Is the UK’s tax burden too high?

Introduction

On December 2 2018, Jacob Rees-Mogg tweeted “The tax burden is too high”. His assertion derived from an analysis of historical data undertaken by the Taxpayers’ Alliance (TPA) which had been commissioned by the Sunday Telegraph. The TPA reported that the tax to GDP ratio had reached a new high of 34.6%, breaking the previous high of 34.3% seen in the early 1960s.

What does “too high” mean?

It seems reasonable to assume that “too high” in this context means that the tax level is impeding GDP growth; it’s not easy to think of a second reason for tax to be too high. This made me wonder whether there is an objective basis for asserting that tax is too high and prompted me to investigate whether a link between a nation’s GDP and its tax level exists.

Methodology

I chose the year 2016 (for which complete data exists), and because it is recent, to examine whether a link exists. I used all 35 countries comprising the OECD (Lithuania was not then a member) to get a sampling frame of sufficient size and because these countries are considered to be developed. The UK is a member of the OECD.

To measure the tax level of a country I used “tax as a percentage of GDP” published by the World Bank for the year 2016. I then classified each country as “high tax” if the country’s measure was higher than the OECD average (published by the World Bank) and “low tax” if the measure was below.

To measure the affluence of a country, I used “GNI per capita” (at PPP) for 2016, also published by the World Bank. I classified each country’s affluence as “rich” if its GNI/capita was above the published OECD average and “poor” if the GNI/capita was below. The terms “rich” and “poor” to denote a county’s affluence have been assigned for convenience and are not intended to be literal.

I then set up a 2 x 2 contingency table and applied a Chi-squared test with one degree of freedom to test whether a significant link between tax level and affluence existed. I used Yates’ continuity correction  in calculating the test statistic as recommended by the literature. The contingency table is show below.

Chi Squared table

Results

The Chi-squared test statistic, adjusted for Yates’ continuity correction, came to 0.00288.   This is well below the 5% significance level of 3.84 for a Chi-squared variable with one degree of freedom. A test statistic value of above 3.84 would be strong evidence that a nation’s tax level and national income are linked (one influences the other). Because the test statistic returned such a low value there is insufficient evidence to support a hypothesis that national income and a nation’s tax level are linked, at least for OECD members. In plain English, there is no discernible link between a nation’s level of taxation and its national income.

Conclusions

The claim made by Jacob Rees-Mogg and the Taxpayers’ Alliance that UK tax is too high does not stand up  when a cross sectional analysis is undertaken. A simple time series analysis on the UK’s “tax as a percentage of GDP”, as conducted by the TPA, is insufficient to conclude whether tax is either too high or too low. This is because the time series analysis says nothing about the consequences of tax levels on national income (or some other variable of interest).

Jacob Rees-Mogg is remunerated (rather well) by taxpayers. Many voters would say they deserve better than his shoddy, scantily-evidenced assertion.  It is also disappointing to discover that the study by the Taxpayers’ Alliance lacks sufficient rigour to support a meaningful conclusion. The TPA’s audiences should be wary – this example shows it does not seem to engage in research of sufficient depth to support its conclusions!  Is the TPA subordinating sound methodology to ideology  here? It seems so. Readers beware!

Appendix: World Bank source data

World bank data

 

 

Self-built assets and value added

Dealing with capitalised costs

Instead of purchasing non-current assets from third party suppliers, a firm may choose to itself construct or erect an asset for use in its own business. In these cases, costs and expenses which would otherwise be revenue in nature should be capitalised. Capitalised costs will not appear in a firm’s statement of profit or loss and hence materials and labour costs will be understated in this account, notwithstanding disclosure by way of a note.

Example

ca[italised costs profit or loss

During the period, a new warehouse was constructed by the firm’s workforce for the firm’s own use at a cost of £4m. The materials cost of the construction was £1m and the labour cost assigned to the construction came to £3m. These costs were capitalised and hence do not appear in the above statement of profit or loss. A value added statement brings these costs in to view because the construction is part of the value created by the firm during the period.

Capitalisation of costs value added statement

Workings and notes

Bought in materials, goods, and services

Purchases of all materials, goods, and services whether or not capital or revenue but excluding depreciation.

To pay employees

All wages and employment on-costs including labour costs assigned to the construction of the new warehouse.

