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on Econometrics |
| By: | Dennis Kristensen (Institute for Fiscal Studies and University College London); Bernard Salanie (Institute for Fiscal Studies and Columbia) |
| Abstract: | Many modern estimation methods in econometrics approximate an objective function, for instance, through simulation or discretisation. These approximations typically affect both bias and variance of the resulting estimator. We provide a higher-order expansion of such 'approximate' estimators that takes into account the errors due to the use of approximations. This expansion allows us to establish general conditions under which the approximate estimator is first-order equivalent to the exact estimator. Moreover, we use the expansion to propose adjustments of the approximate estimator that remove its first-order bias and adjust its standard errors. These adjustments apply to a broad class of approximate estimators that includes all known simulation-based procedures. We also propose another approach to reduce the impact of approximations, based on a Newton-Raphson adjustment. A Monte Carlo simulation on the mixed logit model shows that our proposed adjustments can yield spectacular improvements at a low computational cost. |
| Date: | 2013–09 |
| URL: | http://d.repec.org/n?u=RePEc:ifs:cemmap:45/13&r=ecm |
| By: | Hess , Wolfgang (Department of Economics, Lund University); Schwarzkopf , Larissa (Institute of Health Economics and Health Care Management, Helmholtz Zentrum); Hunger , Matthias (Institute of Health Economics and Health Care Management, Helmholtz Zentrum); Holle , Rolf (Institute of Health Economics and Health Care Management, Helmholtz Zentrum) |
| Abstract: | Multi-state transition models are widely applied tools to analyze individual event histories in the medical or social sciences. In this paper we propose the use of (discrete-time) competing-risks duration models to analyze multi-transition data. Unlike conventional Markov transition models, these models allow the estimated transition probabilities to depend on the time spent in the current state. Moreover, the models can be readily extended to allow for correlated transition probabilities. A further virtue of these models is that they can be estimated using conventional regression tools for discrete-response data, such as the multinomial logit model. The latter is implemented in many statistical software packages, and can be readily applied by empirical researchers. Moreover, model estimation is feasible, even when dealing with very large data sets, and simultaneously allowing for a flexible form of duration dependence and correlation between transition probabilities. We derive the likelihood function for a model with three competing target states, and discuss a feasible and readily applicable estimation method. We also present results from a simulation study, which indicate adequate performance of the proposed approach. In an empirical application we analyze dementia patients’ transition probabilities from the domestic setting, taking into account several, partly duration-dependent covariates. |
| Keywords: | Competing risks; Dementia; Discrete-time duration model; Multinomial logit; Random effects; Transition |
| JEL: | C41 I10 |
| Date: | 2013–09–09 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:lunewp:2013_028&r=ecm |
| By: | Grant Hillier (Institute for Fiscal Studies and University of Southampton); Federico Martellosio |
| Abstract: | The (quasi-) maximum likelihood estimator (MLE) for the autoregressive parameter in a spatial autoregressive model cannot in general be written explicitly in terms of the data. The only known properties of the estimator have hitherto been its first-order asymptotic properties (Lee, 2004, Econometrica), derived under specific assumptions on the evolution of the spatial weights matrix involved. In this paper we show that the exact cumulative distribution function of the estimator can, under mild assumptions, be written down explicitly. A number of immediate consequences of the main result are discussed, and several examples of theoretical and practical interest are analysed in detail. The examples are of interest in their own right, but also serve to illustrate some unexpected features of the distribution of the MLE. In particular, we show that the distribution of the MLE may not be supported on the entire parameter space, and may be nonanalytic at some points in its support. Supplementary material relating to this working paper can be viewed here |
| Keywords: | spatial autoregression, maximum likelihood estimation, group interaction, networks, complete bipartite graph |
| JEL: | C12 C21 |
| Date: | 2013–09 |
| URL: | http://d.repec.org/n?u=RePEc:ifs:cemmap:44/13&r=ecm |
| By: | Dariusz Grech; Grzegorz Pamu{\l}a |
| Abstract: | We provide an alternative method for analysis of multifractal properties of time series. The new approach takes into account the behaviour of the whole multifractal profile of the generalized Hurst exponent $h(q)$ for all moment orders $q$, not limited only to the edge values of $h(q)$ describing in MFDFA scaling properties of smallest and largest fluctuations in signal. The meaning of this new measure is clarified and its properties are investigated for synthetic multifractal data and real signals taken from stock market. We show that the proposed new measure is free of problems one can meet in real nonstationary signals, while searching their multifractal signatures. |
| Date: | 2013–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1309.5466&r=ecm |
| By: | Rama Cont (Laboratoire de Probabilités et Modèles Aléatoires CNRS); Lakshithe Wagalath (IESEG School of Management) |
| Abstract: | We propose a tractable framework for quantifying the impact of fire sales on the volatility and correlations of asset returns in a multi-asset setting. Our results enable to quantify the impact of fire sales on the covariance structure of asset returns and provide a quantitative explanation for spikes in volatility and correlations observed during liquidation of large portfolios. These results allow to test for the presence of fire sales during a given period of time and to estimate the impact and magnitude of fire sales from observation of market prices: we give conditions for the identifiability of model parameters from time series of asset prices, propose an estimator for the magnitude of fire sales in each asset class and study the consistency and large sample properties of the estimator. We illustrate our estimation methodology with two empirical examples: the hedge fund losses of August 2007 and the Great Deleveraging following the default of Lehman Brothers in Fall 2008. |
| Date: | 2013–08 |
| URL: | http://d.repec.org/n?u=RePEc:ies:wpaper:f201301&r=ecm |
| By: | Greene, William H.; Gillman, Max; Harris, Mark N. |
| Abstract: | We propose a Tempered Ordered Probit (TOP) model. Our contribution lies not only in explicitly accounting for an excessive number of observations in a given choice category - as is the case in the standard literature on inflated models; rather, we introduce a new econometric model which nests the recently developed Middle Inflated Ordered Probit (MIOP) models of Bagozzi and Mukherjee (2012) and Brooks, Harris, and Spencer (2012) as a special case, and further, can be used as a specification test of the MIOP, where the implicit test is described as being one of symmetry versus asymmetry. In our application, which exploits a panel data-set containing the votes of Bank of England Monetary Policy Committee (MPC) members, we show that the TOP model affords the econometrician considerable flexibility with respect to modeling the impact of different forms of uncertainty on interest rate decisions. Our findings, we argue, reveal MPC members. asymmetric attitudes towards uncertainty and the changeability of interest rates. |
| Keywords: | Monetary policy committee, voting, discrete data, uncertainty, tempered equations |
| JEL: | C3 E50 |
| Date: | 2013–09 |
| URL: | http://d.repec.org/n?u=RePEc:hit:hitcei:2013-05&r=ecm |
| By: | Pierre Blanc; R\'emy Chicheportiche; Jean-Philippe Bouchaud |
| Abstract: | We decompose, within an ARCH framework, the daily volatility of stocks into overnight and intraday contributions. We find, as perhaps expected, that the overnight and intraday returns behave completely differently. For example, while past intraday returns affect equally the future intraday and overnight volatilities, past overnight returns have a weak effect on future intraday volatilities (except for the very next one) but impact substantially future overnight volatilities. The exogenous component of overnight volatilities is found to be close to zero, which means that the lion's share of overnight volatility comes from feedback effects. The residual kurtosis of returns is small for intraday returns but infinite for overnight returns. We provide a plausible interpretation for these findings, and show that our IntraDay/Overnight model significantly outperforms the standard ARCH framework based on daily returns for Out-of-Sample predictions. |
| Date: | 2013–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1309.5806&r=ecm |