Econometrics & Economic Data
CollegeEvery model in this course made claims — that demand slopes down, that MPC is around 0.8, that minimum wages sometimes raise employment. How do economists actually check claims like these against real-world data? This closing chapter introduces econometrics: the statistical toolkit that turns economic theory into testable, falsifiable science.
At a glanceOrdinary least squares
The workhorse tool is linear regression: model an outcome Y as a linear function of a variable X plus an error term, Y = β0 + β1X + ε. Ordinary least squares (OLS) chooses the intercept and slope that minimise the sum of squared residuals, giving:
β̂₁ estimates how much Y changes, on average, for a one-unit increase in X. R² measures the share of the variation in Y explained by X (0 = none, 1 = all). Because β̂₁ is estimated from a limited sample, we attach a standard error and test whether it is statistically distinguishable from zero (a t-test), reporting a p-value — the probability of seeing a coefficient this large by chance alone if the true effect were zero.
Correlation is not causation
A regression coefficient measures association, not automatically causation. Three classic traps: omitted variable bias (a third factor drives both X and Y — ice-cream sales and drowning deaths are correlated only because both rise with summer heat); reverse causality (does X cause Y, or Y cause X — does police spending cause crime, or crime cause police spending?); and measurement error. In a multiple regression, each coefficient can be read ceteris paribus — holding the other included variables constant — but only if nothing important was left out.
Modern applied economics leans heavily on strategies that mimic a true experiment: randomised controlled trials (assign treatment randomly, as in medicine); natural experiments and instrumental variables (find a source of variation in X that is unrelated to other causes of Y — e.g. Card & Krueger's comparison of neighbouring US states after a minimum-wage rise in only one, a difference-in-differences design); and regression discontinuity (compare observations just above and just below an arbitrary policy cutoff). These are the tools that let economists move from "X and Y move together" to "X causes Y."
Worked example: estimating the marginal propensity to consume
Five households report income (X, $000) and consumption (Y, $000):
| Income (X) | Consumption (Y) |
|---|---|
| 10 | 8 |
| 20 | 15 |
| 30 | 20 |
| 40 | 26 |
| 50 | 31 |
Q1A regression finds ice-cream sales strongly predict drowning deaths. Should we ban ice cream?
No — this is the textbook case of omitted variable bias. Hot weather independently raises both ice-cream sales and swimming (hence drownings). Once you control for temperature or season, the direct relationship between ice cream and drowning likely vanishes. The regression coefficient was picking up a confound, not a causal channel.
Q2What two conditions must a valid instrumental variable satisfy?
Relevance: the instrument must be meaningfully correlated with the endogenous variable X you're trying to instrument for. Exogeneity: the instrument must affect Y only through its effect on X, not through any other channel. Finding a variable satisfying both is hard — which is why credible instruments are prized and heavily scrutinised in applied economics.
Q3Why do economists like difference-in-differences designs, such as Card & Krueger's minimum-wage study?
Comparing a "treated" region before and after a policy change, against a similar "control" region that didn't get the policy, differences out both the effect of trends common to both places (so it isn't confused with the policy) and fixed differences between the two places. What's left over — the difference in the change — is a much more credible estimate of the policy's causal effect than a simple before/after comparison in the treated region alone.
Q4Can a low R² regression still be scientifically useful?
Yes. R² measures how much of the outcome's variation the model explains — but many valid causal effects (especially in human behaviour) are real, statistically significant, and policy-relevant even when other unmeasured factors dominate the outcome's overall variation. A precise, well-identified estimate of a modest R² relationship (e.g. how much an extra year of schooling raises wages) can be far more useful than a high-R² regression built on invalid, correlational assumptions.
How the ideas connect
Every key idea in this chapter, branching from the core concept — use it to see the whole picture at a glance.
The key facts, visualised
Worked problems, step by step
Follow each solution line by line, then try to reproduce it on paper before moving on.
Example 1A regression gives consumption = 100 + 0.57 x income. If income rises $1000, how much does predicted consumption rise?
- The coefficient 0.57 is the marginal effect per $1 of income.
- Change = 0.57 x 1000.
- That equals $570.
Example 2A coefficient is 2.0 with a standard error of 1.0. Roughly, is it statistically significant?
- t-statistic = coefficient / standard error = 2.0 / 1.0 = 2.0.
- A t around 2 corresponds to a p-value near 0.05.
- So it is roughly significant at the 5% level.
Now you try
Work each one out first, then tap to reveal the worked answer.