airtraffickonomics

Glossary

This page defines the technical terms used in the field notes, findings and methods in plain English, most with an aviation example. No statistics training is assumed. Field notes and the Methods & Data page link here when they use a term.

The core ideas

Elasticity

How much one thing moves, in percentage terms, when another moves by one percent. A GDP elasticity just below one means that when the economy grows, air travel grows almost exactly in step with it. Above one, flying grows faster than the economy; below one, slower.

Elasticity ladder

This site’s cross-market comparison chart: the GDP elasticities of the ranked markets from lowest to highest, with a status label on every rung. A market shown without a rank comes last, and markets with no reliable estimate are left off it.

Unit elasticity

An elasticity of exactly one: the two quantities move by the same percentage, so a one percent rise in national income goes with one percent more flying. The elasticity ladder draws it as a reference line. A bar above the line means flying outgrows income, and a bar below it means flying lags behind. Whether a market’s elasticity differs from one depends on its confidence interval, since a range that straddles the line cannot rule out flying keeping pace.

Cointegration

A long-run lock-step between two series that both trend upward. GDP and passenger traffic each grow over decades; cointegration tests ask whether they drift apart or stay tethered, so that when one wanders, the other pulls it back. If they are tethered, an elasticity estimated between them measures a real relationship. If not, the estimate may just be a coincidence of two rising lines.

Error-correction model

A model built for cointegrated series (usually abbreviated ECM). It separates the long-run relationship (where traffic should sit given GDP) from short-run bumps, and includes a pull-back term measuring how fast traffic returns to that long-run level after straying.

Unit root (and the ADF test)

A series has a unit root when shocks never fade: bump it and it wanders off from wherever it lands, the way passenger traffic or GDP drifts over decades. The ADF (augmented Dickey–Fuller) test checks for this. It matters because regressing one wandering series on another produces impressive-looking but meaningless fits.

Integration order: I(0), I(1)

Shorthand for how many times a series must be differenced (converted to period-to-period changes) before it stops wandering. An I(0) series is already stable around a level; an I(1) series (like log passenger traffic or log GDP) wanders in levels but its quarterly changes are stable. Long-run methods (cointegration, ECMs, ARDLs, DOLS) exist to estimate relationships between I(1) series without being fooled by their shared drift.

Trend-stationary

A series that fluctuates around a steady straight-line trend: knock it off course and it drifts back toward the trend line. A unit-root series wanders wherever shocks push it instead, and the difference decides whether a fitted trend can be trusted. Trend lines fitted to wandering series come out looking significant with p-values that mean nothing, while a trend-stationary series supports a valid one. A yearly count of routes that wanders, for example, gives no sound basis for saying the network is steadily shrinking.

Structural break

A date at which the relationship itself changes. COVID and the global financial crisis are the obvious ones; tests like Bai–Perron search the data for break dates without being told where to look. Ignoring a real break makes a model average two different relationships.

Bai-Perron break test

The standard way of letting the data nominate its own break dates. It tries every candidate date, refits the model on each side of the split, and reports where splitting improves the fit most, judged against critical values that allow for the fact that many dates were searched. Run on a passenger series, it can pick out the quarter of a border closure without being told the date.

Seasonal adjustment

Air travel has a strong calendar rhythm (a summer peak, a winter trough) that repeats every year. Seasonal terms in a model strip out that rhythm so that it compares like quarter with like quarter.

Dummy variable

An on-off switch that marks an episode (the pandemic quarters, a recession, a border closure) so the model can absorb the event without it distorting the underlying relationship. A “transitory dummy” is a switch that turns on and then off again.

Lag

A past value used as an input: “four lags of traffic” means the model sees the last four quarters. Results should not hinge on the exact lag count chosen.

The models

ARDL

Short for autoregressive distributed lag: a regression where this quarter’s traffic depends on recent quarters of both traffic itself and GDP, letting the response build over time. The paired numbers in the notation count the lags: traffic’s first, then GDP’s.

