The Riskiness of Risk Models

URL des Documents de travail : http://centredeconomiesorbonne.univ-paris1.fr/bandeau-haut/documents-de-travail/Documents de travail du Centre d'Economie de la Sorbonne 2011.20 - ISSN : 1955-611XWe provide an economic valuation of the riskiness of risk models by directly measuring the impact of model risks (specification and estimation risks) on VaR estimates. We find that integrating the model risk into the VaR computations implies a substantial minimum correction of the order of 10-40% of VaR levels. We also present results of a practical method - based on a backtesting framework - for incorporating the model risk into the VaR estimates.Nous proposons une évaluation économique du risque de modèle, en mesurant directement son impact (risques d'estimation et de spécification) sur les estimations des VaR. Nous montrons que l'intégration du risque de modèle dans les calculs de VaR implique une correction minimum relativement importante, de l'ordre de 10 à 40% du niveau des VaR. Nous présentons également une illustration de notre méthode fondée sur les résultats de backtests pour introduire le risque de modèle dans les estimations de VaR corrigées

Short Run and Long Run Causality in Time Series: Inference

We propose methods for testing hypothesis of non-causality at various horizons, as defined in Dufour and Renault (1998, Econometrica). We study in detail the case of VAR models and we propose linear methods based on running vector autoregressions at different horizons. While the hypotheses considered are nonlinear, the proposed methods only require linear regression techniques as well as standard Gaussian asymptotic distributional theory. Bootstrap procedures are also considered. For the case of integrated processes, we propose extended regression methods that avoid nonstandard asymptotics. The methods are applied to a VAR model of the U.S. economy. Nous proposons des méthodes pour tester des hypothèses de non-causalité à différents horizons, tel que défini dans Dufour et Renault (1998, Econometrica). Nous étudions le cas des modèles VAR en détail et nous proposons des méthodes linéaires basées sur l'estimation d'autorégressions vectorielles à différents horizons. Même si les hypothèses considérées sont non linéaires, les méthodes proposées ne requièrent que des techniques de régression linéaire de même que la théorie distributionnelle asymptotique gaussienne habituelle. Dans le cas des processus intégrés, nous proposons des méthodes de régression étendue qui ne requièrent pas de théorie asymptotique non standard. L'application du bootstrap est aussi considérée. Les méthodes sont appliquées à un modèle VAR de l'économie américaine.time series; Granger causality; indirect causality; multiple horizon causality; autoregression; autoregressive model; vector autoregression; VAR; stationary process; nonstationary process;integrated process; unit root; extended autoregression; bootstrap; Monte Carlo; macroeconomics;money; interest rates; output; inflation, séries chronologiques; causalité; causalité indirecte; causalité à différents horizons; autorégression; modèle autorégressif; autorégression vectorielle; VAR; processus stationnaire; processus non stationnaire; processus intégré; racine unitaire; autorégression étendue; bootstrap; Monte Carlo; macroéconomie; monnaie; taux d'intérêt; production; inflation

The Optimality of the US and Euro Area Taylor Rule

The purpose of this paper is to examine the optimality of the monetary authorities reaction function in the two-area medium size model MARCOS (US and euro areas). The parameters and the horizons of output gap and inflation expectations of the Taylor rule are computed in order to minimise a loss function of the monetary authorities. However, investigating the optimality of the Taylor rule in the context of a large scale macroeconomic model raises several difficulties: the model is non-linear and all the state variables potentially enter the optimal monetary policy rule. Furthermore, the optimality of the Taylor rule is assessed by the minimisation of the loss function under the constraint of a large forward-looking model. To overcome these problems, Black, Macklem and Rose [1998] propose a stochastic simulation based method which has been applied to single-country macroeconomic models. To study the optimality of the Taylor rule in the case of a two-area model, we suppose that the economy is stochastically hit by numerous shocks (supply, demand, monetary, exchange rate and world demand) in each area and simulate MARCOS stochastically.Monetary Policy, Computational Techniques, International Policy Transmission

Conditional Logit with one Binary Covariate: Link between the Static and Dynamic Cases

Disentangling state dependence from unobserved heterogeneity is a common issue in economics. It arises for instance when studying transitions between different states on the labor market. When the outcome variable is binary, one of the usual strategies consists in using a conditional logit model with an appropriate conditioning suitable for a dynamic framework. Although static conditional logit procedures are widely available, these procedures cannot be used directly in a dynamic framework. Indeed, it is inappropriate to use them with a lag dependent variable in the list of regressors. Moreover, reprogramming this kind of procedures in a dynamic framework can prove quite cumbersome because the likelihood can have a very high number of terms when the number of periods increases. Here, we consider the case of a conditional logit model with one binary regressor which can be either exogenous or the lagged dependent variable itself. We provide closed forms for the conditional likelihoods in both cases and show the link between them. These results show that in order to evaluate a conditional logit model with one lag of state dependence and no other covariate, it is possible to simply generate a two variable dataset and use standard procedures originally intended for models without state dependence. Moreover, the closed forms help reduce the computational burden even in the static case in which preimplemented procedures usually exist.conditional logit, state dependence, binary model, incidental parameter

