Instrumental Variables Regression (1) Flashcards

1
Q

goal of instrumental variables

A
  • to know the causal relationship between the response variable Y and X
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2
Q

consistency

A

an estimator is consistent if it get closer to the true parameter values with higher probability as the sample size increases

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3
Q

potential sources of endogeneity

A
  • Omited varaible bias from a variable that is correlated with X but is unobserved ( so cannot be included in the regression) and for which there are inequate control variables
  • simultaneous causality bias ( X causes Y, Y causes X)
  • Errors-in-variables bias ( X is measured with error)
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4
Q

if you have omitted variables

what type problem you have?

possible solution

A
  • endogeneity problem

- solution: instrumental variables (IV)

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5
Q

Symbol for instrumental variable

A

variable Z

IV regression require Z

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6
Q

conditions for a valid instrument

A
  • Relevanve

- Exogeneity

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7
Q

how to use IV Z?

Two-stage Least Square Estimation

A

Stage 1: Run OLS regression of the suspected variable X on z and constant. (then use X^)

Stage 2: Run OLS regression of Y on X^ and a constant

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8
Q

The idea of IV estimator

A

IV regression breaks X into two parts:

  • a part that might be correlated with u
  • a part that is not
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9
Q

Endogenous variable

A

Is one that is CORRELATED with u

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10
Q

Exogenous variable

A

Is one that is UNCORRELATED with u

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11
Q

Terminology of Endogenous

A
  • Literally means “determined within the system”

but the definition is too narrow cuz it may fall on IV bias errors in variables bias

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12
Q

Large sample inference

A
  • In large sample, the sampling distribution of the TSLS estimator is normal
  • The idea behind the large-sample normal distribution of the TSLS estimator is that it involves an average of mean zero i.i.d random variables
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