A heterogeneous Bertrand duopoly game with bounded rational and adaptive players manufacturing differentiated products is subject of investigation. The main goal is to demonstrate that participation of one bounded rational player in the game suffices to destabilize the duopoly. The game is modelled with a system of two difference equations. Evolution of prices over time is obtained by iteration of a two dimensional nonlinear map. Equilibria are found and local stability properties thereof are analyzed. Complex behavior of the system is examined by means of numerical simulations. Region of stability of the Nash equilibrium is demonstrated in the plane of the speeds of adjustment. Period doubling route to chaos is presented on the bifurcation diagrams and on the largest Lyapunov characteristic exponent graph. Lyapunov time is calculated. Chaotic attractors are depicted and their fractal dimensions are computed. Sensitive dependence on initial conditions is evidenced.
This paper estimates the magnitude of the Baumol-Bowen and Balassa-Samuleson effects in the Polish economy. The purpose of the analysis is to establish to what extent the differential price dynamics in Poland and in the euro area and the real appreciation of PLN against EUR are explained by the differential in respective productivity dynamics. The historical contribution of the Baumol-Bowen effect to Polish inflation rate is estimated at 0.9 − 1.0 percentage points in the short run. According to estimation results, the Balassa-Samuelson effect contributed around 0.9 to 1.0 percentage point per annum to the rate of relative price growth between Poland and the euro area and 1.0 to 1.2 p.p. to real exchange rate appreciation. The long-run effects are of an approximately twice larger magnitude. Sub-sample calculations and productivity trends over the last decade suggest that this impact should be declining. However, its size is still non-negligible for policymakers in the context of euro adoption in Poland.
The literature on exchange rate forecasting is vast. Many researchers have tested whether implications of theoretical economic models or the use of advanced econometric techniques can help explain future movements in exchange rates. The results of the empirical studies for major world currencies show that forecasts from a naive random walk tend to be comparable or even better than forecasts from more sophisticated models. In the case of the Polish zloty, the discussion in the literature on exchange rate forecasting is scarce. This article fills this gap by testing whether non-linear time series models are able to generate forecasts for the nominal exchange rate of the Polish zloty that are more accurate than forecasts from a random walk. Our results confirm the main findings from the literature, namely that it is difficult to outperform a naive random walk in exchange rate forecasting contest.
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