{"id":12914,"date":"2010-12-30T18:11:31","date_gmt":"2010-12-30T07:11:31","guid":{"rendered":"https:\/\/billmitchell.org\/blog\/?p=12914"},"modified":"2010-12-30T18:11:31","modified_gmt":"2010-12-30T07:11:31","slug":"what-is-the-balanced-budget-multiplier","status":"publish","type":"post","link":"https:\/\/billmitchell.org\/blog\/?p=12914","title":{"rendered":"What is the balanced-budget multiplier?"},"content":{"rendered":"

\t\t\t\tI have been working today on the modern monetary theory text-book that Randy Wray and I are planning to complete in the coming year (earlier than later hopefully). It just happens that I was up to a section on what economists call the balanced-budget multiplier which is a way to provide stimulus without running a deficit when I read an article in the New York Times (December 25, 2010) by Robert Shiller – Stimulus, Without More Debt<\/a>. I also received a number of E-mails asking me to explain the NYT article in lay-person’s language. So a serendipitous coming together of what I have been working on and some requirement for explanation and MMT interpretation. So what is the balanced-budget multiplier?
\n
\nIn the New York Times article, Yale academic Robert Shiller introduced the notion of a balanced budget multiplier<\/em> which he says will allow the US government to provide more stimulus but “does not require deficit spending”. The logic of this is:<\/p>\n

\nWith the unemployment rate at 9.8 percent, more … [stimulus] … will certainly be needed, yet further deficit spending may not be a politically viable option. Instead, we are likely to see a big fight over raising the national debt ceiling, and a push to reverse the stimulus we already have. In that context, here’s some good news extracted from economic theory: We don’t need to go deeper into debt to stimulate the economy more.\n<\/p><\/blockquote>\n

Most people associate a fiscal stimulus with an expansion of the deficit. But there is a curiosity in macroeconomics that a “Keynesian economic stimulus does not require deficit spending”.<\/p>\n

Shiller says that “(u)nder certain idealized assumptions, a concept known as the “balanced-budget multiplier theorem” states that national income is raised, dollar for dollar, with any increase in government expenditure on goods and services that is matched by a tax increase”.<\/p>\n

The history of the concept is interesting but beyond this blog. Shiller notes that during the Great Depression, Keynes and his group developed the national income generation model of macroeconomics and it became standard doctrine to assume that the spending multiplier (discussed in detail below) was above 1.<\/p>\n

This meant that when governments increased net spending the ultimate rise in total income would be more than the initial increase in net public spending:<\/p>\n

\n… because the income generated by deficit spending also induces second and third rounds of expenditure. If the government buys more goods and services and there is no tax increase, people will spend much of the income that they earned from these sales, which in turn will generate more income for others, who will spend much of it too, and so on.\n<\/p><\/blockquote>\n

However, the worries about increasing public debt ratios have never been far below the surface and Keynesian economists in the 1940s started to consider the impact of deficit spending on public debt. Remember, this was an era where governments operated in a convertible currency system with fixed exchange rates and so were financially constrained.<\/p>\n

So unlike now (since 1971) where a sovereign government is never revenue constrained because it is the monopoly issuer of the currency and floats that non-convertible currency on international markets governments had to “finance” their net spending by issuing debt. Now, the act of debt-issuance to match deficit spending is totally unnecessary and voluntary. It is an artefact of a monetary system that most countries abandoned in 1971.<\/p>\n

But back in the 1940s, economists were worried that the accumulated debt from the Great Depression then the prosecution of the Second World War might be so large that it might constrain the capacity of governments to ramp up their deficits again (because the withdrawal of the war-time stimulus might provoke a return to recession).<\/p>\n

Note: no such worry should exist now. A sovereign government can spend what it likes as long as their are goods and services available for sale it its currency regardless of the public debt ratio. The latter is irrelevant in a modern monetary system for determining (or influencing) in a technical sense – government spending.<\/p>\n

All the fears we hear now (which were valid during the 1940s) are simply the echoes of ignorance or conservative ideologies and have no substance in economic\/financial theory or practice.<\/p>\n

