Some Unorthodox Ways To Achieve High GDP Growth

post by johnswentworth, David Lorell · 2024-08-08T18:58:56.046Z · LW · GW · 6 comments

Contents

    A Toy Example
  Some Policy Suggestions
    Policy 1: The See-Saw
    Policy 2: Rotation of Excessive Overpayment
  Other Possibilities?
None
6 comments

GDP growth, as traditionally calculated, is a weird metric [LW · GW]. People interpret it as measuring “economic growth”, but… well, think about electronics. Electronics which would have cost millions of dollars (or more) in 1984 are now commonplace, everyone carries them around in their pockets. So if we calculate GDP growth based on 1984 prices, then GDP has grown multiple orders of magnitude since then, everyone now owns things which would make 1984’s wealthiest people jealous, and practically all of that growth has come from electronics. On the other hand, if we calculate GDP based on 2024 prices, then all of the digital electronics produced before, say, 2004 are worth almost nothing, so electronics contributed near-zero GDP growth throughout the entire internet boom.

Economists didn’t like either of those conclusions, so back in the 90’s, they mostly switched [LW(p) · GW(p)] to a different way of calculating GDP growth: “chaining”. Basically, we calculate 1984-1985 GDP growth using prices from 1984-1985, then 1985-1986 GDP growth using prices from 1985-1986, and so forth. At the end, we multiply them all together (i.e. “chain” the yearly growth numbers) to get a long-term growth line. Chaining gives less dramatic GDP growth numbers when technological changes make previously-expensive things very cheap.

Chaining also opens up some interesting new methods for achieving high GDP growth.

A Toy Example

Suppose we have two goods, A and B. Over the course of five years, the price of each good and the amount consumed evolve as follows:

Year	Price A	Amount A	Price B	Amount B
1	$1	10	$10	1
2	$1	1	$10	10
3	$10	1	$1	10
4	$10	10	$1	1
5	$1	10	$10	1

The main thing to notice about this table is that year 5 is exactly the same as year 1; our toy economy goes full-circle back to where it started.

Now let’s calculate the GDP growth for this toy economy, using the same standard chaining method adopted by the Bureau of Economic Analysis for calculating US GDP back in the 90’s.

Calculation details (click to expand)

To calculate the GDP growth from year $t$ to year $t+1$, we calculate the ratio of year $t+1$ to year $t$ consumption using year $t$ prices, then calculate the ratio of year $t+1$ to year $t$ consumption using year $t+1$ prices, then average those together using a geometric mean. So the formula is:

${\Delta }_t^{t+1}=\sqrt{\frac{{\sum }_i{p}_i^t{q}_i^{t+1}}{{\sum }_i{p}_i^t{q}_i^t}\frac{{\sum }_i{p}_i^{t+1}{q}_i^{t+1}}{{\sum }_i{p}_i^{t+1}{q}_i^t}}$

where:

• $i$ ranges over the goods (here $A$ and $B$)
• $p$ is price
• $q$ is quantity

To get GDP growth over the whole timespan, we multiply together the growth for each year.

Here’s the result:

Year	Price A	Amount A	Price B	Amount B	GDP Growth
1	$1	10	$10	1
2	$1	1	$10	10	5.05
3	$10	1	$1	10	1
4	$10	10	$1	1	5.05
5	$1	10	$10	1	1

So overall, the GDP growth for the five-year period (according to the chaining method) is 5.05*1*5.05*1 = 25.5. Roughly 2450% growth over four years! Pretty impressive, especially considering that prices and consumption in the final year were exactly the same as prices and consumption in the first year. At that point, why not do it again, to maintain that impressive GDP growth?

Some Policy Suggestions

Our toy example raises an exciting possibility for politicians and policymakers^[1]: what if you could achieve high GDP growth without the notoriously difficult and error-prone business of changing long-run prices or consumption? What if everything could just… go in a circle, always going back to where it started, and thereby produce safe, reliable, high GDP growth?

The basic pattern in our toy example is:

• Prices shift: a popular good becomes cheap, a good rarely purchased becomes expensive
• Consumption shifts: consumers buy less of the cheaper good, and more of the expensive good
• Prices shift back
• Consumers shift back

To match the toy example, shifts must happen in that order. What kind of policies could induce such shifts?

Policy 1: The See-Saw

Suppose that the two major US parties find their way to an equilibrium relationship.

Every 4-8 years, when the Democrats come into power, they'll pass a bunch of laws saying that sellers of healthcare, housing, food, vehicles, what have you, must provide various features which are crucial for the welfare of disadvantaged people - dental care, elevators, organic veggies, low emissions, etc. Prices go up. A year or two later, to ensure that everyone has access to all those expensive features, the Democrats will deploy a combination of subsidies and mandates to make sure access to those expensive things is universal. Consumption goes up.

A couple years later the Republicans will come into power, and repeal the onerous dental/elevator/organic/emissions/etc requirements on sellers. Prices go down. A year or two later, they also roll back some of the subsidies and mandates; there's less pushback against e.g. removing subsidies for things which are no longer so expensive or fancy. Consumption and prices return to baseline.

