CARIFORUM and UK EPA Study

whereor PP’; X t then becomes:

1 i X AP P U ¥ - - = = å ( )( t i t

).

1

(11) The impulse response function (IRF) is thus conventionally written as a moving average (MA) representation: 0

0 ( ) j n j n Pe n y = F =

, 0,1, 2, 3,...;

(12)

where ej is an identity matrix. The generalized representation of the IRF is denoted as:

( , , d

)

( E X u |

,

) (

|

)

GIRF n =

E X

W

=

=

d

W -

W

. (13) Equation 13 is usually scaled in standard deviation units. Though strenuous arguments have been made to standardized the atheoretic form, the representations of the disturbances and their dissipations are not fundamental different. The uses of the impulse response functions are diverse, especially from a policy perspective—intricate fiscal and monetary policies (Bernanke and Blinder (1992) and Stock and Watson (2001); see also several working papers of the Bank of England and Warburton, 2012a. When knowledge about a positive or negative relationship between the probability of realization of success and an independent variable is desired, say increases in exports, wages, income, poverty, FDI, or the number of services that can be generated, the logit can be a useful and 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: 1 1 1 X j t t n jt j t t n t - + - + - log ( ) log ; 1 p it p p æ ö = ç ÷ è - ø

æ ç è

ö ÷ ø

Z

Z

1

e

p

e

+

;

p

=

®

=

1

1

1

Z

Z

p

e

e

-

+

+

(8)

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