribution has a long tail, or is skewed, to the right. As thedegrees of freedom m gets larger, however, the distribution becomesmore symmetric and “bell-shaped”. In fact, as m gets larger, thechi-square distribution converges to, and essentially becomes, anormal distribution.
A Short Review of Probability Theory Famous Distributions
The Chi-Square DistributionLet Zi(i = 1, 2, ...,m) be independent random variables, eachdistributed as standard normal. Then a new random variable can bedefined as the sum of the squares of Zi :
X =
m∑i=1
Z2i
Then X has a chi-squared distribution with m degrees of freedomThe form of the distribution varies with the number of degrees offreedom, i.e. the number of standard normal random variables Ziincluded in X.The distribution has a long tail, or is skewed, to the right. As thedegrees of freedom m gets larger, however, the distribution becomesmore symmetric and “bell-shaped”. In fact, as m gets larger, thechi-square distribution converges to, and essentially becomes, anormal distribution.
A Short Review of Probability Theory Famous Distributions
The Chi-Square DistributionLet Zi(i = 1, 2, ...,m) be independent random variables, eachdistributed as standard normal. Then a new random variable can bedefined as the sum of the squares of Zi :
X =
m∑i=1
Z2i
Then X has a chi-squared distribution with m degrees of freedomThe form of the distribution varies with the number of degrees offreedom, i.e. the number of standard normal random variables Ziincluded in X.The distribution has a long tail, or is skewed, to the right. As thedegrees of freedom m gets larger, however, the distribution becomesmore symmetric and “bell-shaped”. In fact, as m gets larger, thechi-square distribution converges to, and essentially becomes, anormal distribution.
A Short Review of Probability Theory Famous Distributions
The Student t Distribution
The Student t distribution can be obtained from a standard normaland a chi-square random variable.Let Z have a standard normal distribution, let X have a chi-squaredistribution with m degrees of freedom and assume that Z and X areindependent. Then the random variable
T =Z√X/n
has has a t-distribution with m degrees of freedom, denoted asT ∼ tn.The shape of the t-distribution is similar to that of a normaldistribution, except that the t-distribution has more probability massin the tails.As the degrees of freedom get large, the t-distribution approaches thestandard normal distribution.
A Short Review of Probability Theory Famous Distributions
The Student t Distribution
The Student t distribution can be obtained from a standard normaland a chi-square random variable.Let Z have a standard normal distribution, let X have a chi-squaredistribution with m degrees of freedom and assume that Z and X areindependent. Then the random variable
T =Z√X/n
has has a t-distribution with m degrees of freedom, denoted asT ∼ tn.The shape of the t-distribution is similar to that of a normaldistribution, except that the t-distribution has more probability massin the tails.As the degrees of freedom get large, the t-distribution approaches thestandard normal distribution.
A Short Review of Probability Theory Famous Distributions
The Student t Distribution
The Student t distribution can be obtained from a standard normaland a chi-square random variable.Let Z have a standard normal distribution, let X have a chi-squaredistribution with m degrees of freedom and assume that Z and X areindependent. Then the random variable
T =Z√X/n
has has a t-distribution with m degrees of freedom, denoted asT ∼ tn.The shape of the t-distribution is similar to that of a normaldistribution, except that the t-distribution has more probability massin the tails.As the degrees of freedom get large, the t-distribution approaches thestandard normal distribution.
A Short Review of Probability Theory Famous Distributions
The Student t Distribution
The Student t distribution can be obtained from a standard normaland a chi-square random variable.Let Z have a standard normal distribution, let X have a chi-squaredistribution with m degrees of freedom and assume that Z and X areindependent. Then the random variable
T =Z√X/n
has has a t-distribution with m degrees of freedom, denoted asT ∼ tn.The shape of the t-distribution is similar to that of a normaldistribution, except that the t-distribution has more probability massin the tails.As the degrees of freedom get large, the t-distribution approaches thestandard normal distribution.
Causal Inference in Social Science The Core of Empirical Studies: Causal Inference
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.So what is about now? Long skirt is resorting?
Causal Inference in Social Science The Core of Empirical Studies: Causal Inference
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.So what is about now? Long skirt is resorting?
Causal Inference in Social Science The Core of Empirical Studies: Causal Inference
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.So what is about now? Long skirt is resorting?
