EDIT
 Compressing Reality

# Consumption or Saving

## Econ 101

You’ve heard it before, consumption is good for economic growth.

This is a myth - though, like all good myths, it contains a grain of truth.

To tease this apart, it helps to split GDP into two parts: potential GDP and the output gap: $$GDP = (Potential GDP) - (Output Gap)$$

In the short-run, companies can meet increased demand by pushing their employees to work more hours or by hiring less and less qualified employees. Likewise, they can cut costs by firing employees or cutting back their hours.

However, in the long run, when lots of companies demand more labor, wages rise, and subsequently the number of hours required fall. Likewise, when companies are cutting back, wages fall until hiring employees becomes productive again. At least, this is what happens in sufficiently free labor markets.

In the long-run, however, we tend always towards an equilibrium, where unemployment is around 5% and where GDP neither exceeds nor falls short of its long-term potential. Ths potential changes not because of the whims of investor/consumer feelings, but due to economic fundamentals.

Economists pretty much all agree that increasing consumption helps a country get out of a recession. When more people spend money, we see inflation, which reduces real wages, which increases labor demanded, causing unemployment to fall, and voila no more recession.

However, our country can’t produce more in the long-run just by wanting to buy more things. To increase potential GDP, we have to actually improve our ability to produce.

## Open and Closed Financial Markets

Are financial markets opened or closed? This may seem tangential, but we’re get back to consumption, saving, investment, and taxes in a bit.

Anyway, open or closed? Obviously, the answer is both - the real question is one of extent. To be more precise, we’d like to know how much US investment increases if US savings increases by a dollar.

Typically economists approximate globalized markets by assuming the nation being analyzed has no market power. This is frequently not the case for large nations (or small markets), but I think we can make that assumption here. The US personal savings rate only accounts for about 3% of worldwide investment, after all. Admittedly US gross investment is significantly higher - at about 13% of global gross investment "title": "List of countries by GDP (PPP)" "title": "Gross capital formation (% of GDP)".

## The Closed Economy

Let’s consider, then, a completely closed economy regulated by the Solow-Swan model "title": "Solow–Swan model" (with $\alpha=0.4$ as is empirically supported "title": "Share of Labour Compensation in GDP at Current National Prices for United States"): $$Y=A \cdot K^{0.4} \cdot L^{0.6}$$ where people save a constant proportion of their income, all savings is invested, and capital depreciates at some fixed rate. In this case, we can prove that long-term consumption is determined by $$C \propto (1-s) \cdot s^{0.6}$$ where $s$ is the percent of income people save. This implies the optimal savings rate should be around 40%.

Gross capital formation in the US is about 21% of GDP "title": "Gross capital formation (% of GDP)" - significantly lower than the 40% goal. While this might seem massive, graphing long-term consumption against the savings rate reveals that there are sharp diminishing returns - to the extent that increasing savings to the optimal rate would only increase long-term consumption by about 17% - about 8 years of economic growth.

Remember, this is (from a utilitarian perspective) a lower bound because we’re assuming a closed economy. Hence, we know that increasing the savings rate by 19% of GDP should yield at least as much benefit as increasing long-run consumption by 17%.

Like I said, however, the diminishing returns are pretty steep. On the margin, an increase in the savings rate by 1% of GDP causes a 1.9% increase in long-term consumption. I want to emphasize how amazing this is. Consumption is 70% of GDP, so if we had to sacrifice \$1 of consumption in order to shift an additional \$1 from consumption to savings, that would nearly be worth it.

Least you think this is all just theoretical, we can look at annual national data. If we let non-residential investment serve as a proxy for $K$ and 15-64-year-olds serve as a proxy for $L$, we can compute the regression line between annual changes in $K$ versus in $Y/L^{0.6}$. It has a slope of 0.49 ($r=0.41$), which is actually even higher than the slope of 0.4 predicted by the Solow-Swan model, implying that our estimates might even be low-balling the importance of investment.

A cross-country analysis of investment in equipment finds that for each 1 percentage point increase in such investment as a percent of GDP, growth increases by an additional third of a percentage point "title": "Equipment Investment and Economic Growth".

Here’s another study that found a strong effect of (foreign) direct investment on growth "title": "Does Foreign Direct Investment Accelerate Economic Growth?".

## Semi-Open Economies

What’s even more impressive is that this result places a lower bound on the value of shifting consumption to saving. If we shift 1% of saving to investment and assume the US is a small, open economy, we assume that all the money is invested overseas, where it does 4 times as much good.

That is, from a utilitarian perspective, while shifting a dollar of consumption to savings creates 1.9 utils if financial markets are closed, it creates 5.3 utils if they’re open. I should note, however, that 40% of those benefits go to the capitalists themselves, so the externality is “only” between 1.14 and 4.54 utils.