As Shiller notes of the 1940s “this worry was unfounded. The Depression did not return after the war”. But the fears spawned the development of the insight that became known as the balanced budget multiplier.<\/p>\n

So what is the balanced-budget multiplier? Several people have written to me asking me to explain this. Serendipitously, I have been working on a section of our textbook which spans this topic this week and so with the stars aligning a corresponding blog seemed appropriate.<\/p>\n

Shiller offers this explanation of the balanced budget multiplier:<\/p>\n

\nThe reasoning is very simple: On average, people’s pretax incomes rise because of the business directly generated by the new government expenditures. If the income increase is equal to the tax increase, people have the same disposable income before and after. So there is no reason for people, taken as a group, to change their economic behavior. But the national income has increased by the amount of government expenditure, and job opportunities have increased in proportion.\n<\/p><\/blockquote>\n

I doubt that will resonate very well with many people. So more explanation is obviously required.<\/p>\n

But first we need to develop some conceptual apparatus in the form of a simple macroeconomic model to first understand what national income determination is all about, then to refresh our memories on how the normal spending multiplier works before we can hope to understand the concept of a balanced budget multiplier.<\/p>\n

Jargon aka terminology<\/strong><\/p>\n

All disciplines invent their own language as a way of making it harder to understand so that they can parade in the public sphere with a semblance of authority even if no such authority is justified by the actual substance of the ideas.<\/p>\n

Here is some terminology (jargon) that is used in the specification of macroeconomic models. All models have a number of equations which are relationships between variables. Each equation has some variables, some coefficients (or parameters). Usually a variable is written on the left-hand side of the equals sign (=) and is then expressed in terms of some other variables on the right-hand side of the equals sign.<\/p>\n

So y = 2x is an equation which says that variable y is equal to 2 times variable x. So if x = 1, then y = 2 as a result of this equation.<\/p>\n

The rule is that what is on the left-side of the equals sign has to be the same in magnitude as what is on the right-side (that is, an equation has equal left and right sides). You solve an equation by substituting values for the unknowns.<\/p>\n

In the above example the 2 is called a coefficient which is an estimate of the way in which y is related to x. A coefficient can also be called a parameter – which is a given in a model and might be estimated using econometric analysis (regression) or assumed by intuition).<\/p>\n

In the specific context, a variable is some measured economic aggregate (like consumption, output etc) which is denoted by some symbol that hopefully makes sense. The correspondence between the short-hand symbol and the variable is not always intuitive but convention rules.<\/p>\n

So Y is often used to denote GDP or National Income (but it can also be used to denote total output). C is usually used to denote final household consumption and I total private investment. X is typically used to denote exports and M imports although in some cases M is used to denote the stock of Money. I always use M for imports.<\/p>\n

There are two types of equations that are used in macroeconomic models: (a) identities which are true by definition – that is, as a matter of accounting – they are indisputable; and (b) behavioural equations which depict relations between variables that model behaviour – for example, consumption behaviour.<\/p>\n

An example of an identity is the national income equation depicting aggregate demand and output:<\/p>\n

Y ≡ C + I + G + X – M<\/p>\n

Note that in strict terms we write an equation that is an identity using the identity sign (three parallel horizontal lines) instead of the equals sign (two parallel horizontal lines). For the rest of this blog I will just use the equals sign irrespective but you should be aware that some of the equations are identities and are thus accounting statements.<\/p>\n

A behavioural equation captures our hypotheses about how some variable is determined. So these equations represent our conjecture (or theory) about how the economy works and obviously different theories will have different behavioural equations in their system of equations (which is what a model is).<\/p>\n

An example of a behavioural equation is the consumption function:<\/p>\n

C = C0<\/sub> + cYd<\/sub><\/p>\n

which says that final household consumption (C) is equal to some constant (C0<\/sub>) plus some proportion (c) of final disposable income (Yd<\/sub>). The constant component (C0<\/sub>) is the consumption that occurs if there is no income and might be construed as dis-saving.<\/p>\n

In macroeconomics, some behavioural coefficients are considered important and are given special attention. So the coefficient c in the consumption function is called the marginal propensity to consume<\/em> (MPC) and denotes the extra consumption per dollar of extra disposable income. So if c = 0.8 we know that for every extra dollar of disposable income that the economy produces 80 cents will be consumed.<\/p>\n

