# Women and the Wealth of Nations

NOTE: The Growth Economics Blog has moved sites. Click here to find this post at the new site.

I discussed a paper by David Cuberes and Marc Teigner at the SEA meetings in New Orleans a few weeks ago. It provides some interesting calculations on the economic cost of discrimination against women in developing countries.

CT set up a simple model of occupational choice, a la Banerjee and Newman, where people can be (a) workers, (b) self-employed entrepreneurs, or (c) firm owners with multiple employees. As in that standard model, there is some distribution of managerial talent, and so the most capable managers become firm owners, and hire lots of employees. Those with medium management skills run firms, but it only makes sense for them to hire themselves (self-employed). Finally, those with low management skills find it more lucrative to work for the firm owners than start their own firms.

What CT add to this is frictions that prevent women from entering those different categories, even though their distribution of managerial talent is similar to that of men. They set this up so that if affects the number of women in each category, but not the distribution of their skills. For example, if 100 men have sufficient management skills to become firm owners, then 100 women presumably also have sufficient management skills, but the friction means that only 20 of them get to be firm owners. The average skill of those 20 is the same as the average skill of the 100 men (the friction discriminates purely on gender, not on talent).

This takes place all down the line. So you have fewer female firm owners, fewer female self-employed entrepreneurs, and fewer female workers. Now, because we have gotten rid of some possible firm owners and entrepreneurs, we are worse off. Fewer firm owners means lower demand for labor, so the wage of workers is lower. Thus more people (men and women) want to become self-employed. So the firms that do exist are smaller (fewer workers are available) and more of the population works as self-employed entrepreneurs. On the other hand, if few enough women are in the labor force, then the wage of the men and remaining women may actually be higher, which also limits the incentive to start a firm. Regardless, we get distortions to the number of firms, distortions to the wage of workers, and distortions to the number of self-employed entrepreneurs. In the end, this results in lower output per capita.

How much lower? That is the real contribution of CT. They take survey data from a set of developing countries that contains information, by gender, on whether people are workers, self-employed entrepreneurs, or firm owners. They then ask what kind of frictions are necessary in their model to generate the observed numbers. Once they know that, they can ask the counter-factual question of what output per capita would be if they removed any or all of the frictions to women.

Their Table 5 shows the percent loss of income per capita due to various frictions. Focus on the long-run loss columns (which have allowed for capital to adjust to the lower supply of labor). The first column, with a 7.06% loss for Central Asia, shows the impact of the frictions that limit women from becoming firm owners and/or self-employed entrepreneurs. As you can see, there is a sizable loss across regions, ranging from about 5-ish% to not quite 10%.

The second column adds in the loss from limiting women from becoming workers. In other words, limiting their labor-force participation rate. This increases the loss in all regions of the world, but there is really wide variation in the effects. The full set of frictions lower output per capita by about 37% in the Mid-East, for example, due to very low labor force participation rates by women. South Asia has a loss of about 25% of output per capita. The other regions have losses that are still sizable, but not quite as large in absolute terms.

For comparison, CT did the same calculations for OECD countries, and report those in their Table 3, shown below. Here, they break the results down by percentile of losses. So Top 25% means the average loss of the quarter of OECD countries with the biggest losses.

While not quite as bad as the Mid-east, the worst OECD countries have losses from frictions towards women’s work that are as costly as in many developing countries. Even the Bottom 25%, representing the countries with the smallest losses, are losing 10% of output per capita from frictions towards women, which is no better or worse than any developing region of the world.

One interesting note about both tables is that the losses associated with just the frictions towards self-employment and firm-ownership (i.e. losses due to ${\mu}$ and ${\mu_0}$) are relatively consistent across all OECD groups and developing regions, at between 5 and 7 percent. Rich countries are not necessarily any better at limiting these frictions than poor countries. When you add in the labor-force participation effects (i.e. losses due to ${\mu}$, ${\mu_0}$, and ${\lambda}$), there we still find that there is not a significant advantage for the OECD. The implications is that the OECD is not richer than developing countries because it treats women better. It is rich despite the fact that it puts up barriers to women participating in the labor force and/or in entrepreneurship.

When I discussed the paper, I threw up the following quote from David Landes’ The Wealth and Poverty of Nations, p. 413:

In general, the best clue to a nation’s growth and development potential is the status and role of women.

