
on Econometrics 
By:  Almeida, R.J.; Basturk, N.; Kaymak, U.; Costa Sousa, J.M. da 
Abstract:  In this work we introduce a new flexible fuzzy GARCH model for conditional density estimation. The model combines two different types of uncertainty, namely fuzziness or linguistic vagueness, and probabilistic uncertainty. The probabilistic uncertainty is modeled through a GARCH model while the fuzziness or linguistic vagueness is present in the antecedent and combination of the rule base system. The fuzzy GARCH model under study allows for a linguistic interpretation of the gradual changes in the output density, providing a simple understanding of the process. Such a system can capture different properties of data, such as fat tails, skewness and multimodality in one single model. This type of models can be useful in many fields such as macroeconomic analysis, quantitative finance and risk management. The relation to existing similar models is discussed, while the properties, interpretation and estimation of the proposed model are provided. The model performance is illustrated in simulated time series data exhibiting complex behavior and a real data application of volatility forecasting for the S&P 500 daily returns series. 
Keywords:  Linguistic descriptions; Volatility forecasting;Conditional density estimation;Fuzzy GARCH models 
Date:  2013–07–31 
URL:  http://d.repec.org/n?u=RePEc:dgr:eureri:1765040785&r=ecm 
By:  Yuichi Kitamura (Institute for Fiscal Studies and Yale University); Jörg Stoye (Institute for Fiscal Studies and New York University) 
Abstract:  This paper develops and implements a nonparametric test of Random Utility Models (RUM) using only nonsatiation and the Strong Axiom of Revealed Preference (SARP) as restrictions on individual level behaviour, allowing for fully unrestricted unobserved heterogeneity. The main application is the test of the null hypothesis that a sample of crosssectional demand distributions was generated by a population of rational consumers. Thus, the paper provides a finite sample counterpart to the classic theoretical analysis of McFadden and Richter (1991). To do so, it overcomes challenges in computation and in asymptotic theory and provides an empirical application to the U.K. Household Expenditure Survey. An econometric result of independent interest is a test for inequality constraints when they are represented in terms of the rays of a cone rather than its faces. 
Keywords:  stochastic rationality 
JEL:  C14 
Date:  2013–08 
URL:  http://d.repec.org/n?u=RePEc:ifs:cemmap:36/13&r=ecm 
By:  Nobuhiro Hosoe (National Graduate Institute for Policy Studies) 
Abstract:  We used 199520002005 linked inputoutput (IO) tables for Japan to examine estimation errors of updated IO tables and the resulting prediction errors in computable general equilibrium (CGE) analysis developed with updated IO tables. As we usually have no true IO tables for the target year and therefore need to estimate them, we cannot evaluate estimation errors of updated IO tables without comparing the updated ones with true ones. However, using the linked IO tables covering three different years enables us to make this comparison. Our experiments showed that IO tables estimated with more detailed and recent data contained smaller estimation errors and led to smaller quantitative prediction errors in CGE analysis. Despite the quantitative prediction errors, prediction was found to be qualitatively correct. As for the performance of updating techniques of IO tables, a crossentropy method often outperformed a leastsquares method in IO estimation with only aggregate data for the target year but did not necessarily outperform the leastsquares method in CGE prediction. 
Date:  2013–08 
URL:  http://d.repec.org/n?u=RePEc:ngi:dpaper:1316&r=ecm 
By:  Samuel Hurtado (Banco de España) 
Abstract:  Modern DSGE models are microfounded and have deep parameters that should be invariant to changes in economic policy, so in principle they are not subject to the Lucas critique. But the literature has already established that misspecification issues also cause parameter instability after policy changes in DSGE models. This paper will look at the implications of parameter shifts for econometric policy evaluation, to see whether policy advice derived from DSGE models would have differed fundamentally from that which the policymakers of the 1970s derived from their reducedform Phillips curves. The results show drift in most parameters, including those that are supposedly structural (such as the share of capital in production, habits or the elasticity of labor supply to the real wage), and major shifts in the impulse response functions derived from the realtime estimation of the model. After the expansionary monetary shocks of the early 1970s, a standard DSGE model would have behaved very similarly to an oldstyle Phillips curve, with marked shifts in parameter values and impulse response functions. 
Keywords:  keyword, keyword, Macroeconomics, DSGE, Lucas Critique 
JEL:  C11 C32 E32 E60 
Date:  2013–08 
URL:  http://d.repec.org/n?u=RePEc:bde:wpaper:1310&r=ecm 
By:  Erhan Bayraktar; Sergey Nadtochiy 
Abstract:  In this paper, we develop a new mathematical technique which can be used to express the joint distribution of a Markov process and its running maximum (or minimum) through the distribution of the process itself. This technique is an extension of the classical reflection principle for Brownian motion, and it is obtained by weakening the assumptions of symmetry required for the standard reflection principle to work. We call this method a weak reflection principle and show that it provides solutions to many problems for which the classical reflection principle is typically used. In addition, unlike the standard reflection principle, the new method works for a much larger class of stochastic processes which, in particular, do not possess any strong symmetries. Here, we review the existing results which establish the weak reflection principle for a large class of timehomogeneous diffusions on a real line and, then, proceed to develop this method for all L\'evy processes with onesided jumps (subject to some admissibility conditions). Finally, we demonstrate the applications of the weak reflection principle in Financial Mathematics, Computational Methods, and Inverse Problems. 
Date:  2013–08 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1308.2250&r=ecm 
By:  Andrew Binning (Norges Bank (Central Bank of Norway)) 
Abstract:  In this paper I derive the matrix chain rules for solving a second and a thirdorder approximation to a DSGE model that allow the use of a recursive Sylvester equation solution method. In particular I use the solution algorithms of Kamenik (2005) and Martin & Van Loan (2006) to solve the generalised Sylvester equations. Because I use matrix algebra instead of tensor notation to find the system of equations, I am able to provide standalone Matlab routines that make it feasible to solve a medium scale DSGE model in a competitive time. I also provide Fortran code and Matlab/Fortran mex files for my method. 
Keywords:  Solving dynamic models, Secondorder approximation, Thirdorder appeoximation, Secondorder matrix chain rule, Thirdorder matrix chain rule, Generalised Sylvester equations 
Date:  2013–08–05 
URL:  http://d.repec.org/n?u=RePEc:bno:worpap:2013_18&r=ecm 