Central European Journal of Economic Modelling and Econometrics

Arrow and Debreu proved that, if in the mathematical model of the economy that they defined some conditions are satisfied, then there is a price system under which there is Walras equilibrium in this economy. We examine a procedure, defined on the basis of a continuous mapping, of transformation of production sets of the Arrow-Debreu economies in which at least one of the assumptions concerning the production sets is not satisfied. Finally, we get a class of ArrowDebreu economies in which, after modification, there is Walras equilibrium. The research methods are based on the analysis of the linear mappings in real vector space of finite dimension, and the results have the form of mathematical theorems.

This paper attempts to find out what is the role of competitive environment in shaping the sensitivity of growth in banking to the business cycle. To answer this question, we apply a large set of individual bank level data including over 8000 banks operating in more than 100 countries. This study uses the growth of assets, loans, deposits and leverage as proxies of bank growth and Lerner index as a proxy for the competitive environment. The analysis shows that decreased competition is associated with increased procyclicality of bank growth. However, in a perfectly competitive environment the growth turns out to be countercyclical. This effect differs between high- and lowincome countries. A perfectly competitive environment is associated with countercyclical growth in high-income countries. The opposite result is found for low-income countries. Our results for Central Eastern European countries show that increased competition is associated with enhanced procyclicality of growth.

In a national economy, are individual subnational regions business cycle takers or setters? We address this important regional policy question by investigating regional business cycles at NUTS-3 granularity in Poland (N = 73), using two metrics in parallel: GDP dynamics and unemployment. To extract the business cycle, we use a spatial Markov switching model that features both idiosyncratic business cycle fluctuations across regions (as a 2-state chain), as well as spatial interactions with other regions (as spatial autoregression). The posterior distribution of the parameters is simulated with a Metropolis-withinGibbs procedure. We find a clear division into business cycle setters and takers, the latter being largely (but not only) non-metropolitan regions.