Tests for causality between integrated variables using asymptotic and bootstrap distributions: theory and application

Abstract

Causality tests in the Granger's sense are increasingly applied in empirical research. Since the unit root revolution in time-series analysis, several modifications of tests for causality have been introduced in the literature. One of the recent developments is the Toda-Yamamoto modified Wald (MWALD) test, which is attractive due to its simple application, its absence of pre-testing distortions, and its basis on a standard asymptotical distribution irrespective of the number of unit roots and the cointegrating properties of the data. This study investigates the size properties of the MWALD test and finds that in small sample sizes this test performs poorly on those properties when using its asymptotical distribution, the chi-square. It is suggested that use be made of a leveraged bootstrap distribution to lower the size distortions. Monte Carlo simulation results show that an MWALD test based on a bootstrap distribution has much smaller size distortions than corresponding cases when the asymptotic distribution is used. These results hold for different sample sizes, integration orders, and error term processes (homoscedastic or ARCH). This new method is applied to the testing of the efficient market hypothesis.

Two Deficits and Economic Growth: Case of CEE Countries in Transition

“…The bootstrap procedure applied in this paper was based on resampling leveraged residuals, which minimizes the undesirable influence of heteroscedasticity ( [18]). 11 This approach has often been applied in recent empirical causality investigations conducted on basis of relatively small datasets (see e.g.…”

Temporal causality between house prices and output in the US: A bootstrap rolling-window approach

“…Moreover, evaluation of properties of the RBB method in VAR systems with cointegrated time series establishes robust RBB critical values when compared to asymptotic ones (Mantalos and Shukur, 1998 (Mantalos, 2000). Moreover, Hacker and Hatemi-J (2006) confirm that the modified Wald test based on a bootstrap distribution exhibits smaller size distortions irrespective of sample sizes, integration orders, and error-term processes (Balcilar et al, 2010). Therefore, based on these findings, this paper uses the RBB based modified-LR statistic to examine the causality between the real house price index and real GDP per capita in the U.S., because this method applies to cointegrated and non-cointegrated I(1) variables (Hacker and Hatemi-J, 2006).…”

Housing and the business cycle in South Africa

“…The outstanding performance (in terms of power and size) of the residual based bootstrap (RB) method over standard asymptotic tests, regardless of cointegration or not, has been demonstrated in a number of Monte Carlo simulations studies (Horowitz ,1994;Mantalos, 1997a, 1997b;Mantalos and Shukur, 1998;Shukur and Mantalos, 2000;Mantalos, 2000;Hacker and Hatemi-J, 2006). Therefore, following Balcilar and Ozdemir (2013) and , this current study resorts to the RB based modified-LR statistics to examine the causality between housing variables and GDP in South Africa.…”

“…In this paper, we employ the bootstrap approach with the Toda and Yamamoto (1995) modified causality tests, because of several advantages. In particular, this test applies to both cointegrated and non-cointegrated I (1) variables (Hacker and Hatemi-J, 2006). 5 Granger non-causality tests assume that parameters of the VAR model used in testing are constant over time.…”