Sectoral Balances and Keynesian Causation

Macroeconomists often start their analysis from an accounting identity or set of identities. Since identities are true by definition, they can provide a good framework for analysis, including a way to detect any errors in logic or inconsistent conclusions. A theory that conforms to an identity is not necessarily correct but is at least potentially correct. To constitute a theory, though, it is necessary to do more than just invoke identities. This is because identities in themselves tell us nothing about causation.

Once we begin to make behavioral assumptions, the ground becomes contestable. Identities are incontestable, at least if we accept the principles of double-entry book keeping, whereas behavioral assumptions are not.

The sectoral balances

An important identity emphasized in Modern Monetary Theory (MMT) concerns the sectoral balances:

(T – G) + (S – I) + (X – M) = 0

The difference between taxes T and government spending G is the government balance. Private domestic saving S minus private gross investment I is the domestic private balance (or net private saving). Imports M minus exports X is the foreign balance.

When a sector, in aggregate, spends less than its income (or revenue), it is said to be in surplus. If it spends more than its income, it is in deficit. The identity makes clear that the sum of the sectoral balances must sum to zero, canceling each other out.

This is an identity, true by definition. It tells us that whatever the net positions of two sectors, the other sector must offset them exactly. If, for instance, the domestic private sector and foreign sector are both in surplus (S > I, M > X), the government must, by definition, be in deficit to an equal extent. Or, referring to the first version of the identity, if the domestic private sector is net saving and the economy is running a trade deficit, the government’s fiscal balance must be in deficit. For an explanation of this point see Government Deficits and Net Private Saving.

This is a very important point to understand, and it is critical that any theorizing conforms to the sectoral balances identity. Nevertheless, the identity in itself does not explain how each sector affects the others, or how the various sectors are likely to respond in different circumstances. Also, although there is a close connection between GDP and the sectoral balances identity, it is not immediately obvious from the identity itself how GDP is likely to move in response to sectoral behavior and interactions between the sectors. To find possible answers to these questions, we need to introduce our behavioral assumptions.

Broadly speaking, in MMT it is usually argued that once the government has formulated its fiscal policy settings, the behavior of non-government (which includes both the domestic private sector and the external sector) will determine the ultimate size of the government deficit (or surplus) through its behavior. In particular, tax revenues will rise and fall endogenously with oscillations in non-government activity. It is further held that if the government’s fiscal settings are not consistent with non-government achieving its intended net saving position at full employment, there will be either unemployment or inflation. Fundamental to this position is that there is no mechanism in a market economy capable of automatically generating full employment, and so in such cases it is up to government to adjust its fiscal settings to provide a better fit with non-government behavior.

Clearly, these theoretical arguments go well beyond what immediately follows from the sectoral balances identity. To arrive at these conclusions, Modern Monetary Theorists employ behavioral assumptions that appear most appropriate from their perspective.

At the most fundamental level, there is the MMT understanding of modern monetary systems (i.e. sovereign-currency systems). The monopoly issuer of the currency is the only entity that can correct a shortage or excess of the one thing that can extinguish (i.e. finally settle) tax obligations or accommodate non-government net saving desires.

There is also the MMT insight that since any issuance of government bonds by the currency issuer is purchased out of funds it has net spent into existence, the notion of financial crowding out is inapplicable. The currency issuer as monopolist sets the price of its own money, and can do so independently of fiscal operations.

The Post Keynesian observation, accepted in MMT, that loans create deposits does away with the inapplicable notion of a money multiplier. The quantity of reserves does not – and cannot – constrain or drive private credit creation. Lending is capital and demand constrained, not reserve constrained. It is the state of the economy that underpins demand for loans from credit-worthy borrowers, and in a world without financial crowding out, the currency issuer can strengthen economic activity through fiscal measures in situations of excess capacity and unemployment.

Keynesian causation

It has been stated that, given the government’s fiscal settings, non-government behavior largely drives the government’s fiscal outcome through its effects on tax revenue. This means that the ultimate fiscal outcome is endogenously determined by the level of economic activity. The endogenous determination operates through the automatic stabilizers. In particular, tax revenue rises and falls with income and employment.

However, at the same time, fiscal policy can have an exogenous influence on economic activity. This will occur whenever the government actively alters its policy settings. This includes changes in government spending measures and alterations of tax policy, such as changing rates, introducing a new tax or removing an old one.

In analyzing these effects, Modern Monetary Theorists are essentially Keynesian or Kaleckian in the behavioral assumptions they make and the causation they envisage. They also draw on various connections between the sectoral balances and the state of the economy studied earlier by Wynne Godley and his circle in Cambridge, UK.

