Source, e.g.: L. R. Klein, Estimation of interdependent systems in macroeconometrics Econometrica 37, No.2, 1969,

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1 1 Model USA 69/5 (Two versions) Source, e.g.: L. R. Klein, Estimation of interdependent systems in macroeconometrics Econometrica 37, No.2, 1969, List of equations On the left hand side you find the endogenous part, and on the right hand side the exogenous part. The numbers (3.k), k = 1, 2,, 20) relate to the specification of Klein Th system is written so that given variable p, as determinded by equation (29), the 19 equations (1)-(19) are a linear model, provide p is given, i.e. A(p)y = b(p), A(p) R 19,19, b(p) R 19, and y to be determinded by inversion: y = A(p)-1b(p). This kind of structure is an illustration of recursive linearization. Non-residential investment I (3.14) (1) I = a 1,1 I t-1 + a 1,2 r t-1 + a 1,3 X t-1 +a 1,4 W g,t-1 +a 1,5 Depreciation D (3.15) (2) D = a 2,1 S(p, I, R) + a 2,2 D u + a 2,3 Interest rate determination r s (3.16) (3) r s = a 3,1 D u + a 3,2 r d + a 3,3 R e,t-1 +a 3,4 Interest rate structure r (3.10) (4) a 4,1 r s + r = a 4,2 r t-1 + a 4,3 Durable consumption C d (3.1) (5) C d + a 5,1 Y = a 5,2 C d,t-1 + a 5,3 Y t-1 + a 5,4 Non-durable consumption C n (3.2) (6) C n + a 6,1 Y = a 6,2 C n,t-1 + a 6,3 Residential investment R (3.3) (7) Y + a 7,1 R = a 7,2 r t-1 + a 7,3 R t-1 + a 7,4 Inventories investment (3.4) (8) H + a 8,1 X = a 8,2 H t-1 + a 8,3 Import demand I m (3.5) (9) I m + a 9,1 X = a 9,2 I m,t-1 + a 9,3 p m + a 9,4 p +a 9,5 Labor demand (wage share) W-W g (3.8) (10) W + a 10,1 X = a 10,2 W t-1 + a 10,3 W g + a 10,4 W g,t-1 + a 10,5 Corporate savings p. S c (3.11) (11) p. P c + a 11,1 p. S c = a 11,2 (p t-1. P c,t-1 )+a 11,3 (p t-1. S c,t-1 ) + T c + a 11,4 T c,t-1 + a 11,5 Non-corporate income (p. Π p. P c ) (3.12) (12) p. P c + p. Π + a 12,1 p. X = a 12,2 (p t-1. P c,t-1 ) + a 12,3 (p t-1. Π t-1 ) + a 12,4 Rentier income p. Π r (3.13) (13) p. I + a 13,1 r + p. R + a 13,2 p. Π r = a 13,3 r t-1 + a 13,4 (p t-1. Π r,t-1 ) + a 13,5 Definition of real GNP (3.17) (14) I C d C n H + I m R + X H t-1 + G + E National income national product identity (3.18) (15) D p. Y + p. X p. S c T c + T i + T

2 2 Definition of profit (3.19) (16) D + p. W + p. Π + p. X + p. Π r T i Production function (3.6) (17) a 17,1 I + a 17,2 R + a 17,3 X + N W + a 17,4 h = a 17,5 X t-1 + a 17,6 N w,t-1 + a 17,7 h t-1 + a 17,8 W g + N g N s + a 17,9 W g,t-1 + a 17,10 N g,t-1 + a 17,11 N s,t-1 + a 17,12 Hours worked h (3.7) (18) a 18,1 N w + h + a 18,2 w = a 18,3 w t-1 +a 18,4 N s + a 18,5 N L + a 18,6 Wage rate determination w w t-1 (3.9) (19) a 19,1 N w + w = w t-1 +a 19,2 N s + a 19,3 N L + a 19,4 p t-1 + a 19,5 p + a 19,6 Wage identity (3.20) (20) w. h. N w p. W 0 There are 20 endogenous variables: I, D, r s, r, C d, C n, Y, H, I m, W, P c, Π, R, X, S c, Π r, N w, h, w, p and 14 exogenous variables. List of variables General notation 54 billions of 1954 dollars (i) Endogenous variables C d consumption of durables,54 Y personal disposable income, 54 C n consumption of nondurables and services, 54 I investment in plant and equipment, 54 X gross national product, 54 r average yield on corporate bonds (Moody s), percent R residential construction, 54 r s yield on prime commercial paper, 4-6 months, percent H stock of inventories, 54 I m imports, 54 N w wage and salary workers, millions h index of hours worked per week, 194 = 1.00 W wages and salaries and supplements to wages and salaries, 54 w annual earnings, thousands of dollars p implicit GNP deflator, 1954 = 100 S c corporate saving, including inventory valuation adjustment, 54 P c corporate profits including inventory valuation adjustment, 54 Π c P c proprietors income, 54 Π r rental income and net interest, 54 D capital consumption allowances, billions of current dollars

