Demand estimation and market definition for broadband Internet services

This paper analyses residential demand for Internet access in Austria with a focus on broadband Internet connections. Austria has cable network coverage of about 50% and is, therefore, a good candidate to analyse the elasticity of demand for DSL where cable is available and where it is not. We also include mobile broadband via UMTS or HSDPA in our analysis and estimate various nested logit models to derive conclusions for market definition. The estimation results suggest that demand for DSL is elastic and that cable networks are likely to be in the same market as DSL connections both at the retail and at the wholesale level. We discuss possible implications for the regulation of wholesale broadband access markets. All views expressed are solely the authors’ and do not bind RTR or the Telekom-Control-Kommission (TKK) in any way nor are they official position of RTR or TKK.     

Convergence rates of density estimators for sums of powers of observations

Densities of functions of independent and identically distributed random observations can be estimated by a local U-statistic. It has been shown recently that, under an appropriate integrability condition, this estimator behaves asymptotically like an empirical estimator. In particular, it converges at the parametric rate. The integrability condition is rather restrictive. It fails for the sum of powers of two observations when the exponent is at least two. We have shown elsewhere that for exponent equal to two the rate of convergence slows down by a logarithmic factor on the support of the squared observation and is still parametric outside this support. For exponent greater than two, and on the support of the exponentiated observation, the estimator behaves like a classical density estimator: The bias is not negligible and the rate depends on the bandwidth. Outside the support, the rate is again parametric.