Questions: Introduction to Econometrics

Question 1

A researcher observes that cities with more police officers have higher crime rates, and concludes that policing causes crime. What is the most likely econometric problem?

• A. Omitted variable bias — a third variable causes both police presence and crime independently
• B. Reverse causation — high crime rates cause governments to deploy more police
• C. Measurement error — crime statistics are underreported in cities with more police
• D. Simultaneity bias — both police and crime are driven by city population size

Answer: (B)

This is reverse causation: police are deployed in response to crime, so crime drives police presence, not the other way around. A simple regression of crime on police conflates causal direction. Omitted variable bias would require a third variable causing both independently (option A is plausible but secondary here). The key diagnostic question is always: does X cause Y, Y cause X, or both — and the deployment pattern strongly suggests Y → X.

Question 2

A student regresses quantity demanded on price using market data collected over time. The positive correlation she observes means the demand curve slopes upward.

• A. True — if quantity increases with price in the data, the demand curve must be upward-sloping
• B. False — the positive correlation reflects simultaneous demand shifts, not movement along the demand curve; it estimates neither slope
• C. False — the student should use a logarithmic regression, which would reveal the true negative slope
• D. True — market data averages across supply and demand movements, giving an unbiased estimate of the demand slope

Answer: (B)

Market data reflects equilibrium price-quantity pairs shaped by both supply and demand shifts simultaneously. Summer ice cream data shows high prices and high quantities — both driven by demand, not a supply curve. Running a regression on these points estimates neither the demand slope nor the supply slope; it estimates the path of equilibrium points across shifting curves. This is the simultaneity problem: the variables are jointly determined, and simple regression cannot disentangle the causal structure.

Question 3

Omitted variable bias occurs whenever a variable that affects the outcome Y is left out of the regression model.

• T. True
• F. False

Answer: False

Omitted variable bias requires the omitted variable to be correlated with BOTH the included regressor X and the outcome Y. If it correlates with Y but not X, it increases the error variance but doesn't bias the coefficient on X. Only when both conditions hold does the omitted variable's effect 'bleed into' the X coefficient. This distinction is critical: not every missing control creates bias — only those correlated with the regressors you're already including.

Question 4

Econometrics is best understood as statistics applied to economic data, with the same goals and methods as other applied statistics.

• T. True
• F. False

Answer: False

Econometrics differs from general applied statistics in its preoccupation with causal identification from observational data. Economic variables are jointly determined — prices and quantities respond to the same underlying forces — so correlation analysis cannot establish causal effects. Econometrics develops specific tools (instrumental variables, natural experiments, regression discontinuity) to find variation that is as-good-as-random, enabling causal inference where experiments are typically impossible. The economic model driving variable selection is as important as the estimation technique.

Question 5

What does it mean for an econometric strategy to 'identify' a causal effect, and why is identification the central challenge of the discipline?

Model answer: Identification means finding a source of variation in the regressor X that is plausibly unrelated to the error term — variation that behaves as-if-randomly assigned, even though it wasn't. This matters because economic variables are jointly determined: prices, wages, and quantities all respond to the same underlying forces, making endogeneity the default rather than the exception. Without a valid identification strategy, regression coefficients measure correlations, not causal effects. Identification strategies include natural experiments, instrumental variables, and regression discontinuity designs.

The core challenge is that in observational data, people and firms make choices that reflect their unobservable characteristics — ability, ambition, risk tolerance. These unobservables correlate with both the treatment (education, job training) and the outcome (wages), biasing naive estimates. Identification is the art of finding variation that is genuinely exogenous: variation in X that happened 'by accident,' unrelated to anything else affecting Y.