# US GDP vs sub-$50/bbl oil How would we expect US GDP to be affected by oil prices dipping into the 30-50 USD/bbl range? If you need to make additional assumptions to answer this question, please note these, but still answer the question. I would expect that this would lower the cost of a major fundamental input and therefore increase the US GDP dramatically. The US is both the largest producer and consumer of oil. However, the US produces more oil these days from more expensive sources (shale) -- so perhaps this is a naive assumption? This article suggests a slight increase -- but perhaps a drop larger than$10 would change this analysis?

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I suppose that in order to answer the question well, we would need to first know why the price decreased. – jmbejara Jan 13 '15 at 5:36
Assume the price of oil is an exogenous variable. – Erik Jan 13 '15 at 5:37
But an exogenous positive supply shock, negative demand shock, or what? – BKay Jan 13 '15 at 13:08
It is exogenous. For unexplained reasons, the price goes from 100 USD to 30-50 USD. – Erik Jan 13 '15 at 15:05

Consider a basic case of linear supply and demand functions for oil.

Demand: $q_d = \alpha + \beta P + \gamma X + \epsilon$ Think of X as a demand shifter, so Z could move around if the Chinese economy goes into recession or changes growth speed, someone invents a cheap hybrid car, or Americans wake up one day and decide to drive less.

Supply: $q_s = \eta + \zeta P + \psi Z + \phi$ Think of Z as a supply shifter, so if Z could move around if we have a shock to oil production like an expansion of fracking, a return of Libyan oil production to market, or the Saudis decide to reduce production for strategic reasons.

Now in equilibrium supply equals demand ($q_d = q_s$):

$\alpha + \beta P + \gamma X + \epsilon = q_d = q_s = \eta + \zeta P + \psi Z + \phi$

Which we can solve for P:

$\Rightarrow P = \frac{(\alpha - \eta) \gamma X - \psi Z + \epsilon - \phi}{\zeta - \beta}$

We can also solve for $\Delta P$: $\Rightarrow \Delta P = \frac{ \gamma \Delta X - \psi \Delta Z + \Delta (\epsilon - \phi)}{\zeta - \beta}$

When we observe that P has fallen, that may be because $\Delta Z>0$ or because $\Delta X<0$

But for the economy, we'd expect quite different results from $\Delta Z>0$ and $\Delta X <0$. A negative demand shock ($\Delta X <0$) for oil probably reflects people being poorer and the economy heading into recession. A positive supply shock ($\Delta Z>0$) probably reflects technological improvements that make oil extraction more cost effective. The former bodes poorly for the economy, the latter bodes well.

So it isn't enough to say that it is an exogenous change in oil prices, we have to know more about why oil prices are changing. Economics blogger Scott Sumner warns about this particular issue, advising his students and readers to never reason from a price change. However, if we can take a stand on where the shock is coming from we can get some place. For example, if we assume it is entirely a oil supply shock then because we have estimates of the price elasticity of demand for oil, we can ask how much the supply curve would have had to move to drop prices as observed. From a supply curve shift and a sense of the demand function we could then calculate the increase in social surplus(measured in dollars) from the movement in the supply curve. Or you could treat it as a pure positive income shock to american consumers, negative to American oil producers, and use estimates of fiscal multipliers and marginal propensity to consume to estimate the effects. I suspect you could do something similar with demand shocks.

As a thought experiment, I tried to think of this as a global supply shock. In my scenario oil prices are lower because production is up but there are no additional knock on effects on demand for exports or the US dollar. We also have to take a stand on if this is temporary or permanent. In general you'll get much bigger effects from permenant shocks. I'm going to assume the price shock lasts a single year. I'm not positive that's a coherent scenario but it gives me something to plug into my calculator.

According to the US Energy Information Administration the US is a net importer of about 5,700,000 barrels of oil and oil products a day. If the price of oil falls from $\approx$\$102 to$\approx$\$40 a barrel that's about \$127 billion in savings by the American public. That works out to about \$410 a person a year or 0.75 percent of GDP. What about the fiscal multiplier you ask? The marginal propensity to consume numbers are like 4% in representative agent models, which means that if everyone were the same and we have a multiplier of 2 we'd get something like 0.81 percent of GDP. Which suggests that the direct effect of oil price changes can't be very important. That is, if the distributional consequences are not important.

The aggregate net export numbers obscure that some people are huge net exporters (the people in oil business) but the vast majority of us are modest net importers. Aggregate production was something like 3.4 billion barrels produced by about 600,000 workers call it an even two million to include support staff and that's a massive \$100,000 less per worker (noting that capital will bear much of the adjustment here, but still, that's huge). With 9.1B barrels (5.7B imports + 3.4B domestic production) in domestic consumption , that works out to more generous /$1,800 a year in savings for the 308 million or so of us who don't work in the oil business. But if everyone is the same, none of that really matters, income losses buy the oil guys are offset but income gains by consumers except to the extent that we are net importers. Do we think that's true here?