Bounds test

The ARDL’s built-in check for cointegration, read from a single statistic called the bounds F. Above an upper critical bound, a long-run link (between traffic and GDP, say) is confirmed; below a lower bound, there is none; in between, the test cannot say.

UECM

Short for unrestricted error-correction model: the ARDL rewritten so that the long-run relationship and the short-run adjustments appear as separate terms in a single equation. Nothing new is estimated; it is the same model rearranged into the form where the long-run link can be tested directly. The bounds test F statistic is computed on this form, which is why bounds-test write-ups mention it.

Johansen test

A second, different test for cointegration, run on the same two series as the bounds test. It counts how many long-run relationships (the “rank”) a set of series shares: a rank of one between traffic and GDP means exactly one stable long-run link, which is the clean result. Finding as many relationships as there are series (full rank) is a warning, not a stronger pass: it says the series were already individually stable, so there was no shared drift for the test to tie together, and the result cannot be read as a long-run link.

Engle-Granger test

The classic two-step check for cointegration: fit the long-run relationship, then test whether its leftovers (residuals) wander or settle. If the residuals settle, the two series are tethered; if they wander, the fitted relationship may be a coincidence of two trends. For freight and GDP, say, the question is whether the gap between them settles back or keeps drifting.

VECM

A vector error-correction model: the multi-equation form of the error-correction model. It lets every series in the system (say, traffic and GDP) respond when the group drifts away from its long-run relationship, and then measures which of them does the correcting.

DOLS

Dynamic ordinary least squares (the Stock–Watson method): a refinement for measuring the long-run elasticity once cointegration is at least plausible. It adds leads and lags of GDP’s quarter-to-quarter changes to absorb short-run noise, so the elasticity’s reported confidence interval means what a confidence interval should mean, which a naive levels regression between two trending series cannot promise.

NARDL

An ARDL that lets increases and decreases have different effects. It is used to ask whether fares climb quickly when fuel gets expensive but fall slowly when fuel gets cheap, the pattern known as “rockets and feathers”.

SARIMAX

A statistical forecaster that models a series’ own momentum and seasonal rhythm; the X stands for exogenous inputs, outside variables fed in to help predict, such as GDP in a traffic forecast. It uses those inputs for prediction only and estimates no structural elasticities, so its coefficients carry no economic interpretation.

Fixed effects

Comparing entities to themselves. Giving every airport (or carrier, or state) its own baseline means the estimate comes from changes within each one over time, not from differences between them, so a busy hub and a small regional field can sit in the same regression without the size gap contaminating the answer.

Hedonic regression

Pricing a product by its attributes. A hedonic fare model asks what a route “should” cost given its distance, passenger volume, competition, and mix of fare restrictions; routes priced far above or below that prediction have large residuals. The same technique prices houses by bedrooms and postcode.

Engel curve

The relationship between a household’s income and the share of its budget it spends on something. A budget share that falls as income rises marks a necessity; one that rises marks a luxury. For air travel, the question is whether richer households spend a larger or a smaller share of their budget on airfares.

Multinomial logit

A regression for outcomes that are unordered categories. A carrier’s choice among keeping, growing, or shrinking a fleet type is one such outcome: each driver gets a coefficient for each choice, read as the pull toward that choice relative to a reference choice. Converting those coefficients into probabilities gives marginal effects.

Kaplan-Meier survival curve

A way to estimate how long things last when most of them have not finished yet. Most aircraft in the fleet data are still flying, so their service lives are known only to exceed their current age (they are “censored”); the Kaplan-Meier estimator uses that partial information and traces the share of a cohort still in service at each age. What counts as an exit, scrapping only or a sale abroad as well, is a modelling choice, and a stricter definition gives longer lives.

Mundlak device

A check on whether a random-effects panel model is safe to use. It adds each entity’s own average of the time-varying variables (each airline’s, in a panel of carriers) to the regression and tests those averages jointly: if they matter, the entity effects are correlated with the regressors and random effects is the wrong estimator. It stands in for the classical Hausman comparison between fixed effects and random effects, which is not valid once both models use clustered standard errors.