Investment adjustment

The capitalised cost of materials (£1m) and labour (£3m)

Inventory adjustment

Closing inventory minus opening inventory. This represents additional investment in inventory if positive or disinvestment in inventory if negative.

Depreciation adjustment

The total of the depreciation charges shown in the profit or loss statement. This is a measure of capital consumption during the period. In the national accounts, the government may substitute its own figure for a firm’s measure of capital consumption.

Link to the national income accounts

The total of the adjustments will be shown as an investment activity in the national income accounts where it will be denoted as I

 

I is for investment

How is the investment component, denoted by I, of national income determined? An explanation is proffered here by converting the following simple statement of profit or loss into a value added statement.

Investment and VAS

Additional information

During the period, the firm replaced some plant and machinery at a cost of £10m.

Points to note

A statement of profit or loss does not record purchases of a capital nature. Hence the purchase of plant and machinery for £10m is not reported in the statement of profit or loss.

A value added statement does report purchases of a capital nature.

Example

Investment and VAS 2

Working

Working for investment and VAS

National Income Accounts

If every firm prepared a value added statement the total of the net investment adjustments would represent the nation’s periodic investment activity shown in the national accounts prepared by the government. This figure for the periodic investment activity is shown as I in the national accounts.  

NB. The government may substitute its own standard calculation of the depreciation adjustment so as to achieve consistency.

 

Value Added Statements for Dummies

This is a short presentation to demonstrate how value added statements are prepared and to explain how they differ from the accountant’s traditional profit or loss account. A single example will be used which will capture the essential differences.

Example

Below is shown a firm’s statement of profit or loss and value added statement. The two statements are shown side-by-side for ease of comparison.

During the period, the firm purchased plant and machinery for use within the business at a cost of £30m. Because this is capital expenditure, there is no entry in the statement of profit or loss to record this purchase. In the value added statement, the £30m cost appears against “bought-in materials, goods, and services” to obtain the “net value of output” figure. The firm’s investment activity is then shown by the investment adjustment to arrive at “net value added.”

VAS for dummies

Derivation of value produced figures

Bought-in materials, goods and services is equal to the purchases figure taken from the profit or loss statement (£80m) plus the capital expenditure (£30m).

The inventory adjustment is equal to the closing inventory minus the opening inventory. If this figure is positive then it represents additional investment in inventory. If negative then it represents disinvestment in inventory.

The depreciation adjustment is the total depreciation charged to the profit or loss account. This will usually be shown as a negative figure in the value added statement and represents consumption of capital in the period.

The investment adjustment is equal to the capital expenditure during the period. If this adjustment is positive then investment in new productive capacity has occurred. If negative, then disinvestment in productive capacity has occurred. The new productive capacity may consist of either tangible or intangible assets or some mixture.

Derivation of value distributed figures

To pay employees is the wages figure taken from the profit or loss account. The figure should include employer’s on costs, including employer’s National Insurance Contributions, and other employment taxes where they exist

To pay government is the sum of business rates and corporation tax charged to the profit or loss account. The figure represents the contribution the firm makes to the upkeep of the nation’s infrastructure and public services that enable firms to flourish.

To pay rentiers is the sum of property rents, licence fees, patent and copyright charges and the like. Payments to parties who derive income from ownership rather than from provision of a service or goods are recorded under this heading.

To pay financiers is the sum of interest charges in the profit and loss account plus dividends paid in the year. Payments of interest and dividends paid should be offset by interest and dividends received. Interest and dividends received are distributions of  value added produced by other firms. 

Undistributed value is equal to the retained profits shown in the profit or loss statement.

Negative Income Tax For Dummies

Personal Allowances

The UK income tax system ostensibly gives all income tax payers an identical allowance which exempts the first slice of an individual’s market income from income tax. This exemption is known as the personal allowance and is set by parliament each year. For the current year it stands at £11,500.

Basic Rate (20%) Tax Payers

The personal allowance typically reduces the amount of income tax a basic rate tax payer must pay on their market income by £2,300 pa. However, if a basic rate tax payer’s market income is below £11,500 p.a. they do not receive the full benefit of the annual personal allowance. This is arguably a weakness with the UK’s current income tax arrangements.

Example

Susan earns £10,000 p.a. Her tax-free personal allowance is £11,500 p.a. This means she currently pays no income tax and her disposable income (ignoring her National Insurance Contribution) is £10,000.

