Bootstrap prediction mean squared errors of unobserved states based on the Kalman filter with estimated parameters

Prediction intervals in State Space models can be obtained by assuming Gaussian innovations and using the prediction equations of the Kalman filter, where the true parameters are substituted by consistent estimates. This approach has two limitations. First, it does not incorporate the uncertainty due to parameter estimation. Second, the Gaussianity assumption of future innovations may be inaccurate. To overcome these drawbacks, Wall and Stoffer (2002) propose to obtain prediction intervals by using a bootstrap procedure that requires the backward representation of the model. Obtaining this representation increases the complexity of the procedure and limits its implementation to models for which it exists. The bootstrap procedure proposed by Wall and Stoffer (2002) is further complicated by fact that the intervals are obtained for the prediction errors instead of for the observations. In this paper, we propose a bootstrap procedure for constructing prediction intervals in State Space models that does not need the backward representation of the model and is based on obtaining the intervals directly for the observations. Therefore, its application is much simpler, without loosing the good behavior of bootstrap prediction intervals. We study its finite sample properties and compare them with those of the standard and the Wall and Stoffer (2002) procedures for the Local Level Model. Finally, we illustrate the results by implementing the new procedure to obtain prediction intervals for future values of a real time series

Endogenous Growth and Comparative Standards of Living between Mexico and the US

This paper calibrates an AK model of growth for Mexico. Investment financing is modeled considering the domestic savings ratio as well as net factorial income and capital inflows of the balance of payments. Productivity A and the rate of depreciation of capital are found using econometric techniques. According to this model, actual parameters determining growth in Mexico are compatible with a sustained long run rate of growth of about 3.6%. At the same time, under these circumstances the ratio of the Mexican GDP to US GDP would be growing in time. The model is very sensible to the parameters and depends strongly of Mexicans living in the US and transferring remittances to Mexico, nonetheless. If remittances were eliminated, the actual rate of domestic savings would not be compatible with positive growth in the long run, which implies that relatively speaking the domestic savings rate in Mexico is very low. The paper concludes that to assure a positive growth that improves standards of living and the relative size of Mexico with respect to the US, it is necessary to implement policies oriented to increase the domestic savings rate and productivity. Otherwise there are high risks of macroeconomic crises in the future.

Learning Externalities and Economic Growth

It is a well known fact that not all countries develop at the same time. The industrial revolution began over 200 years ago in England and has been spreading over the world ever since. In their paper Barriers to Riches, Parente and Prescott notice that countries that enter the industrial stage later on grow faster than what the early starters did. I present a simple model with learning externalities that generates this kind of behavior. I follow Lucas (1998) and solve the optimization problem of the representative agent under the assumption that the external effect is given by the world leader's human capital.

Bootstrap prediction mean squared errors of unobserved states based on the Kalman filter with estimated parameters

Prediction intervals in State Space models can be obtained by assuming Gaussian innovations and using the prediction equations of the Kalman filter, where the true parameters are substituted by consistent estimates. This approach has two limitations. First, it does not incorporate the uncertainty due to parameter estimation. Second, the Gaussianity assumption of future innovations may be inaccurate. To overcome these drawbacks, Wall and Stoffer (2002) propose to obtain prediction intervals by using a bootstrap procedure that requires the backward representation of the model. Obtaining this representation increases the complexity of the procedure and limits its implementation to models for which it exists. The bootstrap procedure proposed by Wall and Stoffer (2002) is further complicated by fact that the intervals are obtained for the prediction errors instead of for the observations. In this paper, we propose a bootstrap procedure for constructing prediction intervals in State Space models that does not need the backward representation of the model and is based on obtaining the intervals directly for the observations. Therefore, its application is much simpler, without loosing the good behavior of bootstrap prediction intervals. We study its finite sample properties and compare them with those of the standard and the Wall and Stoffer (2002) procedures for the Local Level Model. Finally, we illustrate the results by implementing the new procedure to obtain prediction intervals for future values of a real time series.NAIRU, Output gap, Parameter uncertainty, Prediction Intervals, State Space Models

La metodología de rating “through the cycle”: aplicación para la estimación de ratings soberanos

This paper analyses the through-the-cycle rating concept; basically, we try to specify its main characteristics, focusing on the differences with point-in-time ratings. We also discuss the effects of this methodology on the prediction power of default probabilities, on the stability of those ratings, and their impact on the capital requirements that emerge from Basel II, in terms of their potential procyclicality. On the other hand, we argue how predictable rating changes are, and the ability of the agencies to look through the cycle when assigning qualifications. Based on that, we conclude about the way that economical fundamentals must be incorporated in rating calculations. We estimate a panel data model with random effects ordered probit, using data for the period 1997-2007.Credit Rating Methodology, Panel Data Ordered Probit,

Zeta-like Multizeta Values for higher genus curves

We prove or conjecture several relations between the multizeta values for positive genus function fields of class number one, focusing on the zeta-like values, namely those whose ratio with the zeta value of the same weight is rational (or conjecturally equivalently algebraic). These are the first known relations between multizetas, which are not with prime field coefficients. We seem to have one universal family. We also find that interestingly the mechanism with which the relations work is quite different from the rational function field case, raising interesting questions about the expected motivic interpretation in higher genus. We provide some data in support of the guesses.Comment: Expository revisions plus appendices containing proofs of more cases of conjecture