Is U.S. real output growth non-normal? A tale of time-varying location and scale

Matei Demetrescu and Robinson Kruse-Becher

Journal of Economic Dynamics and Control, 2025, vol. 171, issue C

Abstract: Testing distributional assumptions is an evergreen topic in applied economics and econometrics. A key assumption is stationarity of the series of interest, however time-varying moments are common in economic data. Yet, under time-varying moments, falsely treating data as homogeneous results in apparent distributions belonging to a mixture family. Therefore, tests consistently reject when stationarity assumptions are violated, even under correct specification of the baseline distribution. We propose robust tests building on local standardization (by flexible nonparametric estimators), in particular we use raw moments of probability integral transformations of locally standardized series. Probability integral transforms accommodate a wide range of null distributions and imply simple raw moment restrictions. We demonstrate our approach in detail for normality, while our main results are extended to general location-scale models without essential modifications. Short-run dynamics are accounted for by the fixed-bandwidth approach which leads to robustness of the proposed test statistics to the estimation error induced by the local standardization. We propose a simple rule for choosing the tuning parameters and an effective finite-sample adjustment. Monte Carlo experiments show that the new tests perform well in terms of size and power and outperform alternative tests even under stationarity. We find – in contrast to other studies building on stationarity – no evidence against normality of U.S. real output growth after accounting for time-variation.

Keywords: Distribution testing; Probability integral transformation; Local standardization; Nonparametric estimation; Heteroskedasticity and autocorrelation robust inference (search for similar items in EconPapers)
JEL-codes: C12 C14 C22 E01 E32 (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:dyncon:v:171:y:2025:i:c:s0165188924002240

DOI: 10.1016/j.jedc.2024.105032

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