These numbers seem to indicate that this might not necessarily be right. It is not necessarily true that rich countries put women to work in a more efficient manner than poor countries.

One way that Landes’ point could manifest itself is in which women are discriminated against. The CT model has frictions that apply in a blanket manner to all women, regardless of managerial ability or worker skill. If rich countries discriminate against low-skill women, but allow high-skill women to enter the various categories of professions CT use, then this would limit the loss of output per worker.

On the other hand, even if high-skilled women are not discriminated against in entering certain professions, they may still be discriminated against within those professions, and that would create further losses. Perhaps rich countries do less of this kind of discrimination? I don’t know for sure, I’m simply trying to take Landes’ idea seriously and think of how why CT’s results might not be capturing it.

For the US, Hsieh, Hurst, Jones, and Klenow calculated that 15-20 percent of US growth in output per worker from 1960 to 2008 could be due to the improved allocation of talent across occupations due to the alleviation of discrimination. Again, they don’t have measure of specific discriminatory practices, but use the fact that the race and gender composition of occupations is converging over time towards the aggregate composition. In their calculations, about 3/4 of the total gains from reduced discrimination are due to white women entering professions they previously were underrepresented in. 90% of the gains are due to reduced discrimination against all women (their table 10).

Landes’ point could be valid if we think of the US (and other OECD countries?) doing better than poor countries in the allocation of women across occupations, conditional of them being allowed to work in the first place. Where we do not see major differences between rich and poor, as CT show, is in allowing women to work in the first place. The losses from this type of friction are roughly equivalent around the world, with a few notable exceptions (the Mid-East and maybe South Asia).

Now, it is simply implicit frictions that CT (and HHJK) calculate, and not a measure of the respect, status, or treatment of women in general. Landes may be right that the position of women is a good indicator of growth, even if the frictions that CT calculate are not much different in the OECD than in other regions. The position of women in society may well be an indicator of development (economic or otherwise) that is simply not captured in statistics on labor force participation or rates of entrepreneurship. But even leaving aside Landes’ point, the CT results indicate a significant amount of money left on the table because of limitations on women’s participation in economic life.

# Describing the Decline of Capital per Worker

NOTE: The Growth Economics Blog has moved sites. Click here to find this post at the new site.

The last post I did on the composition of productivity growth documented that recently we appear to be using productivity to reduce our capital/worker, as opposed to increasing the growth of output per worker. The BLS measure of ${K/L}$ is actually shrinking in 2011-2013. That is an anomaly in the post-war era, and seems worth digging into further. Here is some more detail on what is driving the negative growth in ${K/L}$.

• Let me start with a correction. I said in the last post that the BLS was including residential capital in their calculation of ${K}$, but that imputed income from owner-occupied housing was not included in ${Y}$, and that seemed strange. The BLS includes tenant-occupied residential capital in their calculation of ${K}$, and tenant-occupied rents as part of their measure of ${Y}$. They exclude owner-occupied residential housing from ${K}$, and imputed owner-occupied rents from ${Y}$. In short, it seems kosher.

• The decline in ${K/L}$ in the last few years is a function of ${L}$ growing faster than ${K}$, but ${K}$ is still growing. The figure below shows the separate growth rates of both ${K}$ and ${L}$ over the last 20 years.

The growth in ${L}$ is relatively large compared to ${K}$. Why is ${L}$ growth so large? This is a composite measure created by the BLS that measures hours worked, and is weighted by worker type (education, etc..). So it is quite possible to have very strong growth in ${L}$ because hours worked of those employed are higher, even though the absolute number of workers is not growing rapidly. Regardless, ${K/L}$ is falling because growth in ${K}$ is relatively slow. But it is not negative.

• Is the slow growth in ${K}$ caused by any particular type of capital? The BLS has separate measures of equipment, structures (think warehouses), intellectual property (think software), land, rental housing, and inventories. We can look and see which, if any, of these are particularly responsible for the slow growth in ${K}$. What I’ve plotted here is the weighted growth rate of each category of capital. The weighting is their share in total capital income, which is how the BLS weights them to add up total capital growth. This makes the different colors comparable in how they influenced the growth of ${K}$ in a given year.

Looking over the last 4-5 years, there was clearly shrinking inventories (grayish/green) and land (red) during the recession. Since then, there has been negative growth in rental housing capital (yellow) over the last 4 years, but this is a really small effect on aggregate ${K}$ growth.