The MPC is intrinsically related to the marginal propensity to save<\/em> (MPS) which is the amount of every extra dollar generated that is saved (after households decide on their consumption). So the MPS = 1 – MPC by definition.<\/p>\n

The importance of MPC is that is one of the key determinants of the expenditure multiplier (more about which later). Please read my blog – Spending multipliers<\/a> – for more discussion on this point.<\/p>\n

The other piece of jargon that we encounter is the difference between exogenous (pre-determined or given) variables and endogenous variables (which are determined by the solution to the system of equations).<\/p>\n

An exogenous variable is known in advance of “solving” the system of equation. We take its value as given or pre-determined. We might say that government spending (G) is equal to $100 billion which means that its value is known and not determined by the values that the other variables take or are solved to.<\/p>\n

But in a system of equations, the values of some variables are unknown and are only revealed when we “solve” the model for unknowns.<\/p>\n

So if we have these two equations which comprises a “system”:<\/p>\n

(1)     y = 2x
\n(2)     x = 4<\/p>\n

Then x is a pre-determined variable (with the value 4) and is thus exogenous. You do not know the value of y in advance and you have to solve the equations to reveal its value – so it is endogenous. It is determined by the solution to the system.<\/p>\n

To solve this system we substitute the value of x in Equation (2) into Equation (1) so we get:<\/p>\n

y = 2 times 4<\/p>\n

y = 8<\/p>\n

So the solution of a system merely involves substituting all the known values of the coefficients (in this case the 2 on the x) and the exogenous variables (in this case x = 4) into the equations that depict the endogenous variables (which in this case is only Equation (1) but there will typically be multiple endogenous variable equations).<\/p>\n

In real modelling it becomes very complicated as to which variables can be considered endogenous and which are truly exogenous. At the extreme, everything might be considered endogenous and then things get mathematically complex and there is a whole body of theory in econometrics relating to the identification problem, which is well beyond this blog.<\/p>\n

A simple macroeconomic model<\/strong><\/p>\n

In macroeconomics we know that expenditure equals income (output). This fundamental relationship is covered in the national accounting framework.<\/p>\n

The national income identity which relates income (Y) to expenditure (E) is written:<\/p>\n

(1)     GDP ≡ Y ≡ E ≡ C + I + G + (X – M)<\/p>\n

where C is final household consumption, I is private capital formation (investment), G is government spending, X is total export spending and M is total import spending. The right-hand side of the identity is total expenditure in a given period (a flow).<\/p>\n

Another accounting statement is the relationship between disposable income (Yd<\/sub>) and total income (Y):<\/p>\n

(2)     Yd<\/sub> ≡ Y – T<\/p>\n

where T is total tax revenue net of transfers (pensions etc). This is the government’s share of national income. So Y is pre-tax income and Yd<\/sub> is after tax income.<\/p>\n

Our simple behavioural equations are:<\/p>\n

(3) Consumption function      C = C0<\/sub> + cYd<\/sub><\/p>\n

Consumption is the determined by some fixed amount independent on income plus the MPC (c) times disposable income. The MPC lies between 0 and 1. The higher the MPC the higher is the proportion of new income generated that is consumed. So if c = 0.8 then there will be an extra 80 cents in consumption for every extra dollar generated.<\/p>\n

Clearly the MPC = 1 – MPS. So if c = 0.8 then 20 cents in every extra dollar generated after tax is saved.<\/p>\n

(4) Investment function      I = I<\/p>\n

While in the real world investment is likely to depend on interest rates, expected income and other variables in this simple model we assume it to be fixed in each period – that is, it is considered exogenous.<\/p>\n

(5) Export function      X = X<\/p>\n

While in the real world exports are depend on local and external influences in this simple model we assume them to be fixed in each period – that is, they are considered exogenous.<\/p>\n

(6) Import function      M = mY<\/p>\n

Imports are considered proportional to total income where the proportion (m) is the marginal propensity to import<\/em>. In the real world, imports will be influenced by other factors including the real exchange rate. If m = 0.20 then imports will increase imports by 20 cents for every real GDP dollar produced.<\/p>\n

