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Vector error-correction models (VECMs) have become increasingly important in their application to financial markets. Standard full-order VECM models assume non-zero entries in all their coefficient matrices. However, applications of VECM models to financial market data have revealed that zero entries are often a necessary part of efficient modelling. In such cases, the use of full-order VECM models may lead to incorrect inferences. Specifically, if indirect causality or Granger non-causality exists among the variables, the use of over-parameterised full-order VECM models may weaken the power of statistical inference. In this paper, it is argued that the zero–non-zero (ZNZ) patterned VECM is a more straightforward and effective means of testing for both indirect causality and Granger non-causality. For a ZNZ patterned VECM framework for time series of integrated order two, we provide a new algorithm to select cointegrating and loading vectors that can contain zero entries. Two case studies are used to demonstrate the usefulness of the algorithm in tests of purchasing power parity and a three-variable system involving the stock market.

The purpose of this paper is to provide an extensive review of the monetary model of exchange rate determination which is the main theoretical framework on analyzing exchange rate behavior over the last 40 years. Furthermore, we test the flexible price monetarist variant and the sticky price Keynesian variant of the monetary model. We conduct our analysis employing a sample of 14 advanced economies using annual data spanning the period 1880–2012.

The theoretical background of the paper relies on the monetary model to the exchange rate determination. We provide a thorough econometric analysis using a battery of unit root and cointegration testing techniques. We test the price-flexible monetarist version and the sticky-price version of the model using annual data from 1880 to 2012 for a group of industrialized countries.

We provide strong evidence of the existence of a nonlinear relationship between exchange rates and fundamentals. Therefore, we model the time-varying nature of this relationship by allowing for Markov regime switches for the exchange rate regimes. Modeling exchange rates within this context can be motivated by the fact that the change in regime should be considered as a random event and not predictable. These results show that linearity is rejected in favor of an MS-VECM specification which forms statistically an adequate representation of the data. Two regimes are implied by the model; the one of the estimated regimes describes the monetary model whereas the other matches in most cases the constant coefficient model with wrong signs. Furthermore it is shown that depending on the nominal exchange rate regime in operation, the adjustment to the long run implied by the monetary model of the exchange rate determination came either from the exchange rate or from the monetary fundamentals. Moreover, based on a Regime Classification Measure, we showed that our chosen Markov-switching specification performed well in distinguishing between the two regimes for all cases. Finally, it is shown that fundamentals are not only significant within each regime but are also significant for the switches between the two regimes.

The results are of interest to practitioners and policy makers since understanding the evolution and determination of exchange rates is of crucial importance. Furthermore, our results are linked to forecasting performance of exchange rate models.

The present analysis extends previous analyses on exchange rate determination and it provides further support in favor of the monetary model as a long-run framework to understand the evolution of exchange rates.

Conventional methods to test for long-term PPP based on the theory of cointegration are typically undertaken in the framework of vector error correction models (VECM). The standard approach in the use of VECMs is to employ a model of full-order, which assumes nonzero entries in all the coefficient matrices. But, the use of full-order VECM models may lead to incorrect inferences if zero entries are required in the coefficient matrices. Specifically, if we wish to test for indirect causality, instantaneous causality, or Granger non-causality, and employ “overparameterised” full-order VECM models that ignore entries assigned a priori to be zero, then the power of statistical inference is weakened and the resultant specifications can produce different conclusions concerning the cointegrating relationships among the variables. In this paper, an approach is presented that incorporates zero entries in the VECM analysis. This approach is a more straightforward and effective means of testing for causality and cointegrating relations. The paper extends prior work on PPP through an investigation of causality between the U.S. Dollar and the Japanese Yen. The results demonstrate the inconsistencies that can arise in the area and show that bi-directional feedback exists between prices, interest rates and the exchange rate such that adjustment mechanisms are complete within the context of PPP.

The “Fed Model” postulates a cointegrating relationship between the equity yield on the S&P 500 and the bond yield. We evaluate the Fed Model as a vector error correction forecasting model for stock prices and for bond yields. We compare out-of-sample forecasts of each of these two variables from a univariate model and various versions of the Fed Model including both linear and nonlinear vector error correction models. We find that for stock prices the Fed Model improves on the univariate model for longer-horizon forecasts, and the nonlinear vector error correction model performs even better than its linear version.

