{"id":13640,"date":"2011-02-28T06:00:22","date_gmt":"2011-02-27T19:00:22","guid":{"rendered":"https:\/\/billmitchell.org\/blog\/?p=13640"},"modified":"2011-02-28T06:00:22","modified_gmt":"2011-02-27T19:00:22","slug":"us-fiscal-stimulus-worked-more-evidence","status":"publish","type":"post","link":"https:\/\/billmitchell.org\/blog\/?p=13640","title":{"rendered":"US fiscal stimulus worked – more evidence"},"content":{"rendered":"

\t\t\t\tI am travelling today and then have commitments at the other end. So very little time to write. But I did read some interesting papers over the weekend which bear on the question of whether fiscal policy in the US was effective or not. The neo-liberals (mainstream macroeconomists) claim that fiscal policy is not effective. The extremists among them invoke – Ricardian Equivalence – which claims that private households and firms fear that the rising deficits will require higher tax rates and so they save more now – which means that for every dollar of new government spending there is a dollar less of private spending – so no effect. All the evidence contradicts the extreme view. There is also mounting evidence that the recent fiscal interventions have been very effective. A study I read yesterday went a step further and analysis the impact of targetting low income groups. They found that type of public spending was very expansionary. Their results support my contention that a Job Guarantee<\/a> would be a very effective (and cheap) fiscal solution (as a first step) to a private spending collapse. But for all the naysayers – sorry, the evidence is mounting that fiscal policy saved the world.
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\nI have covered the topic of expenditure multipliers before. Please read my blog – Spending multipliers<\/a> – for more discussion on this point.<\/p>\n

If you have trouble with symbols and a bit of algebra then you might gain by reading this blog first – What is the balanced-budget multiplier?<\/a> – where I explain in simple terms how to interpret these constructs in English.<\/p>\n

The expenditure multiplier is the change in national income for a unit increase in some component of exogenous spending (government, private investment, or exports). So what is an exogenous variable as opposed to an endogenous variable?<\/p>\n

Jargon is a vehicle that every discipline uses to obfuscate and maintain authority (and in economics to largely suppress challenge) but can usually be rendered benign with some simple explanation.<\/p>\n

An economic model is just a series of algebraic statements (equations) that relate one variable to others. So, for example, we say that consumption is related to income. These models have exogenous and endogenous variables.<\/p>\n

An exogenous (pre-determined or given) variables are known in advance of “solving” the system of equations whereas endogenous variables are determined by the solution to the system of equations.<\/p>\n

We take the value of an exogenous variable as given or pre-determined. We might say that discretionary 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. These are endogenous variables.<\/p>\n

So if we have a little model consisting of two equations (we call this a “system”):<\/p>\n

(1) y = 2x
\n(2) x = 4<\/p>\n

Given we know the value of x already – it 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, which in this case is y = 2 times 4 = 8.<\/p>\n

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

The standard textbook model of the simple expenditure multiplier is usually derived from a simple macroeconomic model. Here is a very standard model. You can skip to the next section if you already know all of this.<\/p>\n

In macroeconomics, by definition, 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

The c is called the marginal propensity to consume<\/em> (MPC) which tells you how much of every extra dollar of income received is consumed.<\/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 of disposable income 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

Some people might consider this should be modelled in terms of disposable income so M = mYd. If imports were only confined to household consumption then this might be sensible given that the government takes its tax out of total income and households only have disposable income to spend.<\/p>\n

However, imports in the National Accounts covers the spending of households, firms and government and thus should be considered a function of total income (Y). This also impacts on how we interpret the impacts of exogenous spending through the multiplier process.<\/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

The following discussion is summarised in the following Table.<\/p>\n

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

<\/div>\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 times 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

This relates to Period 2 in the previous Table.<\/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

The results in derived here are final results and while I have related them to Period 2 the reality is that it might take several months or years before these full results are achieved. We abstract from the adjustment path in this table.<\/p>\n

How does the multiplier work?<\/strong><\/p>\n

The multiplier describes the adjustment path from one “equilibrium” to another.<\/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 private 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 in Period 1 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 multiplier works as an adjustment process. 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

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

So the initial rise in income stimulates further consumption which is called induced consumption<\/em> because it is induced by an initial increase in exogenous spending.<\/p>\n

This consumption then leads to more output and subsequent spending. At each point in the adjustment process tax revenue, import spending, saving is rising as income rises.<\/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

Latest evidence about the impact of the US fiscal stimulus<\/strong><\/p>\n

In February 2011, the Congressional Budget Office (CBO) put out their latest publication which pertains to the effectiveness of the fiscal stimulus – Estimated Impact of the American Recovery and Reinvestment Act on Employment and Economic Output from October 2010 Through December 2010<\/a>.<\/p>\n

They found that the American Recovery and Reinvestment Act (ARRA):<\/p>\n

\n… funded more than 580,000 full-time-equivalent (FTE) jobs.\n<\/p><\/blockquote>\n

A full breakdown of the data is available at www.recovery.gov<\/a>. The estimates do not necessarily provide an accurate (controlled) estimate of the fiscal impact on employment because:<\/p>\n