Stock-Flow Consistent Monetary Economics

Abstract

The focus in this chapter is on Wynne Godley and Marc Lavoie’s contribution to stock-flow consistent macroeconomics. The Godley and Lavoie models describe economies as systems of shifting and interlocking balance sheets, evolving through time. A simplified open economy stock-flow consistent model of a growing economy is outlined, used to carry out a policy experiment concerning the relative effectiveness of monetary and fiscal policy, in order to show that fiscal policy is the appropriate demand management tool for the maintenance of full employment and sustainable prosperity. This is linked to the use of a job guarantee to identify the appropriate fiscal stance for this purpose.

Appendix

The Simulation Model

We start with the national income accounting identity for GDP.

$$Y = C + I + G + {\text{NX}}\,{\text {.}}$$

(A1)

Non-financial sector firm profits before interest (EBIT) are given by (A2)

$${\text{EBIT}} = \frac{\mu }{1 + \mu }*Y\,{\text {.}}$$

(A2)

The parameter $\mu$ is Kalecki’s gross markup over direct costs, which in this model are entirely labour costs.

$${\text{WB}} = Y{-}{\text{EBIT}}\,{\text {.}}$$

(A3)

The wage bill is that part of GDP which is not EBIT, so that $Y = {\text{EBIT}} + {\text{WB}} \,{\text {.}}$. Banking sector services do not directly make up a part of GDP in this model, and bank earnings are instead treated as a transfer, and a use to which a part of GDP is put.

$${\text{NX}} = - \psi \,.\,\left( {C + I} \right).$$

(A4)

This country is assumed to be running a trade and current account deficit , since the country is in receipt of net capital inflows, driving the real exchange rate to a level at which the trade balance is in deficit . Given the dominance of financial flows in the determination of floating exchange rates in the modern world—where the turnover of the foreign exchange market in recent times has been approximately 100 times the value of trade flows (BIS 2013)—the capital and financial account is viewed as the primary cause of the trade balance being in deficit. In the model, the trade deficit is a proportion of private-sector spending, where the proportion is a parameter. This assumption is made to keep the model compact.

$$I = \delta \,.\,K_{ - 1} + g_{k} K_{ - 1}\,{\text {.}}$$

(A5)

Gross investment spending is the sum of replacement investment and net investment. Replacement investment is a fixed proportion of the previous period’s value of the capital stock, where that proportion $\delta$ is a parameter. Net investment is again a proportion of the prior capital stock, but the rate of accumulation coefficient $g_{k}$ is given by an equation, similar to the Kalecki–Steindl–Keynes–Minsky equation used in Lavoie and Godley .

$$g_{k} = a_{0} + a_{1} \left( {u_{ - 1} - u^{*} } \right) + a_{2} \left( {\frac{{{\text{FU}}_{ - 1} }}{{K_{ - 1} }}} \right) + a_{3} \left( {q_{ - 1} - q^{*} } \right)\,{\text {.}}$$

(A6)

I have omitted the rate of interest on loans from this equation, although the rate of interest will still influence the rate of accumulation, though its direct impact earnings net of interest, and through its impact on the propensity to consume and on household wealth.

$u_{ - 1}$ is to the utilisation ratio of the previous period.

$$u = Y/Y_{\text{cap}}\,{\text {,}}$$

(A7)

$$Y_{\text{cap}} = K_{ - 1} /{\text{COR}}\,{\text {.}}$$

(A8)

$a_{0} , a_{1} , a_{2} \,{\text{and}} \,a_{3}$ are all parameters in the model, as is the capital output ratio, COR.

$q_{ - 1}$ is the valuation ratio for the previous period.

$$q = \frac{{p_{\text{e}} \,.\,e}}{{K - L_{\text{f}} }} \,{\text {.}}$$

(A9)

The higher the utilisation ratio and the stock market valuation ratio, the higher the rate of capital accumulation. Though a utilisation ratio of 70% and valuation ratio of 100% are included in the equation, this does not mean there is any tendency in the model towards a steady state at either (or both) of these benchmarks.