The rest of the categories are growing. But if you compare them to pre-2007 rates, they are all growing slowly. Equipment grew at about 1.8% per year, for example, in 2011-2013, but at 2.6% per year prior to 2007. Structures grew at 0.6% per year 2011-2013, but 1.5% prior to 2007. IP grew at 2.9% 2011-2013, and 5.2% prior to 2007. Rental housing shrinks at 0.6% 2011-2013, and grew at 1.1% prior to 2007. Inventories and land growth rates are roughly similar in the pre-Great Recession and post-Great Recession periods.

The overall decline in ${K/L}$ is thus not driven by any one single category of capital. Even the reduction in rental housing stock is not really that meaningful in absolute size, and it never was that big of a contributor to ${K}$ growth to begin with. This is a broad-based decline in capital growth rates.

What that indicates about the source of this change, I don’t know. I have to think harder on that. It certainly seems to indicate a secular change in investment behavior, though, rather than reallocation away from some category and into another. So explanations that build on a common drop in savings/investment rates are likely to be successful here.

• Because I love you all, I extracted the BLS aggregate labor input data from a PDF, to see what was going on. The figure shows that the BLS labor input measure (the blue bars) contracts sharply in 2008/09, and then has grown at a relatively normal rate of about 2.5% per year since then. This is driven almost entirely by changes in the growth rate of hours (red bars). The growth rate of labor “composition” (green bars) is basically consistently positive over this whole period, but at a low rate of growth. Composition is capturing the quality of labor; think education levels.

In 2011-2013 you can see that the labor input is growing at really robust rates compared to the historical series. This is the strong ${L}$ growth that, combined with the slow growth in ${K}$, is part of the slow growth in ${K/L}$. Why does it appear that labor input is growing so robustly in the BLS data? This is private business sector data only, excluding the government, which is a huge employer and has not been expanding employment much. So the private business sector labor input has been growing robustly, even though the labor input at the national level may not be growing as fast.

• The labor data and capital data seem to indicate that this is some kind of broad slow-down in investment in capital goods, and not some temporary adjustment by one type of capital. This drop occurs exactly when the Great Recession ends, so it seems that the changing financial conditions since then (ZIRP? Credit tightness?) may be responsible, as opposed to something like demographics. If it was demographics, why did all of the sudden after the GR did people decide to stop investing? Did all the Boomers get old all at once?

Whatever the cause, let me just remind everyone that there is no a priori reason that the decline in ${K/L}$ is a bad thing. A perfectly reasonable response to higher productivity is to reduce the use of inputs. But it an an anomaly, and it seems unlikely that everyone decided all at once that they’d like to shed inputs rather than increase output. Whether it has a detrimental long-run effect on growth is not something I can say given the data I’ve got.

# The Changing Composition of Productivity Growth

NOTE: The Growth Economics Blog has moved sites. Click here to find this post at the new site.

After the post I did recently on profit shares and productivity calculations, I’ve been picking around the BLS, OECD, and Penn World Tables methodologies for calculating productivity growth. This has generated several interesting facts. Interesting in the sense that they raise even more questions than I had starting out. Today’s post is just one of those things that I dug up,and will throw out there in case anyone has some ideas about how to explain this.

The BLS provides a measure of private business-sector multi-factor productivity (MFP). “Multi-factor productivity” is what I’d call “total factor productivity” (TFP), but to be consistent I’ll refer to it as MFP here. Because the BLS is working only with information on private business sector output and inputs, they can do more detailed work building up capital stocks and labor inputs. The cost is that they exclude the government (all labor, no capital) and housing services (all capital, no labor) from their measures of output. So the BLS productivity number isn’t going to line up exactly with a measure of productivity based on aggrete GDP, capital, and labor stocks.

That caveat aside – and that caveat may be part of the explanation for the interesting fact I outline below – here’s the BLS series on MFP growth over the long and short run. I apologize for the x-axis in these – it was hard to get Stata to format these into a readable font size.

The basic story is familiar. MFP growth was relatively high from 1960. MFP growth has been relatively slow in the last 8 years, and I’d guess that when we have final numbers for 2014 and 2015 they’ll look similar. A decade of relatively low productivity growth.

Why?