Comment

If Susan had no personal allowance she would have paid income tax of £2,000 (£10,000 x 20%).  The personal allowance has saved Susan £2,000. Had Susan earned £11,500 in the year she would have saved £2,300 in income tax. Because she had only £10,000 of income to offset against her personal allowance of £11,500 Susan has £1,500 of unused personal allowance remaining. In the UK personal allowances can not be carried forward to be utilised in following years. Nor can personal allowances normally be transferred  to someone else or be traded –  it’s a case of use or lose.   

Is there a better way of administering income tax whereby surplus personal allowances would not be wasted if they remain unused at the end of a tax year? An answer to this question is “Yes, negative income tax”.

Negative Income Tax

Giving a taxpayer an annual personal allowance of £11,500  costs the government up to £2,300 in lost tax revenue. In Susan’s case, because her market income is below £11,500, the cost to the government of Susan’s personal allowance is £2,000 in lost tax.

Negative income tax departs from the current income tax system by paying out the value of the personal allowance (the tax shield) in cash to each and every qualifying citizen. To  help fund this apparent largesse, income tax would be collected and calculated without reference to personal allowances.

In Susan’s case, income tax of £2,000 would be deducted by her employer and remitted to HMRC. Susan’s net pay from her employer would therefore be £8,000.  Susan, along with all qualifying citizens, would receive from HMRC an annual amount equal to the value of her tax shield (£11,500 x 20%)  The following table summarises:

Tables

At the year end Susan’s income is £300 higher than her gross market income. This £300  is the value of her surplus personal allowance (£1,500 x 20%). So effectively Susan has been allowed to claim back the value of her unused personal allowance as a “refund” from HMRC. 

Cost

In Susan’s case, HMRC has paid out to Susan £300 more than she has paid to HMRC. So HMRC has a deficit while Susan has a surplus. So how will HMRC fund its deficit? 

Firstly, because Susan is on a low income there is a probability that she is on a means tested benefit, such as the dreaded Universal Credit, to augment her low market income. The benefits agency (DWP) may reassess Susan’s financial circumstances and adjust her award to take account of Susan;s additional source of non-market income. So the government may claw back all or part of Susan’s increased income to eliminate its deficit at HMRC.

Secondly, although Susan has a surplus with HMRC, many taxpayers will have a deficit. It is only qualifying citizens with market incomes below £11,500 who will be receiving more from HMRC than they pay in income tax.  Many taxpayers will be paying income tax far in excess of the £2,300 they will be receiving each year from HMRC. Deficits and surpluses would offset  each other

Purposes of Negative Income Tax

Firstly, to make the income tax system fairer. Currently, those with a market income of above £100,000 do not receive a personal allowance. Introducing a non-means tested negative income tax would enable policy makers to restore the tax shield to high income recipients. 

Secondly, to provide an enhancement to low incomes,  albeit a modest one.

Thirdly, to give every qualifying citizen a guaranteed, obligation-free income, although a small one. It should help individuals to better absorb and weather the shocks that humans are heir to, including those shocks administered by DWP.

Unlike Universal Basic Income (UBI), the purpose of NIT is not to replace contingent benefits, although some means’tested benefits may be reduced as a consequence of NIT’s introduction.

Qualifying Criteria

Every natural person of working age AND registered to vote in UK elections should qualify, irrespective of income. Qualifying individuals would include job seekers, students, disability benefit claimants, employees, self-employed persons, stay-at-home parents, rough sleepers, and prisoners (subject to voting rights). People of state pension age would be excluded.

Summary and Conclusions

The aims of the particular NIT scheme discussed are modest. The scheme is specific to the UK’s income tax system. The scheme provides an opportunity to equalise treatment of different income groups in respect of the operation of personal allowances, otherwise referred to as a tax shield. The parameters of the proposed scheme, that is the NIT rate and the size of the personal allowance, are under the control of the UK parliament and can be altered to suit. The scheme shares features of Basic Income, eg, it is obligation-free, it is not means tested, its coverage is universal (subject to fraud safeguards), and it supports active enfranchisement of disengaged voters. It also provides a small cushion against  loss of income and failure of the social security system. Although modest, the benefits would be real and in excess of its costs. 