The consumption function is as follows:

$$C = \alpha_{1} Y_{{{\text{r }} - 1}} \left( {1 - \theta } \right) + \alpha_{1} \Delta L_{{{\text{h}} - 1}} + \alpha_{2} V_{ - 1} - \alpha_{1} r_{{{\text{l}} - 1}} L_{{{\text{h}} - 1}}\,{\text {.}}$$

(A10)

Household consumption depends on the previous period’s after-tax regular income, on the net additional loans household took out last period, on household wealth in the previous period and on the interest households have to pay on their existing debts. Consumption perhaps ought to depend on expected values of regular income and wealth this period, but it is in the nature of these models that such a change does not make a significant difference to the operation of the model over time.

The marginal propensity to consume out of regular income depends on the lagged rate of interest on loans:

$$\alpha_{1} = \alpha_{10} + \alpha_{11} r_{{{\text{l}} - 1}}\,{\text {.}}$$

(A11)

Gross regular income includes wage income, interest received on deposits, dividends from firms and dividends from banks:

$$Y_{r } = {\text{WB}} + r_{ - 1} \cdot D_{ - 1} + {\text{FD}} + {\text{FDB}}\,{\text {.}}$$

(A12)

Household wealth (V) is the net worth of households, excluding bank reserves, and as identified in the balance sheet matrix:

$$V = D + p_{\text{e}} e - L_{\text{h}}\,{\text {.}}$$

(A13)

The rate of interest on loans is given by adding a bank profit margin onto the rate of interest on deposits (which by assumption is set at the rate of interest on bills here).

$$r_{\text{l}} = r + \pi_{\text{b}} \,{\text {.}}$$

(A14)

The official interest rate, or rate of interest on bills, is set at 2% in the base case, with a bank profit margin of 2%.

The amount of new household borrowing $\Delta L_{\text{h}}$ is assumed to depend on another measure of income—Haig–Simons income, $Y_{\text{hs }}$, which includes (after-tax) capital gains, but excludes debt interest payments.

$$Y_{\text{hs}} = Y_{\text{r }} \left( {1 - \theta } \right) + {\text{CG}}\left( {1 - \frac{\theta }{2}} \right) - r_{{{\text{l}} - 1}} L_{{{\text{h}} - 1}}\,{\text {.}}$$

(A15)

CG denotes capital gains on shares, which are the only speculative asset in this model:

$${\text{CG}} = \Delta p_{\text{e}} \, \cdot \,e_{ - 1}\,{\text {.}}$$

(A16)

It is assumed that all capital gains are taxed, whether realised or not, but that they are taxed at a concessional rate of half the marginal tax rate on regular income. New household borrowing is then given as a proportion of any increase in Haig–Simons income over the period:

$$\Delta L_{\text{h}} =\upzeta \left( {Y_{\text{hs}} - Y_{{{\text{hs}} - 1}} } \right)\,{\text {.}}$$

(A17)

$\alpha_{10} ,\alpha_{11} , \alpha_{2} , \theta ,\pi_{\text{b}} \,{\text{and}} \,\upzeta$ are further values which need to be selected. $\theta$ is of course a key policy variable.

The distributed profits of firms are a proportion of the entrepreneurial earnings F of the previous period, which are themselves EBIT net of interest payments to banks, given that there are no taxes on corporate profit in this model. That proportion is the dividend payout ratio (POR), which is a further parameter:

$$F = {\text{EBIT}} - r_{{{\text{l}} - 1}} L_{{{\text{f}} - 1}} \,{\text {,}}$$

(A18)

$${\text{FD}} = {\text{POR}}\,\cdot\,F_{ - 1}\,{\text {.}}$$

(A19)

Retained earnings are given as a residual by,

$${\text{FU}} = F - {\text{FD}}\,{\text {.}}$$

(A20)

The proportion of planned investment to be funded through the issue of new shares depends on the lagged valuation ratio, so that the number of new shares issued in each period is given by,

$$\Delta e_{\text{s}} = \frac{{\gamma q_{ - 1} I}}{{p_{{{\text{e}} - 1}} }}\,{\text {.}}$$

(A21)

The remaining source of funding for investment is additional borrowing by firms from the banking sector:

$$\Delta L_{\text{f}} = I - {\text{FU}} - p_{{{\text{e }} - 1}} \Delta e \,{\text {.}}$$

(A22)

The only market-clearing price in the model is the price of an equity share. This is set by equating the supply of shares from (A21) with the demand for shares, to determine p. The proportion of the previous period’s household wealth which is invested into the share market in this period is given by an equation similar to the Tobin ‘pitfalls equation’ used in Lavoie and Godley , except for the omission of a term relating to the transactions demand for money.