3 3 (ii) Exogenous variables W g government wages and salaries, 54 p m implicit price deflator for imports, 1954 = 1.00 N g government employees, millions N s self-employed workers, millions N L total labor force, millions T c corporate profits taxes, billions of current dollars D u Dummy variable, 0 for , 1 for r d average discount rate at all Federal Reserve Banks, percent R e year end ration of member banks excess to required reserves G government expenditures, billions of 1954 dollars E exports, billions of 1954 dollars T i reconciling item between net national product and national income, billions of current dollars T personal taxes plus contributions for social insurance less government and business transfer payments less interest on government debt, billions of current dollars 20 S(p, I, R) = Σ p t s (I t s +R t s ) s=1

4 4 Model USA 69/5 (version 2) Source: M. F. Perruchoud-Massy, Analyses et previsions regionales, a l'aide d'un modèle econometrique: Le canton du Valais de 1960 a 1980, Peter Lang, Berne- Francfort/Main, 1985, (Some specifications of regional models) Les equations du modèle de Klein Elles sont au nombre de vingt: (1) C = f 1 ( Y ) pc Fonction de la consommation (2) I = f 2 (X, r, K t-1 ) Fonction des investissements (3) G = f 3 (T, N, r) Fonction des depenses publiques p (4) E = f 4 (Xn, pmi ) (5) Im = f 5 (X, p pmi ) Fonction des exportations Fonction des importations (6) pc. C + q. I + G + Gn + pei. E - pmi. Im p. X Produit regional brut (7) Tp = f 7 (wl, s) Fonction des impôts directs (8) Tx = f 8 (px) Fonction des impôts indirects (9) Tn = f 9 (wl, s) Fonction des impôts federaux (10) Tr = f 10 (U, N) Fonction des paiements de transferts (11) D = f 11 (K t-1 ) Consommation de capital (12) Y = p. X - Tp - Tx - Tn + Tr - qd Revenu disponible (13) X = f 13 (L, K) Fonction de production (14) p = f 14 (P, w, pmi) Niveau des prix (15) pei = f 15 (P, w, pmi) Prix à l'exportation (16) w = f 16 (U, Un, pc) Taux des salaires régionaux (17) K K t-1 + I - D Stock de capital (18) T Tp + Tx Impôts régionaux totaux (19) s p. X - q. D - w. L - Tx Revenu non salarial (20) U o. N - L Chômage Les variables endogènes: C Dépenses de consommation Y Revenu disponible I Formation de capital X Produit régional brut S Dépenses des pouvoirs publics T Recettes des pouvoirs publics E Exportations de biens et services pei Indice des prix a l'exportation Im Importations de biens et services p Déflateur du produit régional brut Tp Impôts directs w Taux de salaire L Emploi

5 5 s Profits et revenus du capital Tx Impots indirects Tn Impots fédéraux Tr Paiements de transferts U Chômage D Consommation de capital K Stock de capital Les variables regionales exogènes: N Population Gn Dépenses fédérales dans la région o Taux de participation de la population Les variables nationales: pc Indice des prix a la consommation r Taux d'intérêt p Déflateur du produit régional brut pmi Indice des prix a l'importation X Produit national brut Un Chômage national (ORDERING, LINEARIZATION)