Instrumental Variables

Instrumental Variables are called one of the usual econometric tricks with panel data with fixed effects, natural experiments ,differences-in-differences and the like. And I have once been told that the skill of finding good IVs is one of the most important skill that an empirical economist should master.  This post thus will gather the materials about IV.

(e.g. reliance on cross-sectional, OLS regressions is a poor way to study effects of the institutional environment on organizations ← not only because of endogeneity, the economist’s usual worry, but also because the proxies are too crude and the complex interactions are not easily captured → thus small-n, in-depth investigations ← above quantitative approaches might be used)


method of instrumental variables (IV) is used to estimate causal relationships when controlled experiments are not feasible or when a treatment is not successfully delivered to every unit in a randomized experiment. Intuitively, IV is used when an explanatory variable of interest is correlated with the error term. A valid instrument induces changes in the explanatory variable but has no independent effect on the dependent variable. (Wiki)

Recapitulating Instrumental Variables

A major complication that is emphasized in micro-econometrics [and political science] is the possibility of inconsistent parameter estimation caused by endogenous regressors. Then regression estimates measure only the magnitude of association, rather than the magnitude and direction of causation.

=> The instrumental variables estimator provides a way to nonetheless obtain consistent parameter estimates. This method, widely used in econometrics and rarely used elsewhere, is conceptually difficult and easily misused. (Cameron&Trivedi 2005, pp. 95)

Instrumental Variables in Cameron&Trivedi(2005)

An Introduction to Instrumental Variables

Instrumental Variables Regression


Chapter 7. Endogeneity and Instrumental Variables

This chapter covers endogeniety and the two-stage least squares estimation. Related materials can be found in Chapter 3 of Hayashi (2000), Chapter 4 of Cameron and Trivedi (2005), Chapter 9 of Hansen (2007), and Chapter 5 of Wooldrige (2010).

Sample Selection and Related Models

This chapter describes 3 models: the sample selection model, the treatment effect model, and the instrumental variables approach.

Heckman’s (1974, 1978, 1979) sample selection model was developed using an econometric framework for handling limited dependent variables. (e.g. estimating the average wage of women using data collected from a population of women in which housewives were excluded by self-selection→incidental truncation of a dependent variable)  => Maddala (1983) extended the sample selection perspective to the evaluation of treatment effectiveness, which offers practical solutions to various types of evaluation problems. => Although the instrumental variables approach is similar in some ways to the sample selection model, it is often conceptualized as a different method.

Stata example:

Instrumental Variables Short Guides to Microeconometrics Fall 2016 (Implementation in Stata 14)

Instrumental Variables Estimation Lecture Notes on Advanced Econometrics


Instrumental variables and the search for identification: From supply and demand to natural experiments J Angrist, AB Krueger – 2001

The method of instrumental variables was first used in the 1920s to estimate supply and demand elasticities, and later used to correct for measurement error in single-equation models. Recently, instrumental variables have been widely used to reduce bias from omitted variables in estimates of causal relationships such as the effect of schooling on earnings. Intuitively, instrumental variables methods use only a portion of the variability in key variables to estimate the relationships of interest; if the instruments are valid, that portion is unrelated to the omitted variables. We discuss the mechanics of instrumental variables, and the qualities that make for a good instrument, devoting particular attention to instruments that are derived from ‘natural experiments.’ A key feature of the natural experiments approach is the transparency and refutability of identifying assumptions. We also discuss the use of instrumental variables in randomized experiments.

The bad, the weak, and the ugly: Avoiding the pitfalls of instrumental variables estimation MP Murray – 2006

A note on the theme of too many instruments D Roodman – Oxford Bulletin of Economics and statistics, 2009

On the use of instrumental variables in accounting research DF Larcker, TO Rusticus – Journal of Accounting and Economics, 2010

Identification of causal effects using instrumental variables JD Angrist, GW Imbens, DB Rubin – Journal of the American Statistical Association, 1996

Empirical Case:

Instrumental variables estimates of the returns to schooling

What are some examples of really clever instrumental variables approaches in econometrics?

