Ordinary Least Squares: chooses coefficients that minimise the sum of squared residuals. Unbiased and BLUE under the classical assumptions. Lec 1

Framework for testing claims about parameters via a test statistic, a null/alternative, and a significance level (5% throughout). Lec 1

Joint-significance test comparing nested models; built from the residual sum of squares of the restricted vs unrestricted model. Large $F$ (small $p$) ⇒ reject that the dropped regressors are jointly zero. PP1 Q1a

Gauss–Markov conditions: linearity, random sampling, no perfect collinearity, zero conditional mean $E[u\mid X]=0$, and homoskedasticity. Under them OLS is BLUE. Lec 2

Error variance depends on $x$ (Var$(u\mid x)$ not constant); violates A5, so classical SEs are wrong (usually too small). Lec 2

Heteroskedasticity-consistent ("sandwich"/HC) standard errors; give correct inference when errors are heteroskedastic — mandatory for the LPM. Lec 2

An estimator converges in probability to the true value as $n\to\infty$. Weaker than unbiasedness. Lec 5

A regressor is correlated with the error, Cov$(x,u)\neq0$, making OLS biased and inconsistent. Sources: omitted variables, simultaneity, measurement error. Lec 4

Bias from leaving out a variable that both affects $y$ and correlates with an included regressor; the omitted effect loads onto the included coefficient. PS4

Estimating the effect of a cause — the counterfactual change in $y$ from changing $x$ — as opposed to mere correlation. Lec 1

Directed acyclic graph (DAG) of assumed causal relationships; used to spot confounders and backdoor paths. PS2

Binary 0/1 indicator for a category; its coefficient is the mean difference versus the omitted base group. Lec 2

Study of strategic decision-making; here the backdrop for binary-choice experiments. Lec 2

Proposer offers a split, responder accepts/rejects; rejecting "unfair" offers violates pure self-interest. The motivating LPM example (Andersen et al. 2011). Lec 2

Difference between a unit's outcome with vs without treatment, $(Y\mid T=1)-(Y\mid T=0)$; never observable for one unit (the fundamental problem of causal inference). Lec 10

The unobserved potential outcome — what would have happened under the other treatment status. The central missing quantity in causal inference. Lec 10

ATT: the mean treatment effect among treated units; the estimand that difference-in-differences recovers. Lec 10

LATE: IV identifies the effect only for "compliers" — units whose treatment status responds to the instrument. Lec 4

OLS on a binary outcome; the fitted value is $P(y=1\mid x)$ and coefficients are marginal effects in percentage points. Drawbacks: predictions can leave $[0,1]$, and errors are inherently heteroskedastic. Lec 2

Outcome coded 0/1 (accept/reject, chose B/A); modelled with the LPM, logit, or probit. Lec 2

Binary model using the logistic CDF to keep $P(y=1)$ in $(0,1)$; estimated by maximum likelihood. Lec 3

Binary model using the normal CDF $\Phi(\cdot)$; coefficients give sign and significance, not the marginal effect. Lec 3

The partial derivative $\partial P(y=1)/\partial x$. In the LPM it equals the coefficient (constant); in logit/probit it is $\beta\cdot\text{density}(\mathbf{x}'\beta)$ and varies with $x$. Lec 3

Estimates parameters by maximising the likelihood of the observed data; used for logit/probit. Consistent and asymptotically normal. Lec 3

Tests restrictions in MLE models by comparing log-likelihoods of restricted vs unrestricted models — the MLE analogue of the F-test. Lec 3

IV: uses an instrument $z$ to isolate exogenous variation in an endogenous regressor, restoring consistency when Cov$(x,u)\neq0$. Lec 4

2SLS: regress $x$ on $z$ (first stage), then $y$ on the fitted $\hat x$ (second stage); the practical IV estimator. Lec 4

Regression of the endogenous regressor on the instrument(s) and exogenous controls; its strength gauges relevance. Lec 4

Regression of the outcome on the first-stage fitted values, giving the IV/2SLS estimate. Lec 4

The instrument must be correlated with the endogenous regressor, Cov$(z,x)\neq0$ (testable, e.g. first-stage $F$). Lec 4

The exclusion restriction: the instrument affects $y$ only through $x$, Cov$(z,u)=0$ (untestable; argued conceptually). Lec 4

Instruments only weakly correlated with $x$ (first-stage $F<10$); produce biased, imprecise IV estimates. Lec 4

Tests for endogeneity; rejection ⇒ OLS is inconsistent and IV is needed. Lec 8

Sargan/Hansen test, available only when instruments outnumber endogenous regressors (overidentified); tests the joint null that all instruments are valid (uncorrelated with the error). Rejection ⇒ at least one instrument violates the exclusion restriction (assuming ≥1 is valid). PP3 Q2c