Appendix 

The impact of Negative Income Tax on higher and additional rate taxpayers

Higher Rate (40%) Taxpayers

 

Example

Stephen has an annual market income of £80,000

Stephen 1

Stephen 2

Stephen would pay £2,300 more under this particular NIT scheme than he does under the current income tax system. This is because HMRC is paying out at 20% x £11,500 while the lost personal allowance brings in 40% x £11,500 to HMRC.  HMRC is in surplus.

 

Additional Rate (45%) Tax Payers

For annual incomes above £150,000 the income tax rate rises to 45% and no personal allowance is available. 

Example

Frances has an annual market income of £170,000

Frances 1

 Frances 2

Frances would pay £2,300 less under this particular NIT scheme. This is because in the current income tax regime taxpayers with market incomes above £100,000 have had their personal allowances completely withdrawn. The receipt of NIT of £2,300 from HMRC consequently would reduce tax payable in cases such as this. 

How to do a heli drop

Purpose of this piece

This piece proposes and illustrates a scheme whereby helicopter money can be delivered within existing legal and accounting constraints. It shows that it is legally and technically feasible to deliver.

Legal constraints

The chief legal constraint is on the UK government which is forbidden to borrow from its banker, the Bank of England. This means the UK government is restricted to raising funds either from taxation or by borrowing from private investors. Neither method is currently popular with the government or its voters.

Accounting constraints

All organisations must follow the rules of double entry. Accounting concepts and standards must also be adopted and complied with. Even the Bank of England must comply with these accounting constraints. The Bank of England’s accounts are audited and where departures are detected they will be reported upon. Serious consequences could potentially arise from an adverse auditor’s report.

Assumptions of the scheme

  1. The government would issue bonds to private investors to fund the helicopter drop.
  2. HMRC would deliver the helicopter drop via tax rebates.
  3. Bonds in issue held by the private sector would be purchased using QE.
  4. The government would not overdraw on its deposits held at the Bank of England.

Procedure

  1. The government issues bonds to the private sector in the sum of the proposed helicopter drop.
  2. The government then uses the proceeds from the bond issue to give fixed sum tax rebates to household and firms.
  3. The central bank does QE for an amount equal to the bond issue.

The scheme in double entry form

The government issues bonds to private investors

Books of the Government £bn
Debit Deposit at Bank of England (asset increase) 30
Credit Bonds (liability increase) 30
Books of Commercial banks £bn
Debit Deposits by investors (liability decrease) 30
Credit Deposits at Bank of England (asset decrease) 30
Books of Investors £bn
Debit Bonds (asset increase)) 30
Credit Deposits at Commercial banks’ (asset decrease) 30
Books of the Bank of England £bn
Debit Deposits by Commercial banks (liability decrease) 30
Credit Deposits by government (liability increase) 30

The government gives a tax rebate of £30bn

Books of the Government £bn
Debit Income statement (expense) 30
Credit Deposit at Bank of England (asset decrease) 30
Books of Households and Firms £bn
Debit Deposits at Commercial banks (asset increase) 30
Credit Income statement (income) 30
Books of Commercial banks £bn
Debit Deposits at Bank of England (asset increase) 30
Credit Deposits by Households and Firms (liability increase) 30
Books of Bank of England £bn
Debit Deposits by Government (liability decrease) 30
Credit Deposits by Commercial banks (liability increase) 30
  1. Bank of England does QE for £30bn

Books of Bank of England £bn
Debit Bonds (asset increase) 30
Credit Deposits by Commercial banks (liability increase) 30
Books of Investors £bn
Debit Deposits at Commercial Banks (asset increase) 30
Credit Bonds (asset decrease) 30
Books of Commercial banks £bn
Debit Deposits at Bank of England (asset increase) 30
Credit Deposits by Investors (liability increase) 30

Summary

Here is a snapshot of the net changes to the respective balance sheets once all the transactions have been completed.  A table for Investors does not exist because the net changes amount to zero between their starting and end positions.

Heli money summary

Reversing QE

Because QE has effectively been used to fund the helicopter money (the tax rebates), at some point in the future the tax rebates must be reversed alongside the QE.  To defer this day far ino the future, long dated bonds could be used in both the bond issue and in the QE “buy back”. Long dating should eliminate the scuppering potential of Ricardian Equivalence.

