CARIFORUM and UK EPA Study

( ) ( | )* ( ) . f D f D f d q q q = ò

(6) Equation 6 shows that the posterior estimation is proportional to the product of the likelihood of

( | )

( ) p D T p D

( ), the likelihood ratio

an occurrence, and the prior information; where D is for the available data, and T is for the parameter that estimates the variable of interest. The likelihood function gives the joint probability of events, conditional on any parameter of interest be it exports, wages, income, poverty or the amount of services that can be generated; that is, the probability that the data is useful, given the parameter of interest, p (D| θ ). The Bayesian model has been pervasively used for similar and unrelated empirical challenges (see Bayarri and Berger (2004) and Zyphur and Oswald (2012)). When knowledge about a positive or negative relationship between the probability of realization of success an independent variable is desired, say increases in exports, wages, income, poverty, FDI, or the amount of services that can be generated, the logit can be an alternative estimating methodology: (7) where p is for probability. Our primary regression model, Equation 3 (say Z for the sake of brevity), can be subjected to probabilistic evaluation when the parameters are les intuitive or useful by using the base e for natural log conversion: log ( ) log ; 1 p it p p æ ö = ç ÷ è - ø

æ ç è

ö ÷ ø æ ç

Z

Z

1

e

p

e

+

;

p

=

®

=

1

1

1

Z

Z

p

e

e

-

+

+

(8)

ö

p

ln

;

Z

=

1 ÷ è - ø p

therefore,

or the odds of occurrences, which can be converted into probabilities.

Note 4: Vector Autoregressive (VAR) models are generally utilized to accomplish such tasks. A representative model, say Equation 3, can be specified in the form of a moving average function:

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