A Cross-Country Analysis of Institutions and Performance
Appendix C: mathematical analog for impact-transmission channels The purpose of this Appendix is to show the derivation of the mathematical analog for the 63 impact-transmission channels associated with the exogenous variables listed in Table 10.1. The mathematical analog of the channels is represented in terms of the partial derivatives of the 10 equations in Model B with respect to the exogenous variables as well as to some of the endogenous variables entering as independent variables in a few equations. To compactly represent the partial derivatives, notations, rather than full names, are used to denote the variables. Thus, the 16 exogenous variables in the model are denoted by Xi (i = 1, 2, . . ., 16) and the 10 endogenous variables by Yj (j = 1, 2, . . ., 10). For ready reference, the names and notations used for these variables are tabulated below. Variable name LPRSRF PGPIUP POELWL POPAWE AIBDWP PGPIPP LOEPRV AACCME ABALFS AARINF LTRWSA LINTRE LOECEN PPSCRI AORGBA AEXTST LCRMEE PIRSWE PCOREC 359 Notation used X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 Y1 Y2 Y3 360 The Institutional Economics of Water Variable name ASBUDC LACPRE LOEFWL POEFWP AOEFWA WIPOEV WSPOEV Notation used Y4 Y5 Y6 Y7 Y8 Y9 Y10 With the assigned notations for all the exogenous and endogenous variables, the 10 equations of Model B can be equally represented as: Y1 = F1(X1, X2, X4, X9, X10, X16) Y2 = F2(X1, Y1, X2, X16) Y3 = F3(X1, X2, X4, X5) Y4 = F4(X2, X5,...
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