The Influence of Age and Size on Family-Owned Firms’ Financing Decisions: Empirical Evidence Using Panel Data

Based on four samples of Portuguese family-owned firmsdi) 185 young, low-sized family-owned firms; ii) 167 young, high-sized familyowned firms; iii) 301 old, low-sized family-owned firms; and iv) 353 old, high-sized family-owned firms d we show that age and size are fundamental characteristics in family-owned firms’ financing decisions. The multiple empirical evidence obtained allows us to conclude that the financing decisions of young, low-sized family-owned firms are quite close to the assumptions of Pecking Order Theory, whereas those of old, high-sized family-owned firms are quite close to what is forecast by Trade-Off Theory. The lesser information asymmetry associated with greater age, the lesser likelihood of bankruptcy associated with greater size, as well as the lesser concentration of ownership and management consequence of greater age and size, may be especially important in the financing decisions of family-owned firms. In addition, we find that GDP, interest rate and periods of crisis have a greater effect on the debt of young, low-sized family-owned firms than on that of family-owned firms of the remainder research samples.

Temperature-averaged and total free-free Gaunt factors for κ and Maxwellian distributions of electrons

Aims. Optically thin plasmas may deviate from thermal equilibrium and thus, electrons (and ions) are no longer described by the Maxwellian distribution. Instead they can be described by κ-distributions. The free-free spectrum and radiative losses depend on the temperature-averaged (over the electrons distribution) and total Gaunt factors, respectively. Thus, there is a need to calculate and make available these factors to be used by any software that deals with plasma emission. Methods. We recalculated the free-free Gaunt factor for a wide range of energies and frequencies using hypergeometric functions of complex arguments and the Clenshaw recurrence formula technique combined with approximations whenever the difference between the initial and final electron energies is smaller than 10−10 in units of z2Ry. We used double and quadruple precisions. The temperature- averaged and total Gaunt factors calculations make use of the Gauss-Laguerre integration with 128 nodes. Results. The temperature-averaged and total Gaunt factors depend on the κ parameter, which shows increasing deviations (with respect to the results obtained with the use of the Maxwellian distribution) with decreasing κ. Tables of these Gaunt factors are provided.