Acemoglu and Robinson have really turned the use of instrumental variables into an art:

Using the Colombian colonial royal road network to estimate the effect state capacity on development: Page on
Using access to the Atlantic to understand trade and development: AER (95,3) p. 546 – The Rise of Europe: Atlantic Trade, Institutional Change, and Economic Growth
Using the tragedy of the Holocaust to estimate the effect of middle class on development: Social Structure and Development: A Legacy of the Holocaust in Russia

Stephen Levitt, of the Freakonomics fame (and his co-authors), is also a master of clever IV:
Using prison overcrowding to estimate the effect of prison populations on crime: The Effect of Prison Population Size on Crime Rates: Evidence from Prison Overcrowding Litigation
Using Electoral Cycles in Police Hiring to Estimate the Effect of Police on Crime(though there is a controversy about the results: Page on
Using campaign spending to understand when incumbent politicians make an effort: The Impact of Federal Spending on House Election Outcomes

Other papers that use clever IVs include:
Using human wealth to test the permanent income hypothesis: Page on
Using dams to understand the relationship between agricultural productivity and vulnerability to weather: Dams (Duflo and Pande)
Using characteristics of indirect friends to estimate peer effects in networks: Identification of peer effects through social networks (Bramoulle et al.)
Using military draft to estimate economic returns to education: Estimating the Payoff to Schooling Using the Vietnam-Era Draft Lottery (Angrist & Krueger; of the “weak” September birthday instrument fame in another answer).
Using rivers to see whether school choice affect school quality: Does Competition Among Public Schools Benefit Students and Taxpayers? (Hoxby; this paper was also very controversial: Does Competition Among Public Schools Benefit Students and Taxpayers? A Comment on Hoxby (2000)).
Using judge assignment to understand the effect of prison on education and recidivism (Aizer & Doyle Jr., Juvenile Incarceration, Human Capital, and Future Crime: Evidence from Randomly Assigned Judges*)
Using droughts to tease out the effect of revolutionary insurgency on development in Mexico (Dell, Page on

Examples of instrumental-variables research in economics:

Author(s) Year* Instrument How it worked Conclusion Link
Joshua Angrist 1990 Vietnam draft lottery Randomly made some people more likely to serve in the military than others Being drafted into the Vietnam-era military reduced future earnings for white males N.A.
Joshua Angrist and Alan Krueger 1991 Season of a student’s birth Compulsory education laws forced people with later birthdates to stay in high school longer Extra time in high school positively affected future earnings N.A.
Steven Levitt 1997 Election cycles Politicians tend to hire more police before election day Additional police reduce violent crime Read the paper8
Caroline Hoxby 2000 Number of streams in metropolitan areas Led some metropolitan areas to have more school districts than others Greater competition among school disctricts leads to better academic results Read the paper9
Lakshmi Iyer 2004 Deaths of heirless rulers of Indian regions Made region more likely to fall under British rule Colonial administrators did a poorer job of providing public goods, such as schools and medical care, than did local rulers Read the paper10
James Feyrer and Bruce Sacerdote 2006 Wind patterns Blew European colonizers’ ships to some islands earlier than to others Earlier colonization had a positive effect on islands’ future wealth Read the paper11
Emily Oster 2006 Distance from the origin of the HIV virus in Africa Caused some Africans to confront the HIV virus earlier than others Wealthier Africans, and in general those who have reason to expect long lives, have cut back on risky sex in response to HIV Read the paper12
Morten Bennedsen, Kasper Meisner Nielsen, Francisco Pérez-González and Daniel Wolfenzon 2006 Gender of CEO’s first-born child, among Danish firms The presence of a first-born son makes the management of a family firm more likely to stay within the family Nepotism harms firms’ profitability Read the paper13
Ben Olken 2006 Signal strength in Indonesia People with better reception watch more TV and listen to more radio TV and radio have had a negative effect on social capital in Indonesia Read the paper14



Some helpful hints on using instruments:

How to think about instrumental variables when you get confused




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