Did the association between fertility and female employment within OECD countries really change its sign?

Recent literature finds that in OECD countries the cross-country correlation between the total fertility rate and the female labor force participation rate, which until the beginning of the 1980s had a negative value, has since acquired a positive value. This result is (explicitly or implicitly) often interpreted as evidence for a changing sign in the time-series association between fertility and female employment within OECD countries. This paper shows that the time-series association between fertility and female employment does not demonstrate a change in sign. Instead, the reversal in the sign of the cross-country correlation is most likely due to a combination of two elements: First, the presence of unmeasured country-specific factors and, second, country-heterogeneity in the magnitude of the negative time-series association between fertility and female employment. However, the paper does find evidence for a reduction in the negative time-series association between fertility and female employment after about 1985.I benefited from stimulating discussions with Arnstein Aassve, Pau Baizan, Francesco Billari, Henriette Engelhardt, Hans-Peter Kohler and Alexia Prskawetz and a seminar in Rostock. Further, I am grateful to two anonymous referees for very useful suggestions that improved essentially the content of the paper. In addition, I thank Susan Masur, Susann Backer, and Elizabeth Zach for language editing. The views expressed in this paper are the authors own views and do not necessarily represent those of the Max Planck Institute for Demographic Research. Responsible editor: Junsen Zhang.     

Trust games: A meta-analysis

We collect data from 162 replications of the Berg, Dickhaut, and McCabe Investment game (the “trust” game) involving more than 23,000 participants. We conduct a meta-analysis of these games in order to identify the effect of experimental protocols and geographic variation on this popular behavioral measure of trust and trustworthiness. Our findings indicate that the amount sent in the game is significantly affected by whether payment is random, and whether play is with a simulated counterpart. Trustworthiness is significantly affected by the amount by which the experimenter multiplies the amount sent, whether subjects play both roles in the experiment, and whether the subjects are students. We find robust evidence that subjects send less in trust games conducted in Africa than those in North America.     

Likelihood ratio ordering of order statistics,mixtures and systems

Let X=(_X1,_X2,…,_Xn)$\mathit{X}=(X_1,X_2,\dots ,X_n)$ be an exchangeable random vector, and denote _X1:i=min{_X1,_X2,…,_Xi}$X_{1:i}=\min \{X_1,X_2,\dots ,X_i\}$ and _Xi:i=max{_X1,_X2,…,_Xi}$X_{i:i}=\max \{X_1,X_2,\dots ,X_i\}$, 1?i?n$1?i?n$. These order statistics represent the lifetimes of the series and the parallel systems, respectively, with component lifetimes _Xi$X_i$. In this paper we obtain conditions under which _X1:i$X_{1:i}$ (or _Xi:i$X_{i:i}$) decreases (increases) in i in the likelihood ratio (lr) order. An even more general result involving general (that is, not necessary exchangeable) random vectors is also derived for general series (or parallel) systems. We show that the series (parallel) systems are not necessarily lr-ordered even if the components are independent.     

Prediction in moving average processes

For the stationary invertible moving average process of order one with unknown innovation distribution F, we construct root-n   consistent plug-in estimators of conditional expectations E(h(_Xn+1)|_X1,…,_Xn)$E(h(X_{n+1})|X_1,\dots ,X_n)$. More specifically, we give weak conditions under which such estimators admit Bahadur-type representations, assuming some smoothness of h or of F. For fixed h it suffices that h   is locally of bounded variation and locally Lipschitz in _L2(F)$L_2(F)$, and that the convolution of h and F   is continuously differentiable. A uniform representation for the plug-in estimator of the conditional distribution function P(_Xn+1?·|_X1,…,_Xn)$P(X_{n+1}?·|X_1,\dots ,X_n)$ holds if F has a uniformly continuous density. For a smoothed version of our estimator, the Bahadur representation holds uniformly over each class of functions h that have an appropriate envelope and whose shifts are F-Donsker, assuming some smoothness of F. The proofs use empirical process arguments.     

Asymptotic results in canonical discriminant analysis when the dimension is large compared to the sample size

This paper deals with the distributions of test statistics for the number of useful discriminant functions and the characteristic roots in canonical discriminant analysis. These asymptotic distributions have been extensively studied when the number p   of variables is fixed, the number q+1$q+1$ of groups is fixed, and the sample size N tends to infinity. However, these approximations become increasingly inaccurate as the value of p increases for a fixed value of N. On the other hand, we encounter to analyze high-dimensional data such that p is large compared to n. The purpose of the present paper is to derive asymptotic distributions of these statistics in a high-dimensional framework such that q   is fixed, p→∞$p\to \infty$, m=n-p+q→∞$m=n-p+q\to \infty$, and p/n→c∈(0,1)$p/n\to c\in (0,1)$, where n=N-q-1$n=N-q-1$. Numerical simulation revealed that our new asymptotic approximations are more accurate than the classical asymptotic approximations in a considerably wide range of (n,p,q)$(n,p,q)$.     

