Extra Lecture: Instrumental Variables

Olaf J. De GrootNOTE: The content of this lecture is not part of the exam. It is meant to make you UNDERSTAND the concepts of Instrumental Variables… Do NOT study the content, just use it to make sure you understand the concepts

Outline

• Quick discussion of OLS Estimation• Examples of in- and outputs from OLS• Instrumental Variables Estimation:

– Why– How– Problems

• Examples:– Tabellini– Other Examples

OLS Estimations 1

A B

X YC

D

OLS Estimations 1

Capital Labour

Conflict GDPExport

demandGDP0

OLS Estimations 2

• Next step is to operationalize the expected linkage into a testable regression:

Y=β0+ β1*K+ β2*L+ β3*K+ β4*GDP0+ β5*NX + β6*conf+ε

Or, to put it more generally:Y= β0+ β*X+ β6*conf+ε

Goal of the estimation is to fit the β’s in such a way so that the residual is minimized.

OLS: Typical inputCountry GDP(%) K(%) L(%) NX($) GDP0($p) Conf(bin)

A 4 10 1 100 10,000 0

B 3 7 2 50 13,000 0

C 2 9 0 -50 8,000 1

D 5 6 3 -10 3,000 0

E -1 -5 -1 -20 12,000 1

F 0 2 0 30 19,000 0

G 2 8 -1 20 9,000 0

H 6 15 3 50 6,000 0

I 7 11 3 40 7,000 0

J 3 6 2 -40 10,000 0

K 1 4 0 -20 15,000 0

L 0 4 -1 0 9,000 1

OLS: Typical Outputvariable Estimated Beta Standard errors P-value

constant 0.825 0.125 0.001

K 0.012 0.006 0.052

L 1.201 0.485 0.023

Ln(GDP0) 1.524 0.357 0.008

NX 0.102 0.097 0.857

conflict 2.103 1.002 0.046

Adjusted R-Squared 0.523

Export Demand and Capital growth are not significant. That is, it is impossible the reject the null hypothesis that there is no effect. GDP0, on the other hand, it is certain with more than 99% that there is an effect.

Instrumental Variables: Why

• Sometimes the linkages you want to research are not as clear-cut.

• Ex.1: X Y (endogeneity)• Ex.2: X? Y (measurement)• Ex.3: Omitted variables• Solution: IV estimation:

ZX Y

Instrumental Variables: How

• There are two ways in which you can employ IV-estimation:– Easy way, by replacing X with Z, but requires strict

conditions from the data:1) Instrument has to be truely exogenous2) Z has to correlate with X very strongly• Not often feasible

– Harder way, by using a 2-stage Least Squares (2SLS estimation), which we are going to discuss today.

Instrumental Variables: 2SLS

• Obviously, 2SLS uses 2 stages.• In first stage, the influence resulting from Y->X

is excluded and a new X is calculated (X-hat) whose value merely includes the value as a result of a change in Z

• During the second stage, X-hat is regressed on Y.

Instrumental Variables: graphical 1

Z A

X Y

B

Instrumental Variables: graphical 2

Stage 1Z A

X Y

BX= λ0+λ1*A+λ2*B+λ3*Z+μ, then estimate X-hat

Instrumental Variables: graphical 3

Stage 2Z A

X Y

BY= β0+ β1*A+ β2*B+ β3*X-hat+ ε

Instrumental Variables: Problems

• Biggest problem is finding a good IV.• Good IVs meet the following criteria:

– Strong causal effect from Z on X.– No relation between Z and Y in either direction– Preferably no strong effects of Z on A or B

• Researcher using IV spends most time explaining why that particular IV is appropriate.

Instrumental Variables: Easy Example

You want to know influence of operating cost on distance driven (by car). Problem of endogeneity, so use fuel price as instrument

1)regress: (oper.costs)=λ+θ(fuel price)+μ2)Calculate (oper.costs)=λ+θ(fuel price)3)Regress (distance)=α+β(oper.costs)+ε

Instrumental Variables: Example

• Tabellini’s paper on the effect of culture on economic growth is one example.

• Question: Does Culture influence economic development– Culture is measured with World Values Survey– Culture: trust, respect, confidence, etc– Economic development also influences culture (in

low-growth environment, maybe less confident)

Tabellini: graphical 1

Historical determinants Urbanization rate

Culture GDP growth

Education

Background idea: Tabellini

Historical HistoricalDeterminants Culture

Current CurrentDeterminants Culture

Current Development

Other IV examples 1

• Somebody wants to research the influence of economic growth on Probability of civil war.

• But, GDP Pr(conflict)• So, want to use IV, but which one?

• Looking at Africa, they realise that African agricultural economies are dependent on Rainfall. There is no relationship between rainfall and conflict, so this is a proper IV.

• Miguel et al., 2004, JPE

Other IV examples 2

• Somebody wants to research the influence of information technology on corruption in USA.

• But, IT corruption• So, want to use IV, but which one?

Idea: lightning voter information

IT usage costscorruption

IT usage WP, Andersen et al, 2008

Other IV examples 3

• Somebody wants to know what the influence of education on later wage is.

• But: education abilitywage

So, are you measuring return to educ or ability?

• Several authors have used wars as IV that influences education level, independent of ability. E.g. Large EU wage database and use dummy for people born in Germany during 1930s: born(G,1930s) Educ wage

Other IV examples 4

• Somebody wants to study the wage penalty for mothers pay at return to labour market.

• You have: working women sample, wages, dummy for women with 6-12 month old baby, controls. BUT, motherhood may be endogenous.

• You look at gender of previous children. Pr(second child) increases if first was girl.

So: (firstborn=girl) secondbornwage

Other IV examples 5

• Somebody wants to study the influence of Aid on Economic Growth. But there is reverse causality, so an exogenous effect on aid is to be found as IV

• One idea is to look at natural disasters, which are always good exogenous variables.

• Natural disaster also has direct effect, so use disaster in OTHER nations as IV

disaster in –X aid for –X aid for X

growth in X

Conclusion

• Instrumental Variables are good way to deal with endogeneity.

• When reading IV-paper, think:– Is the IV truely exogenous to the final result?– Is the correlation between the IV and X good

enough.

• Be very creative in finding ways to use IVs in your estimations.