If we let $\beta$ indicate how much domestic investment changes given a change in savings in the US, we can interpolate between these and state “increasing US savings by \$1 is ethically equivalent to creating$5.3 - 3.4 \beta$utils. So. Now all we have to do is estimate$\beta$. Here’s a list of some estimates from the literature:  Estimate Years Source Citations 0.809 1950 - 1959 "title": "Domestic Saving and International Capital Flows Reconsidered" 125 "title": "International Capital Mobility: What Do Saving-Investment Correlations Tell Us?" 529 0.914 1960 - 1969 "title": "National Saving and International Investment" 524 0.913 1960 - 1969 "title": "National Saving and International Investment" 524 0.870 1960 - 1969 "title": "Saving-Investment Correlations and Capital Mobility: On the Evidence from Annual Data" 346 0.903 1960 - 1969 0.89 1960 - 1974 "title": "Domestic Saving and International Capital Flows" 4062 0.94 1960 - 1974 "title": "Domestic Saving and International Capital Flows" 4062 0.57 1960 - 1984 174 0.805 1970 - 1979 "title": "National Saving and International Investment" 524 0.864 1970 - 1979 "title": "National Saving and International Investment" 524 0.815 1970 - 1979 346 0.763 1970 - 1979 0.69 1960 - 1992 "title": "The saving-investment correlation puzzle is still a puzzle" 83 0.607 1980 - 1986 "title": "National Saving and International Investment" 524 0.792 1980 - 1986 "title": "National Saving and International Investment" 524 0.527 1980 - 1989 "title": "Saving-investment correlations in developing countries" 91 0.682 1980 - 1989 "title": "Saving-Investment Correlations and Capital Mobility: On the Evidence from Annual Data" 346 0.451 1990 - 1999 0.973 2000 - 2009 Remember, that$\beta = 0$would indicate a perfectly global financial market, while$\beta = 1$would indicate a perfectly closed financial market. It looks like financial markets steadily become more open between 1960 and 1990 "title": "National Saving and International Investment" "title": "Saving-Investment Correlations and Capital Mobility: On the Evidence from Annual Data". Sadly, I couldn’t find data after this point. One might want to extrapolate and deduce that the effect of domestic savings on domestic investment has dropped to around 0.5ish. However, there are two significant problems with this: 1. Extrapolation is always dangerous. 2. The US is one of the two largest economies in the world and (more importantly) that it isn’t part of the EU, which makes it more isolated than other OECD countries. This means that we should expect significantly higher correlations for the US than the above estimates would indicate. This is born out: one study found an average correlation of 0.57 in OECD countries and a 0.91 correlation in the US specifically "title": "Estimating saving-investment correlations: evidence for OECD countries based on an error correction model". Conversely, it’s possible that US financial markets are significantly more global now than in the 1990. The most obvious reasons to believe this is that NAFTA was negotiated in 1994 "title": "North American Free Trade Agreement". There’s also the potential for improved financial flows in the future with the potential TPP and a Transatlantic partnership with Europe. For these reasons, finding the true strength of savings’ effects on investment are difficult. However, given the estimates above, I feel confident placing the connection at between 0.5 and 1. These conclusions imply that shifting \$1 from consumption to savings is ethically equivalent to creating between 1.9 and 3.6 utils, for an externality of between 1.14 and 2.84 utils.

There is one final thing to account for. It appears many authors find significantly lower domestic-saving-investment correlations for developing countries "title": "Saving–investment correlations in developing countries", which implies that these countries have more open financial markets. This suggests that the portion of US savings that gets invested overseas probably heads disproportionately to poor countries, which could potentially make saving even more good.

This makes the model significantly more complicated, so I’m going to ignore it, but this suggests that the upper bound of 3.6 utils per dollar is conservative.

## Counter Arguments

There are a number of arguments against economic growth:

1. It boosts greenhouse gas emissions.
2. It harms the environment.
3. It might cause greater inequality - e.g. by replacing low-skilled workers

Now, I think (1) is pretty insignificant. While I think global warming is a big problem, the best estimates place the total social cost of US carbon emissions at less than 1% of GDP. It’s possible that other forms of environmental damage are more important than global warming, but the connection between economic growth in a service-based economy and ecological damage seems tenuous at best.

I do, however, think argument #3 might have significant merit. While I pointed out that roughly 60% of the benefits of investment go to laborers rather than investors, this doesn’t account for labor-income inequality. If it turned out that every \$1 of growth investment creates is canceled out by greater inequality, then the whole “investment increases utility” argument falls rather flat. Even if inequality doesn’t wipe out the gains of investment entirely, it could still put a damper on things. Common wisdom appears to be torn here. The Kuznets curve finds that poor countries tend to be relatively equal, middle-income countries tend to be relatively unequal, and then rich countries tend to be equal again "title": "Kuznets curve". This suggests that in developed countries like the US, investment will probably reduce inequality. The idea that economic growth causes inequality in poor countries is well-supported by the literature as 14 out of 15 studies found that foreign direct investment caused an increase in inequality "title": "Is Foreign Direct Investment Good for the Poor? A Review and Stocktake". Likewise, we find that higher incomes predict lower pre-tax-and-welfare inequality in Europe. On the other hand, we have the historical Great Divergence. As we’ve discussed before, growing inequality in American incomes is almost entirely driven by pay-based inequality. This could plausibly be driven by improvements in technology, capital, or “culture”, or even by increasing inequality in education. It’s hard to tell for sure. ## Conclusions Given all this, it seems clear that the optimal taxation system should promote savings over consumption. The next couple posts will consider how to do that. However, I have one last point to make. If you finance tax-cuts with deficit-spending, you reduce private investment whether abroad or overseas pretty much dollar-for-dollar. There are literally 0 taxes that reduce savings by \$1 for each \\$1 in revenue, so it should always be a bad idea to finance tax-cuts with deficits for long-term growth. Now you might argue that if these deficits finance public investment, then it’s okay, but

1. Public investment doesn’t tend to have as high returns as private investment "title": "Infrastructure Investment and Economic Growth".
2. It’d be better still to finance public investment projects through tax hikes or spending cuts.

Of course, none of this implies that stimulus spending/tax-cuts during recessions is a bad idea. During recessions, such measures can stimulate good inflation and economic growth.