What I’m going to work through here is not a causal explanation, but simply an accounting one. But it may be a useful accounting exercise just because it highlights that the composition of productivity growth in the last decade, and in particular for the last few years, has been different than in the past.

To get started, we need to establish how exactly you measure MFP growth. We can write growth in multi-factor productivity (MFP) as the difference between growth in output per worker and growth in inputs per worker,

$\displaystyle g_{MFP} = g_{Y/L} - \alpha g_{K/L}. \ \ \ \ \ (1)$

By itself, this is pretty straightforward. If output per worker has a high growth rate, but inputs per worker has a low growth rate, then it must be that MFP is growing quickly. We are getting more output per worker even though we aren’t adding lots of inputs per worker.

• ${\alpha}$ is the weight on inputs (${K}$) in the production function, which we are assuming is Cobb-Douglas. If ${\alpha}$ were zero, then inputs like ${K}$ don’t matter at all, and all growth in output per worker is, by definition, driven by growth in MFP. The size of ${\alpha}$ influences how much the growth rate of MFP depends on the growth rate of inputs per worker.
• If ${g_{K/L}<0}$, then notice this adds to MFP growth. If we have some growth in output per worker, ${g_{Y/L}}$, but we used fewer inputs to get it, then by implication it must be that MFP was growing very quickly.

Look at what happened to ${g_{K/L}}$ over the last few years. The figure below is the growth rate of ${K/L}$ year-to-year, from 1996 until now. You can see that we have this atypical shrinking of capital per worker in this period.

If you extend the series out to 1961, you get a similar message. It is pretty atypical for ${K/L}$ to shrink, and unprecendented in the post-war era for it to shrink 4 years in a row.

Flip over to look at ${\alpha}$. Here, I have to dip in and remind everyone that this weight is not something that we can observe. We can infer it from capital’s share of costs. One reason working with the BLS data is nice is that they specifically report capital’s share of costs, not just capital’s share of output (that’s a different question for a different post). Take a look at what happens to ${\alpha}$ in the last few years.

There is a clear, completely out of the ordinary, surge in capital’s share of costs in the last few years. Thus the ${\alpha}$ that goes into the calculation of MFP growth is rising. This means that whatever is happening to input per worker is getting amplified in it’s effect on MFP growth.

Combine those two facts: ${g_{K/L}<0}$ and ${\alpha}$ rising. What do you get? You get a distinct positive effect on MFP growth. The composition of MFP growth is different than it used to be.

What we’ve got going on in the last few years is that MFP growth reflects our economy using fewer inputs to produce the same output, rather than producing more output using our existing inputs. You can see the difference in these figures. I’ve plotted ${g_{Y/L}}$ (blue bars) and ${\alpha g_{K/L}}$ (red bars) for each year. The difference between these bars is MFP growth.

Up until about 2005, we generally had high input per worker growth. MFP growth allowed us to use inputs more efficiently, and we took advantage of that by using our increasing inputs to increase output by a lot. In the last few years, though,we have taken advantage of MFP growth by shedding inputs while increasing output only a little. Those red bars below zero from 2009-2013 all imply positive MFP growth.

There is nothing inherently right or wrong about this change. But it is different. A good question is whether this is something that represents a temporary change, or whether we’ve entered on a long-run path towards lower and lower input use while output per worker only grows slowly.

From a pure welfare perspective, there is nothing to say that lowering input use makes us worse off. We have to provide fewer inputs, which is nice. But an economy that is shedding inputs rather than expanding output sure seems like a different animal. What does it imply for asset prices, for example, if we are actively letting capital stocks run down?

It is one of those asset stocks that may play a role in explaining what is going on here, by the way. Remember that caveat I made above. The BLS excludes housing services from it’s measure of output, and by housing services I mean the implicit flow of rents that home-owners receive. However, the BLS does, according to their documentation, include residential capital as part of their measure of ${K}$. The decline in housing investment since 2006/07 is going to actively drag down ${K}$, perhaps so much that it explains most of the ${g_{K/L}<0}$ – I can’t find the detailed breakdown from the BLS to be sure.

If the decline in housing stock is responsible for ${g_{K/L}<0}$, then it is implicitly responsible for a large part of the measured MFP growth that we have enjoyed in the last few years. Will that continue? It’s hard to think of a decline in the housing stock as a permanent state of affairs, so it may be a temporary deviation.

