Kaleckian models of growth in a coherent stock-flow monetary framework: A Kaldorian view

Outline Traditions The matrices The main behavioural equations Main experiments

The model draws its inspiration from six (mainly Post-Keynesian) traditions 1. The Kaleckian growth models (Rowthorn 1981, Dutt 1990). 2. The “neo-Pasinetti” model of Kaldor (1966):  Its distinction between households and firms;  Its consumption function based on current income and capital gains (instead of past wealth);  Its valuation ratio (Tobin’s q ratio);  Finance through retained earnings and equity issues. 3. The Kaldorian theory of endogenous credit-money (1970, 1982). 4. Tobin’s portfolio theory (1969). 5. National accounts that include flow-of-funds. 6. Procedural rationality, based on gradual adjustments to observed disequilibria (Duménil and Lévy 1995).

The model does not include: Circulating capital and inventories; Social classes (capitalists, rentiers, workers); Technical progress; Inflation and unemployment; A government sector and the central bank;

Stock matrix HouseholdsFirmsBanksSum Money+ M − M0 Equities+ e.pe − e.pe0 Tangible capital + K Loans − L+ L0 Balance − V − K + (L+e.pe) 0 − K Sum0000

Transactions matrix: Sources +; Uses - Hous’ldsFirmsBanksSum CurrentCapitalCurrentCapital Consumption − C+ C0 Investment + I− I0 Salaries + W− W0 Net profits +Fd− F+Fu0 Interests − rl.L(-1)+ rl.L(-1)0 Interests +rm.M(-1) 0 Change in money − dM− dM+ dM0 Change in loans + dL− dL− dL0 Issues of equities − de.pe+de.pe0 Sum

The monetary circuit Hous’ldsFirmsBanksSum CurrentCapitalCurrentCapital Consumption 0 Investment + I− I0 Salaries + W− W0 Net profits 0 Interests 0 0 Change in money − dM− dM+ dM0 Change in loans + dL− dL− dL0 Issues of equities 0 Sum

Le circuit monétaire: financement initial MénagesEntreprisesBanquesSomme CourantCapitalCourantCapital Consommation Investissement + I- I0 Salaires + W- W0 Profits nets Intérêts Changt en monnaie - - dM+ dM0 Changt en prêts + dL - - dL0 Émission de titres Somme 00000

The investment function Based on the empirical research of Ndikumara (1999) and Fazzari. (21) g = γ0+ γ1.rcf(-1) - γ2.rl.l(-1) + γ3.q(-1) + γ4.u(-1) The rate of accumulation depends on:  A constant (animal spirits)  The cash-flow (retained earnings ) to capital ratio  The weight of interest payments relative to capital  Tobin’s q ratio (or Kaldor’s valuation ratio) q = (L+pe.e)/K  The rate of utilization of capacity

Other decisions of the firm The distribution of dividends Fd = (1-sf)[FT(-1)-rl(-1).L(-2)] Issuing equities d(e).pe = x.I(-1)

The consumption function (25) Cd = a1.Yhr* + (a1/α).G(-1) Consumption, as in Kaldor (1966), depends on:  (expected) current income of the period;  Yhr = W + FD + rm.M(-1)  Capital gains of the previous period.  G = d(pe).e(-1) It is not required to suppose, as must be the case in a stationary model, that consumption depends on the stock of wealth of households.

The portfolio decisions (pe.ed)* / V* = λ0 - λ1.rm + λ2.re(-1) - λ3.(Yhr*/V*) Md */V* = (1 - λ0) + λ1.rm - λ2.re(-1) + λ3.(Yhr*/V*) re = (FD + G)/(pe(-1).ed(-1) ) Households wish to hold a proportion λ0 of their expected wealth in the form of equities, But this proportion is modified positively by past rates of return on equities, And negatively by the interest rates on deposits, as well as demand for money arising from transactions.

(7A)Ms = Md redundant equation (2B)Md - Md* = (Yhr - Yhr*) In the model, although the supply of additional money is exactly equal to the supply of new loans to firms, and despite the fact that the demand for money depends on portfolio decisions, the accounting constraints are always such the supply of money is always equal to the demand for money. Although the supply of money and the demand for money are apparently determined by two independent mechanisms, these two variables always turn out to be equal. They seem independent of each other, but the accounting is such that they are dependent.

Experiments Normal regime: utilization rates have a strong effect on the rate of accumulation; Puzzling regime: Tobin’s q ratio has a strong effect on the rate of accumulation.