The presented paper aims to analyse both statistical and economic aspects of the model with I(2) variables. The statistical foundations of such models are introduced. The enlargement of possible statistical interpretation is discussed. The economic interpretation of both VECM parameters and common stochastic trends representation is considered in the I(2) domain. The returns of I(2) approach in terms of stock-flows, nominal-real analysis and diasggregation into both long-, short and even medium-run analysis are proved. Potential complications under reflecting I(3) variables are presented.

The concept of cointegration that enables the proper statistical analysis of long-run comovements between unit root processes has been of great interest to numerous economic investigators since it was introduced. However, investigation of short-run comovement between economic time series seems equally important, especially for economic decision-makers. The concept of common features and based on it the idea of two additional reduced rank structure forms in a VEC model (the strong and the weak one) may be of some help. The strong form reduced rank structure (SF) takes place when at least one linear combination of the first differences of the variables exists, which is white noise. However, when this assumption seems too strong, the weaker case can be considered. The weak form appears when the linear combination of first differences adjusted for long-run efects exists, which is white noise.

The main focus of this paper is a Bayesian analysis of the VEC models involving the weak form of reduced rank restrictions.

After the introduction and discussion of the said Bayesian model, the presented methods will be illustrated by an empirical investigation of the price – wage spiral in the Polish economy.

The paper analyses the consequences of structural change in the presenceof non-stationary stochastic processes I(1) or I(2). The structural change mayconcern the deterministic structure (in particular, the trend and the constantterm) as well as the process generating the stochastic part. The focus of thepaper is on the case of a discrete change in a regime for which the momentof switch is known. A change in the deterministic part does not alter thecharacter of the cointegration relationships but its consequences for cotrendingand cobreaking are interesting. The consequences of a change in the stochasticpart are more complex, because then the stochastic process as well as thedeterministic structure of the VECM are modified. The restrictions are analysedfor both cases.

The paper aims at comparing forecast ability of VAR/VEC models with a non-changing covariance matrix and two classes of Bayesian Vector Error Correction – Stochastic Volatility (VEC-SV) models, which combine the VEC representation of a VAR structure with stochastic volatility, represented by the Multiplicative Stochastic Factor (MSF) process, the SBEKK form or the MSF-SBEKK specification.

Based on macro-data coming from the Polish economy (time series of unemployment, inflation and interest rates) we evaluate predictive density functions employing of such measures as log predictive density score, continuous rank probability score, energy score, probability integral transform. Each of them takes account of different feature of the obtained predictive density functions.

A review of the contemporary mainstream literature on exchange rate modelling clearly indicates that the rational expectations hypothesis (RE) is almost invariably taken as a point of reference in empirical investigations. This paper tests the RE hypothesis for the Polish foreign exchange market within the Roman Frydman and Michael Goldberg model that builds on the hypothesis of imperfect knowledge economics (IKE). The employed modelling strategy consists in the formulation of assumptions about the persistence of nominal rate, prices and interest rates and of the verification of competing scenarios congruent with RE and IKE. As a result of the analysis, the RE hypothesis is rejected in favour of the IKE alternative.

In this paper we present the Bayesian model selection procedure within the class of cointegrated processes. In order to make inference about the cointegration space we use the class of Matrix Angular Central Gaussian distributions. To carry out posterior simulations we use an alorithm based on the collapsed Gibbs sampler. The presented methods are applied to the analysis of the price – wage mechanism in the Polish economy.

Poland is expected to enter the Exchange Rate Mechanism II (ERM II). The European Central Bank recommends that the ERM II central rate should reflect the best possible assessment of the equilibrium exchange rate. Since the equilibrium rate is changing in time, it is important to identify the pushing and pulling forces of the exchange rate. This knowledge will let the authorities to defend only the exchange rate that is in equilibrium and to assess outcomes of their actions. We use the VEC approach of Johansen to estimate the behavioral equilibrium exchange rate and to identify the pushing forces of the Polish zloty/euro rate. We apply the Gonzalo-Granger decomposition to calculate the permanent equilibrium exchange rate and to identify the pulling forces of the zloty exchange rate. We demonstrate that this approach may be useful for Polish authorities while entering the ERM II as well as within that mechanism.

This article analyses fuel pricing in Poland in the period January 2000 – March 2011. Two levels of prices are considered: wholesale prices set by Polish refineries and retail prices paid at petrol stations. Because refinery product prices are strongly dependent on the zloty exchange rate, a large part of the article deals with the modelling of the PLN/EUR exchange rate, in which process a CHEER model is used.

The multivariate cointegration analysis showed that the wholesale and retail prices of fuels and the exchange rate are linked through long-run relationships. As demonstrated, the wholesale price of fuel depends on the crude-oil price and the PLN/EUR exchange rate. Another finding is that changes in the wholesale price are fully transmitted to retail prices. As far as the exchange rate is concerned, the real interest rate parity hypothesis has been confirmed, as well as the significance of the risk as perceived by financial investors.

The main goal of the paper is the Bayesian analysis of weak form polynomial serial correlation common features together with cointegration. In the VEC model the serial correlation common feature leads to an additional reduced rank restriction imposed on the model parameters.

After the introduction and discussion of the model, the methods will be illustrated with an empirical investigation of the price-wage nexus in the Polish economy.

Additionally, consequences of imposing such additional short-run restrictions for permanent-transitory decomposition will be discussed.

This paper studies the long-run relationship between consumption, labour income and asset wealth in Poland. Within cointegrated VAR model dynamic responses of the variables in the system to shocks are studied. In addition, series are decomposed into permanent and transitory components on the basis of the cointegrating relation found in the system.