Gravity model

Trade economics borrowed from physics: traffic between two airports rises with their sizes and falls with the distance between them, just as gravity rises with mass and falls with separation. PPML (Poisson pseudo-maximum likelihood) is the standard way to estimate one: it fits traffic in levels, not logarithms, which keeps the estimate reliable when busier routes are also noisier. It can also handle airport pairs with zero traffic.

Multilateral resistance

The trade-literature name (from Anderson and van Wincoop) for the fact that traffic between two airports depends on the alternatives each endpoint has as well as on the pair itself: a route from a hub with many substitute destinations behaves differently from an equally long route from an isolated airport. Gravity models handle it by giving every origin and every destination its own fixed effect, so the distance effect is measured by comparing routes that share an endpoint.

Instrumental variable

A method for estimating an effect when cause and outcome influence each other. If GDP drives air travel but air travel also feeds GDP, an ordinary regression mixes the two; an instrument is an outside variable that moves GDP without affecting aviation directly, which isolates the one-way effect. A weak instrument, one only loosely tied to GDP, can give estimates less reliable than the ordinary regression it was meant to correct.

Conformal prediction

A way to build forecast ranges that are guaranteed to contain the truth a stated share of the time, judged purely by how wrong the model has been before, with no bell-curve assumption. The guarantee holds only if future errors resemble past ones, and a shock such as COVID breaks that resemblance.

Reading the statistics

P-value

The probability of seeing an effect at least this large if the true effect were zero: a measure of surprise, not of importance. By convention, below one chance in twenty counts as “statistically significant.” A large p-value on a coefficient means the data are consistent with no effect.

Confidence interval

The range of values consistent with the data, usually at the ninety-five percent level. An interval that crosses zero means the data cannot rule out no effect, and an elasticity whose interval runs from below one to above it cannot say whether flying grows faster or slower than income.

Standard error

How much an estimate would vary if the data could be collected again. Confidence intervals and p-values are built from it, so when a standard error is computed the wrong way, everything downstream is too.

Delta method

A way to put a standard error on a quantity that is calculated from other estimates. A long-run elasticity, for example, is a ratio of fitted coefficients, so its uncertainty has to be propagated from theirs; the delta method does that propagation analytically. Intervals labelled “delta CI” are built this way; the bootstrap is the alternative when the formula’s assumptions fail.

HAC standard errors

Standard errors computed to survive two common real-world failures: errors whose size changes over time (heteroskedasticity) and errors that echo from one quarter into the next (autocorrelation), hence heteroskedasticity-and-autocorrelation-consistent. Quarterly aviation data have both, so a textbook standard error would overstate the precision; HAC (often “Newey–West”) widens it to allow for both.

Wald test

A general-purpose test of whether a fitted model’s coefficients satisfy some claim: equal before and after a break (the same seasonal pattern of travel before and after COVID, say), zero, or symmetric. It measures how far the estimated coefficients sit from the claim, scaled by their uncertainty, and can check several coefficients at once. In its robust form it is built from standard errors that survive changing volatility.

R-squared

The share of the variation a model explains, from zero to one. A high value means the model tracks most of the movement in, say, quarterly traffic; a low one means most of the variation, in route-level fares for instance, comes from things outside the model.

RMSE

Root mean squared error: the typical size of a model’s forecast miss, with bigger misses penalised extra. Lower is better. For a model that works in logarithms, an RMSE of a few hundredths corresponds to a typical miss of a few percent.

Out-of-sample

Tested on data the model never saw while being fitted, abbreviated OOS on some charts. Scored on its own training data, a model looks more accurate than it is.

Nowcast

An estimate of the present, or the very recent past, made before the official figures arrive. Official US passenger counts are published months after the fact, while airport security screening counts arrive daily, so the screening counts can fill in the quarters the official data have not yet covered. Because the two series count the same travellers, such a nowcast is a bridge between two measures of the same traffic rather than a model of why people fly.

Bootstrap

Re-estimating a model thousands of times on reshuffled versions of its own errors to see how much the answer wobbles. It produces valid confidence intervals when the textbook formulas’ assumptions fail; the “wild” bootstrap variant also survives changing volatility, like calm pre-COVID data next to the volatile pandemic quarters.

