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Walk the neighbourhood to see how similar homes acquire different prices before reading the model.
Playback starts only when selected.Housing & the cityHedonic pricing / Urban economicsVideo lesson · 01:33
Why a house price is really a bundle of implicit prices, and how a log-linear regression reads the market's marginal valuation of things like access to a school or a station.
Abstract
This note treats a dwelling as a bundle of location, size, quality, and public-service attributes, then shows how coefficients in a log-linear hedonic model become implicit prices. It also marks the identification boundary: a proximity coefficient describes market valuation, but does not by itself establish the causal effect of building an amenity.
Spatial methodsSpatial econometrics / Method notes
Two different ways geography enters a regression — a neighbour effect versus a relationship that refuses to stay constant — and why the distinction dictates the whole modelling chain.
Abstract
This note separates spatial dependence from spatial heterogeneity. The first concerns correlation between neighboring observations; the second concerns relationships whose parameters vary by location. Because they call for different diagnostics, models, and interpretations, confusing them at the outset can distort every later choice, from the weight matrix to the final claim.
Compare contiguity, distance, and nearest-neighbour rules before treating W as part of the research design.
Playback starts only when selected.Spatial methodsSpatial econometrics / Weights matrixVideo lesson · 01:37
Before any spatial test or model, you have to declare who counts as whose neighbour. The W matrix is that declaration — an assumption, not a fact handed over by the data.
Abstract
This note treats the spatial weight matrix as a research-design choice that must be defended, not as a software default. Contiguity, distance, and nearest-neighbor rules encode different mechanisms. A useful W follows the theory, scale, and data structure, and its conclusions should be checked against plausible alternative definitions of neighborhood.
Separate the global clustering question from the local map before turning to inference and interpretation.
Playback starts only when selected.Spatial methodsSpatial autocorrelation / Moran's IVideo lesson · 01:45
A global autocorrelation statistic tells you clustering exists; its local decomposition tells you where, and of what kind — along with the traps that make both easy to misread.
Abstract
This note places global Moran's I beside local indicators of spatial association. The global statistic asks whether clustering exists overall; the local map locates high-high, low-low, and spatial-outlier areas. The emphasis is also interpretive: significance, multiple testing, and the fact that a cluster map alone cannot identify a mechanism or a causal relation.
Spatial methodsSpatial econometrics / SEM
Spatial error, spatial lag, and the Durbin model that contains both: where the dependence lives, whether there are spillovers, and why the coefficient stops being the marginal effect.
Abstract
This note compares the spatial error and spatial lag models, then uses the more general Durbin form to show how the two can be nested. The central distinction is whether dependence enters the disturbance or the dependent variable, and whether feedback and spillovers follow. With a spatial lag, coefficients must be decomposed into direct, indirect, and total effects.
Move from OLS residuals through classical and robust LM tests to a defensible spatial-model choice.
Playback starts only when selected.Spatial methodsSpatial econometrics / Model selectionVideo lesson · 01:41
Moran's I tells you spatial dependence exists but not which kind. The Lagrange-multiplier tests — and especially their robust variants — are how you decide between a spatial error and a spatial lag.
Abstract
This note organizes the LM decision rule that moves from OLS residual diagnostics to a spatial-model choice. Classical and robust LM-lag and LM-error results help distinguish lag-like from error-like dependence. They provide comparative evidence rather than an automatic answer, and must remain consistent with the mechanism, weight matrix, and residual diagnostics.
Read a coefficient surface as local association, then identify the diagnostics needed before interpretation.
Playback starts only when selected.Spatial methodsGWR / Spatial heterogeneityVideo lesson · 01:50
Geographically weighted regression gives you one coefficient per place instead of one for the whole map. What that surface says — and the three ways it can quietly mislead you.
Abstract
This note explains how to read a local coefficient from geographically weighted regression: it is a local association conditional on a chosen bandwidth and weighting scheme, not an automatically valid local causal effect. Coefficient surfaces can also reflect collinearity, edge samples, and multiple testing, so they need global benchmarks, stability diagnostics, and a stated spatial mechanism.
Spatial methodsspatial methods / GIS
Most of a spatial study happens before the regression: turning raw points and boundaries into one clean layer with real distances, then the OLS → spatial → local modeling ladder that sits on top.
Abstract
A field note on the unglamorous half of spatial analysis: the data engineering that precedes any coefficient. It walks the generic pipeline from raw address points and administrative boundaries to a single analysis-ready layer — text cleaning and composite keys, reprojection to a metric coordinate system, network-based accessibility instead of straight lines, and a circuity check that flags impossible detours without discarding real geography. It then sketches the modeling ladder above that layer — OLS with a Moran's I diagnostic, a global spatial model to absorb dependence, and geographically weighted regression when the relationship itself varies across the map. Examples are textbook-generic; the method travels, the findings do not.
A short distinction between repairing the variance and repairing the model.
Playback starts only when selected.EconometricsWLS / EconometricsVideo lesson · 01:31
Inverse-variance weighting is the right tool for heteroskedasticity and the wrong tool for a biased model. A note on what changing the weights does and does not repair.
Abstract
This note separates the variance problem that weighted least squares can address from the endogeneity problem it cannot. When weights approximate inverse error variance, WLS can improve efficiency and restore valid inference under heteroskedasticity. Bias from omitted variables, reverse causality, or measurement error does not disappear merely because observations are reweighted.
Separate the coefficient estimate from its uncertainty, then see what the sandwich estimator actually repairs.
Playback starts only when selected.EconometricsEconometrics / InferenceVideo lesson · 01:35
The sandwich estimator repairs OLS standard errors under heteroskedasticity while leaving the coefficients untouched — what it does, the HC0–HC3 variants, and when to reach for weighting instead.
