Instrumental Variables (2SLS) Lab

Explore bias from endogeneity and how a valid instrument recovers the causal effect. Adjust instrument strength, endogeneity, and noise; compare OLS vs. IV; and check the first-stage F-statistic for weak instruments.

Controls

True Effect β: 1.5

-13

Instrument Strength π₁: 0.9

01.6

Use Second Instrument (z2)

Endogeneity ρ (corr(u, ε)): 0.6

00.95

Sample Size n: 300

801000

σᵤ

σₑ

Quick Scenarios

OLS fit

IV (2SLS) fit

1.240

IV (2SLS) Estimate

True β = 1.50

1.988

OLS Estimate

Bias from corr(x, ε) when ρ > 0

297.33

First-Stage F

Rule-of-thumb: F ≥ 10

First Stage: x on z1

R² (first stage) = 0.499, F = 297.33

Stata Implementation

* 2SLS with robust SEs
clear all
use "your_data.dta", clear

* First stage diagnostics (x on instruments)
regress x z1, vce(robust)
estat firststage

* Second stage (2SLS)
ivregress 2sls y (x = z1), vce(robust)

* Over-ID test (only when >1 instrument)
* estat overid  // (needs >1 instrument)

When does IV work?

Two key conditions:

Relevance: instruments explain variation in x (check first-stage F).
Exogeneity: instruments affect y only through x, uncorrelated with ε.

Good practice:

Report first-stage results and F-statistic.
Use robust or clustered SEs; consider LIML for weak IVs.