Granger causality

A test of whether knowing one series’ past helps predict another’s future: does past GDP predict traffic better than traffic’s own history alone? It establishes the direction of prediction, not physical cause and effect. (The Toda–Yamamoto version is a variant of the same test built to stay valid on trending data.)

Weak exogeneity

A variable is weakly exogenous when it drives the system without being driven by it: it does not adjust when the relationship goes off track. For aviation, the claim is that GDP is weakly exogenous: when traffic and GDP drift apart, traffic does the correcting while GDP carries on. A single-equation model of traffic assumes it and treats GDP as an input.

SHAP values

A way to see what a machine-learning model’s prediction rests on. For any single prediction, SHAP splits the outcome across the input variables: this quarter’s forecast is up a little because GDP rose, down a little because fuel spiked. Named for the Shapley value, a fair-division idea from game theory.

AUC

For a yes/no classifier, the probability that it ranks a randomly chosen true case above a randomly chosen false one: a coin flip scores a half, perfection scores one. For a model that flags which airlines will post a loss, it is the chance that a carrier that did lose money was ranked above one that did not.

Market structure

HHI

The Herfindahl–Hirschman Index, the standard market-concentration score: square each competitor’s percentage market share and add them up. A monopoly route scores the maximum; two equal carriers score half of it. Scales differ between charts: most freight and non-US concentration charts square shares as fractions and so run from zero to one, while others (India’s carrier concentration among them) use the full points scale antitrust practice quotes.

CASM, RASM, and yield

The three unit economics of an airline. CASM and RASM are measured per available seat mile (one seat flown one mile, whether or not anyone sat in it). CASM is cost per seat mile: what it costs to fly the seat. RASM is revenue per seat mile: what the seat brings in. Yield is the average fare paid per mile a passenger actually flies, so it is measured per passenger mile, not per seat mile. An airline earns money when RASM exceeds CASM.

Status labels on the elasticity ladder

Every rung of the cross-market ladder carries a label saying how much to trust it. In plain terms, for using the number:

Markets whose estimates cannot be reliably identified (Japan, Mexico, South Korea, India) are excluded from the ladder; the grounds include a nearly flat GDP series and structural breaks in short samples. The United Kingdom is excluded on a different ground: the source data have a gap of several years, and too few unbroken quarters lie between that gap and a later structural break, so the estimate that used to span the gap was withdrawn, and the quarters after the gap do not pass the long-run test. Canada is excluded on a third: its passenger and passenger-kilometre series both pass the bounds test but give elasticities far apart, so no single figure can be ranked. China is shown on the ladder but not ranked, because its test is inconclusive on a short pre-COVID window.

Findings and chart captions use further labels beyond the ladder’s. Descriptive covers associations published without a causal or structural claim (the hedonic fare model and the freight panel). Exploratory covers estimates on restricted samples, or under caveats strong enough that they should inform intuition rather than decisions (for example the Japan and Mexico demand models).

Projection covers a forward path computed from stated assumptions about income and population, or from an assumed growth rate. It is not a tested finding and not a forecast with a calibrated interval.

Null result is the strictest label on the site. It says the quantity was pinned down closely enough to conclude it is not big enough to matter: the range of values consistent with the data sits near zero and excludes an effect large enough to change the answer to the question being asked, and the tests agree. A statistical test cannot prove an effect is exactly zero; it can only fail to find one, and a failure to find is worth reporting only when the search was sharp enough to have found the effect had it been there. A result that merely comes back as not significant does not earn this label.

Inconclusive covers the other results in which nothing is significant, and it means the evidence cannot settle the question either way: the range consistent with the data is wide enough to still contain an effect worth caring about, or the tests disagree, or the identifying assumption fails, or the specification does not support the conclusion being drawn. It carries the same meaning off the ladder as on it. The fuel pass-through chain sits here, since its interval spans zero and its cointegration is not established, and so does the fare-asymmetry test built on one of that chain’s stages. Where a chart and a finding rest on the same number, they carry the same label.