Public Finance — Budget Systems and Cost-Benefit Analysis

Public Finance — A Budget Records Choices; Cost-Benefit Analysis Calculates Them

Chapter 3 showed that the size of spending is set by voting and by incentives inside government. This chapter covers the institution that holds that process — the budget — and the tool for judging whether an individual project is worth doing: cost-benefit analysis.

1. Budget systems differ in what they make visible

Comparing budget systems
System	Basis of classification	What it shows well	Weakness
Line-item budgeting	Input items such as personnel and supplies	Spending control, financial accountability	Does not show what was achieved
Performance budgeting	Programmes and activities with unit costs	Workload and efficiency	Outputs are not the same as outcomes
Planning-programming-budgeting (PPBS)	Links between goals, programmes and budgets	Long-term goals and comparison of alternatives	Heavy analytical burden, hard to coordinate across ministries
Zero-based budgeting (ZBB)	Every programme reviewed from scratch each year	Clearing out programmes that persist by inertia	High review costs; applied only partially in practice

Whatever the system, actual budgets tend to be set by adding and subtracting a little from last year’s budget. This is called incrementalism. It is a rational response to the lack of information and time to compare every alternative afresh each year, but it is also why programmes, once created, continue regardless of performance. Performance evaluation and sunset clauses are devices to break this inertia.

The budget process also embodies principles of fiscal democracy. Parliament scrutinizes and approves the budget; if the budget is not passed before the fiscal year begins, only essential spending is carried out on the basis of the previous year’s budget (a provisional budget); and supplementary budgets respond to changes in circumstances after the budget is adopted. These procedures hold the executive accountable for justifying spending.

2. The skeleton of cost-benefit analysis

Whether a public project should go ahead is judged by converting society’s total benefits and costs into money at the same point in time and comparing them.

Net present value

NPV = \sum_{t=0}^{T} \frac{B_t - C_t}{(1+\rho)^t}

ρ is the social discount rate. If NPV > 0, the project raises social welfare. Under a budget constraint, projects are chosen in order of their benefit-cost ratios.

Suppose building a bridge costs 100 billion won today and yields benefits (time savings, fewer accidents) of 8 billion won a year for 30 years.

At a 4.5% discount rate: the present value of benefits is $8\times\frac{1-1.045^{-30}}{0.045}\approx 8\times 16.29\approx 130.3$ billion won, so $NPV\approx 30.3$ billion won
At a 7% discount rate: the present value of benefits is $8\times 12.41\approx 99.3$ billion won, so $NPV\approx -0.7$ billion won

The same project passes or fails depending on the discount rate. The more a project’s benefits lie in the distant future (climate action, basic research), the more sensitive it is to the discount rate.

3. What should the discount rate reflect?

There are two views of the social discount rate.

Opportunity cost view: money spent on public projects crowds out private investment, so the pre-tax return on private investment should be used.
Social time preference view: the rate should reflect how willing society is to trade future for present consumption. The Ramsey formula gives $\rho = \delta + \eta g$ (pure time preference plus the elasticity of marginal utility times the growth rate of consumption per person).

With $\delta=1\%$ , $\eta=1.5$ and $g=2\%$ , $\rho=4\%$ . Whether pure time preference $\delta$ should be close to zero (intergenerational equity) or aligned with market interest rates is at the heart of the climate policy debate. Korea’s preliminary feasibility studies set the social discount rate by guideline (4.5% since 2017), and some countries use discount rates that decline with the time horizon for long-term projects.

4. Valuing things without market prices

Methods for setting shadow prices
Item	Method	Example
Time	A fixed share of the wage rate	Valuing commuting time saved at 50% of the hourly wage
Labour of the unemployed	Its opportunity cost is below the market wage	Setting a low shadow wage for idle labour
Environment	Hedonic pricing, travel cost, contingent valuation	Differences in house prices near parks
Life	Value of a statistical life (VSL)	Willingness to pay for risk reductions

The value of a statistical life is not the price of a particular person’s life but the sum of what people are willing to pay for small reductions in the risk of death. If 10,000 people are each willing to pay 500,000 won to cut their risk of death by 1 in 10,000, together they are willing to pay 5 billion won to prevent one expected death. The VSL is 5 billion won. It is estimated from wage premiums in risky jobs or from purchases of safety products.

5. Common calculation errors

Double counting: if a new road shortens travel times and nearby land prices rise as a result, the rise in land prices is the time-saving benefit capitalized. Adding the two counts the same benefit twice.
Counting job creation as a benefit: labour employed on construction is a cost. If it would have worked elsewhere, its full opportunity cost is a cost; if it was idle, only the shadow wage is.
Counting transfers as benefits: tax reliefs and subsidies are one party’s gain and another’s loss, so they net to zero for society. The excess burden of the taxes that finance a project (Chapter 2) should instead be added to its costs.

Check your understanding

What is the NPV at a 5% discount rate of a project with an initial cost of 50 billion won and benefits of 7 billion won a year for 10 years? The annuity factor is $\frac{1-1.05^{-10}}{0.05}\approx 7.72$ , so the present value of benefits is about 54 billion won and the NPV about 4 billion won. If the excess burden of the taxes that finance it is 0.2 won per won, the cost becomes 60 billion won and the NPV turns to about −6 billion won.

References

Anthony Boardman et al., Cost-Benefit Analysis: Concepts and Practice
Harvey Rosen and Ted Gayer, Public Finance, ch. 8
HM Treasury, The Green Book: Appraisal and Evaluation in Central Government
KDI Public and Private Infrastructure Investment Management Center, general guidelines for preliminary feasibility studies (Korean)