1 Model USA 69/5 (Two versions) Source, e.g.: L. R. Klein, Estimation of interdependent systems in macroeconometrics Econometrica 37, No.2, 1969, 171-192 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 1969. 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 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 (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 1929-1946, 1 for 1947-1962 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 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, 56-58 (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 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)