In general, we think that poorer people have a higher marginal propensity to consume than richer people, which generally means that shocks that affect poor people have stronger short-run economic effects than shocks of the same size affecting rich people. The people who work in the petroleum business are much higher paid than the average American (about 91k a year compared with say 43k for the typical worker and of course not everyone works).

Imagine America had one guy (some trillionare) who owned all domestic oil production and consumed so little of his money that oil price shocks didn't influence his consumption (MPC = 0). Everyone else was a consumer of oil. In that world the short run aggregate effects would be more like that of giving everyone the \$1,800 wealth effect from cheaper oil. So something like 3-4% of income is a non-trivial shocks, and by some accounts lower income people have MPC as high as 0.5, so that could be say 1.5 - 2 percent of GDP directly. You'd also get a knock on effect of whatever you think the fiscal multiplier is. Some people would say about 2. So that tells you 3-4 percent of GDP stimulus effect should be the upper bound. So in my thought experiment I'd say something between 0.75 - 4% of GDP effect from the oil price drop of \$62 a barrel from a pure supply effect.

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I see your point on why the cause of the oil price changes has happened is important -- if you are talking about global GDP. But if I assume that prices are exogenous, I am also implying that global supply and demand are large compared to domestic supply and demand (which of course is not true). Thus, it would seem that the effect on US GDP would be something that expresses the ratio of supplier surplus vs. consumer surplus at a given price point. I would expect US consumers to benefit more than US suppliers lose for example. Nice approach I think though. – Erik Jan 14 '15 at 2:48
That doesn't seem like a good model for the USA, which is a huge producer of oil, a huge consumer of oil, and deeply interlocked with the global economy through trade. Yes, the direct price effect makes American consumers better off and producers worse off. But there are clearly both negative demand and positive shocks going on. Oil is about 8% of exports and a smaller part of GDP, so direct effects of oil may easily be swamped by whatever is causing the change in oil prices. – BKay Jan 14 '15 at 11:20
I appreciate your analysis, but you never really answer the question. If you must make an assumption about the cause, note it and carry on. – Erik Jan 18 '15 at 22:01

# Requested assumptions

Like @BKay pointed out, the answer really depends on what caused the price decrease. Also, along this point, I think it would be more appropriate to ask for us to assume that the cost of oil has gone down. As far as jargon goes, a "price" is the number that defines an equilibrium where markets clear---where supply equals demand. So, as I'm sure you understand, I feel like a price should always be considered endogeneous. On the other hand, it seems more appropriate to assume that cost has gone down in the sense that the cost just represents, e.g., the cost of extraction. I'll make this assumption.

Also, in a comment you made on @BKay's answer, you talk about wanting to make the assumption that the domestic supply of oil is small in comparison with the global supply. So, I'll make this assumption as well.

# Two Extreme Cases

I think a simple analysis would be as follows. I believe that the logic will show two extreme cases in which GDP could go up or down. The idea is that we could be somewhere in between and it's hard to say without more data and a more careful analysis.

### GDP could go up

Assuming that domestic supply of oil is small (infinitesimal) compared to the global supply, assuming a small open economy with no trade barriers in a perfectly competitive market, domestic owners of oil will have no market power and so when the cost of foreign oil does down, people will substitute away from domestic oil until the price of domestic oil is equal to the price of foreign oil. If we assume that the value of the domestic supply of oil represents a negligible fraction of the value of domestic endowments, then the lower cost of oil will only serve to slacken the budget constraints of households and firms who purchase oil (as a good of final demand or as an intermediate factor of production). In this sense, the US has become richer and GDP will go up.

### GDP could go down

On the other hand, suppose the extreme case where the US's only endowment is oil (you notice that we're just assuming a simple endowment economy here). Then, because we have assumed that domestic owners of oil have no market power (domestic supply small compared to global), the price and therefore the value of the US's only endowment has gone down. Because we've assumed a friction-less, perfectly competitive market, the lower value of the US's endowment can only cause GDP to go down. Essentially, the lower price of oil has made the US a poorer country.

# Somewhere in between?

There were a lot of unrealistic assumptions made in the above argument, but it just serves to show ways in what ways that GDP could go up or down given the "requested assumptions" discussed above.

Also, for what it's worth, I think this line of reasoning is particularly nice because it's a little more transparent. The logic is essentially built on how the cost change affects the budget constraint. It's easy to see that this line of reasoning is internally consistent. In essence, the question just amounts to this: does the lower cost of oil make the US richer or poorer in terms of its natural endowments?

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