As an aside, this could imply that measured MFP growth in the early 2000’s may have been lower because of the run-up of housing capital in that period.

Regardless, it seems odd that the BLS uses residential capital in their calculation of ${K}$, while excluding housing services from their calculation of ${Y}$. I’d love to see some kind of alternative series of MFP growth where residential capital is excluded from ${K}$.

But if the change in the nature of MFP growth is true regardless of how we treat residential capital, then there is something very odd going on. Remember, I didn’t make any causal claim, solely an accounting claim. The composition of MFP growth has changed demonstrably, and now reflects declining input use per worker. Could it represent a change in the kind of technological change that we pursue or are exposed to? Are we now inventing things to eliminate the need for inputs, where before we used to invent things that made inputs more valuable? If yes, that represents a real change from several decades (and probably even longer) of productivity growth.

# Tyler, Noah, and Bob walk into a Chinese bar…

NOTE: The Growth Economics Blog has moved sites. Click here to find this post at the new site.

I know that in internet-time I’m light-years behind this discussion, but Tyler Cowen recently put up a post questioning whether Chinese growth could be explained by Solow catch-up growth, and Noah Smith had a reply that said, “Yes, it could”. I just wanted to drop in on that to generally agree with Noah, and to indulge in some quibbles.

Tyler says that

It seems obvious to many people that Chinese growth is Solow-like catch-up growth, as the country was applying already-introduced technologies to its development.

and Noah rightly says that this isn’t what Solow-like catch-up growth is about.

Solow catch-up growth (convergence) is just about capital investment. That’s the convergence mechanism. And that mechanism says that if you are well below your potential, you’ll grow really fast as you accumulate capital rapidly. So the Solow story for China is that there was a profound shift(s) starting in the late 1970’s, early 1980’s that created a much higher potential level of output. That generates really rapid growth.

Does 10% growth make sense as being due to convergence? We can use my handy convergence-growth calculating equation from earlier posts to figure this out. In this case, Tyler was talking about aggregate GDP growth, so in what follows, ${y}$ represents GDP.

$\displaystyle Growth = \frac{y_{t+1}-y_t}{y_t} = (1+g)\left[\lambda \frac{y^{\ast}_t}{y_t} + (1-\lambda)\right] - 1. \ \ \ \ \ (1)$

The term ${\lambda}$ is the convergence parameter, which dictates how fast a country closes the gap between actual GDP (${y_t}$) and potential GDP (${y^{\ast}}$). The rate ${g}$ is the steady state growth rate of aggregate output.

${g}$ might be something like 3-4% for China, the combination of about 2% growth in output per capita, along with something like 1-2% population growth. The convergence term ${\lambda}$ is around 0.02. We know that Chinese growth was around 10% per year for a while (not any longer). So what does ${y^{\ast}}$ have to be relative to existing output to generate 10% growth? Turns out that you need to have

$\displaystyle \frac{y^{\ast}_t}{y_t} = 4.4 \ \ \ \ \ (2)$

to get there. That is, starting in 1980-ish, you need Chinese potential GDP to be 4.4 times as high as actual GDP. If that happened, then growth would be 10%, at least for a while.

Is that reasonable? I don’t know for sure. It’s really a statement about how inefficient the Maoist system was, rather than a statment about how high potential GDP could be. GDP per capita in China was only about $220 (US 2005 dollars) in 1980. That’s really, really, poor. A 4.4 fold increase only implies that potential GDP per capita was$880 (US 2005 dollars) in 1980. We’re not talking about a change in potential that is ludicrous. There is a good reason to think that standard Solow-convergence effects could explain Chinese growth.

But not entirely. One issue with this Solow-convergence explanation is that growth should not have stayed at 10% for very long after the reforms. That is, the Solow model says that you close part of the gap between actual and potential GDP every year, so the growth rate should slow down until it hits ${g}$. That happens pretty fast.

After 10 years of convergence – about 1990 – China’s growth rate should have been about 6.7%, and it was lower in the early 90’s than in the 1980s. But after 20 years – about 2000 – China’s growth rate should have been down to 5.3%. Yet Chinese GDP growth has been somewhere between 8-10% since 2000, depending on how you want to average growth rates, and what data source you believe.