The behavioural policy equations are:<\/p>\n

(7) Government spending      G = G<\/p>\n

So we assume government spending is fixed in each period.<\/p>\n

(8) Tax rule      T = tY<\/p>\n

Tax revenue is a simple function of total income where t is the marginal (and average) tax rate. We could make the rule more complex by adding in, for example, lump-sum taxes and other taxes independent of income.<\/p>\n

So if t = 0.2 then Yd<\/sub> = (1 – t)Y = 0.8Y.<\/p>\n

The system of equations (1) to (8) define our macroeconomic system or model. You will note that the system reduces very quickly to the following model (because several of the variables are given in this simple model). We will also assume that C0<\/sub> = 0 for further simplicity.<\/p>\n

Y = C + I + G + (X – M)<\/p>\n

C = cYd<\/sub><\/p>\n

T = tY<\/p>\n

M = mY<\/p>\n

In mathematics if you have a system of equations, to get a solution you need to have as many equations as there are unknowns. We have four variables which are unknown here Y, C, T and M and four equations so we should be able to find a solution. In fact we can simplify the model even further by substituting (“putting”) the equations for C, T and M into the national income equation as follows:<\/p>\n

Y = cYd<\/sub> + I + G + X – mY<\/p>\n

We also know that Yd<\/sub> = Y – T = Y – tY, so our simple model reduces to a single equation with one unknown (Y) which will allow us to solve for Y and then subsequently we will know what C, T and M are.<\/p>\n

Y = c(Y-tY) + I + G + X – mY<\/p>\n

We simplify this further by collecting all the Y terms on the left hand side:<\/p>\n

Y – c(1 – t)Y + mY = I + G + X<\/p>\n

Note: all the exogenous variables in our model are on the right-hand side.<\/p>\n

This simplifies further (non-mathematicians please bear with me – it is just a matter of understanding a few simple rules of algebra, applying them and re-arranging terms):<\/p>\n

(9)      Y[1 – c(1 – t) + m] = I + G + X<\/p>\n

Therefore our model solves for total output and income (Y) as:<\/p>\n

(10)      \"\"<\/a><\/p>\n

<\/div>\n

We could simplify this further by denoting the exogenous right-hand expenditures are A (autonomous spending) such that:<\/p>\n

(11)      \"\"<\/a><\/p>\n

<\/div>\n

So a change in A will generate a change in Y according to the this formula:<\/p>\n

(12)      ΔY = kΔA<\/p>\n

where k = 1\/(1 – c*(1-t) + m) and is the expression for the expenditure multiplier.<\/p>\n

A model solution<\/strong><\/p>\n

Assume that c = 0.8; m = 0.2; t = 0.15. This will give a multiplier value of approximately 1.9. It is in fact equal to 1.92307692.<\/p>\n

This means that if A changes by 1 (that is, there is an extra dollar of spending) then national income will rise by $1.92. National income would fall by $1.92 if A fell by 1.<\/p>\n

Clearly A could rise if investment and\/or government spending and\/or exports increased. A can increase even if private investment falls as long as government spending and\/or exports rises by more than the fall in investment. You can tell a myriad of different stories about the way the government sector, the private domestic sector and the external sector is performing and how these sectors impact on aggregate demand (spending) and hence national income (GDP).<\/p>\n

With these behavioural coefficient values, and if we know that I = 100; G = 100 and X = 150 then we can solve for national income as follows:<\/p>\n

Y = kA<\/p>\n

Y = 1.92307692(350)<\/p>\n

Y = 673<\/p>\n

C = c(1-t)Y = 0.8(1-0.15)673 = 458<\/p>\n

S = (1-t)Y – C = 0.85(673)-458 = 114<\/p>\n

T = tY = 0.15(673) = 101<\/p>\n

M = mY = 0.2(673) = 135<\/p>\n

We can then deduce the following balances:<\/p>\n

Government budget balance = (G – T) = (100-101) = -1 (that is, a small budget surplus)<\/p>\n

Private domestic balance = (I – S) = (100-114) = -14 (that is, a surplus because saving is higher than investment spending)<\/p>\n