For instance, it was primarily the understanding that persistent fiscal austerity in trade-deficit economies during the 1990s corresponded, as a matter of accounting, to domestic-private sector deficits and an unsustainable accumulation of private debt that enabled some to foresee the global financial crisis of 2007. It is this understanding that also informs the depiction of the current malaise as a balance-sheet recession. A heavily indebted private sector (primarily the household sector) needs to work down its debt before it can be the driver of a sustainable recovery. But in the absence of an orderly cancellation or write down of private debts, debt repayment will require substantial net saving by the private sector, which in trade-deficit economies is only possible alongside ongoing government deficits.

Keynesian or Kaleckian causation suggests that fiscal stimulus can boost output and income when, as now, there is excess capacity and unemployment. Modern Monetary Theorists point out, in addition, that a failure to do so will impede the private sector’s attempts to net save.

It may be instructive to elaborate on the kind of causation Modern Monetary Theorists have in mind, and the behavioral assumptions, many of them Keynesian, that are involved in the formulation of this theoretical perspective.

First, the notion that there is a connection between the behavior of the various sectors on the one hand, and GDP and employment on the other, is suggested by the fact that the sectoral balances identity is simply a reworking of an identity pertaining to GDP. In the sectoral balances identity

(T – G) + (S – I) + (X – M) = 0

private saving, S, is disposable income not consumed; i.e. S = Y – T – C, where Y is income, Y – T is disposable income and C is private consumption expenditure. If we substitute this expression for S into the sectoral balances identity and solve for Y, we get:

Y = C + I + G + (X – M)

Real income, Y, is real GDP, so this suggests that the connection between real GDP and the sectoral balances is close. But what are the causal connections?

MMT, following Keynes, assumes that tax revenue, saving desires and import spending are endogenously influenced by the state of the economy, specifically by the level of income. In more elaborate models it is recognized that these variables have both endogenous and exogenous influences. For example, import spending depends endogenously on income but is also susceptible to other factors exogenous to the circular flow of income, such as exchange rates. For present purposes, we can keep things simple by assuming tax revenue, desired saving and imports can be expressed as positive fractions of income, ignoring the exogenous factors:

Sd = s(Y – Td), Td = tY, Md = mY

These expressions reflect the behavioral assumption that desired saving (Sd), taxes (Td) and imports (Md) rise with income. In this regard, s, t and m are marginal propensities to ‘leak’ from the circular flow of income and all take values between zero and one. It is being assumed that, within a reasonable range of income, a fraction s of each additional dollar of disposable income will be saved, and that fractions t and m of an additional dollar of income will be taxed and spent on imports, respectively.

Often reference is also made to the marginal propensity to consume, c, which is the proportion of extra disposable income that households desire to devote to private consumption, Cd. The marginal propensity to consume, c, and the marginal propensity to save, s, sum to one by definition. That is, whatever disposable income is not consumed is saved. Desired consumption is typically assumed to be primarily determined by income but also by exogenous factors such as interest rates and asset prices. Since, for simplicity, desired saving is being treated simply as a fraction of disposable income, this implies the same is true of desired consumption. From Sd = Y – Td – Cd it follows that:

Cd = Y – Td – Sd

Substituting for Sd we get:

Cd = Y – Td – s(Y – Td) = (1 – s)(Y – Td) = c(Y – tY) = c(1 – t)Y

In contrast to the leakages (taxes, saving and imports), it is assumed that desired investment, government spending and exports are exogenous ‘injections’ into the economy originating from outside the circular flow of income.

From the MMT perspective, it makes sense to consider government expenditure in this way. It is injected into the economy by the monopoly issuer of the currency. The act of government spending injects a flow of expenditure and adds to the circular flow of income. The level of government expenditure is not constrained by current income. It is referred to as an autonomous expenditure, because its level is assumed to be determined independently of current income.

The same is assumed to be true of private investment and exports. Desired investment can be financed out of past profits or private credit creation of the banking system, and so is not constrained by current income. In Keynes influenced approaches, the level of investment is assumed to depend on expected profitability, which at the aggregate level is considered to be a function of expected aggregate demand. For instance, the Kalecki profit equation – which follows immediately from the sectoral balances identity (see Thinking in a Macro Way) – indicates that aggregate profit is equal to the sum of capitalist expenditures, the government deficit and net exports, minus saving out of wage income.

