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This survey focuses on two families of nonlinear vector time series models, the family of vector threshold regression (VTR) models and that of vector smooth transition regression (VSTR) models. These two model classes contain incomplete models in the sense that strongly exogeneous variables are allowed in the equations. The emphasis is on stationary models, but the considerations also include nonstationary VTR and VSTR models with cointegrated variables. Model specification, estimation and evaluation is considered, and the use of the models illustrated by macroeconomic examples from the literature.

This paper proposes an efficient test designed to have power against alternatives where the error correction term follows a Markov switching dynamics. The adjustment to long run equilibrium is different in different regimes characterised by the hidden state Markov chain process. Using a general nonlinear MS-ECM framework, we propose an optimal test for the null of no cointegration against an alternative of a globally stationary MS cointegration. The Monte Carlo studies demonstrate that our proposed tests display superior powers compared to the linear tests. In an application to price-dividend relationships, our test is able to find cointegration while linear based tests fail to do so.

Purpose – This chapter aims to investigate the stock market comovements between Mexico and the world capital market using nonlinear modeling tools.

Methodology/approach – We apply recent nonlinear cointegration and nonlinear error correction models (NECMs) to investigate the comovements between stock prices over the recent period.

Findings – While the previous literature only highlights some evidence of time-varying comovements, our chapter aims to specify the mechanism characterizing the comovement process through the comparison of two nonlinear error correction models (NECMs). It shows a nonlinear relationship between stock prices that are activated per regime.

Originality – Studying the integration hypothesis between stock markets over the recent financial crisis, our findings highlight strong evidence of significant comovements that explain the global collapse of stock markets in 2008–2009.

The purpose of this paper is to examine the relationship between financial inclusion (FI) and economic growth in India.

To measure FI, a multidimensional time-varying index is proposed following the Human Development Index method. The long-run relationship between FI and economic growth is examined by using the autoregressive distributed lag (ARDL) approach to cointegration and nonlinear ARDL approach. Further, the direction of causality is investigated by employing the Toda–Yamamoto Granger causality test.

The linear cointegration test confirms a long-run relationship between FI and economic growth for India. The improvement in both demand-side and supply-side financial services has a positive impact on economic growth. These results suggest that India can attain long-run economic growth by improving the coverage of FI. However, there is no evidence of nonlinear cointegration, indicating that there is no asymmetric effect of FI on economic growth. Further, the causality test shows that FI granger causes economic growth but not vice versa.

The major limitation of the study is the availability of time series data for all important variables. The index for both demand- and supply-side indicators can be extended with several other important variables in later date once the data are available for those variables.

As the study confirms that FI is one of the main drivers of economic growth, it is suggested that the policy maker emphasizing on financial sector reforms can enjoy economic growth in the long run, especially in developing countries. Therefore, the government and policy makers need to address the issues involved in access to financial services to spur economic growth.

The study examines the long-run relationship between FI and economic growth employing ARDL bound testing approach and nonlinear ARDL approach, separately for demand-side and supply-side indicators. Further, the study uses the Toda–Yamamoto granger causality to find the direction of causal flow between FI and economic growth.

The purpose of this paper is to explore the dynamic interdependence structure and risk spillover effect between the Chinese stock market and the US stock market.

This paper mainly uses the multivariate R-vine copula-complex network analysis and the multivariate R-vine copula-CoVaR model and selects stock price indices and their subsector indices as samples.

The empirical results indicate that the Energy, Materials and Financials sectors have leading roles in the interdependent structure of the Chinese and US stock markets, while the Utilities and Real Estate sectors have the least important positions. The comprehensive influence of the Chinese stock market is similar to that of the US stock market but with smaller differences in the influence of different sectors of the US stock market on the overall interdependent structure system. Over time, the interdependent structure of both stock markets changed; the sector status gradually equalized; the contribution of the same sector in different countries to the interdependent structure converged; and the degree of interaction between the two stock markets was positively correlated with the degree of market volatility.