External balance = (X – M) = (150 – 135) = 15 (that is, a trade surplus)<\/p>\n

We know that the balances have to sum to zero which they do (when arranged in the correct way).<\/p>\n

An increase in government spending<\/strong><\/p>\n

Assume that the government wants to increase national income because it considers that employment is too low and unemployment is too high. It can use its fiscal capacity to stimulate aggregate demand (by increasing G).<\/p>\n

If it increases G by $50 – so G now rises to $150 then what is the impact on the system?<\/p>\n

In this case A increases by 50 and is multiplied throughout the economy 1.92 times so that the total increase in national income is 769.<\/p>\n

Consumption rises to 523; Imports rise to 154; Saving rises to 131; Taxes rise to 115.<\/p>\n

In terms of the balances, the budget is now in deficit of 35; the private domestic sector saving overall increases to 31 and net exports records a small deficit (because imports have risen with the rising income).<\/p>\n

So an expansion in government spending which pushes the budget into deficit (even though tax revenue also rises) stimulates national income and promotes increases in both consumption and saving. <\/p>\n

Why does the multiplier work in this way?<\/strong><\/p>\n

Remember the basic macroeconomic rule – aggregate demand drives output with generates incomes (via payments to the productive inputs).<\/p>\n

What is spent will generate income in that period which is available for use. The uses are further consumption; paying taxes and\/or buying imports. We consider imports as a separate category (even though they reflect consumption, investment and government spending decisions) because they constitute spending which does not recycle back into the production process. They are thus considered to be “leakages” from the expenditure system.<\/p>\n

So if for every dollar produced and paid out as income, if the economy imports around 20 cents in the dollar, then only 80 cents is available within the system for spending in subsequent periods excluding taxation considerations.<\/p>\n

However there are two other “leakages” which arise from domestic sources – saving and taxation. Take taxation first. When income is produced, the households end up with less than they are paid out in gross terms because the government levies a tax. So the income concept available for subsequent spending is called disposable income (Yd<\/sub>). So taxation (T) is a “leakage” from the expenditure system in the same way as imports are.<\/p>\n

Finally consider saving. Consumers make decisions to spend a proportion of their disposable income. The amount of each dollar they spent at the margin (that is, how much of every extra dollar to they consume) is determined by the marginal propensity to consume. Saving will be the residual after the spending (and tax) decisions are made. Saving (S) is thus a “leakage” from the expenditure system.<\/p>\n

Economists also define expenditure “injections” as autonomous spending which in our model comprises the sum of investment (I), government spending (G) and exports (X). The injections are seen as coming from “outside” the output-income generating process (they are exogenous or autonomous expenditure variables).<\/p>\n

For GDP (Y) to be stable injections have to equal leakages (this can be converted into growth terms to the same effect). The national accounting statements that we have discussed previous such that the government deficit (surplus) equals $-for-$ the non-government surplus (deficit) and those that decompose the non-government sector in the external and private domestic sectors are derived from these relationships.<\/p>\n

So in our simple model the uses of national income are:<\/p>\n

C + S + T + M = 458 + 114 + 101 + 135<\/p>\n

And the sources of spending are:<\/p>\n

C + I + G + X = 458 + 100 + 100 + 150<\/p>\n

The total leakages are:<\/p>\n

S + T + M = 114 + 101 + 135 = 350<\/p>\n

The total injections are:<\/p>\n

I + G + X = 100 + 100 + 150 = 350<\/p>\n

National income is in equilibrium (that is, will not change) once the leakages equal the injections. Income changes bring that equality into force because the leakages are sensitive to income changes.<\/p>\n

So imagine there is a certain level of income being produced – its value is immaterial. Imagine that the central bank sees no inflation risk and so interest rates are stable as are exchange rates (these simplifications are to to eliminate unnecessary complexity).<\/p>\n

The question then is: what would happen if government increased spending by $50? This is the terrain of the expenditure multiplier. If aggregate demand increases drive higher output and income increases then the question is by how much?<\/p>\n

The spending multiplier is defined as the change in real income that results from a dollar change in exogenous aggregate demand (so one of G, I or X). We could complicate this by having autonomous consumption (C0<\/sub>) as well but the principle is not altered.<\/p>\n