Bias from non-random inclusion in the estimation sample when selection depends on unobservables that affect $y$, Cov(selection, $u)\neq0$. Lec 5

Two-step estimator: model selection (probit), then add the inverse Mills ratio to the outcome regression to correct selection bias. Lec 5

Correction term $\lambda$ added in Heckman step 2; a significant $\lambda$ confirms selection bias. Lec 5

When who appears in the sample depends on unobservables that also drive the outcome. Lec 5

Standard log-wage model: $\log(\text{wage})=f(\text{educ},\text{exper},\text{exper}^2)$; a common setting for selection corrections. Lec 5

System where variables are jointly determined (e.g. supply & demand), creating simultaneity bias. Lec 6

Errors correlated over time, Cov$(u_t,u_{t-1})\neq0$; biases classical SEs in time series. Lec 6

Newey–West standard errors, robust to heteroskedasticity and autocorrelation. Lec 6

Observations indexed by time, where the past can influence the future. Lec 6

$x$ affects $y$ only contemporaneously (no lags). Lec 6

$E[u_t\mid X]=0$ for all time periods (stronger than contemporaneous exogeneity). Lec 6

$y_t$ depends on current and past values of $x$; the lag coefficients trace the dynamic response. Lec 6

$y_t$ depends on its own lagged values; consistent but not unbiased. Lec 6

Regular calendar-driven patterns in a series, controlled with seasonal dummy variables. Lec 6

Seasonal dummy variables added to absorb predictable calendar effects. Lec 6

Predictable systematic drift over time; linear ($\alpha_1 t$) or exponential (linear in logs). Lec 7

Two trending series look correlated in OLS purely from common drift, not a genuine relationship. Lec 7

Removing a trend by regressing on $t$ and using the residuals (equivalently, adding $t$ as a regressor — FWL theorem). Lec 7

Measures the effect of a discrete event by comparing actual vs model-predicted outcomes around it. Lec 7

Actual return minus model-predicted return; the event-study measure of surprise. Lec 7

The pre-event window used to fit the baseline model. Lec 7

The event window in which abnormal outcomes are computed. Lec 7

Repeated observations on the same units over time. Lec 8

Unit/group dummies (intercepts) that absorb all time-invariant characteristics of that unit. Lec 8

OLS on demeaned data; identifies $\beta$ from within-unit variation only. Lec 8

Subtracting each unit's own mean from every variable; annihilates anything constant within the unit (so fixed effects vanish). Lec 8

Variation in unit averages across units; contaminated by cross-unit confounders. Lec 8

Variation within a unit over time; the variation fixed effects exploit. Lec 8

$a_i$: a per-individual intercept capturing all of that individual's time-invariant traits. Lec 8

Per-period dummies absorbing shocks common to all units in that period. Lec 8

Unit and time fixed effects together; the panel form of difference-in-differences. Lec 8

SEs allowing arbitrary correlation within groups; cluster at the level of the fixed effect. Lec 8

OLS on all panel rows ignoring the $i$/$t$ structure; biased when fixed unit traits correlate with the regressor. Lec 8

Exploits a treatment cutoff in a running variable; the jump in the outcome at the cutoff is the effect. Lec 9

The forcing variable whose value relative to the cutoff determines treatment. Lec 9

Threshold of the running variable that switches treatment on/off. Lec 9

Window around the cutoff used for estimation; a bias–variance trade-off. Lec 9

Absent treatment, the outcome would vary smoothly through the cutoff. Lec 9

Treatment probability jumps cleanly $0\to1$ at the cutoff. Lec 9

Crossing the cutoff only changes the probability of treatment; estimated by IV (the Wald estimator). Lec 9

Checks that the density of the running variable is smooth at the cutoff (no manipulation/sorting). Lec 9

Checks that predetermined covariates (or pre-periods) show no jump/effect where none should exist. Lec 9

(Jump in outcome) ÷ (jump in treatment probability); the fuzzy-RDD / IV ratio. Lec 9

(Treatment change) − (control change); nets out common time trends and fixed group gaps to estimate the ATT. Lec 10

Absent treatment, treated and control groups would have followed the same trend; the key DiD identifying assumption. Lec 10

Fresh samples at each period (same individuals not required); sufficient for DiD. Lec 10

Diagnoses two-way-FE DiD under staggered timing as a weighted average of all 2×2 comparisons. Lec 10

DDD: adds a third difference to net out a confounding trend. Lec 10