Rearranging the resulting equation for the household demand for shares to make the market-clearing price of shares the subject, we get,

$$p_{\text{e}} = \left\{ {\lambda_{0} - \lambda_{1} r_{ - 1} + \lambda_{2} r_{{{\text{e}} - 1}} } \right\}V_{ - 1} /e \,{\text {.}}$$

(A23)

Household demand for shares, and therefore the market-clearing price of shares, since the supply this period has already been determined, depends negatively on the lagged return on bank deposits and positively on the lagged return on equities. The $\lambda_{i}$ terms are further parameters.

The return on equities is the simple sum of the dividend yield plus capital gain. In gross terms, this gives us,

$$r_{e } = \frac{{{\text{FD}} + {\text{CG}}}}{{p_{ - 1} e_{ - 1} }}\,{\text {.}}$$

(A24*)

(* in the simulation model as used, FD was adjusted using the marginal income tax rate and CG using the concessional tax rate for capital gains)

It is government spending which drives the sustainable rate of growth of demand in this model, and consequently which drives the growth in GDP . Pure government spending, net of interest payments on government financial liabilities, is taken to grow at some trend rate:

$$G = G_{ - 1} \left( {1 + g_{g} } \right)\,{\text {,}}$$

(A25)

The growth rate in pure government spending is another parameter, which will be set at 4% in the base case of the model.

Taxation is given by,

$$T = \theta \left( {Y_{\text{r}} } \right) + \left( {\theta /2} \right){\text{CG}}\,{\text {.}}$$

(A26)

The fiscal deficit is given by,

$$\Delta B = T - G - r_{ - 1} B_{ - 1}\,{\text {.}}$$

(A27)

Part of this reflects a demand for domestic financial assets on the part of the rest of the world, due to the current account deficit :

$$\Delta B_{\text{o}} = - \left( {\text{CA}} \right) = - \left( {\text{TB}} \right) + r_{ - 1} B_{{{\text{o}} - 1}}\,{\text {.}}$$

(A28)

The rest is taken up by domestic banks. Government financial liabilities in this context equate to additional exchange settlement reserves or federal funds for the banking sector, so that there is no question of securities needing to be sold in a market to ‘fund’ the fiscal deficit . Banks must take up as settlement reserves whatever government financial liabilities are not taken up by other sectors, as in real life (in this model, the only other sector to hold government liabilities directly is the overseas sector). Should insufficient net government liabilities be issued to meet the demand for them from the foreign sector, then banks go short in bills in this model, which equates to central bank lending to the banks at the official interest rate:

$$\Delta B_{\text{b}} = \Delta B - \Delta B_{\text{o}}\,{\text {.}}$$

(A29)

Distributed earnings from banks are given by bank earnings, less bank retained earnings:

$${\text{FDB}} = {\text{FB}} - \Delta R \,{\text {.}}$$

(A30)

Bank earnings are given by the gap between interest received on assets and interest paid on liabilities:

$${\text{FB}} = r_{{{\text{l}} - 1}} L_{{{\text{f}} - 1}} + r_{{{\text{l}} - 1}} L_{{{\text{h}} - 1}} + r_{ - 1} B_{{{\text{b}} - 1}} - r_{ - 1} D_{ - 1}\,{\text {.}}$$

(A31)

Bank retained earnings depend on the necessary increase in reserves to meet a lagged solvency ratio requirement, where SOLR is the required solvency ratio:

$$\Delta R = \left( {{\text{SOLR}} - {\text{SOL}}} \right)\, \cdot \,\left( {L_{{{\text{f}} - 1}} + L_{{{\text{h}} - 1}} } \right)\,{\text {.}}$$