So why didn’t Chinese growth slow down as fast as the Solow model would predict? That requires us to think of potential GDP, ${y^{\ast}}$, taking even further jumps up over time. Somewhere in the time frame of 1995-2000, another jump in potential GDP took place in China, which then allowed growth to remain high at 8-10% until now. And now, we see growth in China starting to slow down, as we’d expect in the Solow convergence story.

I think I would take Tyler’s post as being about the source of that additional “jump” in potential GDP that kept growth up around 8-10%. It may be that China had some kind of special ability to absorb foreign technology (perhaps just it’s size?). But then again, in the late 1990’s, China actively negotiated for WTO accession, which took place in 2001. Hong Kong also reverted to Chinese control in 1997. Both could have created big boosts to potential GDP.

We do not necessarily need to think of some kind of special Chinese ability to absorb or adapt technology to explain it’s fast growth. Solow convergence effects get us most of the way there. Whatever happened in the 1990’s may reflect some unique Chinese ability to absorb technology, but I’d be wary of going down that route until I exhausted the ability of open trade and Hong Kong to explain the jump in potential.

Okay, last quibble. In Noah’s post, he said that we’d expect Chinese capital per worker to level off as they get close to potential GDP. No, it wouldn’t! The growth of capital per worker will slow down, yes, but will settle down to a rate about equal to the growth rate of output per worker. The growth rate of capital per worker won’t reach zero, if the Solow model is at all right about what is happening.

# More on the Effect of Social Policy on Innovation and Growth

NOTE: The Growth Economics Blog has moved sites. Click here to find this post at the new site.

My last post was on the false trade-off between social policies and growth. In particular, I took a shot at an essay by Michael Strain, but his essay is simply a good example of an argument that gets made very often: social policies will lower growth. I said this was wrong, and a number of responses I got questioned my reasoning. So this post is meant to spell out the logic more clearly, and point out why precisely I think that Strain’s argument (and others like it) is flawed. Consider this an uber-response to comments on the site, some e-mails I got, and the discussion I had with my neighbor (who probably won’t read this, but whatever).

First, we need to be clear that we have to distinguish the effect of social policies on innovation from the effect of social policies on growth in GDP. They need not be identical, which I’ll get too in more detail below. So to begin, let’s think about the effect of these policies on innovation, which is what Strain and others acknowledge is the source of improvements in living standards.

I’m an economist, so I think of the flow of innovations as responding to incentives. When the value of coming up with a new idea goes up, we get more new ideas. Simple as that.

What’s the value of an idea? That depends on the flow of net profits that it generates. The profits of owning an idea are

$\displaystyle \pi = (1-\tau)(\mu-1)wQ \ \ \ \ \ (1)$

where ${\tau}$ is the “tax rate”, and this tax rate is meant to capture both formal taxation and any other frictions that limit profits (e.g. regulations).

${\mu>1}$ is the markup that the owner can charge over marginal cost for their idea. ${(\mu-1)>0}$ is therefore the difference between price and marginal cost. The more indispensable your idea, the higher the markup you can charge. For instance, there are big markups on many heart medications because your demand for them is pretty inelastic. The markup on a new type of LCD TV is very low because there are lots and lots of almost identical substitutes.

${w}$ is the marginal cost, which here we can think of as the wage rate you pay to run the business that produces the good or service based on your idea. ${Q}$ is the number of “units” of the idea that you sell (pills or TVs or whatever). Together, ${wQ}$ represents “market size”. If the wage rate or quantity purchased go up, then your absolute profits rise. The effect of ${Q}$ makes sense, but why do profits rise when wages rise? Because of the markup. If your costs are higher, the price you can charge is higher too.

The profits from an idea are the incentive to innovate. So anything that makes ${\pi}$ goes up should generate more ideas. My issue with Michael Strain’s article, and others like it, is that when they think of “progressive social policy”, they think only of the cost ${\tau}$ of funding that policy. So there is a direct trade-off between funding these social policies and innovation (and possibly growth).

My point is that those social policies have direct, positive, effects on market size, ${w}$ and ${Q}$. Profits should be written as

$\displaystyle \pi = (1-\tau)(\mu-1)w(\tau)Q(\tau). \ \ \ \ \ (2)$

If we raise ${\tau}$ to pay for social policies that educate people or raise their living standards, there is a positive effect on market size. The wage goes up, either directly because we have higher-skilled workers, or indirectly because they have some kind of viable outside option.

