Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/89250
Authors: 
Broda, Simon A.
Kan, Raymond
Year of Publication: 
2014
Series/Report no.: 
Tinbergen Institute Discussion Paper 13-211/III
Abstract: 
A large number of exact inferential procedures in statistics and econometrics involve the sampling distribution of ratios of random variables. If the denominator variable is positive, then tail probabilities of the ratio can be expressed as those of a suitably defined difference of random variables. If in addition, the joint characteristic function of numerator and denominator is known, then standard Fourier inversion techniques can be used to reconstruct the distribution function from it. Most research in this field has been based on this correspondence, but which breaks down when both numerator and denominator are supported on the entire real line. The present manuscript derives inversion formulae and saddlepoint approximations that remain valid in this case, and reduce to known results when the denominator is almost surely positive. Applications include the IV est imator of a structural parameter in a just identified equation.
Subjects: 
Characteristic Function
Inversion Formula
Saddlepoint Approximation
Simultaneous Equations
Instrumental Variables
Weak Instruments
Bootstrap
JEL: 
C15
C26
C46
C63
Document Type: 
Working Paper

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