Abstract
This note explains why heteroskedasticity-robust standard errors change the covariance matrix while leaving OLS coefficients untouched. HC0 through HC3 mainly differ in finite-sample adjustment and their treatment of high-leverage observations. Robust errors repair inference; they do not make an inefficient estimate efficient or solve misspecification and endogeneity.
Follow the path from endogeneity to the first stage, exclusion restriction, and two-stage least squares.
Playback starts only when selected.EconometricsEconometrics / Causal inferenceVideo lesson · 02:09
If an explanatory variable is correlated with the error, OLS is inconsistent. An instrument that moves the regressor without touching the error restores identification — under one assumption you can never test.
Abstract
This note begins with the endogeneity that makes OLS inconsistent and shows how relevance and the exclusion restriction allow an instrument to restore identification. It connects the first stage, reduced form, and two-stage least squares, while emphasizing weak instruments and the untestable core of exclusion: computation can be automated, but credibility still comes from research design.
See how within-group demeaning removes time-invariant confounding while discarding between-group variation.
Playback starts only when selected.EconometricsEconometrics / Panel dataVideo lesson · 01:14
The within estimator sweeps out every time-invariant group confounder at once — a lot of omitted-variable bias for free — at the price of discarding all the between-group variation.
Abstract
This note uses the within transformation to show how fixed effects make each individual or group its own control, removing every unobserved factor that does not change over time. The cost is that time-invariant regressors cannot be estimated and between-group information is discarded; identification comes entirely from change within the same group.
Move from preference rankings to utility, indifference curves, and the marginal rate of substitution.
Playback starts only when selected.FoundationsMicroeconomics / Consumer theoryVideo lesson · 01:38
Foundations note — the axioms that let a preference ordering be written as a utility function, and what the indifference curve and the MRS actually encode.
Abstract
This note explains when completeness, transitivity, continuity, and related conditions allow preferences to be represented by a utility function, while keeping ordinal utility separate from a measurable psychological quantity. Indifference curves and the marginal rate of substitution then become geometric expressions of ranking, preparing the ground for budget constraints and optimal choice.
See the slope, parallel shift, and pivot of the budget line before reading the full note.
Playback starts only when selected.FoundationsMicroeconomics / Consumer theoryVideo lesson · 01:11
Foundations note — the budget line, why its slope is a pure relative price, and the difference between a parallel shift and a pivot.
Abstract
This note reconstructs the budget line from income and two prices, then distinguishes the parallel shift caused by an income change from the rotation caused by a change in one price. It translates the diagram back into relative prices and purchasing power, establishing the constraint used in later analysis of consumer choice.
Move from the feasible set to the chosen bundle before working through the tangency conditions.
Playback starts only when selected.FoundationsMicroeconomics / Consumer theoryVideo lesson · 01:28
Foundations note — the consumer's optimum as a tangency, the equal-marginal 'bang per buck' principle, the Lagrange multiplier as the marginal utility of income, and when the tangency fails.
Abstract
This note combines preferences and the budget constraint into the consumer's optimization problem. It derives the tangency condition for an interior solution, the equal-marginal-utility-per-dollar rule, and the interpretation of the Lagrange multiplier. Corner solutions, kinks, and nonconvexity show why MRS equals the price ratio only under specific conditions.
Connect inputs to output, diminishing marginal product, and the geometry of isoquants.
Playback starts only when selected.FoundationsMicroeconomics / Producer theoryVideo lesson · 01:59
Foundations note — output from inputs, marginal versus average product, why returns diminish in the short run, and what the isoquant's slope encodes.
Abstract
This note uses the production function to connect inputs with output, separating total, marginal, and average product and explaining why fixed inputs eventually generate diminishing marginal returns in the short run. Isoquants and the marginal rate of technical substitution then express multi-input choice geometrically, providing the technical basis for cost minimization.
Use the average test to connect marginal, average, and long-run cost before reading the full note.
Playback starts only when selected.FoundationsMicroeconomics / Producer theoryVideo lesson · 01:35
Foundations note — the short-run cost family, why marginal cost cuts the average minima, and how the long-run average cost is the envelope of every plant the firm could build.
Abstract
This note derives fixed, variable, average, and marginal cost from production technology and explains why marginal cost crosses AVC and ATC at their minima. Long-run average cost is then read as the envelope of short-run curves for different plant sizes, clarifying economies of scale, efficient scale, and capacity choice.
Trace the price-taking firm's output choice, shutdown rule, and zero-profit long-run equilibrium.
Playback starts only when selected.FoundationsMicroeconomics / Market structureVideo lesson · 01:40
Foundations note — the four assumptions, why the firm sets P = MC, the short-run shutdown rule, and how free entry drives long-run profit to zero at the efficient scale.
Abstract
Under price taking, homogeneous products, sufficient information, and free entry, this note derives the competitive firm's output choice. In the short run, price, marginal cost, and average variable cost determine production or shutdown. In the long run, entry and exit drive economic profit toward zero and the industry toward efficient scale.
See why a monopolist chooses quantity first, reads price from demand, and leaves a deadweight loss.
Playback starts only when selected.FoundationsMicroeconomics / Market structureVideo lesson · 02:18
Foundations note — why marginal revenue falls below price, the two-step quantity-then-price optimum, the Lerner markup, and the deadweight loss against the competitive benchmark.
Abstract
Starting from a downward-sloping demand curve, this note derives the monopolist's marginal revenue and the two-step choice of quantity where MR equals MC, followed by price on the demand curve. The markup over marginal cost, the Lerner index, and deadweight loss together show how market power changes distribution and total surplus.
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