Post Script

I have stuck to the technical aspects of making a helicopter drop. My intention has been to show that it is technically and legally possible within current constraints. Whether it would be successful in pulling the UK out of its current economic quagmire is moot and resolving that question is beyond my pay grade.

Fallacies of Modern Monetary Theory (MMT)

Fallacies of Modern Monetary Theory (MMT)

Taxation does not fund government spending

It does! Governments can fund public spending in just three ways: 

  1. Through taxation;
  2. By borrowing from the private sector;
  3. By borrowing from its banker (the central bank).

The last option on this list is forbidden in most advanced economies. This leaves taxation and borrowing from the private sector as the only available funding sources.

Money is a liability of the government

No it’s not! Customer deposits held by retail banks are liabilities of those retail banks. These customer deposits are not liabilities of the government or of the central bank. As an aside, money deposited with these banks is an asset to the depositor (customer).

Government spending precedes taxation

This could be true if money was created and injected into the economy by the government. But this condition does not hold. Most money in circulation is created and injected into the economy by private banks. 

Taxation alone determines a currency’s value

It is true that governments require taxes to be paid in the national currency and this creates demand for the currency. However, a nation’s international trading performance and capital flows also affect demand for a nation’s currency and its value. So tax is not the sole determinant. 

Conclusion

The “magic money tree” does not exist!

Image

Basic Income and Welfare

Background

A recent Guardian piece by Declan Gaffney asserts that a Universal Basic Income could not replace the UK’s social security (or welfare) system. The piece can be read here:

http://www.theguardian.com/commentisfree/2015/dec/10/finland-universal-basic-income-ubi-social-security

A basic income that replaced the UK’s social security system would need to be so generous that it would disincentivise the jobless from looking for work. Hence a punitive social security system that relies on sanctions is necessary because otherwise the jobless will not look for work. In short, such a Basic Income would make life too comfortable for the lazy and workshy.

Well perhaps this is true. given Declan’s assumption of a universal and unconditional basic income intended to replace the social security system. Such a basic income would need to be very generous and might well have the effect that Declan fears. A valid  inference of Declan’s fine piece is that Basic Income is a nice idea but infeasible; so let’s keep means tested and contingent benefits. and rely on Universal Credit to provide the right balance between carrot and stick.

Should the idea of Basic Income be abandoned?

Given Declan’s point, that UBI could not, or should not, replace the social security system, is Basic Income simply a nice but impracticable idea?

I agree that it would be too expensive for basic income to replace all social security, at least in the UK’s circumstances. UK housing costs, for example, are far too high and would need to fall massively before a Basic Income could be anywhere near sufficient to cover housing costs. Until such time as the high cost of housing in the UK  is addressed, a system of means tested benefits for housing costs will be needed.

Similarly, the social security system also provides contingent benefits, that is benefits which compensate for disability, unemployment, old age, and child rearing. It would not make sense for a uniform basic income to be set at a level  which covers contingent costs  of minorities – it would be far too expensive. In any case, the National Insurance Fund insures against some of these contingencies via contributions.

So Declan says (and others say) that the current social security system accommodates the variegated needs of the population and that a basic income is unnecessary and inadequate. However, I do not believe Declan’s argument is dispositive.  A modest basic income scheme, that is, one which does not seek to replace all social security benefits, is a practical  and worthwhile option.

Proposal for a modest basic income

A hat tip to Mike Gist (@mgist) who suggested that I calculate the net tax liability at different income levels before and after introduction of a basic income. I have done this analysis for the tax year 2015/2016, assuming an annual personal allowance of £10,600, which, to help fund the scheme, would be scrapped. So post tax income after implementation of basic income and after scrappage of the personal allowance is being compared with post tax income before scrappage of personal allowance. Tax credits have been excluded from the analysis.

The analysis shows that no one, whatever their income level would be left worse off if annual basic income were to be set at £4,240. Below is a graph of the results.

  1. The graph shows that for market incomes of below £45k (approx) tax payers would be better off post tax after abolition of annual personal allowance under basic income of £4,240 p.a.
  2. For incomes between £45k approx and £100k, there is no gain or loss. For incomes over £100k there is a gain which stabilises at £4,240 when income reaches £120k approx.
  3. The gain for incomes over £100k arises because personal allowances are currently restricted or non-existent at this level. Scrapping the annual personal allowance as per the scheme thus causes all income levels to be treated equally with respect to personal allowances.