Further, the size of the market increases because people appear to have non-homothetic preferences. That is, they buy a few essential goods no matter what. They only spend money on other goods once those essentials are dealt with. With non-homothetic preferences, the distribution of income matters a lot to the size of the market for your idea. If lots of people are very poor, or if the cost of essentials is very high, then they have little or no money to spend on your idea, and ${Q}$ is small. If you provide them with more income or make essentials cheaper, they have more income to spend on your idea, and ${Q}$ goes up.

To be clear, I think that the positive effects of ${\tau}$ on ${w}$ and ${Q}$ outweigh the direct negative effect of ${\tau}$. That’s what I mean when I say progressive social policies are good for innovation, and why I said that there is not a direct trade-off between funding social policies and innovation (and possibly growth).

That doesn’t mean that funding social policies is always positive. There is a Laffer-curve type relationship here, and if ${\tau}$ were too high the incentives to innovate would go to zero and that would be bad. But the innovation-maximizing level of ${\tau}$ is not zero.

As an aside – there are plenty of costs that comparies or innovators have to pay that would have no direct benefit for wages or ${Q}$. Think of useless red tape regulations. I’m all for getting rid of those. But getting rid of red tape is not something that requires us to sacrifice social policies. It does not cost anything to remove red tape.

But wait, there’s more. The speed of innovation in an economy – ${g_A}$ – is going to be governed by something like the following process

$\displaystyle g_A = \frac{R(\pi,H)}{A^{\phi}} \ \ \ \ \ (3)$

where ${R(\pi,H)}$ is a function that describes how many resources we put towards innovation, like how much time is spent doing R&D, or how much is spent on labs. That allocation depends on profits, ${\pi}$, which dictate how lucrative it is to come up with an innovation. But it also depends on the stock of resources available to do innovation, and here I think specifically of the amount of human capital available, ${H}$. Social policies can not only raise ${\pi}$ indirectly, but can directly act to raise ${H}$. Education spending is the obvious case here. But policies that lower uncertainty (income support, health care coverage) allow people to either undertake risky innovation projects themselves, or work for those who are pursuing those projects, because they don’t have to worry about what happens if the risk fails to pay off. Social policy can act directly to raise ${H}$. Which means that social policies can, for two reasons, raise the growth rate of innovation, ${g_A}$. Even if the effect on profits is zero, innovation can still rise because the stock of innovators has been increased.

Aside: The term on the bottom, ${A^{\phi}}$, is a term that captures the effect of the level of innovation, ${A}$, on the growth rate, ${g_A}$. If you are of the Chad Jones semi-endogenous growth opinion, then ${\phi>0}$, and this means that the growth rate will end up pinned down in the long run, and social policies will have a positive level effect on innovation. If you are of the opinion that ${\phi=0}$, then policies have permanent effects on the growth rate. It isn’t important for my purposes which of those is right.

What does this mean for GDP growth? I said in the prior post that it isn’t clear that GDP growth is the right metric. We really want to encourage innovation, not necessarily GDP growth. Why? Because growth in GDP, ${g_Y}$, is just

$\displaystyle g_Y = g_A + g_{Inputs}. \ \ \ \ \ (4)$

If we raise ${g_A}$, then what happens to ${g_Y}$ depends on what happens to ${g_{Inputs}}$. We might imagine that ${g_{Inputs}}$ remains constant, so ${g_Y}$ rises when ${g_A}$ goes up. But there is no reason we couldn’t have ${g_{Inputs}}$ fall while ${g_Y}$ remains constant. What if we take advantage of innovations to only work 30 hours a week? Then GDP growth could remain the same, ${g_{Inputs}}$ falls, and yet we’re all better off. Or if innovation allows us to dis-invest in some capital (parking garages?) while still enjoying transportation services (self-driving cars?). GDP may not grow any faster, but we’d be better off by using fewer inputs to produce the same GDP growth rate.

The point is that the right metric for evaluating the effect of social policies is not GDP growth per se, it is the rate of innovation. It is ${g_A}$ that dictates the pace of living standard increases, not ${g_Y}$. In lots and lots of models, we presume that growth in inputs is invariable, but that doesn’t mean it is how the world actually works.