Desired exports are regarded as primarily influenced by exogenous factors, especially the state of the global economy – the level of the rest of the world’s income – and other factors including exchange rates.

The assumption that the injections are exogenous is signified by a subscript “o”:

Id = Io, Gd = Go, Xd = Xo

Introducing the Keynesian assumptions into the sectoral balances identity we have:

[tY – Go] + [s(1 – t)Y – Io] + [mY – Xo] = 0

This can be rearranged to get an expression for income in terms of the exogenous and endogenous variables:

Y = (Io + Go + Xo) / (s + (1 – s)t + m)

This expression is in the form:

Y = k.A


k = 1 / (s + (1 – s)t + m)

A = Io + Go + Xo

Here, k is referred to as the expenditure multiplier. This billy blog post provides a good introduction on spending multipliers.

In words, the expression for Y says that equilibrium income can be expressed as a multiple of the sum of autonomous demands. The idea is that once private firms, the government and foreigners have made their spending decisions, the resulting expenditure flows will be received as income by other participants in the economy. A portion of the income will be dedicated to consumption, while other portions will leak out of the circular flow of income to saving, tax payments and imports. The portion dedicated to consumption will create additional income, which again is used partly for consumption while the remainder drains to taxes, saving and imports, and so on. At each stage of the multiplier process, the amount of consumption and income shrinks until it is insignificant.

As can be inferred from the expression for k, the multiplier will be larger when the propensities to leak are small, and vice versa.

A stylized example

A simple numerical example may help to illustrate some features of the MMT perspective on the lead up to the balance-sheet recession and the effects of different policy responses to the crisis. It may also help to crystallize the connection envisaged in MMT between the sectoral balances and the economy’s performance in terms of output and employment.

We have our simple model:

Y = k.A

where k is the expenditure multiplier and A the sum of autonomous expenditures. We also know that:

k = 1 / (s + (1 – s)t + m)

A = Io + Go + Xo

and that the leakages are:

Sd = s(Y – Td), Td = tY, Md = mY

For calculation purposes we can rearrange the expression for private saving:

Sd = s(Y – Td) = s(1 – t)Y

Suppose initially the following behavioral parameters and exogenous spending levels:

Io = 10, Go = 20, Xo = 10
s = 3/32, t = 1/5, m = 1/8

The figures for the components of autonomous demand can be regarded as in millions, billions or trillions depending on the country and currency we have in mind. Or, in fact, for the initial part of the example, the expenditures can be thought of as percentages of GDP.

The propensities to leak indicate that private households are currently saving just under 10% of disposable income, being taxed 20% of GDP and spending the equivalent of 12.5% of GDP on imports.

Plugging these figures into our model reveals an expenditure multiplier of 2.5, autonomous demand of 40 and GDP (= Y) of 100.

Let’s assume this GDP of 100 corresponds to full employment. We can see how this situation breaks down at the sectoral level by calculating the government deficit, net private saving and the trade deficit using the equations in our model for the leakages. Doing so reveals that Td = 20, Sd = 7.5 and Md = 12.5. Since Go = 20, Io = 10 and Xo = 10, we can see that the sectors break down as follows:

(T – G) [0] + (S – I) [-2.5] + (M – X) [2.5] = 0

Although the economy is at full employment, a trade deficit in combination with a balanced fiscal outcome implies that the domestic private sector desires to be in deficit, spending more than it earns. Whether this is of concern depends on how long the situation has prevailed.

Suppose the economy has been performing somewhat like this for an extended period of time. Although highly stylized, this is kind of what happened in the US and many other countries in the lead up to the global financial crisis. Over time, this pushes the domestic private sector increasingly into debt as it runs down financial wealth to maintain its deficit (spending more than its income).

At some point the situation proves unsustainable. The domestic private sector is likely to respond by trying to increase its saving rate and get its debt under control and balance sheets in better shape.

We can reflect this behavior in our model by assuming that there is an increase in the marginal propensity to save. Imagine it increases to s = 7/32, or a bit over 20% of disposable income. We’ll assume this occurs before any change in government policy settings.

For simplicity, assume that exogenous investment and exports also remain unchanged. If the downturn in demand resulting from the increased saving rate is more or less global – as it was in the Great Recession – these expenditure flows would actually be likely to decrease. But including these changes would only further underscore most of the points to be made.

We can recalculate the outcome of our model using the new, higher propensity to save. The effect is to reduce the size of the multiplier from 2.5 down to 2 and income from 100 to 80. The steepness of the decline in output (a 20% drop) is not the point. As mentioned, this example is highly stylized. It is the direction of the change that is relevant.