Ordered ranked set samples and applications to inference

Ranked set sampling (RSS) was first proposed by McIntyre [1952. A method for unbiased selective sampling, using ranked sets. Australian J. Agricultural Res. 3, 385–390] as an effective way to estimate the unknown population mean. Chuiv and Sinha [1998. On some aspects of ranked set sampling in parametric estimation. In: Balakrishnan, N., Rao, C.R. (Eds.), Handbook of Statistics, vol. 17. Elsevier, Amsterdam, pp. 337–377] and Chen et al. [2004. Ranked Set Sampling—Theory and Application. Lecture Notes in Statistics, vol. 176. Springer, New York] have provided excellent surveys of RSS and various inferential results based on RSS. In this paper, we use the idea of order statistics from independent and non-identically distributed (INID) random variables to propose ordered ranked set sampling (ORSS) and then develop optimal linear inference based on ORSS. We determine the best linear unbiased estimators based on ORSS (BLUE-ORSS) and show that they are more efficient than BLUE-RSS for the two-parameter exponential, normal and logistic distributions. Although this is not the case for the one-parameter exponential distribution, the relative efficiency of the BLUE-ORSS (to BLUE-RSS) is very close to 1. Furthermore, we compare both BLUE-ORSS and BLUE-RSS with the BLUE based on order statistics from a simple random sample (BLUE-OS). We show that BLUE-ORSS is uniformly better than BLUE-OS, while BLUE-RSS is not as efficient as BLUE-OS for small sample sizes (n<5$n<5$).     

Characterizations based on record values and order statistics

Consider a sequence of independent and identically distributed random variables {_Xi,i?1}$\{X_i,i?1\}$ with a common absolutely continuous distribution function F  . Let _X1:n?_X2:n???_Xn:n$X_{1:n}?X_{2:n}???X_{n:n}$ be the order statistics of {_X1,_X2,…,_Xn}$\{X_1,X_2,\dots ,X_n\}$ and {_Yl,l?1}$\{Y_l,l?1\}$ be the sequence of record values generated by {_Xi,i?1}$\{X_i,i?1\}$. In this work, the conditional distribution of _Yl$Y_l$ given _Xn:n$X_{n:n}$ is established. Some characterizations of F   based on record values and _Xn:n$X_{n:n}$ are then given.     

A note on the queue with a random set-up time under a restricted admissibility policy with a Bernoulli vacation schedule

This paper deals with the queue size distribution of an M^x/G/1 queue with a random set-up time and with a Bernoulli vacation schedule under a restricted admissibility policy. This generalizes the model studied by Madan and Choudhury [Sankhyá 66 (2004) 175–193].     

Gesellschafterausstieg in großen Familienunternehmen

Zusammenfassung  Dieser Beitrag befasst sich mit dem Ausstieg von Gesellschaftern aus Familienunternehmen als bedeutendes Corporate Governance-Problem. Im Mittelpunkt steht die Untersuchung der Wirkung von Ausstiegsmotiven, Rahmenbedingungen sowie Ausstiegsbarrieren auf die Belastung von Unternehmen und Familie durch den Gesellschafterausstieg. Eine explorative empirische Untersuchung von 55 gro?en deutschen Familienunternehmen liefert Ans?tze für eine Organisationstheorie des Familienunternehmens und für praktische Empfehlungen bei der Gestaltung von Satzung und Ausstiegsverhandlung.

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Summary  This article deals with the exit of shareholders in family owned businesses as an important corporate governance problem. We mainly analyse the effect of exit motivations, exit conditions, and barriers to exit on the exit’s burden for the company and the family. An explorative empirical study of 55 large German family owned businesses comes up with ideas for an organization theory of family owned businesses as well as some practical recommendations for statutes and exit negotiations.

     

A sequential design for a clinical trial with a linear prognostic factor

We study a randomized adaptive design to assign one of the L$L$ treatments to patients who arrive sequentially by means of an urn model. At each stage n$n$, a reward is distributed between treatments. The treatment applied is rewarded according to its response, 0?_Yn?1$0?Y_n?1$, and 1-_Yn$1-Y_n$ is distributed among the other treatments according to their performance until stage n-1$n-1$. Patients can be classified in K+1$K+1$ levels and we assume that the effect of this level in the response to the treatments is linear. We study the asymptotic behavior of the design when the ordinary least square estimators are used as a measure of performance until stage n-1$n-1$.