Firms initially react to the $50 order from government at the beginning of the process of change. They increase output (assuming no change in inventories) and generate an extra $50 in income as a consequence – so Y increases initially by the full injection of new government spending ($50).<\/p>\n

The government taxes this income increase at 15 cents in the dollar (t = 0.15 in our example) and so disposable income only rises by $42.50.<\/p>\n

There is a saying that one person’s income is another person’s expenditure and so the more the latter spends the more the former will receive and spend in turn – repeating the process.<\/p>\n

Households spend 80 cents of every disposable dollar they receive which means that consumption rises by $34 in response to the rise in production\/income. Households also save $8.50 of the initial increase in disposable income as a residual.<\/p>\n

Imports also rise by $10 given that every dollar of GDP leads to a 20 cents increase imports (by assumption here) and this spending is lost from the spending stream in the next period.<\/p>\n

So the initial rise in government spending has induced<\/strong> new consumption spending of $42.50 which then triggers further production increases.<\/p>\n

At the end of the first period (before the induced consumption spending starts to take effect), the total leakages (S + T + M) equal 26 (that is, 8.50 + 7.50 + 10) and they are well below the initial injection of 50. So the system is not yet at rest because the leakages have not yet matched the initial injection.<\/p>\n

This is where the multiplier begins. The workers who earned that initial increase in income increase their consumption by $42.50 and the production system responds. So consumption spending in the next period rises by 0.8(1-0.15)42.50 = $29.90. Firms react and generate and extra $29.90 of extra output and income to meet the increase in aggregate demand.<\/p>\n

And so the process continues with each period seeing a smaller and smaller induced spending effect (via consumption) because the leakages are draining the spending that gets recycled into increased production.<\/p>\n

Eventually the process stops and income reaches its new “equilibrium” level in response to the step-increase of $50 in government spending. At that point the leakages will have risen in total (accumulated over the period of adjustment) to match the initial 50 injection in government spending.<\/p>\n

The new national income is $769 a rise of $96 after the government increased its spending by $50. The extra $46 in income came about by the successive induced consumption increases as the multiplier played out.<\/p>\n

Please read my blog – Spending multipliers<\/a> – for more discussion on this point.<\/p>\n

The balanced budget multiplier<\/strong><\/p>\n

Now we can see how the balanced budget multiplier works and is different to the normal expenditure multiplier.<\/p>\n

What we will see is that Shiller is making very large assumptions about the external sector. But to see that we need to go back to our simple macroeconomic model.<\/p>\n

There is also a complexity that I will abstract from which is whether the budget neutrality is to be achieved at the time of the spending (so initially) or at the end of the multiplier process. The latter is much harder to explain in a blog and so I will assume that the government decides to initiate a budget neutral spending increase which is in the spirit of Shiller’s proposal.<\/p>\n

The other complexity is how the tax increase is accomplished. Clearly we could increase the tax rate such that at the current level of income the tax revenue rises by the amount of extra government spending. Or we could simply impose a lump-sum tax of $50 and leave the income tax component alone. The final result is dependent of which choice is made. In this example we assume a lump-sum tax equal to the rise in government spending is imposed – it keeps the model and the explanation simpler and is the way most of the old text-books used to explain it anyway. If there is sufficient interest I can write the model out where I change the tax rate to accomplish the same end.<\/p>\n

So if we go back to our example where the government increases its spending by $50 but taxes are simultaneously increased by $50 so that the deficit is unchanged and there is no debt-issuance required (even under the voluntary practices that are used in today’s modern monetary system).<\/p>\n

What is the net impact of national income of the increase in government spending and the matching increase in tax revenue? The balanced budget multiplier theorem tells us that the impact is not neutral. In fact, national income rises by exactly as much as the increase in government spending.<\/p>\n

Clearly this has to work via the separate impacts that the increase in government spending and the increase in taxes have on aggregate demand. Remember aggregate demand (spending) equals income (changes equal changes).<\/p>\n

The initial rise in aggregate demand (and income) attributable to the increase in government spending is ΔG = 50. If there was no tax rise, then this increase in income would induce further consumption spending and the expenditure multiplier (k) would determined the final increase in output (income).<\/p>\n