The decline in output implies a collapse in employment below the full employment level on the assumption that productivity has not declined as sharply as output. We can suppose that unemployment has increased significantly, much like the experience of the US and other economies since the onset of the crisis.

The decline in income will impact on tax revenue and import spending, and also thwart the private sector’s attempt to save to a significant degree.

If we suppose that the private sector’s new, higher marginal propensity to save was initially arrived at on the expectation that output would remain at the full-employment level, the saving rate would have translated into saving of 17.5 and net private saving of 7.5, considering investment is 10. We can think of 7.5 as the domestic private sector’s desired level of net saving at full employment.

Instead, because of the onset of recession, the domestic private sector has only saved 14, indicating net private saving of 4. Admittedly, if investment had been allowed to decline exogenously, this would contribute to net private saving. This would have exacerbated the downturn in demand and output even further, but would help to boost net private saving. The current example most resembles a situation where private households feel the pinch first, due to unsustainable debt levels, perhaps on mortgages and credit cards, and firms do not anticipate the decline in consumer demand before it occurs. As mentioned, we are also ignoring the likely decline in export income, which would also impact negatively on income and subtract from net private saving.

Plugging the numbers into our model reveals the following breakdown by sector:

(G – T) [-4] + (S – I) [4] + (M – X) [0] = 0

Overall, the domestic private sector has begun to mend its balance sheets. The fiscal automatic stabilizers have kicked in to support private-sector net saving, even though the government has not responded to the crisis at this stage.

From the MMT perspective, the emergence of unemployment is a clear sign that the government’s net expenditure is insufficient to enable private sector net-saving intentions alongside full employment. Our simple model indicates that an increase in autonomous demand of 10 would be necessary to restore output to 100, which we have assumed is consistent with full employment.

According to the logic of the model, it wouldn’t matter if this extra exogenous spending came from government spending, private investment or export demand. However, since investment is considered to be sensitive to expected profitability, which Keynesians regard as a function of aggregate demand, stronger investment seems unlikely in the midst of weak demand and high unemployment. This is especially true, in terms of MMT, given that the domestic private sector is intent on increasing its net saving, and this can be achieved through reductions in investment as well as through a higher saving rate.

In a global downturn, exports are also an uncertain source of demand. They may provide a boost in demand for some countries, but only at the expense of lower demand in other countries, since at the global level net exports cancel to zero.

The solution, within the model, is for the government to increase its net spending, through increased spending and/or tax cuts.

By increasing government spending by 10 to 30, and leaving all other parameters unchanged, the model indicates output would be restored to the full employment level of 100 with the following sectoral composition:

(T – G) [-10] + (S – I) [7.5] + (M – X) [2.5] = 0

By running a fiscal deficit equal to 10% of GDP, the government has underpinned net private saving of the desired level (7.5% of full-employment GDP) and a trade deficit (2.5% of GDP).

Alternatively, the model indicates that the government could have left government spending at 20 and cut taxes, which would have the effect of reducing the propensity to tax below its current level of 1/5.

But maybe the government doesn’t want its fiscal deficit to widen. Suppose that instead of introducing fiscal stimulus, the government responded to the onset of the balance-sheet recession by attempting to balance its spending and taxing. Recall that at the onset of the crisis, GDP had fallen to 80, with the government deficit at 4 (5% of GDP) and net private saving at 4 (also 5% of GDP). The foreign sector was in balance.

Imagine for whatever reason that the government chose to cut spending from 20 down to 15. Through the multiplier, this would reduce GDP further to 70, implying lower employment. We are assuming private investment remains unchanged for simplicity, but for Keynes influenced economists, the depressed conditions would probably result in a collapse in investment. The impact on the various sectors, according to our simple model, is:

(T – G) [-1] + (S – I) [2.25] + (M – X) [-1.25] = 0

The government has almost succeeded in reducing its deficit to zero and there is a small trade surplus (foreign deficit). But the policy has also frustrated private-sector net saving efforts.

The model indicates, as MMT suggests, that the unemployment would persist until either the government quit trying to eliminate its deficit or the domestic private sector altered its desired level of net saving.

But, in a balance-sheet recession, if the domestic private sector cannot net save sufficiently to pay down its debts to sustainable levels, it will be in no position to drive sustainable recovery through credit expansion and private demand.

This, in any case, is a rough outline of the MMT perspective on causation, and why fiscal stimulus rather than austerity is regarded as the appropriate policy under current circumstances.

Related post

Introduction to the Sectoral Financial Balances Model