Main conclusion of this paper is that deviations of the three variables from their estimated long-run relationship are better explained with uctuations of labour income than assets. A tentative explanation of this nding is presented. Additionally, the magnitude of the asset wealth eect in Poland is calculated and compared with other studies for European countries and for the U.S.

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 abrupt depreciation of the zloty during the subprime crisis and fastrising prices are serious problems, because Poland, having to fulfil five Maastricht criteria, makes the dependence of her domestic inflation on price increases in the EU countries the central point of the discussion about the optimal monetary and fiscal policy rules for the next few years. The primary objective of the paper is to test out some hypotheses about the main sources of the volatility of the Polish zloty / euro exchange rate and inflation in Poland. Because several competing theoretical models describing inflationary processes are widely used, special attention is paid to their empirical verification. The working-hypotheses allowing for the country-specific features of the consumer and producer price inflation are formulated and verified in the paper.

The aim of the study is to discuss the relationship of the crude oil price, speculative activity and fundamental factors. An empirical study was conducted with a VEC model. Two cointegrating vectors were identified. The first vector represents the speculative activity. We argue that the number of short non-commercial positions increases with the crude oil stock and price, decreases with the higher number of long non-commercial positions. A positive trend of crude oil prices may be a signal for traders outside the industry to invest in the oil market, especially as access to information could be limited for them. The second vector represents the crude oil price under the fundamental approach. The results support the hypothesis that the crude oil price is dependent on futures trading. The higher is a number of commercial long positions, the greater is the pressure on crude oil price to increase.

Small sample properties of unrestricted and restricted canonical correlation estimators of cointegrating vectors for panel vector autoregressive process are considered when the cross-sectional dependencies occur in the process generating nonstationary panel data. It is shown that the unrestricted Box-Tiao estimator is slightly outperformed by the unrestricted Johansen estimator if the dynamic properties of the underlying process are correctly specified. The comparison of performance of the restricted canonical correlation estimator of cointegrating vectors for the panel VAR and for the classical VAR applied independently for each cross-section reveals that the latter performs better in small samples when the cross-sectional dependence is limited to the error terms correlations, even though it is inefficient in the limit, but it falls short in comparison to the former when there are cross-sectional dependencies in the short-run dynamics and/or in the long-run adjustments.

The national total expenditure of a country is precipitated on several factors of which revenue generated could be one and very significant. This paper therefore examines the contribution of some selected sources of Nigerian government revenue to total national expenditure. Statistical and econometric techniques used for the data analysis are unit root test, cointegration test, combined estimators’ analysis, the error correction model (ECM) and the feasible generalized linear (FGLS) estimators. Results showed that the variables are non stationary but are stationary at first difference. The long-run relationship of total expenditure on oil revenue, non-oil revenue, federation account and federal retained revenue revealed that the variables are co-integrated and required the use of combined estimators. The effect of non-oil revenue and federal retained revenue is very significant. Investigations on the short-run modeling necessitated the use of FGLS estimators. The effect of ECM and federal retained revenue is very significant. Consequently, other sources of revenue apart from federal retained revenue need to be enhanced and tailored towards improving economic growth and development through national expenditure.

In 1993 Engle and Kozicki proposed the notion of common features of which one example is a serial correlation common feature. We say that stationary, non-innovation processes exhibit common serial correlation when there exists at least one linear combination of them which is an innovation. Later on in 1993 Vahid and Engle combined the notions of cointegration among I(1) processes with common serial correlation within their first differences. It is commonly known that cointegrated time series have vector error correction (VEC) representation. The existence of common serial correlation leads to an additional reduced rank restriction imposed on the VEC model’s parameters. This type of restriction was later termed a strong form (SF) reduced rank structure, as opposed to a weak one introduced in 2006 by Hecq, Palm and Urbain.

The main aim of the present paper is to construct the Bayesian vector error correction model with these additional strong form restrictions.

The empirical validity of investigating both the short- and long-run co-movements between macroeconomic time series will be illustrated by the analysis of the price-wage nexus in the Polish economy.

The purpose of the article is to verify a hypothesis about the asymmetric pass-through of crude oil prices to the selling prices of refinery products (unleaded 95 petrol and diesel oil). The distribution chain is considered at three levels: the European wholesale market, the domestic wholesale market and the domestic retail market. The error correction model with threshold cointegration proved to be an appropriate tool for making an empirical analysis based on the Polish data. As found, price transmission asymmetry in the fuel market is significant and its scale varies depending on the level of distribution. The only exception is the wholesale price transmission to the domestic refinery price. All conclusions are supported by the cumulative response functions. The analysis sheds new light on the price-setting processes in an imperfectly competitive fuel market of a medium-sized, non-oil producing European country in transition.

Foreign direct investment (FDI) and foreign portfolio investment (FPI) have been long considered as independent forms of international capital flows. This paper analyzes the mutual relationship between FDI and FPI and attempts to answer the question whether they complement or substitute for each other from a foreign investor’s point of view. The paper describes the main characteristics of FDI and FPI in terms of their volatility and profitability. We analyze the long-run and short-run relationships between FDI and FPI using vector error correction (VEC) regressions on data for Poland as it is the largest country in Central and Eastern Europe and receives the lion’s share of these two forms of capital in the region. Our investigation suggests that FDI and FPI may be regarded as substitutes. In economically stable periods FDI tends to dominate over FPI but during insecurity and economic distress FPI starts to gain importance.