Basic income simulation

Other points

  1. The analysis shows that the cost of even this modest scheme will exceed the current (pre-scheme) income tax take. To establish the cost of the scheme it is necessary to know how many people will gain how much for all income groups.
  2. A basic income set at £4,240 is sufficient to replace Job Seekers’ Allowance for the unemployed, and Working Tax Credits for those in work. Hence the aggregate spend on JSA and WTC can be deducted from the additional cost calculated in point 1.
  3. The basic income would replace working tax credits without the cliff edges and complexity that the existing system contains.
  4. The graph’s U shape is caused by the kinks in the current income tax schedule, and not by the properties of the basic income scheme itself. The withdrawal rate is a constant 20%. There is thus a strong incentive for workers at lower pay rates to increase their market earnings.
  5. The scheme has been formulated with the same parameters as are used in the existing income tax regime. That is the bands and rates (20%, 40%, and 45%) on which income tax is charged are identical as those which are in current use.
  6. Some of the annual gains of £4,240 accruing to 45% tax payers (those earning more than £150k p.a.), could, if a government had a mind to, be taxed away by raising the rate to 50%.
  7. The scheme should be acceptable to the electorate since there are no losers.

Summary and conclusions

An ambitious basic income scheme, that is, one that seeks to replace all social security benefits, is probably incontrovertibly infeasible.

However, because an ambitious scheme may be infeasible this is not necessarily a good ground for rejecting the concept of Basic Income completely. A modest scheme may be both feasible and worthwhile.

A modest scheme, as outlined above, could replace Job Seekers’ Allowance and Working Tax Credits. Withdrawal rates would be at the basic rate of income tax of 20%.

A need for other social security benefits would continue. Incentives to work could be improved by addressing housing costs which are currently so high that without Housing Benefit support it does not pay people to work.

Replacing Job Seekers’ Allowance and Working Tax Credits with an unconditional basic income removes the threat of starvation (which JSA sanctions represent) as an instrument of government policy.  Starving people is wrong and most people would agree that starvation should not be used by governments as a weapon against civilian populations.

Acknowledgements

@mgist for his suggestion that inspired the analysis

@cjfdillow for his comprehensive descriptions of how basic income works.

All errors are mine.

Appendix:

Calculation of post-tax income 

Appendix Basic Income calculations.png

 

 

 

 

Ricardian Equivalence is dead. Long live Keynes!

Introduction

In this piece, I show how government spending on capital projects can be beneficial to the private sector. The demonstration shows the oft-cited objection to government spending, so called Ricardian Equivalence, is not correct. I use an example, which hints at the proposed HS2 rail project, to make my point. I also use accepted investment appraisal techniques.

An example

A government proposes to invest in a high speed rail line which will cost £30 billion to build. The government will commission a consortium of private sector firms to undertake the work. The consortium will be paid £30 billion and this will be treated as income in their financial accounts and for GDP measurement purposes.

The government proposes to fund the project by borrowing £30 billion from the City at a rate of 6% per annum. The bonds must be repaid at the end of 20 years. Once built, the line will be operated by a private rail company. The line is expected to last for 50 years after which time it must be replaced.

Methodology

A prudent government should ensure the borrowed money will be repaid to the lenders when due and that interest payments are met. This can be done by calculating an “annual equivalent” of the interest payments and the loan repayment. The government can then levy the amount of the annual equivalent as an annual taxation charge on the private sector over the 20 years of the loan. This stream of annual tax receipts, which are additional to other tax receipts, will then be sufficient to pay the annual interest charges to the lenders and to repay the amount initially borrowed (the principal) when it falls due at the end of 20 years. In short, the government will be able to break even.

Annual Equivalent

The annual equivalent is obtained from a formula which converts an uneven stream of cash flows into an even stream of cash flows (an annuity). In this particular case, there are 20 payments of £1.8 billion for interest (6% p.a. x £30 billion) and a final payment of £30 billion by way of repayment of the principal to the lenders. The annual equivalent is £2.616 billion (3 d.p.).  So this amount should be the additional annual tax charge to fund this particular project. It will be enough to provide for the annual interest charge of £1.8 billion for 20 years plus £30 billion repayment of principal. See appendix.

