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Throughout this series of blog posts, I use a small set of recurring acronyms and symbols to keep the discussion readable (and to avoid rewriting definitions every time we move from intuition to estimation). The tables below are quick glossaries: if, in later posts, a symbol like LGDP or output gap (or a test name like CIPS or Westerlund) feels momentarily unclear, come back here and treat it as the reference card for the entire series.
Glossary table: acronyms and symbols used across the Okun blog series
| Acronym or Symbol | Definition |
| GDP | Gross Domestic Product: a measure of total economic output (overall production of goods and services). In the series it is used as the core indicator of economic activity (often real GDP, i.e., adjusted for price changes). |
| GDP per capita | GDP divided by population: a per-person measure of economic output used to compare living-standard–type output levels over time or across places. |
| UR | Unemployment rate: the share of the labour force that is unemployed (not working but actively seeking work). The main labour-market outcome in Okun’s Law. |
| LGDP | Log GDP (often log real GDP or log real GDP per capita): the natural logarithm of GDP. Logging is used to interpret changes approximately as percentage changes and to stabilise scale over long samples. |
| DLGDP | First difference of LGDP, i.e., (\(\Delta \log(GDP)\)). Interpreted approximately as GDP growth over the period (for annual data: annual growth; for quarterly: quarterly growth). |
| DUR | First difference of the unemployment rate, i.e., (\(\Delta UR\)). Interpreted as the change in unemployment in percentage points over the period (annual or quarterly, depending on the dataset). |
| Output gap | A cyclical measure of economic slack: the deviation of (log) output from estimated potential/trend output. Typically: (\(\text{Output gap}_t = \log(GDP_t) – \log(\widehat{GDP}^{trend}_t)\)). Positive values imply output above trend; negative values imply output below trend. In these posts, gaps are typically constructed using the HP filter when stated. |
| DOutput gap | First difference of the output gap, i.e., (\(\Delta(\text{Output gap})\)). Interpreted as the change in cyclical output slack from one period to the next. |
| Unemployment gap | A cyclical measure of labour-market slack: the deviation of unemployment from its estimated “natural” or trend level (as defined by the report). Typically: (\(\text{Unemployment gap}_t = UR_t – \widehat{UR}^{trend}_t\)). Positive values imply unemployment above trend (more slack); negative values imply unemployment below trend (tight labour market). |
| DUnemployment gap / Dunemployment gap | First difference of the unemployment gap, i.e., (\(\Delta(\text{Unemployment gap})\)). Interpreted as how quickly labour-market slack is widening or narrowing. |
| Δ (Delta) | The “first difference” operator: (\(\Delta x_t = x_t – x_{t-1}\)). Used to represent changes (growth rates for logged variables; level changes for rates). |
| L (prefix) | “Log” indicator: (\(Lx = \log(x)\)). In this series it signals the natural log unless explicitly stated otherwise. |
| D (prefix) | “Difference” indicator: (\(Dx = \Delta x\)). A leading D means the variable is expressed as a first difference (change). |
| β (beta) | Slope coefficient in a regression model. In Okun contexts it is the Okun coefficient: the estimated mapping from output (or output slack) to unemployment (or unemployment slack). |
| α (alpha) | Intercept/constant term in a regression model (baseline level when explanatory variables are zero). |
| ε (epsilon) | Regression error term (residual): the portion of the dependent variable not explained by included regressors. |
| t (time index) | Time period index (year (t), quarter (t)). |
| i (unit index) | Cross-sectional unit index in panels (e.g., country (i), county (i)). |
Methods and model acronyms (used in methodology + results posts)
| Acronym or Symbol | Definition |
| HP filter | Hodrick–Prescott filter: a smoothing method used to decompose a time series into a trend component and a cyclical component; the cycle is commonly used as an “output gap” (or analogous “unemployment gap”). |
| OLS | Ordinary Least Squares: baseline linear regression estimation method used for simple relationships and illustrative “line-through-the-cloud” regressions. |
| ARDL | Autoregressive Distributed Lag model: a dynamic regression with lags of the dependent variable and lags of explanatory variables; used to model short-run dynamics and (when applicable) infer long-run relationships via an error-correction representation. |
| NARDL | Nonlinear ARDL: ARDL extended to allow asymmetric effects, typically by decomposing an explanatory variable into positive and negative changes and estimating separate dynamic responses. |
| ECM / ECT | Error-correction model / error-correction term: the component that measures how quickly deviations from a long-run equilibrium are corrected. The ECT coefficient is usually expected to be negative (convergence). |
| F-bounds / t-bounds | Bounds testing statistics used in ARDL frameworks (Pesaran–Shin–Smith style) to assess whether a long-run (level) relationship is present. |