This paper employs the methods of nonlinear cointegration and the R-vine copula function to explore the interactive relationship and risk spillover effect between the Chinese stock market and the US stock market. This paper proposes the R-vine copula-complex network analysis method to creatively construct the interdependent network structure of the two stock markets. This paper combines the generalized CoVaR method with the R-vine copula function, introduces the stock market decline and rise risk and further discusses the risk spillover effect between the two stock markets.

This chapter develops an asymptotic theory for a general transformation model with a time trend, stationary regressors, and unit root nonstationary regressors. This model extends that of Han (1987) to incorporate time trend and nonstationary regressors. When the transformation is specified as an identity function, the model reduces to the conventional cointegrating regression, possibly with a time trend and other stationary regressors, which has been studied in Phillips and Durlauf (1986) and Park and Phillips (1988, 1989). The limiting distributions of the extremum estimator of the transformation parameter and the plug-in estimators of other model parameters are found to critically depend upon the transformation function and the order of the time trend. Simulations demonstrate that the estimators perform well in finite samples.

This paper aims to examine the effects of the real exchange rate on trade balance in Algeria and investigates whether it represents a viable tool to sustain and improve trade performance using the nonlinear autoregressive distributed lag (NARDL) estimation technique and data from Algeria over the period 1980–2018. This study also highlights the role of trading partners with large income endowments in enhancing the trade balance.

The NARDL model is used to unveil potential short and long run nonlinear responses of the trade balance to shocks in real exchange rates and detect whether these responses are different in terms of sign and magnitude. The paper also provides a dynamic multiplier analysis that tests the existence of a J-Curve pattern in Algeria with several policy recommendations.

The findings confirm the existence of a J-curve pattern in Algeria where domestic currency depreciation will worsen the trade balance in the short run and improve it in the long run. The authors also find that the asymmetrical effect of real exchange rate on trade balance is different in sign and magnitude. Finally, the results indicate that an increase in trade partners' income increases the trade balance in Algeria. The findings are of utmost importance with several policy implications.

While some works investigated the nonlinear response of trade balance to real exchange rate movements, their results remain inconclusive and seem to depend on the characteristics of the country/region of study. Moreover, the role of trade partners and their potential impact on trade balance has been relatively overlooked in the literature. The authors fill this gap by examining the asymmetric impacts of real exchange rate and the effect of trade partners' income on trade balance in Algeria.

This paper investigates the causality among gold prices, crude oil prices, bitcoin and stock prices by using daily data from January 2014 to December 2021. The study also examines the data during the COVID-19 outbreak from January 2020 to December 2021.

To estimate the long- and short-run causality, this study considers the nonlinear autoregressive distributed lag (NARDL) cointegration test.

The analysis found the existence of an asymmetric long-run cointegration among selected assets. Findings indicate that positive changes in bitcoin do not affect stock market in the long term. Changes in crude oil prices have a significant impact on stock prices. Moreover, it is observed that variations in the stock prices trigger a negative impact on gold prices. During the COVID-19 period, the study notices the presence of an asymmetric long-term cointegration between selected assets except bitcoin. Besides, findings revealed that negative price adjustments in gold lead to significant positive shocks in stock market.

These results provide critical information for policy performers and researchers to develop new strategies. Policy regulators can also consider the potential effects of the COVID-19 outbreak while developing strategies for investment decisions.

Departing from the expansionary austerity literature, this study aims at examining how fiscal consolidation affects the economic growth in Tunisia using annual data over the period 1970–2018.

To revisit the fiscal consolidation-economic growth nexus, the ambiguous empirical findings in previous literature make useful the adoption of alternative econometric techniques. The authors use an extended nonlinear autoregressive distributed lag (ARDL) cointegration approach developed by Shin et al. (2014) and the Diks and Panchenko's (2006) nonlinear Granger causality test. Furthermore, a traditional approach based on changes in cyclically-adjusted primary balance was applied to define the fiscal consolidation episodes in Tunisia.