This chapter analyzes the exchange rate pass-through (ERPT) into different prices for 12 euro area (EA) countries. We provide new up-to-date estimates of ERPT by paying attention to either the time-series properties of data and variables endogeneity. Using VECM framework, we examine the pass-through at different stages along the distribution chain, that is, import prices, producer prices, and consumer prices. When carrying out impulse response functions analysis, we find a higher pass-through to import prices with a complete pass-through (after one year) detected for roughly half of EA countries. These estimates are relatively large compared to single-equation literature. We denote that the magnitude of the pass-through of exchange rate shocks declines along the distribution chain of pricing, with the modest effect recorded for consumer prices. When assessing for the determinant of cross-country differences in the ERPT, we find that inflation level, inflation volatility, and exchange rate persistence are the main macroeconomic factors influencing the pass-through almost along the pricing chain. Thereafter, we have tested for the decline of the response of consumer prices across EA countries. According to multivariate time-series Chow test, the stability of ERPT coefficients was rejected, and the impulse responses of consumer prices over 1990–2010 provide an evidence of general decline in rates of pass-through in most of the EA countries. Finally, using the historical decompositions, our results reveal that external factors, that is, exchange rate and import prices shocks, have had important inflationary impacts on inflation since 1999 compared to the pre-EMU period.

This paper proposes a Bayesian procedure to investigate the purchasing power parity (PPP) utilizing an exponential smooth transition vector error correction model (VECM). Employing a simple Gibbs sampler, we jointly estimate the cointegrating relationship along with the nonlinearities caused by the departures from the long-run equilibrium. By allowing for nonlinear regime changes, we provide strong evidence that PPP holds between the US and each of the remaining G7 countries. The model we employed implies that the dynamics of the PPP deviations can be rather complex, which is attested to by the impulse response analysis.

This paper investigates forecasting US Treasury bond and Dollar Eurocurrency rates using the stochastic unit root (STUR) model of Leybourne et al. (1996), and the stochastic cointegration (SC) model of Harris et al. (2002, 2006). Both models have time-varying parameter representations and are conceptually attractive for modelling interest rates as both allow for conditional heteroscedasticity. I find that for many of the series considered STUR and SC models generate statistically significant gains in out-of-sample forecasting accuracy relative to simple orthodox models. The results obtained highlight the usefulness of these extensions and raise some issues for future research.

In this chapter, we apply an efficient subset of vector error correction model (VECM) using the forgetting factor to examine the cointegration under climate change of the time series of the gross domestic product (GDP) and the industrial production and that of the utilization and consumption of important metals such as copper and steel in some important OECD countries as well as some selected newly industrialized Asian and Latin American countries. Both the long-term and the short-term dynamic relations among these variables are examined and the implications are discussed.

Recent evidences show that terrorism is becoming frequent in Nigeria, ranging from incessant Boko Haram activities in the North East; Independent People of Biafra (IPOB) activities in the South-East states, kidnapping and vandalizing oil pipes in the South-South, Fulani-herdsmen attacks in the Middle Belt, among others. In an attempt to tackle terrorism, the Federal Government at different times adopted military actions with little or no lasting solution. The Have and Have-nots hypothesis (Shahbaz, 2013) stresses the role of economic phenomenon in determining the causes of terrorism. It is on this note that this chapter investigates the linkages between economic growth proxy by gross domestic product per capita (GDPPC) and other fundamental variables such as inflation, unemployment, and inequality gaps, among others; and terrorism in Nigeria. We intend to know whether cointegration exists between the two constructs; and if it does, is there causality? The study employed both the autoregressive distributed lag (ARDL) and the vector error correction model (VECM) approaches to examine the existence of or otherwise a long-run relationship as well as causality among the constructs. Results reveal that a compelling cointegrating relationship exists among the variables. It is further revealed that unemployment, inequality, poverty, inflation, among others, Granger cause terrorism. It stresses that the Have-not hypothesis explained the causes of terrorism in Nigeria. The study therefore suggests that policy makers should, in order to prevent or combat terrorism, focus on improving the economy by creating job opportunities through provision of conducive environment that supports businesses and reduces inequality gaps.

Industry 5.0 has shown a new approach to integrating enterprises, particularly fintech firms. It would be interesting to see whether we are ready to implement Industry 5.0 across domains and enterprises while there are still obstacles to overcome, such as cybercrime impacting fintech organizations. Using empirical analysis of the fintech stocks that make up the KBW index, the author uncovered the influence of cybercrime on investor herding behavior in a highly interdependent environment provided by Industry 4.0. The cross-sectional standard deviation has been shown to rise after a cyber attack on a company anywhere on the globe. Furthermore, the author established the long-term equilibrium of the volatilities of gold and bitcoin returns, as well as the volatility of Keefe, Bruyette, and Woods (KBW) returns, in the sample after the firms’ cyber assault using Vector Auto Regressive (VAR) and Vector error correction model (VECM) models. Following the cyber assault, there is a decrease in the volatility of KBW returns while the volatility of bitcoin returns rises, suggesting a volatility transfer from one market to the other. These results show that during times of crisis, investors should be more careful in their approach to investment diversification, and any Industry 5.0 implementations should be done with the constraints in mind.