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.

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