Causal Inference in Social Science The Core of Empirical Studies: Causal Inference
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.So what is about now? Long skirt is resorting?
Causal Inference in Social Science The Core of Empirical Studies: Causal Inference
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.So what is about now? Long skirt is resorting?
Causal Inference in Social Science The Core of Empirical Studies: Causal Inference
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.So what is about now? Long skirt is resorting?
Causal Inference in Social Science The Core of Empirical Studies: Causal Inference
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.So what is about now? Long skirt is resorting?
Causal Inference in Social Science The Core of Empirical Studies: Causal Inference
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.So what is about now? Long skirt is resorting?
Causal Inference in Social Science The Core of Empirical Studies: Causal Inference
Causality v.s. Forecasting
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)
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)
Causal Inference in Social Science The Core of Empirical Studies: Causal Inference
Causality v.s. Forecasting
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)
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)
Causal Inference in Social Science The Core of Empirical Studies: Causal Inference
Causality v.s. Forecasting
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)
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)
Causal Inference in Social Science The Core of Empirical Studies: Causal Inference
Causality v.s. Forecasting
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)
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)
Causal Inference in Social Science The Core of Empirical Studies: Causal Inference
Causality v.s. Forecasting
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)
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)
Causal Inference in Social Science The Core of Empirical Studies: Causal Inference
Causality v.s. Forecasting
Even though forecasting need not involve causal relationships,economic theory suggests patterns and relationships that mightbe useful for forecasting.
Econometric analysis(times series) allows us to quantifyhistorical relationships suggested by economic theory, tocheck whether those relationships have been stable overtime, to make quantitative forecasts about the future, and toassess the accuracy of those forecasts.
The biggest difference between machine learning andeconometrics(or causal inference).
Causal Inference in Social Science The Core of Empirical Studies: Causal Inference
Causality v.s. Forecasting
Even though forecasting need not involve causal relationships,economic theory suggests patterns and relationships that mightbe useful for forecasting.
Econometric analysis(times series) allows us to quantifyhistorical relationships suggested by economic theory, tocheck whether those relationships have been stable overtime, to make quantitative forecasts about the future, and toassess the accuracy of those forecasts.
The biggest difference between machine learning andeconometrics(or causal inference).
Causal Inference in Social Science The Core of Empirical Studies: Causal Inference
Causality v.s. Forecasting
Even though forecasting need not involve causal relationships,economic theory suggests patterns and relationships that mightbe useful for forecasting.
Econometric analysis(times series) allows us to quantifyhistorical relationships suggested by economic theory, tocheck whether those relationships have been stable overtime, to make quantitative forecasts about the future, and toassess the accuracy of those forecasts.
The biggest difference between machine learning andeconometrics(or causal inference).
Causal Inference in Social Science The Central Question of Causality
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.
Causal Inference in Social Science The Central Question of Causality
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.
Causal Inference in Social Science The Central Question of Causality
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.
Causal Inference in Social Science The Central Question of Causality
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.
Causal Inference in Social Science The Central Question of Causality
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.
Causal Inference in Social Science The Central Question of Causality
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,工作的工资)
Then make a difference. This is the right answer to ourquestion.
Difficulty in Identification: only one state can be observed
Causal Inference in Social Science The Central Question of Causality
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,工作的工资)
Then make a difference. This is the right answer to ourquestion.
Difficulty in Identification: only one state can be observed
Causal Inference in Social Science The Central Question of Causality
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,工作的工资)
Then make a difference. This is the right answer to ourquestion.
Difficulty in Identification: only one state can be observed
Causal Inference in Social Science The Central Question of Causality
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,工作的工资)
Then make a difference. This is the right answer to ourquestion.
Difficulty in Identification: only one state can be observed
Causal Inference in Social Science The Central Question of Causality
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,工作的工资)
Then make a difference. This is the right answer to ourquestion.
Difficulty in Identification: only one state can be observed
Causal Inference in Social Science The Central Question of Causality
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,工作的工资)
Then make a difference. This is the right answer to ourquestion.
Difficulty in Identification: only one state can be observed
Causal Inference in Social Science The Central Question of Causality
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,工作的工资)
Then make a difference. This is the right answer to ourquestion.
