Applied Econometrics · Problem set 4

Immigration & house prices

From OLS to IV, in four pictures.

X = change in immigrant population / last year’s population.
Y = change in log house prices, approximately house-price growth.

01 · THE OLS PROBLEM

Another force can move both.

A local jobs boom can confound the immigration–house-price relationship. A local jobs boom points to both immigration and house-price growth. Immigration also points to house-price growth: this is the causal effect we want to learn, not an effect established by OLS.
A local jobs boom can attract immigrants and raise housing demand. OLS may mix immigration’s effect with the effect of the boom.

02 · OUR FIXED-EFFECTS OLS

Fixed effects help, but not with everything.

Controlling for area and year effects leaves changing local shocks uncontrolled. The double-ringed area and year node is controlled for. Its paths to immigration and house-price growth are shown in gray. A separate local jobs shock still points to both, leaving a possible source of confounding.
We account for persistent area differences and common year shocks. A changing local shock can still affect both X and Y.

OLS coefficient: −0.178. An adjusted association, not automatically causal.

reg Dlnhpyear imms i.year i.svar, vce(cluster svar)

03 · THE IV IDEA

Find a different source of immigration.

An ideal instrument affects immigration without sharing the unobserved local shock. Predicted immigration Z points to actual immigration X, which points to house-price growth Y. A local jobs shock still affects X and Y, but has no connection to Z. This is an assumed valid-IV structure, not proof of instrument validity.
Use the part of immigration driven by Z. Z must move X (relevance) and be unrelated to unobserved local shocks (independence).

Here, Z uses earlier immigrant settlement patterns and national inflows by origin, scaled by last year’s local population. Area and year effects remain in the model.

IV coefficient: −1.786. Causal interpretation requires the IV assumptions.

04 · THE EXCLUSION RESTRICTION

No route around immigration.

A path from the instrument to house prices that bypasses immigration violates exclusion. The valid chain is Z to immigration X to house-price growth Y. A red dashed arrow from Z directly to Y, marked with a cross, shows a forbidden additional path. It must be absent, whether the bypass is direct or runs through another variable.
Z must affect house prices only through immigration. If it also changes housing demand through another route, exclusion fails.

The crossed-out path must be absent in reality—not just left out of the regression. A strong first stage does not prove this.