Valuing economic growth

Introduction

Sometimes, we come across interventions whose main path to impact is increasing economic growth. This memo outlines how we value an increase in economic growth in our research framework.

I’ll first present our simple model of how to value economic growth for back-of-the-envelope calculations (BOTECs), making a few assumptions on the way. This will gloss over some details but aims to provide some intuition as to how economic growth relates to individual consumption increases. Part II discusses each assumption, giving reasons why they are a good approximation on average and sketching in what circumstances we should deviate from them. In the last part, I’ll outline considerations that we plan to look into further in the future and that are likely to change our conclusions substantially, i.e., the value of growth by at least 25% in our research framework.

The immediate term recommendation of this memo is to use the model outlined in Part I: Simple model. The medium-term recommendation is to investigate the questions outlined in Part III: Extensions more as they have a good chance of changing our conclusions substantially.

Part I: Simple model

Economic growth is defined as an increase in the Gross Domestic Product (GDP) of a country. GDP in short stands for the market value of all the final goods and services that an economy produces. So, when countries grow economically, it means that they produce more/higher-value goods and services in aggregate than they did previously. For a short primer on economic growth, see, e.g., this post.

One thing to keep in mind is that, in practice, GDP can be reported in both real and nominal terms (for a short introduction, see the IMF’s Gross Domestic Product: An Economy’s All). Nominal GDP in a given year refers to the value of the economy using that year’s prices, whereas real GDP uses a fixed year’s prices. When measuring growth in real GDP, for example using 2010 price levels, we measure only the increase in the value of goods and services. If we measured growth in nominal GDP, we would also include a general increase in the prices of the same goods over time (inflation). In short, real GDP corrects for inflation, i.e., an increase in prices that is not due to increases in the underlying value. Whenever we talk about economic growth, we refer to increases in real GDP. If you only have data on nominal GDP in an evaluation, it is easiest to convert it to real GDP before continuing (how-to instructions).

In our research, we assign moral weight to doubling consumption for one person for one year. How do we get from economic growth to individual consumption increases?

We assume that:

To give an example, suppose there is an intervention that leads to a 1 percentage-point increase in economic growth in Gabon in 2024. In our model, this will increase every resident’s consumption by 1%. There are 2.3 million people in Gabon. So, the impact of the 1 percentage-point growth rate increase is 2.3 million times ln(1.01)/ln(2) = 33,017 consumption doubling equivalents¹ in 2024.

We can make the simplification that an increase in growth equals % increases in each person’s consumption because of the following three assumptions:

• A % increase in GDP causes the same % increase in total² disposable personal income in a country.
• Increases in disposable income are distributed equally (in % terms) to everyone in society.
• Disposable income increases equal consumption increases.

Broadly speaking, they allow us to think about growth like this: when the value of what everyone in society produces goes up, people are compensated for those value increases. In % terms, these gains to society flow to everyone equally. And once people have the income, they can spend it on consumption. The next part of the memo discusses each assumption in more detail.

Part II: Justifying the assumptions

For the simple model we made the following assumption: An x percentage-point increase in economic growth causes an x% increase in each person’s consumption.

This assumption relies on the three approximations below³. The reasoning to go from a rise in GDP to individual consumption increases goes as follows.

1. An x percentage-point increase in the growth rate is equal to an x% increase in GDP⁴.
2. An x% increase in GDP leads to an x% increase in nation-wide aggregate personal disposable income (Approximation 1).
3. This increase in total personal disposable income is distributed equally (in % terms) to everyone in society (Approximation 2).
4. Individuals will gain at least as much wellbeing/utility from their income gain as they would if they spent all of it on consumption (Approximation 3).
5. As a result, the value from an x percentage-point increase in the growth rate approximates the value from an x% increase in everyone’s consumption.

We discuss each of these assumptions in turn, why they are plausible in expectation, and for what types of interventions they might break down: read more in the full report.

Conclusion

This memo is the first version of an outline of our economic growth valuation methodology. It laid out a simple model that can be used for BOTECs: counting an x percentage-point increase in economic growth as an x% increase in everyone’s consumption. Part II discussed the three assumptions necessary for this model to hold and concluded that they were reasonable in most cases though should be adjusted for specific interventions (e.g., growth interventions that mostly target high-income people).

The final part of this memo sketched five questions that might substantially change our valuation of economic growth in the future:

• How far into the future should we count benefits from growth?
• What is the impact of including population projections?
• What is the consumption vs existential risk trade-off in frontier growth?
• What is the value of increased government revenue and spending?
• How do we value new goods and services independently of income?

The immediate recommendation is to use the simple model for our current cost-effectiveness calculations. The medium-term recommendation is to use Part III: Extensions as a starting point to investigate where our current approach might be significantly deficient—likely by undercounting the benefits of growth or by understating the existential risk from frontier technological development.

Notes

1. If you’re unsure about the ln(1.01)/ln(2) term: this term represents how much utility a person gets from a 1% compared to a 100% consumption increase (consumption doubling). It is significantly more than 1/100 (about 1.4/100) because people experience declining marginal utility from consumption—the more they consume, the less an increase in consumption improves their wellbeing. To see why ln(1.01)/ln(2) in particular is the right term to use, note that we assume constant utility from consumption doublings (by using a constant moral weight for consumption doublings). The functional form of utility compatible with this is u(x) = log_2(x) = ln(x)/ln(2). Starting from any initial point x_0 > 0, the value of a consumption doubling equals u(2 * x_0) - u(x_0) = ln(2*x_0)/ln(2) - ln(x_0)/ln(2) = ln(2)/ln(2) = 1. The value of a consumption increase in general (x > x_0) is u(x) - u(x_0) = ln(x/x_0) / ln(2). Since x/x_0 is equal to 1 + % consumption increase, the share of impact from a consumption increase is ln(1 + % increase)/ln(2) the value of a consumption doubling. ↩

2. Summed over all individuals. ↩

3. Another way of structuring the assumptions is to start from the claim that under certain conditions, Net National Product equals the present discounted value of future consumption (Weitzman 1976—I thank a reviewer for this reference). On the one hand, such an argument would be simpler. On the other hand, it would abstract from some features (taxes, distributional effects of growth, the household share of income, etc.). ↩

4. This is just the definition of economic growth in terms of GDP. ↩