Optimal Inattention to the Stock Market With Information Costs and Transactions Costs

Information costs, which comprise costs of gathering and processing information about stock values and costs of deciding how to respond to this information, induce a consumer to remain inattentive to the stock market for finite intervals of time. Whether, and how much, a consumer transfers assets between accounts depends on the costs of undertaking such transactions. In general, optimal behavior by a consumer facing both information costs and transactions costs is state‐dependent, with the timing of observations and the timing and size of transactions depending on the state. Surprisingly, if the fixed component of the transactions cost is sufficiently small, then eventually, with probability 1, a time‐dependent rule emerges: the interval between observations is constant and on each observation date, the consumer converts enough assets to liquid assets to finance consumption until the next observation. If the fixed component of transactions costs is large, the optimal rule remains state‐dependent indefinitely.     

Is Psychological Well-Being Linked to the Consumption of Fruit and Vegetables?

Little is known about the influence of people’s diet on their psychological well-being. This study provides evidence of a link between the consumption of fruit and vegetables and high well-being. In cross-sectional data, happiness and mental health rise in an approximately dose–response way with the number of daily portions of fruit and vegetables. Well-being peaks at approximately 7 portions per day. We document this relationship in three data sets, covering approximately 80,000 randomly selected British individuals, and for seven measures of well-being (life satisfaction, WEMWBS mental well-being, GHQ mental disorders, self-reported health, happiness, nervousness, and feeling low). The pattern is robust to adjustment for a large number of other demographic, social and economic variables. Reverse causality and problems of confounding remain possible. We discuss the strengths and weaknesses of our analysis, how government policy-makers might wish to react to it, and what kinds of further research—especially randomized trials—would be valuable.     

Note on an extension of rational bounds for the t-tail area to arbitrary degrees of freedom

The bounds of Soms (1980a) for the tail area of the t-distribution with integral degrees of freedom are extended to arbitrary positive degrees of freedom, Comparisons are made with the bounds of Shenton and Carpenter (1965) and some numerical examples are provided.     

Applications of schur theory to reliability inference for k of n systems

The results of Hoeffding (1956), Pledger and Proschan (1971), Gleser (1975) and Boland and Proschan (1983) are used to obtain Buehler (1957) 1-α lower confidence limits for the reliability of k of n systems of independent components when the subsystem data have equal sample sizes and the observed failures satisfy certain conditions. To the best of our knowledge, for k ≠ 1 or n, this is the first time the exact optimal lower confidence limits for system reliability have been given. The observed failure vectors are a generalization of key test results for k of n systems, k ≠ n (Soms (1984) and Winterbottom (1974)). Two examples applying the above theory are also given.     

Dynamic Savings Decisions in Agricultural Environments With Incomplete Markets

We develop a methodology for examining savings behavior in rural areas of developing countries that explicitly incorporates the sequential decision process in agriculture. The approach is used to examine the relative importance of alternative forms of savings in the presence and absence of formal financial intermediaries. Our results, based on stage-specific panel data from Pakistan, provide evidence that the presence of financial intermediaries importantly influences the use of formal savings and transfers for income smoothing. We also find that there are significant biases in evaluations of the savings-income relationship that are inattentive to the within-year dynamics of agricultural production.     

The Modeling and Seasonal Adjustment of Weekly Observations

Several important economic time series are recorded on a particular day every week. Seasonal adjustment of such series is difficult because the number of weeks varies between 52 and 53 and the position of the recording day changes from year to year. In addition certain festivals, most notably Easter, take place at different times according to the year. This article presents a solution to problems of this kind by setting up a structural time series model that allows the seasonal pattern to evolve over time and enables trend extraction and seasonal adjustment to be carried out by means of state-space filtering and smoothing algorithms. The method is illustrated with a Bank of England series on the money supply.     

Interval Estimation for the Difference of Two Independent Variances

Analytical methods for interval estimation of differences between variances have not been described. A simple analytical method is given for interval estimation of the difference between variances of two independent samples. It is shown, using simulations, that confidence intervals generated with this method have close to nominal coverage even when sample sizes are small and unequal and observations are highly skewed and leptokurtic, provided the difference in variances is not very large. The method is also adapted for testing the hypothesis of no difference between variances. The test is robust but slightly less powerful than Bonett's test with small samples.     

Regenerative Markov Chain Monte Carlo for Any Distribution

While Markov chain Monte Carlo (MCMC) methods are frequently used for difficult calculations in a wide range of scientific disciplines, they suffer from a serious limitation: their samples are not independent and identically distributed. Consequently, estimates of expectations are biased if the initial value of the chain is not drawn from the target distribution. Regenerative simulation provides an elegant solution to this problem. In this article, we propose a simple regenerative MCMC algorithm to generate variates for any distribution.     

Efficient estimators for the good family

We consider the problem of estimating the two parameters of the discrete Good distribution. We first show that the sufficient statistics for the parameters are the arithmetic and the geometric means. The maximum likelihood estimators (MLE's) of the parameters are obtained by solving numerically a system of equations involving the Lerch zeta function and the sufficient statistics. We find an expression for the asymptotic variance-covariance matrix of the MLE's, which can be evaluated numerically. We show that the probability mass function satisfies a simple recurrence equation linear in the two parameters, and propose the quadratic distance estimator (QDE) which can be computed with an ineratively reweighted least-squares algorithm. the QDE is easy to calculate and admits a simple expression for its asymptotic variance-covariance matrix. We compute this matrix for the MLE's and the QDE for various values of the parameters and see that the QDE has very high asymptotic efficiency. Finally, we present a numerical example.