The duration of fixed exchange rate regimes

duration t_i . The probability of ending a regime in the interval t + dt given that the spell
lasts up to time t is given by

λ(ti) = d                                            (2)

ni

Parametric estimation requires an assumption about the underlying distribution of the
random variable T . Suppose that the distribution of durations is known up to a vector
of parameters θ. The density of a duration is f (t, θ). The only information available on
a censored duration at time tj is that this duration was at least tj . The contribution
to likelihood is then given by the value of the survivor function, S(tj , θ). We can again
construct a dummy variable δ , taking a value of unity when the observation is censored
and zero otherwise. The log-likelihood function is given by

nn

ln L*(θ) = £(1 - δi) ln f (ti, θ) + £ δi ln S(ti, θ)
i=1                         i=1

which can be rewritten in terms of the hazard and integrated hazard functions

nn

ln L*(θ) = £(1 - δi) ln λ(ti, θ) - £ Λ(ti, θ)                       (3)

i=1                         i=1

In practice, the sample of durations is rarely homogeneous and is affected by various ex-
planatory factors. A convenient specification is the proportional hazard (PH) specification
which is written as

λ(t, x, β, λ0) = λ0(t)φ(x, β)                                 (4)

= λ₀(t)exp(x'β )

where x is a vector of explanatory variables, and β is a vector of unknown parameters
to be estimated. The so-called baseline hazard λ0 corresponds to the case where φ(.) = 1
and represents the hazard function for the mean individual. Explanatory variables affect
the hazard function by multiplying the baseline hazard by a time-invariant factor φ(.).
This specification is convenient for two reasons. First, to the extent that both λ(.) and λ₀

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