So long as the parties time their changes correctly, this can all result in lots of GDP growth! Prices of some goods go up, subsidies and mandates push people to buy more of the newly-expensive goods, prices of those goods goes down, and then removal of the subsidies and mandates causes consumption to return to baseline. That's basically the cycle from the toy example.

However, this is still a rather unreliable method. The separation between price-changing and consumption-changing steps won't be clean, people will sometimes respond in weird ways, the economists' accounting might not recognize the more expensive versions of things as the same good, etc. Can we find a more reliable, controllable strategy?

Policy 2: Rotation of Excessive Overpayment

The US government is itself a major consumer over which government policy has a relatively high degree of control. So, why not try a similar strategy with the consumption of the US government itself?

The federal procurement system is already notorious for massively overpaying for goods. In order to leverage that overpayment into massive GDP growth, it needs to be rotated: the US government needs to shift which goods it's massively overpaying for every couple of years. And to match our toy model, they need to stage the changes in the correct order: in one year, dramatically increase the amount paid for some good. In the next year, buy a much larger amount of that good. In the third year, actually negotiate the price down to something reasonable. In the fourth year, dial amount back down to baseline.

By strategically timing excessive overpayment and delivery of goods, this method should allow the US government to boost GDP growth, using only the tools (and budget) already available.

How much could overpayment rotation boost GDP growth, at what level of resource commitment? Let's do a back-of-the-envelope estimate. Assume the resources involved in rotation are small relative to total dollar value of economic production, and both prices and quantities in the whole economy do not change much year-to-year. Then we can use a linear approximation to estimate the marginal GDP growth contribution from performing overpayment rotation with two goods, along the same price/quantity pattern as our toy example.

Linear expansion details (click to expand)

Let $V_{\tau }^t$ be the value of goods produced at time $t$, in time $\tau$ prices. Then, as the previous box walked through, the GDP growth from time $t$ to $t+1$ is

$\sqrt{\frac{V_t^{t+1}}{V_t^t}\frac{V_{t+1}^{t+1}}{V_{t+1}^t}}=e^{\frac{1}{2}(ln{V}_t^{t+1}-ln{V}_t^t+ln{V}_{t+1}^{t+1}-V_{t+1}^t)}$

If we take a first-order expansion with respect to all the $V$'s, then evaluate the expansion at $V_t^t=V_t^{t+1}=V_{t+1}^t=V_{t+1}^{t+1}$ (i.e. ignore changes in the underlying economy for purposes of calculating the marginal contribution of our small changes), we get

$\delta e^{\frac{1}{2}(ln{V}_t^{t+1}-ln{V}_t^t+ln{V}_{t+1}^{t+1}-V_{t+1}^t)}$

$=e^{\frac{1}{2}(ln{V}_t^{t+1}-ln{V}_t^t+ln{V}_{t+1}^{t+1}-V_{t+1}^t)}\frac{1}{2}\frac{1}{V_t^t}(\delta V_t^{t+1}-\delta V_t^t+\delta V_{t+1}^{t+1}-\delta V_{t+1}^t)$

We will call the term in parens (multiplied by the factor of $\frac{1}{2}$) the "marginal dollar-value contribution to GDP growth", and the same term divided by $V_t^t$ the "marginal contribution to GDP growth".

Here's what the numbers look like for the toy example:

Year	Price A	Amount A	Price B	Amount B	Marginal Dollar-Value Contribution to Growth
1	$1	10	$10	1
2	$1	1	$10	10	$81
3	$10	1	$1	10	$0
4	$10	10	$1	1	$81
5	$1	10	$10	1	$0

There's about $100 of spending tied up in the toy example (at peak years), and this spending adds about $81/2 $\approx$ $40 (divided by total dollar-value of all goods in the economy) to GDP growth for the average year. So long as the numbers remain low relative to the whole economy, we can scale it up linearly: with $100B of spending involved in peak years, GDP growth would be boosted by about $40B. Using an estimate of $25.44T for US economic output in 2022, that would be an increase of $40B/$25.44T $\approx$ 0.15% on an average year. And - crucially - overpayment rotation with $100B in peak years can continue boosting GDP growth by that amount, again and again, indefinitely.

Since the peak spend is only needed every other year, overpayment rotation on more types of goods could roughly double the GDP growth improvement, to roughly 0.3% with $100B of overpayment rotation.

Could overpayment rotation be performed with $1T? That would be a pretty substantial fraction of US government spending. But the payoff could be HUGE: the GDP growth improvement would be about 3% per year, more than doubling the annual growth rate typically seen in recent years.

And that's just using the technique from our toy example. Could other methods be more efficient?

Other Possibilities?

We're eager to hear of other methods to boost long-term GDP growth without all the challenges of changing long-term prices or consumption. Please leave additional ideas in the comments! This includes both other practical implementations of the cycle illustrated by our toy model, and new toy models with different kinds of cycles.

1. ^{^}

   and econometricians, ML practitioners, Soviet planners, people with MBAs, …

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