Schedule of cash flows

To see how the annual equivalent calculation clarifies and makes tractable the analysis, here is a summary of the cash flows between the government and the private sector using the facts of this example.  Outflows are shown in brackets and inflows without brackets.

Cash Flows

Comment

At this point, a reader may observe that the government and private sectors are mirror images of each other; the flows in and out of the private sector being exactly matched by the flows out and in of the government.  This may induce  the same reader to consider that government spending does not benefit the private sector since the additional tax charges (20 x £2.62) exceed the £30 billion income received at the outset of the project.

Time value of money

However, this conclusion takes no account of the TIME VALUE of money. Very simply put, the time value of money is the preference to receive money sooner rather than later. Most people prefer to receive money sooner rather than later. There are several reasons why individuals, households and firms prefer to receive money sooner rather than later. The list of reasons includes inflation, risk, need and so on. For example, a starving pauper would prefer to receive £1 now, rather than in one week’s time, for otherwise he or she may not be able to eat for a week. The poorer an individual, the greater their time value of money; a millionaire does not really care if they receive  £1 now or in one week’s time since it will make virtually no difference to his or her life.

Discount rate

This is the time value of money expressed as an annual interest rate. The higher a time value is, the higher the discount (or interest) rate. The discount rate allows someone’s preference for immediate money to be linked to future money. For example, someone with a discount rate of 25% would see £125 receivable in one year’s time as having an immediate value of £100. Someone with a higher time value, say with a discount rate of 30%, would value the same £125 as having an immediate value £96.15. The immediate value is called the PRESENT VALUE. In general, the poorer an individual, a household, or a firm is, then the higher their time value of money and their discount rate. The higher the discount rate the stronger the preference to receive a given sum now rather than in the future.

Putting it all together

The above table of cash flows shows the cash flows of the government and private sector to be equal (but opposite). The PRESENT VALUE of the tax cash flows, which arise in the future, may differ between the government and the private sector. In short, the time value of money for the private sector may be different from the government’s time value. In reality, this is highly likely to be true. If the time values, and therefore the discount rates, are different then the PRESENT VALUE of the cash flows shown in the table will be different. We hence need to ascertain the PRESENT VALUE of these future tax payments if we are to conclude whether or not government spending increases private sector income.

We know the government’s discount rate in the example is 6% (its borrowing cost).  However, we do not know the private sector’s discount rate (or time value of money). But we do know the private sector is composed of many households as well as firms. Many households, perhaps the larger part, will struggle day to day to make ends meet. They will be at the poorer end of the income spectrum. Many individuals and households will be borrowing at annual rates in excess of 1000% via Pay Day loans. This fact alone signifies that many households have extremely high discount rates

Firms will often be under pressure from their shareholders to make short term profits. Moreover, firms race risk when investing funds and this risk increases their discount rate. These factors, among others, support a conclusion that the private sector will have a higher average discount rate than the government’s, although we may not be able to quantify it.

If the private sector’s average discount rate is assumed to be 18%, then the following summary table shows the private sector (and GDP) benefits from the government’s spending. This conclusion may run counter to some economists who argue that government spending does not promote growth or income. They believe the private sector’s response will be to immediately save the entire amount of the additional government spending and thereby withdraw the government injection totally and immediately. These economists believe the private sector’s response would be in anticipation of the government clawing back the additional spending via higher future taxation. This analysis shows the conclusion is wrong since it does not correctly adjust for the different time values of the parties to the transaction.

Investment decision summary

The net present value represents the surplus in present value terms. As planned, the net present value accruing to the government is zero (it has broken even). The NPV accruing to the private sector is positive. This means it has gained £16 billion as a consequence of the government’s capital spending of £30 billion. The size of the private sector’s surplus depends on the private sector’s discount rate. The higher the private sector’s discount rate then the higher will be the surplus. A surplus will arise so long as the private sector’s discount rate is higher than the government’s. As explained above, it is almost certain that the private sector’s discount rate is higher than the government’s.

Appendix: 

Repayment schedule for 6% government bonds with a term of 20 years

Repayment schedule

The repayment schedule assumes that surplus funds can be invested at 6% – a realistic assumption because the government will be repaying maturing 6% bonds continuously, thus saving itself 6%.on each bond redemption.