Explaining and Forecasting Inflation in Emerging Markets: The Case of Mexico

The authors apply existing inflation models that have worked well in industrialized countries to Mexico, an emerging market that has recently moved to adopt an inflation-targeting framework for monetary policy. They compare the performance of these models with a mark-up model that has been used extensively to analyze inflation in Mexico. The authors focus on three models that have some theoretical foundations and that can therefore help explain the causes of inflation as well as be used for forecasting purposes: a mark-up model, a money-gap model, and a Phillips curve. The authors' empirical results suggest that the evolution of the exchange rate remains a very important factor for forecasting inflation in Mexico. Indeed, in the best-performing model, the mark-up model, the exchange rate plays the most significant role. The Phillips curve explains and forecasts inflation well when using actual values for the explanatory variables, but does not perform well when using forecasted values for the explanatory variables. The money-gap model does not appear to be useful in its current form, because it is unable to beat even a simple AR1.Inflation and prices; International topics

Learning-by-Doing or Habit Formation?

In a recent paper, Chang, Gomes, and Schorfheide (2002) extend the standard real business cycle (RBC) model to allow for a learning-by-doing (LBD) mechanism whereby current labour supply affects future productivity. They show that this feature magnifies the propagation of shocks and improves the matching performance of the standard RBC model. In this paper, the authors show that the LBD model is nearly observationally equivalent to an RBC model with habit formation in labour (or, equivalently, in leisure). Under the same calibration of the parameters, the two models share the same equilibrium paths of output, consumption, and investment, but have different implications for hours worked. Using Bayesian techniques, the authors investigate which of the LBD and habit models fits the U.S. data best. Their results suggest that the habit specification is more strongly supported by the data.Business fluctuations and cycles; Labour markets; Economic models; Econometric and statistical methods

A systems dynamics model for the urban travel system

This paper describes the development of a model architecture based on systems dynamics and econometrics. The purpose of the system of models is to simulate the medium­ and long­term effects of urban transport policies with reference to sustainable travel. Three models are presented successively with some results from simulation. The first model relates to the regulation of public transport finance and allows for the constraint of the scarcity of public funds. The second is a modal split model based on price­time modelling. The third is a combined assignment and time of departure choice model based on a queuing representation of congestion. Finally, the coupling between the last two models is described.system dynamics ; Econometrics model ; Urban travel system ; finance ; modal split ; assignment ; time of departure

A Structural Small Open-Economy Model for Canada

The authors develop a small open-economy dynamic stochastic general-equilibrium (DSGE) model in an attempt to understand the dynamic relationships in Canadian macroeconomic data. The model differs from most recent DSGE models in two key ways. First, for prices and wages, the authors use the time-dependent staggered contracting model of Dotsey, King, and Wolman (1999) and Wolman (1999), rather than the Calvo (1983) specification. Second, to model investment, the authors adopt Edge's (2000a, b) framework of time-to-build with ex-post inflexibilities. The model's parameters are chosen to minimize the distance between the structural model's impulse responses to interest rate, demand (consumption), and exchange rate shocks and those from an estimated vector autoregression (VAR). The majority of the model's theoretical impulse responses fall within the 5 and 95 per cent confidence intervals generated by the VAR.Business fluctuations and cycles; Economic models; Inflation and prices

Costs, demand, and producer price changes.

We estimate an ordered probit model in order to explain the occurrence and magnitude of producer price changes in the French manufacturing sector. We use data consisting essentially of the Banque de France monthly business surveys, pooled over the years 1998-2005. Our results show that changes in the price of intermediate inputs are the main driver of producer price changes. Firms also appear to react significantly to changes in the producer price index of their industry. Variations in labor costs as well as in the production level also appear to increase the likelihood of a price change but their influence seems to be of a lesser importance. We also show that estimating an unconstrained dynamic model allows improving the estimation results as compared to those associated with a standard state-dependent model. Finally, our results point to an asymmetry in price adjustments. When they face a change in their costs, firms adjust their prices upward more often and more rapidly than they do it downward.Price stickiness, frequency of price changes, price setting-behavior, survey data, ordered probit model.