Glossary

Correlation between a variable and its own past values, or between the errors of a time-series regression in different periods. It does not bias OLS coefficients by itself, but it makes classical standard errors wrong. HAC standard errors account for it.

The change in the predicted outcome from a small change in one regressor, averaged over the observations in the sample. In nonlinear models such as logit, the effect differs from person to person, and the average marginal effect summarises it in the outcome's own units.

A resampling method that estimates the sampling distribution of a statistic by recomputing it on many samples drawn with replacement from the data. Pairs and cluster bootstraps resample observations or whole clusters. A fixed random seed makes the result reproducible.

The difference between the outcome a unit would have with a treatment and the outcome it would have without it. Only one of the two is ever observed, so causal effects are estimated by comparing groups under assumptions. See correlation vs causation.

Standard errors that allow the errors to be correlated within groups, such as students in a school or repeated observations of the same firm, while assuming independence across groups. They need a reasonably large number of clusters. See the standard errors guide.

A number that multiplies a regressor in a model. In a linear regression, it measures how the average outcome changes when that regressor increases by one unit and the other regressors are held fixed.

A range computed from the data by a procedure that, across repeated samples, contains the true parameter a stated share of the time, such as 95%. It shows both the size of an estimate and its precision.

A variable that affects both the treatment and the outcome. If it is left out of the analysis, its influence is wrongly attributed to the treatment.

An estimator is consistent if it converges to the true parameter as the sample size grows. Consistency is a large-sample property; a consistent estimator can still be biased in small samples.

Observations on many units, such as people, firms or countries, at a single point in time.

The number of independent pieces of information left to estimate uncertainty after fitting a model. In OLS it is the number of observations minus the number of estimated coefficients. With clustered standard errors, the number of clusters minus one is often used.

A method that compares the change in outcomes for a group affected by a policy with the change for an unaffected group. It assumes the two groups would have followed parallel trends without the policy.

A variable that takes the value 1 when a condition holds and 0 otherwise, such as being female or living in a region. Its coefficient compares the group with the omitted reference group. Also called an indicator variable.

A regressor is endogenous when it is correlated with the error term, for example because of omitted variables, measurement error or simultaneity. OLS is then biased and inconsistent for the causal effect.

A regressor is exogenous when it is uncorrelated with the error term. Strict exogeneity in panel data requires this for the errors in every period.

A panel-data method that removes each unit's time-constant characteristics by comparing the unit only with itself over time. See what is panel data?

Heteroskedasticity and autocorrelation consistent standard errors, often called Newey–West standard errors. They are used for time series where errors are correlated across periods. They require a choice of kernel and lag length.

A test that compares two estimators, one consistent under weaker assumptions and one efficient under stronger ones. In panel data it is used to compare fixed and random effects.

The variance of the error term differs across observations, for example when the spread of wages grows with education. OLS coefficients remain unbiased, but classical standard errors are wrong. Heteroskedasticity-robust standard errors correct this.

A variable that affects the treatment but has no direct effect on the outcome and is unrelated to the unobserved factors that affect it. Instruments allow causal estimation when the treatment is endogenous.

Models for a binary outcome, such as employed or not. They describe how the probability of the outcome depends on the regressors, using the logistic or the normal distribution.

Strong correlation among regressors. It makes individual coefficients imprecise because the data cannot separate their effects. Perfect multicollinearity makes a coefficient impossible to estimate.

The hypothesis a test evaluates, often that a coefficient equals zero. A test asks whether the data are consistent with it.

The bias in a regression coefficient that arises when a variable that affects the outcome and is correlated with a regressor is left out of the model.

The estimator that chooses the coefficients of a linear regression to minimise the sum of squared residuals. Usually abbreviated OLS. See what is regression analysis?

The probability, computed as if the null hypothesis and the model were true, of a test statistic at least as extreme as the one observed. It is not the probability that the null hypothesis is true. See p-values in economics.

Observations on the same units over several periods, such as workers followed every year. Also called longitudinal data.

The share of the variance of the outcome that a regression's fitted values account for in the sample. A high R-squared does not make a coefficient causal, and a low one does not make it wrong.

A panel-data estimator that treats unit-specific effects as random and uncorrelated with the regressors. It is more efficient than fixed effects when that assumption holds and inconsistent when it fails.

A design that estimates an effect by comparing units just above and just below a threshold that determines treatment, such as a test-score cutoff for a scholarship.

The difference between an observed outcome and the value fitted by the model. Residuals are the sample counterpart of the unobserved errors.

Standard errors that remain valid when the error variance differs across observations. The HC0 to HC3 variants differ in their small-sample adjustments.

Bias that arises when the observed sample is not representative because inclusion depends on the outcome or on factors related to it. Wages, for example, are observed only for people who work.

An estimate of the standard deviation of an estimator across repeated samples. It measures the precision of a coefficient and is the basis of confidence intervals and tests.

A time series is stationary when its statistical properties, such as its mean and variance, do not change over time. Many time-series methods assume stationarity or transform the data to achieve it.

Observations on one unit over many periods, such as monthly inflation or daily exchange rates.

An instrumental-variables estimator. The first stage predicts the endogenous regressor from the instruments. The second stage regresses the outcome on that prediction. Usually abbreviated 2SLS.

A property of a time series in which shocks have permanent effects, as in a random walk. Regressions between unit-root series can show spurious relationships. Dickey–Fuller and similar tests check for a unit root.

Instruments that are only weakly related to the endogenous regressor. They make instrumental-variables estimates biased towards OLS and make conventional confidence intervals unreliable. First-stage F statistics help detect them.

A bootstrap method for clustered data that flips or rescales the residuals of whole clusters with random weights. It gives more reliable tests than conventional clustered standard errors when the number of clusters is small.