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

 

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.

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.

Value Added Statements

Introduction

Being slightly nerdy and having a background in accountancy and an amateur interest in some of the current economic controversies, the topic of value added statements and national income accounting interests me. Hence this post. I hope those with an interest in accounting and bookkeeping for national income will find this interesting and useful.

What is value added?

Value added is a measure of wealth creation. At an individual firm level, value added is measured as sales revenue minus the cost of all goods and services purchased from outside the firm. At an individual firm level, a value added statement provides a useful and interesting alternative to a traditional income statement.

Value added is used in accounting for national income because a nation’s value added is the same as a nation’s GDP. Value added statements can assist in evaluating government spending projects.

Illustration

The government proposes to spend £100 m on a much needed public housing programme. It will borrow funds from wealthy private sector savers to finance the project.

Of the additional GDP created by the project, 10% will be paid to government by way of taxation and 10% will be saved by the private sector. The remaining 80% of additional GDP will be spent on wages and salaries. The recipients of wages and salaries will spend their entire incomes on consumption. This consumption expenditure will be spent 3 parts on imported goods and 5 parts on domestically produced goods and services.

The multiplier effect

The spending in shops, restaurants, cinemas, and on other consumables by workers becomes the income of those supplying the goods and services to the workers. These suppliers will then pay their labour force, who in turn will then spend their wages on consumable goods and services in shops, restaurants etc. However, at each turn of the cycle, the value of transactions will shrink by 50% because the 10% saving rate, the 10% tax rate, and the 30% import rate removes 50% of income received from circulation by the time wages are next paid. This  process will continue until all the additional demand generated by the £100 m initial government injection has disappeared. This will occur when the additional GDP has reached £200m. It stops at this point because the multiplier value used in the illustration is 2*. Had the multiplier value been 1.5 then the process would stop when the additional GDP (value added) reached £150 m (1.5 x £100m)

The following statement reports the additional GDP once all transactions have completed.

Value Added Statement

Some final points

The statement is in two parts. The top part shows how value has been created. The lower part shows how the value has been distributed among the stakeholders. In the above example, providers of finance capital have not been shown as stakeholders. This is a deliberate omission, made to aid exposition

The above example is a simple one. For example, we have assumed that all wages have been spent on consumption. In reality, this is unlikely to be the case because workers may save, just as the firms have done in this example.

Secondly, we are not showing how much of the value added has been distributed to finance creditors and shareholders as interest and dividends respectively. Their share of valued added has been subsumed under savings instead of itemising their respective share of value added .To keep the illustration simple, all consumption expenditure has been assumed to derive from wages and salaries. In reality, dividends and interest payments will impact consumption expenditure.

Another simplification is that all consumption expenditure has been paid for out of income. This is nowadays an unrealistic assumption since it is common for workers to borrow to fund their consumption expenditure. A simplifying assumption has been made in the illustration that workers do not spend more than they have earned.

More elaborate value added statement to incorporate more complex and realistic scenarios are relatively easy to prepare.

The coding shown on the value added statement illustration denotes the item corresponding to the expenditure method of measuring national income, eg G = Government expenditure, C = Consumption, M = Imports and Y = National Income, T = Taxation and S = Savings.

* A multiplier value is calculated as the reciprocal of the sum of leakages. In the illustration, the leakages were tax = 10% + saving  = 10% + imports = 30% = 50%.  The reciprocal of 50% = 2, which is the value of the multiplier used in the illustration