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In this paper, we analyse Okun’s law—a relation between the change in the unemployment rate and GDP growth—using data from Australia, the euro area, the UK and the USA. More specifically, we assess the relevance of non-Gaussianity when modelling the relation. This is done in a Bayesian VAR framework with stochastic volatility where we allow the different models’ error distributions to have heavier-than-Gaussian tails and skewness. Our results indicate that accounting for heavy tails yields improvements over a Gaussian specification in some cases, whereas skewness appears less fruitful. In terms of dynamic effects, a shock to GDP growth has robustly negative effects on the change in the unemployment rate in all four economies.

We derive asymptotic results for the long-horizon ordinary least squares (OLS) estimator and corresponding t-statistic for stationary autoregressive predictors. The t-statistic-formed using the correct asymptotic variance-together with standard-normal critical values result in a correctly-sized test for exogenous predictors. For endogenous predictors, the test is size distorted regardless of the persistence in the predictor and adjusted critical values are necessary. The endogeneity problem stems from the long-run estimation and is distinct from the ordinary persistence-dependent "Stambaugh" bias. The bias for fully stationary predictors appears not to have been previously noted and adds further difficulty to inference in long-run predictive regressions.

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