Estimating rating transition probabilites with missing data

In this article we provide a rigorous treatment of one of the central statistical issues of credit risk management. GivenK-1 rating categories, the rating of a corporate bond over a certain horizon may either stay the same or change to one of the remainingK-2 categories; in addition, it is usually the case that the rating of some bonds is withdrawn during the time interval considered in the analysis. When estimating transition probabilities, we have thus to consider aK-th category, called withdrawal, which contains (partially) missing data. We show how maximum likelihood estimation can be performed in this setup; whereas in discrete time our solution gives rigorous support to a solution often used in applications, in continuous time the maximum likelihood estimator of the transition matrix computed by means of the EM algorithm represents a significant improvement over existing methods.     

Ridge regression: A multivariate analysis of criminal activity

The objective of the paper is to apply the statistical procedure of ridge regression to a multivariate model of criminal activity. The explanatory variables are of an economic, apprehension, and seasonal nature. The Time Shared Reactive On Line Laboratory (TROLL) computer package was used in estimating all regression coefficients and other pertinent statistics. The economic variables, which included per capita personal income, hours worked, and plant closing dummy variable, were found to be statistically related to criminal activity. In addition, police expenditures as well as the three seasonal dummy variables were statistically associated with the dependent variable. A comparison is made between the results obtained from the ordinary least squares procedure and the ridge regression approach.     

The effect of migration on ages at vital events: A critique of family reconstitution in historical demography

Demographic rates of historical populations have usually been calculated using only data from stayers alone. Can they be extrapolated to the population as a whole? Ruggles has recently pointed out, using both logic and a computer simulation, that stayers experience vital events earlier in life than movers due to migration censorship: those who experience them later in life have often migrated away from the community being studied. We show that stayers do indeed marry and die at younger ages than do movers, using a genealogical database on the American North (1620–1880). These differences are caused, however, both by migration censorship and by genuine differences between the two groups and the places they lived. Therefore changes over time among stayers are not good indicators of changes in the population as a whole because they are affected by changing migration rates. Thus no simple “correction factor” can be extrapolated to estimate the general population; neither stayers (nor movers) constitute a “baseline” or “normal” process: both must be considered together in order to gain an accurate picture of the population as a whole.     

Formative Indicators and Effects of a Causal Model for Household Human Capital with Application

Dagum and Slottje (2000) estimated household human capital (HC) as a latent variable (LV) and proposed its monetary estimation by means of an actuarial approach. This paper introduces an improved method for the estimation of household HC as an LV by means of formative and reflective indicators in agreement with the accepted economic definition of HC. The monetary value of HC is used in a recursive causal model to obtain short- and long-term multipliers that measure the direct and total effects of the variables that determine household HC. The new method is applied to estimate US household HC for year 2004.     

Estimation of the Lognormal-Pareto Distribution Using Probability Weighted Moments and Maximum Likelihood

This article deals with the estimation of the lognormal-Pareto and the lognormal-generalized Pareto distributions, for which a general result concerning asymptotic optimality of maximum likelihood estimation cannot be proved. We develop a method based on probability weighted moments, showing that it can be applied straightforwardly to the first distribution only. In the lognormal-generalized Pareto case, we propose a mixed approach combining maximum likelihood and probability weighted moments. Extensive simulations analyze the relative efficiencies of the methods in various setups. Finally, the techniques are applied to two real datasets in the actuarial and operational risk management fields.     

Density approximations and VaR computation for compound Poisson-lognormal distributions

Parametric approximations of the compound Poisson-lognormal distribution are developed and used to compute Value-at-Risk (VaR). As guidelines for finding an approximation, the skewness–kurtosis space and the tail behavior are considered. The Generalized Beta distribution of the second kind (GB2) and a mixture of lognormals are found to provide a good fit. In certain cases, the GB2 can be estimated by moment-matching, thus providing a simulation-free procedure for VaR computation. For confidence levels larger than 99%, extreme value theory approaches are developed. According to extensive Monte Carlo evidence, the proposed approximations are more efficient than crude Monte Carlo.     

Spectral properties of the concurrent and forecasting seasonal linear filters of the X-11-ARIMA method

This study analyzes the properties of the linear filters of the X-11-ARIMA seasonal adjustment method applied for current seasonal adjustment. It provides the general formula for the combined weights that result from the ARIMA model extrapolation filters with the X-11 seasonal-adjustment filters. The three cases studied correspond to the three ARIMA models automatically tested by the X-11-ARIMA program, namely, (0, 1, 1)(0, 1, 1), (0, 2, 2)(0, 1, 1), and (2, 1. 2)(0, 1,1). The parameter values chosen reflect different degrees of flexibility of the trend-cycle and seasonal components. It is shown that the X-11-ARIMA linear filters for current seasonal adjustment are very flexible; they change with both the ARIMA extrapolation model and its parameter values, contrary to those of the X-11 program, which are fixed for a given set of options.     

Engendering migrant networks: The case of Mexican migration

This article compares the impact of family migrant and destination-specific networks on international and internal migration. We find that migrant networks are more important for international moves than for internal moves and that female networks are more important than male networks for moves within Mexico. For moves to the United States, male migrant networks are more important for prospective male migrants than for female migrants, and female migrant networks lower the odds of male migration, but significantly increase female migration. We suggest that distinguishing the gender composition and destination content of migrant networks deepens our understanding of how cumulative causation affects patterns of Mexican migration.