The generalized lognormal distribution and the Stieltjes moment problem

This paper studies a Stieltjes-type moment problem defined by the generalized lognormal distribution, a heavy-tailed distribution with applications in economics, finance and related fields. It arises as the distribution of the exponential of a random variable following a generalized error distribution, and hence figures prominently in the EGARCH model of asset price volatility. Compared to the classical lognormal distribution it has an additional shape parameter. It emerges that moment (in)determinacy depends on the value of this parameter: for some values, the distribution does not have finite moments of all orders, hence the moment problem is not of interest in these cases. For other values, the distribution has moments of all orders, yet it is moment-indeterminate. Finally, a limiting case is supported on a bounded interval, and hence determined by its moments. For those generalized lognormal distributions that are moment-indeterminate Stieltjes classes of moment-equivalent distributions are presented.Comment: 12 pages, 1 figur

A Guide to the Dagum Distributions

In a series of papers in the 1970s, Camilo Dagum proposed several variants of a new model for the size distribution of personal income. This Chapter traces the genesis of the Dagum distributions in applied economics and points out parallel developments in several branches of the applied statistics literature. It also provides interrelations with other statistical distributions as well as aspects that are of special interest in the income distribution eld, including Lorenz curves and the Lorenz order and inequality measures. The Chapter ends with a survey of empirical applications of the Dagum distributions, many published in Romance language periodicals.

The Effect of Ethanol-Driven Corn Demand on Crop Choice

Since the late 1990s, U.S. production of corn ethanol has risen rapidly. In response to high demand, driven in part by rising ethanol production, corn prices and corn production surged in 2007 when corn plantings reached their highest level since 1944. To increase corn acreage, farmers shifted land to corn from other crops or, possibly, returned uncultivated land (e.g., cropland pasture, CRP land) to corn production. Even before 2007, however, "islands" of relatively high corn prices formed around ethanol plants in the Midwest. Price impacts were usually concentrated around an ethanol plant and ranged between 4.6 cents and 19.6 cents, with an average price increase of 12.5 cents at the plant site. Prices were also affected up to an estimated 68 miles from the plant (McNew and Griffith, 2005). Did these price island effects induce producers to shift to crop rotations that include more corn and/or bring in uncultivated land to corn production? If localized changes did occur in the years before 2007, they may persist into the future even though corn prices have declined absolutely and in relation to prices for soybeans and other crop commodities. The question is important because continuous corn, corn-intensive crop rotations, and shifting pasture or hayland into corn, can adversely affect the environment. This paper develops a discrete choice model that incorporates price island effects, local ethanol capacity, and broader land use change to understand the effect of ethanol-driven price islands on corn acreage, corn rotations, and general land use for cultivated crops. The primary data set in estimating the econometric model is the 2005 Corn Agricultural Resource Management Study (ARMS) survey, collected by the Economic Research Service and the National Agricultural Statistics Service. Because ARMS phase II (field-level) data is geo-referenced, spatially explicit data on corn and soybean prices are linked, along with the proximity of farms to ethanol plants and a soil productivity index. The ARMS Corn data is drawn from the traditional Corn Belt, along with some outlier states including North Carolina and North Dakota. A nested multinomial logit model (NML) is used to estimate producer crop mix response to local corn price islands, land quality, and other farm and location-specific factors. The NML model allows us to account for a range of crop production and land use options which vary in terms of similarity and, therefore, substitutability. At the highest level of the nested model, the farmer decides if he will cultivate his land or leave it uncultivated. If he chooses to cultivate his land, he needs to decide what crop to plant, for example, a corn-soybean rotation, wheat, or some “other” crop. The farmer will choose the crop and rotation pattern that will provide him with the greatest return, given prices and inputs. In this paper, the NML estimates the probability that a farmer will choose corn and soybeans (conditional on the choice of corn or soybeans) at the lower level and the choice among corn or soybeans, wheat, and “other” crops at the upper level, where the probability is a function of a corn/soybean price ratio; ethanol capacity index; livestock indicator variable; irrigation; soil quality and protected land statuses (highly erodible land); and household and farm characteristics. Because parameters cannot be directly interpreted in this model, the marginal effects and elasticities are examined. The authors find that in both levels of estimation, soil productivity and livestock value influence a farmer’s decision to plant corn or soybeans, wheat or some other crop. The estimation of our lower level confirms that local prices have a strong influence on whether a farmer will choose to plant corn or soybeans, while our upper level estimation may suggest that an increase in local ethanol capacity will encourage farmers to plant corn or soybean relative to both wheat and “other”. Information on the influence of "price islands" on farm behavior, including farm crop and rotation patterns and individual farmer land use decisions, could have environmental and other implications. This work could be extended by linking land use change to nutrient runoff and loads in water, possible soil erosion, and other environmental impacts from continuous corn rotations.Crop Production/Industries,

The Lorenz curve in economics and econometrics

This paper surveys selected applications of the Lorenz curve and related stochastic orders in economics and econometrics, with a bias towards problems in statistical distribution theory. These include characterizations of income distributions in terms of families of inequality measures, Lorenz ordering of multiparameter distributions in terms of their parameters, probability inequalities for distributions of quadratic forms, and Condorcet jury theorems.Lorenz curve, Lorenz order, majorization, income distribution, income inequality, statistical distributions, characterizations, Condorcet jury theorem.

Reproducible Econometric Simulations

Reproducibility of economic research has attracted considerable attention in recent years. So far, the discussion has focused on reproducibility of empirical analyses. This paper addresses a further aspect of reproducibility, the reproducibility of computational experiments. We examine the current situation in econometrics and derive a set of guidelines from our findings. To illustrate how computational experiments could be conducted and reported we present an example from time series econometrics that explores the finite-sample power of certain structural change tests.computational experiment, reproducibility, simulation, software.

Efficiency, Equity, and Generalized Lorenz Dominance

We decompose the generalized Lorenz order into a size and a distribution component. The former is represented by stochastic dominance, the latter by the standard Lorenz order. We show that it is always possible, given generalized Lorenz dominance between two distributions F and G, to find distributions H1 and H2 such that F stochastically dominates H1 and H1 Lorenz-dominates G, and such that F Lorenz-dominates H2 and H2 stochastically dominates G. We also show that generalized Lorenz dominance is characterized by this property and discuss the implications of these results for choice under risk.Income distribution, welfare dominance, Lorenz order, stochastic dominance, decisions under risk

Validating multiple structural change models : A case study

In a recent article, Bai and Perron (2003, Journal of Applied Econometrics) present a comprehensive discussion of computational aspects of multiple structural change models along with several empirical examples. Here, we report on the results of a replication study using the R statistical software package. We are able to verify most of their findings; however, some confidence intervals associated with breakpoints cannot be reproduced. These confidence intervals require computation of the quantiles of a nonstandard distribution, the distribution of the argmax functional of a certain stochastic process. Interestingly, the difficulties appear to be due to numerical problems in GAUSS, the software package used by Bai and Perron. --structural change,breakpoints,econometric software,numerical accuracy,reproducibility,R,GAUSS