On the bias in flexible functional forms and an essentially unbiased form

A general equilibrium view of global rebound effects

“…which is essentially the expression applied by Saunders (2008) to derive short term rebound for cost functions like Gallant (Fourier) function (Gallant, 1981). Next I will show this expression is consistent with the expression (2) if Shephard's Lemma for capital price also holds, i.e.…”

The impact of macroeconomic news on quote adjustments, noise, and informational volatility

“…The second component, , , captures deterministic volatility patterns around the announcement dates. We refer them to 'time-ofnews' (ton) effects and model them using a flexible Fourier form (Gallant, 1981) of order three. 3 Here = / ∈ [0, 1] is the standardized time during the event window, where denotes the number of (one-minute) time intervals around the announcement.…”

Cost efficiency, economies of scale, technological progress and productivity in Indonesian banks

“…Flexible fourier form of cost function for two output quantities and two input prices used in this study can be written as follows (Gallant, 1981) However, to avoid end points estimation problems around those two limits, Gallant (1981) Lovell, and Schmidt (1977), it is assumed that v it and u it are independently distributed, v it is distributed as two-sided normal distribution with zero mean and variance , 2 v σ , while u it is usually assumed to follow one-sided distribution. It can be either, truncated normal, or exponential or any other distributions.…”