Nonlinear Cointegration Research Articles

Nonlinear Cointegrating Power Function Regression with Endogeneity

This paper develops an asymptotic theory for nonlinear cointegrating power function regression. The framework extends earlier work on the deterministic trend case and allows for both endogeneity and heteroskedasticity, which makes the models and inferential methods relevant to many empirical economic and financial applications, including predictive regression. Accompanying the asymptotic theory of nonlinear regression, the paper establishes some new results on weak convergence to stochastic integrals that go beyond the usual semi-martingale structure and considerably extend existing limit theory, complementing other recent findings on stochastic integral asymptotics. The paper also provides a general framework for extremum estimation limit theory that encompasses stochastically nonstationary time series and should be of wide applicability.

Impact of changes in the level, slope and curvature of interest rates on U.S. sector returns: an asymmetric nonlinear cointegration approach

This article examines the sensitivity of U.S. sector equity indices to changes in nominal interest rates and in the corresponding principal components (level, slope and curvature of the U.S. yield curve) over the period 1990–2013 using factor models and a nonlinear autoregressive distributed lag (N.A.R.D.L.) approach. Furthermore, for robustness, this research analyses whether the sensitivity of sector stock returns is different depending on the stage of the economy, splitting the whole sample period into two sub-periods: pre-crisis and subprime crisis. In general, the empirical results confirm a substantial exposure to interest rate risk that depends on the model used and the period analysed. In addition, considering the three principal components of the U.S. yield curve, the sensitivity to changes in these components tends to be stronger during the subprime crisis sub-period. Finally, in the N.A.R.D.L. context, about 50% of sectors show long-run relations between sector stock returns and the explanatory factors, mainly during the whole sample and the pre-crisis sub-period. Nevertheless, short-run responses may be mostly shown in the subprime crisis sub-period. Therefore, our results evidence that nominal interest rates and its three components would have asymmetric effects on the U.S. stock returns at sector level, depending on the stage of the economy.

Impact of Oil Price Shocks on Stock Market Prices Volatility in Nigeria: New Evidence from a Non-linear ARDL Cointegration

This study examined the impact of oil price shocks on stock market prices volatility in Nigeria using non-linear cointegration approach labelled as Non-linear Autoregressive Distributed Lag (NARDL) which represents one of the major important contribution to the literature on the subject matter. The study was carried out using a quarterly data for the period of 1986 to 2016. The oil price shocks impact was disentangled or decomposed into oil supply shocks, oil demand shocks and oil specific demand shocks and the results from the empirical analysis revealed that, there is long run relationship among the variables and positive oil price shocks in its various forms which exert positive and significant impact on the volatility of stock prices in both long run and short run except for oil supply shock that have negative impact in the long run, while negative oil price shocks exert negative impact on the volatility of stock prices in both short and long run. However, the asymmetric result using Wald test shows that, the positive impact of these shocks on volatility of stock prices differs in both short run and long run. Therefore, the findings from the study affirmed the presence of nonlinear relationship between oil price shocks and stock prices volatility in Nigeria which is an indication that positive and negative oil price shocks affect stock prices volatility differently and this must be taking into consideration when formulating policy

Modelling Time-Varying Income Elasticities of Health Care Expenditure for the OECD

Income elasticity dynamics of health expenditure is considered for the OECD and the Eurozone over the period 1995-2014. This paper studies a novel non-linear cointegration model with fixed effects, controlling for cross-section dependence and unobserved heterogeneity. Most importantly, its coefficients can vary over time and its variables can be non-stationary. The resulting asymptotic theory is fundamentally different with a faster rate of convergence to similar kernel smoothing methodologies. A fully modified kernel regression method is also proposed to reduce the asymptotic bias. Results show a steep increase in the income elasticity for the OECD and a small increase for the Eurozone.

The Causal Dynamics in Indian Agriculture Commodity Prices and Macro-Economic Variables in the Presence of a Structural Break

Agriculture commodity prices have been quite volatile in India. The proposed study explores the effect of structural change on the flow of information between the spot and futures market of agriculture commodities and select macro-economic factors. The volatility in agriculture commodity prices is studied with respect to three dominant macro-economic factors—movement in crude price which serves as an input to agriculture sector, movement in INR/USD exchange rate and movement in Sensex which is considered as a barometer of investment in India. The study uses non-linear cointegration and causality test to understand the direction of causality in volatility of commodities and impact of macro-economic factors. The study observed the agriculture commodities spot and futures prices to be co-integrated with crude, forex and Sensex for majority of the break periods. We find robust evidence that futures market played a leading role in the price discovery function and information processing. Breaks in agriculture commodity prices are attributed to fundamentals of demand and supply in the market and global financial turmoil of 2007. We observed mixed results of influence of the exchange rate, Sensex and crude on agriculture prices in different sub-periods.

