Population, population density and technological change

In a model on population and endogenous technological change, Kremer (1993) combines a short-run Malthusian scenario where income determines the population that can be sustained, with the Boserupian insight that greater population spurs technological change and can therefore lift a country out of its Malthusian trap. We show that a more realistic version of the model, which combines population and population density, allows deeper insights into these processes. The incorporation of population density also allows a superior interpretation of the empirical regularities between the level of population, population density, population growth, and economic development at aggregated and disaggregated levels.

Soziale Ungleichheiten beim Schulstart

Although there is a regular age of school entry in Germany, some children start school later than usual and some children start ahead of schedule. While there has been some decrease in delayed school entries in the last years, the rate of premature school entry has increased substantially. Paradoxically, while the delayed entry is primarily because professionals rate a child as not ready for school, the premature entry is mainly based on parents’ choice. The first aim of the paper is to discover whether kindergarten attendance can reduce the risk of a delayed entry. The arguments and hypotheses are mainly based on the theory on the ecology of human development of Bronfenbrenner. The empirical analyses demonstrate that low educated families profit most by kindergarten attendance, but only if the child begins attending the care institution before reaching age four. The second aim concerns considerations in regard to the decision of prematurely entering school. Socio-economic conditions are not as important at this point as compared with a delay in school entry. However, there are some effects indicating that higher educated parents foster a premature entry to elementary schools. The analyses are based on over 1.400 children in the relevant age group and their parents taking part in the large nationwide German Socio-Economic Panel Study (SOEP).     

Randomized p-values for multiple testing of composite null hypotheses

We are considered with the problem of m simultaneous statistical test problems with composite null hypotheses. Usually, marginal p-values are computed under least favorable parameter configurations (LFCs), thus being over-conservative under non-LFCs. Our proposed randomized p-value leads to a tighter exhaustion of the marginal (local) significance level. In turn, it is stochastically larger than the LFC-based p-value under alternatives. While these distributional properties are typically nonsensical for m  =1, the exhaustion of the local significance level is extremely helpful for cases with m>1$m>1$ in connection with data-adaptive multiple tests as we will demonstrate by considering multiple one-sided tests for Gaussian means.     

Asymptotic Tail Properties of Student's t-Distribution

We investigate the asymptotic behavior of the probability density function (pdf) and the cumulative distribution function (cdf) of Student's t-distribution with ν > 0 degrees of freedom (t _ν for short) for ν tending to infinity when the argument x = x _ν of the pdf (cdf) depends on ν and tends to ± ∞ (?∞). To this end, we consider the ratio of the pdf's (cdf's) of the t _ν- and the standard normal distribution. Depending on the choice of the argument x _ν, the pdf-ratio (cdf-ratio) tends to 1, a fixed value greater than 1, or to ∞. As a byproduct, we obtain a result for Mill' ratio when x _ν → ?∞.