The empirical evidence reveal that fiscal adjustment in Tunisia may hurt the economy, both in the short- and long-run, through its contractionary effect on economic growth. Another important finding concerns the unidirectional nonlinear Granger causality running from fiscal consolidation to economic growth.

Fiscal adjustment in Tunisia is found to play a prominent role in reducing public debt; but at the same time, it may be costly and not beneficial to the economy. This view corroborates with the fact that fiscal consolidation is more likely to end successfully only under specific conditions. This calls for a deeper reflection upon new insights regarding the design of fiscal adjustment in Tunisia. To reach this end, it is suggested to combine the defensive consolidation strategy with offensive components such as investment, infrastructure, education and health.

The existing economic analysis on fiscal policy-growth nexus in Tunisia has often identified fiscal consolidation through the use of the actual fiscal balance. With the goal of more accurate estimation, this study bridges the gap by using the cyclically-adjusted primary balance (CAPB) as a much suitable indicator to investigate the non-Keynesian effect of fiscal consolidation in Tunisia. This indicator eliminates the influence of cyclical fluctuations and many other fixed expenditures such as the interest paid on the public debt.

This paper aims to scrutinize the asymmetric interactions between current account deficit and gross fiscal deficit in case of a growing and dynamically integrated economy, namely, India featured with high inequality and liquidity constraints. Two additional variables, trade-openness and output growth, are also incorporated into the analysis to assess their likely impact on the current account balance.

The study uses a recently developed non-linear autoregressive distributed lag model given by Shin et al. (2014) in its empirical examination. In addition, non-linear cumulative dynamic multipliers are used to understand the route between disequilibrium position of short-run and subsequent long-run equilibrium of the system.

The study confirms the long-run co-movements of current account deficit and gross fiscal deficit and therefore refutes the Ricardian Equivalence proposition and validates the twin-deficit hypothesis. But instead of a linear relationship of the kind examined in the previous studies, the two variables share asymmetric linkages – both in the short run and in the long run. The asymmetry indicates that positive changes are more influential than their negative counterparts in the short run, whereas in the long run, only the positive changes are found to alter the external balance statistically. The asymmetric impact of fiscal deficits on the current account balance of a country may arise due to its asymmetric impact on aggregate demand through consumption inflexibility (ratchet effect) and the existence of liquidity constraints. The other control variables used in the study are also found to have cointegration with the current account deficit, but the relationship is symmetrical in the long run, even though it is asymmetrical in the short run. The study finally uses the asymmetric cumulative dynamic multipliers to examine the route of asymmetries and adjustments over the course of time. The dynamic multipliers also confirm the results documented in the earlier part and therefore demonstrate their robustness.

The asymmetric results obtained in the study provide strong grounds to devise the policies adaptive to changing arenas in domestic and external sectors. Output growth, export promotion and import substitution, increasing integration and fiscal austerity are seen as helpful in achieving a desired (and growth conducive) external balance together with macroeconomic stability. The need for a prudent fiscal policy and avoidance of profligacy is indicated based on the asymmetric results to ward off any unfavorable impact of fiscal deficits on external account. To conduct a sound fiscal policy, the government needs to cut down unproductive consumption expenditure, raise tax revenues and should pay attention to distribution and trickle-down effects to avoid the adversity of high inequality and liquidity constraints in the economy. Moreover, to ameliorate the current account balance, policies aimed at increasing the real competitiveness through control of domestic price fluctuations and improvement in the quality of tradable goods and services (such as productive investments and technological advancements) should be adopted.

Work reported in the present paper is motivated by the fact that there is no study conducted so far in the Indian context which has analyzed the two deficits in a nonlinear framework. The authors have used a well-articulated nonlinear asymmetric technique to examine the relationship between two deficits when asymmetry is incorporated. This paper will, therefore, enrich the existing literature along the lines of asymmetric linkages. Moreover, the traverse of asymmetries and adjustments over the course of time highlights the inherent dynamism of the relationship.