Price convergence in the UK supermarket chains: Evidence from nonlinear cointegration approach

Supermarket chain is an important sector of the UK grocery stores and the growing dominance of supermarket chains has brought public concern over exploitation of market power in the UK retail grocery industry. This paper therefore aims to examine the price convergence of the UK supermarket products. Since the cointegrating relationship between supermarket prices may not be exact or linear, we adopt the rank tests for analysis which do not require prior knowledge and specification of the linear or nonlinear functional form. Our results confirm the evidence of the price convergence of all grocery products and then validate the price competition between the UK supermarket chains. Furthermore, a subset of the cointegration relationships exhibits nonlinear long-run price co-movements.

Oil Prices and Chinese Stock Market: Nonlinear Causality and Volatility Persistence

ABSTRACTThis article mainly focuses on investigating the nonlinear co-integration and nonlinear causality relationships between oil prices and Chinese stock market at the overall and sectoral levels by using nonlinear autoregressive distributed lags (NARDL) model and Diks and Panchenko (DP) test. The empirical results show that there are not significantly asymmetric co-integration effects between oil prices and Chinese stock market for the overall and sectoral levels. However, the significantly nonlinear causality between oil prices and Chinese stock market can be found. Specifically, oil prices can widely affect Chinese stock indices through nonlinear channel. The cases in the reverse also work for overall indices and Mining, Utilities, Financial and Real Estate sectors. Furthermore, the potential sources of these nonlinear causality linkages are examined. The results suggest that volatility persistence rather than asymmetrical co-integration is the major factor that accounts for the nonlinear causality between oil prices and Chinese stock market.

Financial inclusion matters for economic growth in India

PurposeThe purpose of this paper is to examine the relationship between financial inclusion (FI) and economic growth in India.Design/methodology/approachTo 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.FindingsThe 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.Research limitations/implicationsThe 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.Practical implicationsAs 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.Originality/valueThe 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.

Further evidence on the validity of purchasing power parity in selected African countries

This article extended previous studies on testing the validity of purchasing power parity (PPP) in 16 African countries between 1970 M01 and 2017 M01. We employed these approaches: first, we investigated for the presence of unit roots in the real exchange rates (RERs) using the nonlinear ADF unit root test and the modified Wald-type test under an exponential smooth threshold autoregressive (ESTAR) framework; second, we used the detrended fluctuation analysis (DFA) to find out if RERs were mean- reverting by analyzing Hurst estimates of the RERs in absolute form and in a rolling window form. Finally, we used a nonlinear cointegration rank and score test to investigate if nominal exchange rates and relative prices are cointegrated. Our findings showed that RERs of each of the 16 countries in absolute form had unit roots and were not mean reverting. Also, nominal exchange rates and relative prices were not cointegrated. These findings indicate strong evidence against PPP theory in these countries. We, therefore, cannot use PPP as a basis for determining equilibrium exchange rates for these 16 countries. However, a time-varying DFA method on RERs provided mixed conclusions about the validity of PPP in these countries.

Exchange rate volatility and India's cross-border trade: A pooled mean group and nonlinear cointegration approach

This paper offers first-hand commodity-level evidence regarding the effects of exchange rate volatility on India's cross-border trade with the U.S., Germany, Japan, and China. We used autoregressive conditional heteroscedasticity based models to estimate the volatility of the nominal exchange rate. To determine the short and long run relationships, we used pooled mean group estimators. The results show that, in the long run, nominal exchange rate volatility has a significant dampening impact on India's export rates to the U.S., Germany, and China along with imports from the U.S. and China. However, in the short run, the effects of the nominal exchange rate volatility on India's exports and imports were rather mixed. The study also tested the asymmetric effects of exchange rate volatility on India's trade using aggregated data. Although the results do not show much of an asymmetric effect, they do indicate that positive and negative effects differ in terms of their impact on trade volume. Policy recommendations are therefore suggested on the basis of these results.