Difficulty in Identification: only one state can be observed
Causal Inference in Social Science Rubin Causal Model
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)
Causal Inference in Social Science Rubin Causal Model
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)
Causal Inference in Social Science Rubin Causal Model
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)
Causal Inference in Social Science Rubin Causal Model
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)
Causal Inference in Social Science Rubin Causal Model
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)
Causal Inference in Social Science Rubin Causal Model
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)
Causal Inference in Social Science Rubin Causal Model
Causal effect for an Individual
To know the difference between Y1i and Y0i, which can be said tobe the causal effect of going to college for individual i. (Do youagree 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)
Causal Inference in Social Science Rubin Causal Model
Causal effect for an Individual
To know the difference between Y1i and Y0i, which can be said tobe the causal effect of going to college for individual i. (Do youagree 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)
Causal Inference in Social Science Rubin Causal Model
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?
Causal Inference in Social Science Rubin Causal Model
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?
Causal Inference in Social Science Rubin Causal Model
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?
Causal Inference in Social Science Rubin Causal Model
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?
Causal Inference in Social Science Rubin Causal Model
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?
Causal Inference in Social Science Rubin Causal Model
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.
Causal Inference in Social Science Rubin Causal Model
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.
Causal Inference in Social Science Rubin Causal Model
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.
Causal Inference in Social Science Rubin Causal Model
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.
Causal Inference in Social Science Rubin Causal Model
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.
Causal Inference in Social Science Rubin Causal Model
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.
Causal Inference in Social Science Rubin Causal Model
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.
Causal Inference in Social Science Rubin Causal Model
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.
Causal Inference in Social Science Rubin Causal Model
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.
Causal Inference in Social Science Rubin Causal Model
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.
Causal Inference in Social Science Rubin Causal Model
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.
Causal Inference in Social Science Rubin Causal Model
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?
Causal Inference in Social Science Rubin Causal Model
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?
Causal Inference in Social Science Rubin Causal Model
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?
Causal Inference in Social Science Rubin Causal Model
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?
Causal Inference in Social Science Rubin Causal Model
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?
Causal Inference in Social Science Rubin Causal Model
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?
Causal Inference in Social Science Rubin Causal Model
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?
Causal Inference in Social Science Rubin Causal Model
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?
Experimental Design as a Benchmark RCTs Can Solve the Selection Bias
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 andthen 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
Experimental Design as a Benchmark RCTs Can Solve the Selection Bias
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 andthen 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
Experimental Design as a Benchmark RCTs Can Solve the Selection Bias
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 andthen 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
Experimental Design as a Benchmark RCTs Can Solve the Selection Bias
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 andthen 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
Experimental Design as a Benchmark RCTs Can Solve the Selection Bias
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 andthen 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
Experimental Design as a Benchmark RCTs Can Solve the Selection Bias
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 andthen 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
Experimental Design as a Benchmark RCTs Can Solve the Selection Bias
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 andthen 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
Experimental Design as a Benchmark RCTs Can Solve the Selection Bias
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
Experimental Design as a Benchmark RCTs Can Solve the Selection Bias
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
Experimental Design as a Benchmark RCTs Can Solve the Selection Bias
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
Experimental Design as a Benchmark RCTs Can Solve the Selection Bias
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
Experimental Design as a Benchmark RCTs Can Solve the Selection Bias
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
Experimental Design as a Benchmark RCTs Can Solve the Selection Bias
Our Benchmark: Randomized Experiments
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.
Experimental Design as a Benchmark RCTs Can Solve the Selection Bias
Our Benchmark: Randomized Experiments
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.
Experimental Design as a Benchmark RCTs Can Solve the Selection Bias
Our Benchmark: Randomized Experiments
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.
Experimental Design as a Benchmark RCTs Can Solve the Selection Bias
Our Benchmark: Randomized Experiments
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.
Experimental Design as a Benchmark Program Evaluation Econometrics
Program Evaluation Econometrics
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.
Experimental Design as a Benchmark Program Evaluation Econometrics
Program Evaluation Econometrics
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.
Experimental Design as a Benchmark Program Evaluation Econometrics
Program Evaluation Econometrics
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.
Experimental Design as a Benchmark Program Evaluation Econometrics
Program Evaluation Econometrics
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.
