Econometrics
Instrumental variable approach:
Simultaneity bias and Example
Keisuke Kawata
IDEC
Simultaneity bias
Econometrics 2
• Not only omitted variables but also simultaneous relationship between treatments and outcome are
e.g.) The estimation of demand function:
• We ould like to esti ate the effe t of apple pri e o its’ de a d.
• Supposing the following demand function:
= + � + �
where is trading volume of apple, and � is price.
⇒If there are no omitted variables, we can get unbiased estimators? ⇒
Simultaneity bias
• From the economic theory, equilibrium demand and price are determined not only demand function but also supply function as
= + +
If is high⇒ ⇒From the supply function,
⇒ and are ⇒ = ′
Graphical example
Econometrics 4
↑
↑
• To estimate the demand function, we should find IV which have effects on price but not on
⇒We should find
IV
Ho to fi d the a epta le IV
• Practically problem is that what variable can be used as IV.
1. Studying the theory and special knowledge of your interest area. 2. Studying related literature.
E a ple of a epta le IV
Econometrics 6
Explained variable
Explanation variable
Source of problem
IV
Income Education School construction
Proximity to college
Newborn weight Smoking State tax on cigarettes
Crime Policy surveillance Simultaneity Electoral cycles
Conflict GDP Simultaneity Rainfall
Labor supply Fertility Simultaneity Gender composition of children
• The relevance and exogeneity of IV totally depend on social background. O itted
O itted
Clingingsmith et.al. (QJE 09)
Purpose: Estimating the impact of religious event on individual social opinion and behavior
Method: IV approa h: IV = Lotter out o e of isa Data: Individual survey in Pakistan.
Background
Econometrics 8
• E o o i s ha e supposed people’s so ial prefere e is ke fou datio of our society.
⇒ O e of i porta t deter i a ts is religio .
• Religious event may have strong impacts on our preference and world view.
Treatments: Hajj
Hajji: annual Islamic pilgrimage to Mecca (Saudi Arabia).
⇒Gathering so many male and female from various countries and schools, and interact ⇒May affect their opinion.
Problem to identification
Econometrics 10
Joint Hajj Behavior and Opinion (5 to 8 month after the Hajj)
Covariates
• I o e, Faith , fa il a kgrou d,…
IV: Hajj Lottery
• Due to overcrowding on the Hajj, Saudi Arabia has established quotas for the number of Hajj visas for each major Islamic country. ⇒For Pakistan, 150,000 visas in 2006.
• Large part of allo atio of isas is deter i ed lotter ⇒ Instrumental exogeneity.
⇒Authors use survey for applicants of Hajj lottery.
Problem to identification
Econometrics 12
Joint Hajj Behavior and Opinion (5 to 8 month after the Hajj)
Covariates
• I o e, Faith , fa il a kgrou d,… IV: Hajj Lotter
Empirical model
• Main model is
�� � = + ∗ � �� + �
� = + ∗ �� � + �
Balanced check
Econometrics 14
Religion
Tolerance
Econometrics 16
Gender
Well-Being
Econometrics 18
Engagement and Exposure
Werker et.al. (AEJ Macroeconomics 09)
Econometrics 20
Purpose: Estimating the impact of foreign aid on economic performance
Method: Fixed effect & Instrumental variable approach: IV = International oil price. Data: Unit(Country and year); Macro indicator of developing and non-Muslim oil- producing developing countries from World bank.
Problem to identification
Aid Macroeconomic Performance
Covariates
• Bad shock on economy
• Good shock on political stability
Main Idea
Econometrics 22
• For Muslim-developing countries, Gulf oil exporters (Saudi Arabia, United Arab Emirates, and Kuwait) are important donors of foreign aid.
⇒ A ou t of their aid depe d o their udgets ← affected by international price of OIL.
Instrumental relevance
Problem to identification
Econometrics 24
Aid Macroeconomic Performance
Covariates
• Bad shock on economy
• Good shock on political stability Oil Price
Main model
� � = + � ∗ � ∗ � ���� + ∗ � + � � + + �
� = + � ∗ � � + ∗ � + � � + + �
where � is country dummy, is year dummy.
Results in the first stage
Econometrics 26
Results in the first stage
Results in the second stage
Econometrics 28