But the initial rise in taxes ($50) causes consumption to fall because disposable income falls. Note we are assuming a lump-sum tax is imposed and the tax rate (t) is unchanged. Therefore the spending multiplier derived above is unchanged.<\/p>\n

The drop in consumption is the drop in disposable income ΔT times the marginal propensity to consume (c). Thus the fall in consumption is given as:<\/p>\n

(13)     ΔC = -cΔT<\/p>\n

Given that c = 0.8 and ΔT = 50 the initial fall in consumption is $40.<\/p>\n

The tax multiplier is thus given as:<\/p>\n

(14)     ΔY = -kcΔT<\/p>\n

So the fall in consumption (cΔT) which results from the fall in disposable income initially multiplies through the expenditure system via the spending multiplier k = 1\/(1 – c(1-t) + m).<\/p>\n

In our example, other things equal this would lead to a fall in income (Y) of 1.92(40) = $77<\/p>\n

However, aggregate demand is also stimulated by the change in government spending. The rise in income attributable to this is given by Equation (12) so:<\/p>\n

ΔY = kΔG = 1.92(50) = $96.2<\/p>\n

The total change in national income is thus the sum of the tax multiplier impact and the government spending multiplier impact, which is just the net change in aggregate demand multiplied by k:<\/p>\n

ΔY = kΔG -kcΔT<\/p>\n

And because ΔG = ΔT this becomes:<\/p>\n

ΔY = k(1-c)ΔG = 1.92(1-0.8)(50) = $19.2<\/p>\n

Puzzled? Recall that Shiller said that “(u)nder certain idealized assumptions, a concept known as the “balanced-budget multiplier theorem” states that national income is raised, dollar for dollar, with any increase in government expenditure on goods and services that is matched by a tax increase”.<\/p>\n

That is, Shiller is claiming that the balanced-budget multiplier is unity (= 1). In our example, it is positive but certainly not equal to 1. For a rise in government spending of $50 the final rise in national income is only $19.2.<\/p>\n

What gives?<\/p>\n

The reason is simple. Shiller must have dug out an old 1950s or 1960s American macroeconomics text-book which derived all the main macroeconomic results as if the economy was closed. In those days, the external sector and trade were often examined in the closing chapters. This was justified by the fact that the US economy was a large and fairly closed economy.<\/p>\n

This has always been a problem for Australian students and students of other small open economies that were forced to use American textbooks. Most of the analytical results that were derived from the US textbooks were of limited relevance to the Australian setting.<\/p>\n

The balanced-budget multiplier is a classic example. If we consider a closed economy with only lump-sum taxes we would get a simple multiplier of 1\/(1 – c).<\/p>\n

Then the tax multiplier is -c\/(1 – c) and the balanced-budget multiplier is equal to 1 as shown in the following:<\/p>\n

\"\"<\/a><\/p>\n

<\/div>\n

In our example, the closed economy expenditure multiplier with no income tax would be 1\/(1 – c) = 5 and the tax multiplier would be -c\/(1 – c) = 0.8\/0.2 = 4.<\/p>\n

So if we plugged in our example to this model we would get:<\/p>\n

ΔY = 1\/(1-c)ΔG -c\/(1-c)ΔT = 5(50)-4(50) = 50<\/p>\n

So the rise in income is exactly equal to the initial government spending increase, which is Shiller’s case.<\/p>\n

But once you open the economy and have income-sensitive tax revenue then the leakages are much higher and this reduces the overall impact of the spending increase on aggregate demand and while the multiplier remains positive it is much lower than 1.<\/p>\n

I could show more cases to demonstrate this but the algebra can get tricky and I would lose more than I would keep.<\/p>\n

Idealised assumptions?<\/strong><\/p>\n

So Shiller completely ignores the fact that the US is an open economy with positive marginal tax rates. It is questionable whether you would get very much bang for the spending increase.<\/p>\n

Shiller does qualify his proposal by saying that the “balanced-budget theorem is only as good as its assumptions”. But his concerns are do to with the possible prescence of Ricardian agents.<\/p>\n

