Robust Monetary Policy In A Linear Model Of The Polish Economy: Is The Uncertainty In The Model Responsible For The Interest Rate Smoothing Effect?

Estimates of the generalised Taylor rule suggest that monetary policy in Poland can be characterized as having reacted in a moderate fashion to output and in ation gaps and are strongly dependent on the lagged interest rate. Moreover, as for the majority of central banks the short-term rate paths are smooth and only gradual changes can be observed. Optimal monetary policy models in the linear-quadratic framework produce high variability of interest rates, and are hence inconsistent with the data. One can obtain gradual behaviour of optimal monetary policy by adding an interest rate smoothing term to the central bank objective. This heuristic procedure has not much substantiation in the central bank's targets and raises the question: What are the rational reasons for the gradual movements in the monetary policy instrument? In this paper we determine optimal monetary polices in a VAR model of the Polish economy with parameter uncertainty. By incorporating a proper structure of multiplicative uncertainty in the linear-quadratic model of the Polish economy we nd a data consistent robust monetary policy rule. Thus proving that parameter uncertainty can be the rationale for "timid" movements in the short-interest rate dynamics. Finally, we show that there is trade o between parameter uncertainty and the interest rate smoothing incentive

Optimal Goodwill Model with Consumer Recommendations and Market Segmentation

We propose a new dynamic model of product goodwill where a product is sold in many market segments, and where the segments are indicated by the usage experience of consumers. The dynamics of product goodwill is described by a partial di erential equation of the Lotka{Sharpe{ McKendrick type. The main novelty of this model is that the product goodwill in a segment of new consumers depends not only on advertising e ort, but also on consumer recommendations, for which we introduce a mathematical representation. We consider an optimal goodwill model where in each market segment the control variable is the company's advertising e orts in order to maximize its pro ts. Using the maximum principle, we numerically nd the optimal advertising strategies and corresponding optimal goodwill paths. The sensitivity of these solutions is analysed. We identify two types of optimal advertising campaign: `strengthening' and `supportive'. They may assume di erent shapes and levels depending on the market segment. These experiments highlight the need for both researchers and managers to consider a segmented advertising polic

Optymalne strategie polityki pieniężnej dla Polski uwzględniające wrażliwość banku na ryzyko nieosiągnięcia założonego celu

Klasyfikacja JEL: C53, E47, E52, E58Autorska wersja artykułu, który ukazał się w Materiałach i Studiach nr 317 Narodowego Banku PolskiegoGłównym celem niniejszej pracy jest analiza optymalnych - wrażliwych na ryzyko stóp procentowych (risk-sensitive optimal interest rates), które mają za zadanie realizację bezpośredniego celu inflacyjnego oraz stabilizację sfery realnej gospodarki. Dla gospodarki Polski wyznaczamy optymalne strategie banku centralnego charakteryzującego się różnym stopniem wrażliwości na ryzyko nieosiągnięcia założonego celu (dalej nazywanego krótko ryzykiem). Optymalna wrażliwa na ryzyko polityka monetarna poddana jest ilościowej ocenie i porównana z historycznymi ścieżkami. W tym celu porównujemy reakcje zmiennych na impulsy egzogeniczne oraz wyznaczamy i analizujemy horyzonty stabilizujące inflację. Ponadto badamy wrażliwość polityki pieniężnej na zmianę parametru ryzyka oraz horyzontu decyzyjnego. Badanie przeprowadzone jest w oparciu o model wektorowej autoregresji opisujący mechanizm transmisji impulsów polityki pieniężnej w gospodarce Polski. Cel działania banku centralnego zapisany jest przy użyciu wykładniczej funkcji dysużyteczności, w której funkcja straty jest średnią ważoną wariancji zmiennych stanu i zmiennej sterowania, umożliwia uwzględnienie podstawowych zadań banku centralnego. Zaproponowana metodologia badawcza pozwala na skonstruowanie efektywnego narzędzia do wyznaczania optymalnych wrażliwych na ryzyko strategii polityki monetarnej uwzględniających: zarówno realizację bezpośredniego celu inflacyjnego jaki i stabilizację sfery realnej gospodarki. Niniejsze badanie stanowi, zgodnie z wiedzą autorów, pierwszą w literaturze empiryczną analizę optymalnej wrażliwej na ryzyko polityki monetarnej.Projekt badawczy został zrealizowany w ramach konkursu na projekty badawcze NBP, przeznaczone do realizacji w 2014 r., oraz sfinansowany ze środków Narodowego Banku Polskiego

How do loyalty programs affect goodwill? An optimal control approach

This paper examines the long-term impact of loyalty programs on a company’s profit and reputation among customers, and with different durations of product use. We analyze how the launch of loyalty programs may change the profitability of optimal advertising activities. The basis of this study is a modified goodwill model where the market is segmented according to usage experience. The main novelty is the role of loyalty programs and consumer recommendations in the creation of product goodwill, and also their influence on optimal advertising. The dynamics of goodwill are described by a partial differential equation. The firm maximizes the sum of discounted profits by choosing a different advertising campaign for each market segment. For a high-quality product, we observe that there is a trade off between the loyalty program and optimal advertising strategies. For a low-quality product, the loyalty program causes more profitable companies to invest heavily in additional advertising efforts.The authors gratefully acknowledge financial support from the National Science Centre in Poland. Decision number: DEC-2011/03/D/HS4/04269

Measuring uncertainty of optimal simple monetary policy rules in DSGE models

This paper presents a new approach to measure the parameter uncertainty for optimal simple monetary policy rules in the New Keynesian dynamic stochastic general equilibrium models. More precisely, we propose a new algorithm which enables to directly introduce parameter uncertainty into the optimal simple precommitment rule problem. As a result we find distributions of the optimal monetary policy reactions and the minimized welfare losses. To compare the distributions of the monetary policy parameters and the welfare losses we apply the first order stochastic dominance ordering (SD1). The SD1 inequality between the probability distribution is verified by means of the Kolmogorov-Smirnov test. The proposed algorithms are applied to the Erceg, Henderson and Levine (2000) small-scale closed economy model estimated for the Polish economy. For the welfare-loss-minimizing central bank, we examine three types of the dynamic specification of its policy rule: backward-, current- and forward-looking. Finally, for a given set of optimal and implementable monetary policy rules, we show that the fully specified forward-looking monetary policy rule with interest rate smoothing mechanism minimizes the welfare-loss in the sense of the stochastic ordering SD1.This work was supported by the National Science Centre in Poland under Grant No. 2017/26/D/HS4/00942

On the Equivalence of Solutions for a Class of Stochastic Evolution Equations in a Banach Space

Acknowledgments: The author wishes to thank Professor Anna Chojnowska-Michalik and the referee for many helpful suggestions and comments.We study a class of stochastic evolution equations in a Banach space E driven by cylindrical Wiener process. Three different analytical concepts of solutions: generalised strong, weak and mild are defined and the conditions under which they are equivalent are given. We apply this result to prove existence, uniqueness and continuity of weak solutions to stochastic delay evolution equations. We also consider two examples of these equations in non-reflexive Banach spaces: a stochastic transport equation with delay and a stochastic delay McKendrick equation