A Simple Estimator of Two‐Dimensional Copulas,with Applications1

Copulas are distributions with uniform marginals. Non‐parametric copula estimates may violate the uniformity condition in finite samples. We look at whether it is possible to obtain valid piecewise linear copula densities by triangulation. The copula property imposes strict constraints on design points, making an equi‐spaced grid a natural starting point. However, the mixed‐integer nature of the problem makes a pure triangulation approach impractical on fine grids. As an alternative, we study the ways of approximating copula densities with triangular functions which guarantees that the estimator is a valid copula density. The family of resulting estimators can be viewed as a non‐parametric MLE of B‐spline coefficients on possibly non‐equally spaced grids under simple linear constraints. As such, it can be easily solved using standard convex optimization tools and allows for a degree of localization. A simulation study shows an attractive performance of the estimator in small samples and compares it with some of the leading alternatives. We demonstrate empirical relevance of our approach using three applications. In the first application, we investigate how the body mass index of children depends on that of parents. In the second application, we construct a bivariate copula underlying the Gibson paradox from macroeconomics. In the third application, we show the benefit of using our approach in testing the null of independence against the alternative of an arbitrary dependence pattern.     

Impulse buying: A systematic literature review and future research directions

This paper performs a comprehensive analysis of academic research on impulse buying following a systematic literature review approach. Drawing on the TCCM framework suggested by Paul and Rosado-Serrano, we synthesize the impulse buying literature and develop a future research agenda. Accordingly, this review synthesizes impulse buying research in terms of theory development, context, characteristics, and methodologies to examine the development of the literature over time. This systematic review shows that impulse buying research is fragmented and still developing due to its transition from a traditional retail environment into different online channels. Furthermore, this paper proposes a conceptual framework based on the literature synthesis, presenting antecedents and mediators of impulse buying behaviour. Finally, this review identifies overlooked areas in impulse buying literature and provides insightful directions to advance research in the domain. Overall, this research effort makes a significant contribution to consumer behaviour literature, specifically to impulse buying literature.     

Second order bias of quasi-MLE for covariance structure models

For covariance structure models, the QMLE second-order bias is derived and compared with EL and GMM. Surprisingly, QMLE and EL have the same second-order bias if QMLE and GMM(EL) are equally first-order efficient. Other examples favoring QMLE are given.     

Russia’s invasion of Ukraine: assessment of the humanitarian,economic, and financial impact in the short and medium term

What are the economic effects of the Ukraine war for Ukraine, Russia, and the rest of Europe? In this study, the Vienna Institute for International Economic Studies (wiiw) sheds light on the immediate consequences on the one hand, but also on the medium-term structural changes caused by the largest armed conflict in Europe since the Second World War. The Russian invasion of Ukraine has triggered a humanitarian crisis. Pre-war, almost 19 m people lived in those regions that are currently directly affected. Refugee inflows to the rest of Europe are likely to be at least three times greater than in 2015/2016. As Black Sea ports come under Russian assault, Ukraine has lost its ability to sell more than half of its exports, primarily agricultural commodities and metals. Western financial support will become ever more important as the war continues. Turning to Russia, sanctions will have a very serious impact on that country’s economy and financial sector. Despite being partly hamstrung by the fact that a large proportion of Russian reserve assets are frozen in the EU and G7, the central bank managed to stabilise financial markets by a combination of confidence-building and hard-steering measures: capital controls, FX controls, regulatory easing for financial institutions, and a doubling of the key policy rate. The medium-term and long-term outlook is negative. As a result of the war and the sanctions, the rest of Europe faces a surge in already high inflation; this will weigh on real incomes and will depress economic growth. Many European countries rely heavily on Russia for oil and gas imports: import shares are over 75% in Czechia, Latvia, Hungary, Slovakia, and Bulgaria with respect to natural gas; Slovakia, Lithuania, Poland, and Finland with respect to oil and petroleum; and Cyprus, Estonia, Latvia, Denmark, Lithuania, Greece, and Bulgaria with respect to solid fuels. Aside from energy, the fallout via trade for the rest of Europe is likely to be small. Non-energy trade and investment links between Russia and many European countries have declined in importance since 2013. There are four main areas of structural change and lasting impact for the EU (and Europe more broadly) as a result of Russia’s invasion of Ukraine. First, the EU will get more serious about defence. Second, the green transition will gather pace. Third, broader Eurasian economic integration will be unwound. And fourth, the EU accession prospects for countries in Southeast Europe could (and should) improve.