Shiller say that:<\/p>\n

\nOther possible repercussions could make its multiplier something other than 1.0. The number could be less, for example, if people cut consumption because of psychological reactions to higher taxes. Alternatively, it could be greater if income-earning people who are taxed more cut their consumption less than newly employed people increase their spending. We can’t be sure what will happen.\n<\/p><\/blockquote>\n

I dismissed the Ricardian arguments in this blog – Pushing the fantasy barrow<\/a>. They are nonsensical – rely on assumptions that are never found in reality and have no empirical support.<\/p>\n

Shiller’s heart is in the right place. He says:<\/p>\n

\nBut the balanced-budget multiplier is simpler to judge: If the government spends the money directly on goods and services, that activity goes directly into national income. And with a balanced budget, there is no clear reason to expect further repercussions. People have jobs again: end of story.s<\/p>\n

What kind of jobs? Building highways and improving our schools are just two examples …\n<\/p><\/blockquote>\n

There is no doubt that the US government could significantly reduce the entrenched unemployment it has created by its policy failures to date (not net spending enough) by significantly increasing the budget deficit.<\/p>\n

Worrying about the balanced-budget theory, which was apposite in a past monetary system, is not something it should be doing. The US government has no spending constraint and its public debt ratio is irrelevant when it comes to having the capacity to introduce a large-scale job creation program.<\/p>\n

The welfare improvements that such a program would bring would be huge.<\/p>\n

Yes, critics will say that the debt ratio is a political problem even if it is not a financial one. I agree. The polity is failing the American people as polities are failing citizens all around the world. A polity in the grip of neo-liberalism will always produce these poor outcomes for the majority while transferring assets and real income to the elites including the politicians that are captured by the elites.<\/p>\n

Shiller recognises this when he says:<\/p>\n

\nAT present, however, political problems could make it hard to use the balanced-budget multiplier to reduce unemployment. People are bound to notice that the benefits of the plan go disproportionately to the minority who are unemployed, while most of the costs are borne by the majority who are working. There is also exaggerated sensitivity to “earmarks,” government expenditures that benefit one group more than another.<\/p>\n

Another problem is that pursuing balanced-budget stimulus requires raising taxes. And, as we all know, today’s voters are extremely sensitive to the very words “tax increase.”\n<\/p><\/blockquote>\n

When you live in a country that rejects small relief to the most disadvantaged citizens then you are living in a failed state. Again the polity has failed to provide sufficient leadership and the education system has been poisoned by conservative (free market) look-after no-one but myself thinking.<\/p>\n

In these situations, as the oppression of unemployment worsens and the gap between the haves and have-nots widens revolutions occur. In the meantime, crime rates rise, property and life is increasingly threatened and an increasing number of citizens have a very low quality of life.<\/p>\n

It is all unnecessary and the capacity is within the government’s grasp to remedy it. There is just a failure of leadership.<\/p>\n

Conclusion<\/strong><\/p>\n

The balanced budget multiplier was a cute construct in its day. But in an open economy where the government is fully sovereign it is an irrelevant idea to resurrect.<\/p>\n

Sorry to those who hate algebra for all the algebra and I hope you appreciated the message nonetheless.<\/p>\n

That is enough for today!<\/p>\n","protected":false},"excerpt":{"rendered":"

I have been working today on the modern monetary theory text-book that Randy Wray and I are planning to complete in the coming year (earlier than later hopefully). It just happens that I was up to a section on what economists call the balanced-budget multiplier which is a way to provide stimulus without running a…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[18,50],"tags":[],"class_list":["post-12914","post","type-post","status-publish","format-standard","hentry","category-economics","category-teaching-models","entry","no-media"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/billmitchell.org\/blog\/index.php?rest_route=\/wp\/v2\/posts\/12914","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/billmitchell.org\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/billmitchell.org\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/billmitchell.org\/blog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/billmitchell.org\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=12914"}],"version-history":[{"count":0,"href":"https:\/\/billmitchell.org\/blog\/index.php?rest_route=\/wp\/v2\/posts\/12914\/revisions"}],"wp:attachment":[{"href":"https:\/\/billmitchell.org\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=12914"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/billmitchell.org\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=12914"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/billmitchell.org\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=12914"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}