(A32)

The demand for deposits at banks is determined from the balance sheet of households as,

$$D_{\text{d}} = V + L_{\text{h}} - p \cdot e_{\text{d}}\,{\text {.}}$$

(A33)

The supply of deposits by banks comes from the balance sheet of banks and is,

$$D_{\text{s}} = L + B_{\text{b}} - R \,{\text {.}}$$

(A34)

The equation I have no need to write down is the identity between the demand for deposits on the part of households and their supply by banks $(D_{\text{d}} = D_{\text{s}} )$. This identity is a consequence of correct accounting within the model and serves as a check that the model is correctly specified in terms of accounting for stock-flow relationships.

This is sufficient to determine the behaviour of this highly simplified, mechanical and non-stochastic monetary model. It has obvious limitations, but any attempt at a fully realistic model of this kind necessitates at least three times as many equations, and full realism is not the purpose here. The purpose is to design a model which can easily be reproduced on excel, with some institutional realism, which accounts correctly for stocks and flows, and within which a range of useful experiments can be carried out. The experiments are useful if they generate predictions which still hold approximately in much larger and more realistic models, and which are likely to apply in real life also, since they reflect the workings of a correct accounting for stocks and flows within the model.

Since the price level is held constant (at P = 1.65), then any changes in labour productivity (APL) or the Kaleckian markup show up as changes in the (real) wage:

$$\frac{W}{P} = \frac{\text{APL}}{{\left( {1 + \mu } \right)}}.$$

(A35)

Labour productivity is set at 1, the markup is 0.65, and therefore the nominal wage rate W is 1, in the base case.

Employment is given by the wage bill divided by the wage rate:

$$N = \frac{\text{WB}}{W}\,{\text {.}}$$

(A36)

The labour force grows over time, at some trend rate:

$${\text{LF}} = {\text{LF}}_{ - 1} \left( {1 + g_{\text{LF}} } \right){\text {.}}$$

(A37)

In the base case, pure government spending grows in line with the sum of the growth rate of the labour force and the growth of labour productivity, with the growth in labour productivity set equal to zero.

The unemployment rate is given by 1, the ratio of employment to the labour force:

$${\text{UN}} = 1 - \frac{N}{\text{LF}}{\text {.}}$$

(A38)

In the ‘year 2000’, the labour force consists of 7233 workers, and the unemployment rate is 2.96%.

The economy in the simple model looks like a very stable place, and as it stands there is no financial instability in this model, but Minskian financial instability; complexity and nonlinearities; and stochastic behaviour can easily be added. A model like this, and even far more complicated and realistic stock-flow consistent models, provides a canvas on which a variety of scenarios can be described. While almost fully realistic models, with parameters selected for consistency with econometric data, can be used as an aid to economic forecasting, that is not the most important function of these models. They can, at best, as Godley understood, make contingent predictions of possible future outcomes. The power of such models lies in their narrowing down the set of possible futures, to ones consistent with a plausible evolution of stocks and flows, based on correct accounting.

The values of the policy variables and parameters used in Model 7A, base case, were as follows:

$$\begin{aligned} & g_{g} = 0.04;\;\theta = 0.15;\;r = 0.02;\;{\text{SOLR}} = 0. 1 5\\ & \mu = 0.65;\;\psi = 0.02;\;\delta = 0.03;\; a_{0} = 0.01;\;a_{1} = 0.10;\;a_{2} = 0.02;\;a_{3} = 0.02; \\ & u^{*} = 0.7;\;q^{*} = 1;\; = 3.5;\;\alpha_{10} = 0.9;\;\alpha_{11} = 4;\;\alpha_{2} = 0.1;\;\pi_{\text{b}} = 0.02 \\ & \zeta = 1 ;\;{\text{POR}} = 0.5;\;\gamma = 0.1;\;\lambda_{0} = 0.6;\;\lambda_{1} = 0.02;\;\lambda_{2} = 0.38;\;g_{\text{LF}} = 0.04 \\ & W = 1{\text{ (the price level }}P{\text{ is always fixed at 1 in this model);}}\;{\text{APL}} = 1 \\ \end{aligned}$$