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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.

The purpose of this paper is to investigate the behavior peculiarities of the labor force participation in Eastern European countries.

The authors provide the analysis of nonlinearity in dynamics of economic active population and perform the econometric analysis using logistic smooth transition autoregressive models that are flexible and capture various kinds of behavior for different modes. The paper investigates labor markets of six Eastern European countries, Hungary, Bulgaria, Poland, Slovakia, Romania and Croatia that are characterized by lower level of labor force participation rate (LFPR) than average level in EU.

The results of modeling quantitatively characterize smooth changes in the behavior modes of labor force activity for each country and indicate how population economic activity depends on previous labor market states. The estimated slope parameters that determine the smoothness of transition between regimes show that, in all countries, the labor force participation quite quickly reacts to changes that occurred on the labor market in the past. During recession periods, households of European countries that joint EU last decade in order to prevent the depletion of their total income increased labor supply and showed increased activity in job search.

This paper indicates the nonlinearity and asymmetry in LFPR in transition economies, discovers variety of its dynamics in the different regimes and determines the indicators that cause the change of the population economic activity behavior in each country.

Standard economic theory predicts that any increase in public spending is accompanied by a rise in inflation in an economy. This paper presents empirical proof that prices do not always rise with an increase in public expenditure but only up to a certain threshold level. The primary aim of this paper is to unearth the government size-inflation nexus in India for the period from 1971 to 2019.

The logistic STAR (smooth transition autoregression) model is employed to unravel the government size-inflation nexus for the Indian economy from a non-linear perspective.

The finding of our study confirm the non-linear relationship between the size of the government and inflation in India. The estimated threshold level for government size is precisely found to be 9.27%. The size of the government exerts a negative influence on inflation until it reaches the optimal or threshold level. Any further increase in the size of government beyond this threshold level would result in a rise in inflation.

The findings have implications for the conduct of fiscal policy. Policymakers can increase government spending in a regime of small government size without having any inflationary impacts by generating revenues from taxes and other sources instead of relying much on the central bank. In the regime of a large-sized government, adhering strictly to the discipline in the conduct of fiscal and monetary policies would help curb inflation and enhance growth synchronously, hence alleviating any loss of welfare.

To the best of the authors’ knowledge, this study is an attempt to revisit the government size-inflation nexus in India from a non-linear perspective using the Smooth Transition Autoregression (STAR) model for the first time.

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.

The aim of this chapter is to assess the real exchange rate misalignments. A smooth transition autoregressive model (STAR) is used for Tunisian exchange market. This model allows us to see whether these differences are temporary or persistent over the period 1975–2012. We start by defining the exchange rate’s fundamental determinants to provide the equilibrium exchange rate value. Then, we study the observed exchange rate adjustment toward its equilibrium level. Vector autoregressive model and vector error correction model are applied to characterize the joint dynamics of variables in the long run. The results indicate a long-run relationship between variables. In order to consider the nonlinearity for better results, we will move to nonlinear smooth transition model. We found there is a high degree of exchange rate misalignment. We recognized that this difference decreases in the long run and disappears at the end.

The purpose of this paper is to identify the level of natural gas consumption that can be adjudged as capable of improving the growth of the Nigerian economy, to investigate whether natural gas consumption is at optimal level in Nigeria and to examine the nature and rate to which natural gas consumption affects economic growth in Nigeria at low and high regimes.

The tool used to achieve the objectives of the paper is the smooth transition regression (STR) model.

The findings of the paper are that the relationship between natural gas consumption and economic growth in Nigeria is asymmetric, where the natural gas consumption threshold value in the country is 9085.36 standard cubic meters, whereas the level of its consumption in the country is below the optimal level. Further, in both low and high regimes, natural gas consumption has been found to have a positive and significant impact on economic growth in Nigeria.

The policy implication of the paper is that natural gas consumption in Nigeria should not be less than 9085.36 standard cubic meters and the country should intensify efforts to increase the level of natural gas consumption, as it is below the optimal level and its consumption bolsters the growth of Nigerian economy.

What is new in this paper is its ability to use the STR model. To the best of the authors’ knowledge, such methodology has not been adopted before in such a relation.

The purpose of this study is to investigate the nonlinear effects of renewable energy (RE) consumption and economic growth on per capita CO₂ emissions during the time span from 1980 to 2020.

The study uses the logistic smooth transition autoregression (STAR) model to decipher the nonlinear relationship between RE consumption, economic growth and CO₂ emissions in the Indian economy.

The estimated results confirm a nonlinear relationship between India’s economic growth, RE consumption and CO₂ emissions. The authors found that economic growth positively impacts CO₂ emissions until it reaches a specific threshold of 1.81 (per capita growth). Beyond this point, further economic growth leads to a reduction in CO₂ emissions. Similarly, RE consumption positively affects CO₂ emissions until economic growth reaches the same threshold level, after which an increase in RE consumption negatively impacts CO₂ emissions.

The study suggests that India should optimize the balance between economic growth and RE consumption to mitigate CO₂ emissions. Policymakers should prioritize the adoption of RE during the early stages of economic growth. As economic growth reaches the specific threshold of 1.81 per capita, the economy should shift to more sustainable and energy-efficient practices to limit the effect of further CO₂ emissions on further economic growth.

To the best of the authors’ knowledge, this study represents the first-ever endeavor to reexamine the nonlinear relationship between RE consumption, economic growth and CO₂ emissions in India, using the STAR model.