Infrastructure Investment in Network Industries: The Role of Incentive Regulation and Regulatory Independence

disaggregation is limited to three broad categories: first, electricity, gas and water supply; second,
transportation (road, rail, water, air and associated storage); and third, telecommunications (which
also includes postal services). Secondly, capital stock data needed to calculate the investment-to-
capital stock ratio are available only for a limited number of OECD countries and are not fully
comparable across countries. In principle, one could compute capital stock series using
investment flows and the perpetual inventory method, but these estimates are extremely sensitive
to the underlying assumptions. Given long asset lives, one often still needs an estimate of the
value of the capital stock to anchor the series, which is not readily available. As a result, sectoral
value added is used instead to construct an investment to value added ratio at the sectoral level.
Overall, the sectoral dataset covers 13 countries for the three sectoral aggregates.

5. Estimation method: Bayesian averaging of classical
estimates

The main empirical approach is Bayesian averaging of classical estimates of the possible
explanatory variables (e.g. as applied to growth regressions in Sala-i-Martin et al. 2004). For
comparison purposes, results of OLS estimates are also reported. Bayesian averaging is a
comprehensive analytical tool to check the extent to which any given explanatory variable
improves the explanatory power of the estimated models when it is included. In other words, it
investigates the probability with which any given variable would be included in the estimated
models. This approach requires the estimation of all possible combinations of the candidate
explanatory variables (of number K) that is 2^K .

Bayesian averaging of classical estimates (BACE) first determines the (estimated) posterior
probability attributed to each single model M including a given variable, conditioned on the
underlying dataset y ( P (M_i ∣y ) ).

PM P   P(M )T’kj/2SSE^T/2

^p (M∖y ) = ₂k     ---------ⁱ-----

∑ P (M_i )T ⁱ kⁱ/² SSE^{i t}/²
i=1

where SSE is the sum of squared residuals, T is the number of observations, k denotes the number
of explanatory variables included in the specific model and K is the number of all explanatory
variables considered. Expression (2a) shows the extent to which any given model contributes to
explaining the dependent variable as compared to the other models. Expression (2a) is then

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