| FMOLS | Fully Modified OLS: an estimator designed for cointegrated relationships that corrects for endogeneity and serial correlation in the cointegration regression. |
| DOLS | Dynamic OLS: a cointegration estimator that augments the regression with leads/lags of differenced regressors to correct endogeneity/serial correlation issues. |
| MG | Mean Group estimator: estimates separate relationships for each unit (e.g., county/country) and averages coefficients; allows slope heterogeneity. |
| PMG | Pooled Mean Group estimator: allows heterogeneous short-run dynamics across units but imposes a common long-run relationship; often used in dynamic panel ARDL settings. |
| VECM | Vector Error Correction Model: a multivariate system model used when variables are cointegrated, combining short-run changes with error-correction toward long-run equilibria. |
Unit-root / stationarity tests (time-series and panel)
| Acronym or Symbol | Definition |
| Unit root | A property indicating strong persistence/non-stationarity; shocks have long-lasting effects and the series may drift rather than fluctuate around a stable mean. |
| Stationary (I(0)) | A series with stable statistical properties over time (mean/variance) and mean-reverting behaviour. |
| Integrated of order 1 (I(1)) | A non-stationary series that becomes stationary after first differencing. |
| DF-GLS / ERS | Elliott–Rothenberg–Stock DF-GLS test: a unit-root test with improved power in some settings (compared with classic ADF), often used for time-series stationarity checks. |
| KPSS | Kwiatkowski–Phillips–Schmidt–Shin test: a stationarity test where the null is stationarity (often used alongside unit-root tests for complementary evidence). |
| ZA | Zivot–Andrews test: time-series unit-root test allowing one endogenous structural break in the trend and/or intercept. |
| CMR | Clemente–Montañés–Reyes test: time-series unit-root test allowing two breaks (often discussed in additive-outlier vs innovative-outlier forms). |
| LLC | Levin–Lin–Chu panel unit-root test (first-generation; typically assumes cross-sectional independence). |
| IPS | Im–Pesaran–Shin panel unit-root test (first-generation; allows heterogeneous autoregressive coefficients but often assumes cross-sectional independence). |
| ADF–Fisher / PP–Fisher | Panel unit-root approaches that combine individual-unit ADF or Phillips–Perron tests using Fisher-type aggregation. |
| Hadri | Panel stationarity test (null is stationarity; counterpart to panel unit-root tests). |
| CIPS | Pesaran’s Cross-sectionally Augmented IPS test (second-generation panel unit-root test allowing cross-sectional dependence via cross-sectional averages). |
Cross-sectional dependence, breaks, cointegration, and causality
| Acronym or Symbol | Definition |
| CSD | Cross-sectional dependence: correlation across units in a panel (e.g., counties affected by common shocks). Important because it can invalidate first-generation panel tests if ignored. |
| CD / CDw / CD* | Families of panel cross-sectional dependence tests (often associated with Pesaran-type diagnostics and variants). Used to detect whether units share common factors/shocks. |
| Slope homogeneity test | Tests whether coefficients are common across panel units or heterogeneous (i.e., whether each county/country has its own Okun slope). |
| Structural break | A change in the underlying relationship or data-generating process at some time (e.g., crisis periods), implying instability in coefficients or trends. |
| Bai–Perron | Multiple-break framework for detecting structural changes at unknown dates in time series relationships (used to identify multiple regime shifts). |
| Cointegration | A long-run equilibrium relationship among non-stationary (often I(1)) series; despite drifting individually, they move together in a stable way over time. |
| Engle–Granger (EG) | Two-step cointegration test: estimates a long-run regression and tests residuals for stationarity. |
| Gregory–Hansen (GH) | Cointegration test allowing a structural break in the long-run relationship. |
| Johansen | System-based cointegration method for multivariate settings; determines cointegration rank and estimates cointegrating vectors. |
| Pedroni | Panel cointegration test family allowing heterogeneous cointegrating relationships across units (various within- and between-dimension statistics). |
| Kao | Panel cointegration test often imposing more homogeneity structure than Pedroni (useful but potentially restrictive in heterogeneous panels). |
| Westerlund | Panel cointegration tests framed around error-correction; often interpreted as testing whether error-correction is present (i.e., whether adjustment toward equilibrium exists). |
| Granger causality | Predictive causality concept: whether past values of one variable help predict another, beyond the other’s own past. Not a guarantee of deep structural causation. |
| Toda–Yamamoto (TY) | Causality testing approach that can be applied in VAR settings without requiring pre-testing for cointegration in the same way as standard approaches (robust to integration order under conditions). |
| Dumitrescu–Hurlin (DH) | Panel Granger non-causality test allowing heterogeneity across units; used to assess predictive direction in panels. |