The real peso–dollar rate and US–Mexico industry trade: an asymmetric analysis

AbstractIn an attempt to improve upon previous analyses and find further evidence for exchange rate theories such as the ‘J‐curve', numerous studies have introduced novel econometric approaches that might help uncover significant results through disaggregation and nonlinearity. This study applies the nonlinear cointegration method of Shin et al. () to US–Mexican trade balances in 91 individual industries. While the linear model yields support for the ‘J‐curve' effect in 16 industries, the nonlinear model raises this number to 29 which includes the two largest industries that engage in 35% of the trade between two countries. Furthermore, while the short‐run asymmetric effects of exchange rate changes were discovered in almost all industries, short‐run effects translated to significant long‐run asymmetric effects in 52 industries.

A cointegrating polynomial regression analysis of the material kuznets curve hypothesis

This paper investigates the Material Kuznets Curve (MKC) hypothesis, postulating an inverted U-shaped relationship between a country's level of economic development and its intensity of material use, by means of nonlinear cointegration analysis. We use consumption data for aluminum, lead and zinc for eight OECD countries spanning from 1900 to 2006 and employ the tests and estimation techniques for nonlinear cointegration developed by Saikkonen and Choi (2004), Wagner (2013) as well as Wagner and Hong (2016). We find evidence for the prevalence of a cointegrating quadratic MKC for about half of the country-metal pairs.

Time-variation in the relationship between white precious metals and inflation: A cross-country analysis

In recent years, as a result of an increasing financialisation of financial markets, white precious metals have slowly transformed from mere production inputs to investment assets. In order to analyse the characteristics of white precious metals and the consequences of the transition, this paper examines the long-run inflation hedging effectiveness of silver, platinum, and palladium using both linear and non-linear cointegration relationship procedures. This study is the first to formally investigate the inflation hedging effectiveness of white precious metals across different countries. Overall, the results point towards the superiority of palladium as the most reliable inflation hedge. Furthermore, country-specific graphical evidence uncovers time-variation in the inflation hedging potential of white precious metals.

A new Cramer-Von Misses cointegration test with application to environmental Kuznets curve

ABSTRACTThis article introduces a new Cramer-Von Misses (CVM) cointegration test robust to nonlinearities. We characterize nonlinear cointegration in terms of a nonlinear moving-average filter (high pass filter) of a matrix based on permutation matrices on the discrepancy of empirical distributions. A Cramer-Von Misses (CVM) test statistic is proposed for testing the null hypothesis of two independent random walks against a broad range of cointegrating alternatives with monotonic nonlinearities and level shifts in the cointegration relationship. We derive the asymptotic distribution of this induced-order Cramer-Von Misses (CVM) cointegration test. This new non-parametric test statistic has two important properties: the invariance to monotonic transformations of the series and the robustness for the presence of several parameter shifts or structural changes. We analyse the small sample properties of this test by Monte Carlo simulations and evaluate the power of the test. Finally, this CVM test is applied to the analysis of long run environmental Kuznets curve which relates economic growth and pollution. In particular, we consider a nonlinear cointegration between gross domestic product (GDP) and CO2 emissions. Our new CVM test is able to find evidence of cointegration while classical single equation cointegration tests are not.

Nonlinear short-run adjustments between house and stock prices in emerging Asian regions

This study uses the powerful nonparametric cointegration test to examine whether nonlinear cointegration exists between prices of used houses and corresponding stock markets in China and the four Asian Tigers. Then, it uses the smooth transition vector error-correction model (STVECM) to explore the adjustment efficiencies of the short-run house and corresponding stockreturn dynamics when there is disequilibrium between house and stock prices. The empirical results indicate that there is a nonlinear cointegration between the house prices and corresponding stock prices in China, South Korea, Singapore, and Taiwan, and that the speed of price adjustment to equilibrium is always greater for houses than stocks when there are large positive and negative deviations. Moreover, the short-run speed of adjustment of the large negative and positive deviations is equal in China, South Korea, and Taiwan, but unequal in Singapore. With the exception of South Korea, the results of the Granger causality test indicate that stock prices clearly lead used house prices, which means a wealth effect exists in most Asian countries. Our study confirms that the STVECM can be used to analyze the short-run adjustment efficiency of house and stock return dynamics in China, South Korea, Singapore, and Taiwan; thus, supporting models of interaction between noise and arbitrage traders.

