# Ekonomická a finančná matematika

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 Predmet príspevku: Seminár NBS 26.10.2012 - Marián Vávra (NBS)Napísal: Uto Okt 23, 2012 10:08 am

Registrovaný: Uto Okt 04, 2011 9:38 am
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Dobrý deň,

rád by som Vás pozval na seminár odboru výskumu, ktorý sa uskutoční v piatok 26. októbra 2012 o 13:00 v zasadačke na ôsmom poschodí v budove NBS.

Marián Vávra (NBS)
Testing Multivariate Non-linearity in Economic Time Series: linear or non-linear macroeconomic models?

Abstract
Currently used economic models allow for a non-linear state-space (NLSS) representation, which covers both ad-hoc models used in finance (e.g. multivariate GARCH models) and structural models used in macroeconomics (e.g. RE/DSGE models). Although NLSS models are very flexible, their direct use for applied economic modelling is problematic. Therefore, some approximations have been proposed in the literature. Among those successfully applied, the following three classes have attracted much attention recently: (a) linear rational expectation (LRE) models; (b) non-linear rational expectations (NLRE) models; (c) Markov-switching rational expectations (MSRE) models. The main advantage of NLRE and MSRE models is that they are very flexible and may be actually very good approximations to the original NLSS model and, thus, can capture empirically observed phenomena without breaking theoretical concepts or imposing unrealistic assumptions. On the other hand, both NLRE and MSRE models, even if approximative representations to the original NLSS model, are still highly non-linear dynamic multivariate systems, which are difficult to identify, the model solution is computationally intensive and might be non-unique, and the estimation is cumbersome. So, an ultimate question is whether NLRE or MSRE models necessarily lead to significant improvements compared to simple LRE counterparts. A definitive answer is very likely difficult, if not infeasible, to obtain. The main problem is not related to the fact that we deal with non-linear multivariate dynamic models, but rather to the fact that the functional form of the original NLSS model is, in contrast to other branches of science, determined by ad-hoc assumptions about the behaviour of agents in the economy, and thus, pretty arbitrary in economics. As a result, it might actually happen that the NLSS model, following from arbitrary economic assumptions, does not have to be supported by the empirical data set. In such a case, the use of computationally intensive NLRE or MSRE models can do much harm than good, and the use of a simple LRE model may actually provide an adequate approximation. On the contrary, provided that the non-linear representation is correct, then parameters of a simple LRE model, estimated by standard methods such as the MLE, are very likely inconsistent and inefficient. If this is the case, then standard inference (e.g. hypothesis testing, impulse-response functions, point forecasts and confidence bands) is simply invalid. This fact can have serious economic policy implications (e.g. for setting the REPO rate, setting the key policy parameters of labour or pension reforms, or a decision about joining the EMU).

Clearly, a simple test of multivariate non-linearity corresponding to NLRE and/or MSRE models is of the practical importance for economic modelling. The main task of this paper is to modify two standard multivariate non-linearity tests and assess their finite sample properties. In particular, we concentrate on a multivariate extension of the TSAY and ARCH tests in this paper. The main problem with the original multivariate tests is that they run out the number of variables and degrees of freedom very quickly. As a result, the multivariate tests require a large number of observations, which is not feasible to get in applied macroeconomics and sometimes not even in finance. The dimensionality problem is bypassed by principal component analysis. It will be shown that the modified tests have very good size and power properties. Much importantly, the dimensionality problem of the tests is reduced by approximately 70 % without any significant power loss. However, it is clearly demonstrated that a special care must be exercised when determining the number of components. Our results indicate that the BIC approach and the Kaiser rule are very robust and efficient. Finally, empirical findings suggest that the use of linear (DSGE) macroeconomic model is questionable.

Pripájam článok.

Účasť na seminári prosím potvrďte emailom na adrese matus.senaj@nbs.sk.

Prajem pekný deň,

Matúš Senaj
Odbor výskumu
Národná banka Slovenska
tel.: 02 5787 2935
e-mail: matus.senaj@nbs.sk
web: http://www.nbs.sk/sk/publikacie/vyskumne-studie
http://ideas.repec.org/f/pse317.html

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