Experimental Design as a Benchmark Program Evaluation Econometrics
Program Evaluation Econometrics
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.
Experimental Design as a Benchmark Program Evaluation Econometrics
Program Evaluation Econometrics
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 Panel Data, Differences in Differences(双差分) ,Synthetic Control(合成控制法)
Experimental Design as a Benchmark Program Evaluation Econometrics
Program Evaluation Econometrics
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 Panel Data, Differences in Differences(双差分) ,Synthetic Control(合成控制法)
Experimental Design as a Benchmark Program Evaluation Econometrics
Program Evaluation Econometrics
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 Panel Data, Differences in Differences(双差分) ,Synthetic Control(合成控制法)
Experimental Design as a Benchmark Program Evaluation Econometrics
Program Evaluation Econometrics
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 Panel Data, Differences in Differences(双差分) ,Synthetic Control(合成控制法)
Experimental Design as a Benchmark Program Evaluation Econometrics
Program Evaluation Econometrics
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 Panel Data, Differences in Differences(双差分) ,Synthetic Control(合成控制法)
Experimental Design as a Benchmark Program Evaluation Econometrics
Program Evaluation Econometrics
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 Panel Data, Differences in Differences(双差分) ,Synthetic Control(合成控制法)
Experimental Design as a Benchmark Program Evaluation Econometrics
Program Evaluation Econometrics
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 Panel Data, Differences in Differences(双差分) ,Synthetic Control(合成控制法)
Experimental Design as a Benchmark Program Evaluation Econometrics
Program Evaluation Econometrics
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 Panel Data, Differences in Differences(双差分) ,Synthetic Control(合成控制法)
Experimental Design as a Benchmark Program Evaluation Econometrics
Program Evaluation Econometrics
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 Panel Data, Differences in Differences(双差分) ,Synthetic Control(合成控制法)
Experimental Design as a Benchmark Program Evaluation Econometrics
Program Evaluation Econometrics
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 Panel Data, Differences in Differences(双差分) ,Synthetic Control(合成控制法)
Experimental Design as a Benchmark Program Evaluation Econometrics
Program Evaluation Econometrics
These Furious Seven are the most basic and popular methods inapplied econometrics and so powerful that
even if you just master one, you may finish your empiricalpaper and get a good score.if you master several ones, you could have opportunity topublish your paper.If you master all of them, you might to teach appliedeconometrics class just as what I am doing now.
We will introduce essentials of these methods in the class asmany as possible. Let’s start our journey together.
Experimental Design as a Benchmark Program Evaluation Econometrics
Program Evaluation Econometrics
These Furious Seven are the most basic and popular methods inapplied econometrics and so powerful that
even if you just master one, you may finish your empiricalpaper and get a good score.if you master several ones, you could have opportunity topublish your paper.If you master all of them, you might to teach appliedeconometrics class just as what I am doing now.
We will introduce essentials of these methods in the class asmany as possible. Let’s start our journey together.
Experimental Design as a Benchmark Program Evaluation Econometrics
Program Evaluation Econometrics
These Furious Seven are the most basic and popular methods inapplied econometrics and so powerful that
even if you just master one, you may finish your empiricalpaper and get a good score.if you master several ones, you could have opportunity topublish your paper.If you master all of them, you might to teach appliedeconometrics class just as what I am doing now.
We will introduce essentials of these methods in the class asmany as possible. Let’s start our journey together.
Experimental Design as a Benchmark Program Evaluation Econometrics
Program Evaluation Econometrics
These Furious Seven are the most basic and popular methods inapplied econometrics and so powerful that
even if you just master one, you may finish your empiricalpaper and get a good score.if you master several ones, you could have opportunity topublish your paper.If you master all of them, you might to teach appliedeconometrics class just as what I am doing now.
We will introduce essentials of these methods in the class asmany as possible. Let’s start our journey together.
Experimental Design as a Benchmark Program Evaluation Econometrics
Program Evaluation Econometrics
These Furious Seven are the most basic and popular methods inapplied econometrics and so powerful that
even if you just master one, you may finish your empiricalpaper and get a good score.if you master several ones, you could have opportunity topublish your paper.If you master all of them, you might to teach appliedeconometrics class just as what I am doing now.
We will introduce essentials of these methods in the class asmany as possible. Let’s start our journey together.