Co-integration Between Globalisation and Economic Growth

<span class="fontstyle0">This paper analyses the co-integration relationship between globalisation and economic<br />growth of 27 more or less developed countries across almost all Continents for the time period<br />1970–2013. Globalisation is </span><span class="fontstyle2">proxied </span><span class="fontstyle0">by the overall globalisation index and the sub-indices<br />representing economic globalisation, social globalisation and political globalisation, all<br />provided by the Swiss Economic Institute. Economic growth is measured through the natural<br />logarithm of the real Gross Domestic Product, sourced from the World Development<br />Indicators which are provided by the World Bank. Co-integration is tested with quantile cointegration regressions. The results obtained clearly confirm the existence of non-linear cointegration relationships between the considered globalisation indices and the real economic<br />growth.</span>

Co-integration Between Globalisation and Economic Growth

<span class="fontstyle0">This paper analyses the co-integration relationship between globalisation and economic<br />growth of 27 more or less developed countries across almost all Continents for the time period<br />1970–2013. Globalisation is </span><span class="fontstyle2">proxied </span><span class="fontstyle0">by the overall globalisation index and the sub-indices<br />representing economic globalisation, social globalisation and political globalisation, all<br />provided by the Swiss Economic Institute. Economic growth is measured through the natural<br />logarithm of the real Gross Domestic Product, sourced from the World Development<br />Indicators which are provided by the World Bank. Co-integration is tested with quantile cointegration regressions. The results obtained clearly confirm the existence of non-linear cointegration relationships between the considered globalisation indices and the real economic<br />growth.</span>

The impact of interest rate volatility on financial market inclusion: evidence from emerging markets

Interest rate uncertainty adversely affects financial market performance and, eventually, economic growth. This study investigates the relationship between interest rate volatility and financial market inclusion for five selected emerging economies over the period 1980–2015. To do this, we assess the long-run and short-run relationship using Pesaran et al. (J Appl Econ 16:289–326, 2001) bounds testing approach to cointegration and error-correction modeling and Shin et al. (2014) nonlinear cointegration estimation method (NARDAL). The latter method incorporates nonlinearity into the model and enables us to check the asymmetric effects of interest rate variability on financial market inclusion. The findings of our linear models indicate that short-run symmetric effects lead to long-run symmetric effects in four countries (Turkey is the exception) and there is a long-run symmetric effect for the other four countries. On the other hand, estimation of nonlinear models shows the short-run existence of asymmetric effects for all five emerging economies. We found that the long-run effect of interest rate volatility is asymmetric in all countries except for Mexico. We suggest that this group of countries should cautiously pay attention to laws and regulations related to their financial market and interest rate policies. Our estimation results show that interest rate uncertainty significantly affects financial market inclusion and has an important role in financial market development and eventually achieving higher economic growth.

Asymmetric and nonlinear inter-relations of US stock indices

PurposeThe purpose of this paper is to examine the inter-relations among the US stock indices.Design/methodology/approachData of nine US stock indices spanning a period of sixteen years (2000-2015) are employed for this purpose. Asymmetries are examined via an error correction model. Non-linear inter-relations are researched via Breitung’s nonlinear cointegration, a M-G nonlinear causality model, shocks to the forecast error variance, a shock spillover index and an asymmetric VAR-GARCH (VAR-ABEKK) approach.FindingsThe inter-relations are significant. The results are robust across all types of inter-relations. They are highest in the Lehman Brothers sub-period. Higher stability after the EU debt crisis, enhances independence and growth for the US stock indices.Originality/valueTo the best of the knowledge, this is the first study to examine the inter-relations of US stock indices. Most studies on inter-relations concentrate on the portfolio analysis to reveal diversification benefits among various asset markets internationally. Hence this study contributes to this literature on the inter-relations of a specific asset market (stock), and in a specific nation (USA). The evident inter-relations support the notion of diversification benefits in the US stock markets.

Asymmetries, outliers and structural stability in the US gasoline market

By using a recently developed nonlinear cointegration methodology, and a sample that encompasses more than thirty years of monthly data, we investigate whether the transmission of crude oil price variations to gasoline prices in the US market is asymmetric, i.e.,depends on the sign of the change in the explanatory variable, considering both the long- and the short-run. The model is further extended by taking separately into account the effects of extreme and mild changes in crude oil prices. This allows us to verify whether and to what extent the size and shape of any observed asymmetry in pricing is affected by the presence of outliers. Moreover, given the substantial length of the sample considered, we test for the possible presence of multiple structural breaks of unknown timing in the cointegrating vector. Our results indicate that the relationship between the prices of gasoline and crude oil has undergone a single structural break in the late 2008, and that after the break extreme observations have a non-negligible role in shaping asymmetry.