Strain completely ignores the possible positive impacts of social policies on the growth of innovation, and that is what I’m saying is wrong about his essay. We can have a reasonable discussion about what the right level of ${\tau}$ is to maximize the growth rate of innovation, but that answer is not mechanically zero. There is no strict trade-off between innovation growth and social policies. Which means there is even less of a strict trade-off between GDP growth and social policies.

# Progressive Social Goals and Economic Growth

NOTE: The Growth Economics Blog has moved sites. Click here to find this post at the new site.

Someone pointed me towards this Washington Post essay by Michael Strain, of the AEI, on “Why we need growth more than we need democratic socialism“. It’s something of a rebuttal to Bernie Sanders’ positive statements regarding the social democratic systems that are in place in Denmark, Sweden, and several other countries. Strain takes issue with this, suggesting that we cannot purse the progressive social goals that are part of this social democratic system because we would sacrifice economic growth, and that would be bad. The TL;DR version of my post is that Strain is wrong. Wrong about the nature of economic growth, and wrong about the effect of progressive social policies on growth.

To start, Strain engages in some ham-fisted hippie-punching. Except he’s punching Swedes and Danes, so I guess he’s Scandanavian-punching?

Yes, yes, while it didn’t turn out so well under Stalin and Mao, something of the dem-soc variety may work for the good people of Scandinavia.

This is a breathtakingly ridiculous connection to draw. Strain is lumping Stalin’s USSR and Mao’s China together with post-war Denmark and Sweden. These are economies and political systems fundamentally different in kind, not in degree. I’m fairly sure calling Stalin or Mao’s system “democratic” would be a stretch. “Socialist” is also wrong for their economies. I know, it’s confusing, they used “socialist” right there in the name of the USSR! Sometimes labels are wrong. Chilean sea bass ain’t Chilean or a bass.

The USSR and China were committed communist countries, with a lack of private ownership, and centrally planned economies. In contrast, Denmark and Sweden have free, fair elections, a free press, freedom of assembly, freedom of religion, and do not deliberately let giant swathes of their population starve. Oh, they also happen to have marginal tax rates of about 50% at the top, free health care, child care, and education. Which, sure, makes them exactly like the USSR or China under Mao.

Now that we’ve dealt with that, we can actually look at what Strain has to say about growth.

For one, demographic pressures are pushing the potential growth rate of the economy below its historic average. The nation is headed for a period of naturally slower growth, which means that we need to take pro-growth policies even more seriously now than in previous decades.

Why? If the economy is naturally slowing down due to demographic changes, then what precisely is the issue I am worried about? No one gets utility from the growth rate. If we have people getting utility from retiring, and the growth rate is lower, then explain why I should care. Is this an argument that the demographic pressures will put a greater burden on those still working to pay for Social Security and Medicare? Then we should be having an argument about the optimal tax rate, or benefits, or eligibility ages.

True, public policy cannot deliver 6 percent growth, no matter how great a deal Trump makes with the economy. But policy can get rid of a bad regulation (or 20) here, encourage people to participate in the workforce there, make savings and investment a bit more attractive, make entrepreneurship and innovation a bit more common, make the government’s footprint in the economy a bit smaller — on the margin, a range of policies can increase the rate of economic growth. And when you add up all those marginal changes, good policy can make the economy grow at a non-trivially faster rate.

If by “non-trivially” you mean by about 0.2% faster a year, then I might believe that. But notice that Strain tries to sound reasonable (“public policy cannot deliver 6 percent growth”), but never bothers to try and say how much pro-growth policies can actually raise the growth rate. Does he think pro-growth policies – and what precisely are those, by the way – mean growth of 3%, 4%, or 5%? The answer is that it would be a little over 2%, just a smidge higher than growth is today. And that is assuming that Strain’s non-specified growth policies actually have an incredibly massive effect of potential GDP. There is no magic fairy dust to make growth accelerate dramatically. It’s even plausible that pro-growth policies that raise the profit share of output to induce innovation would lower measured productivity growth simply due to how we calculate that productivity.

And the measured growth rate of GDP doesn’t even matter, really. What matters is the availability of innovations that improve living standards. Strain almost gets this right in the next quote:

Over the past two centuries, growth has increased living standards in the West unimaginably quickly. Many more babies survive to adulthood. Many more adults survive to old age. Many more people can be fed, clothed and housed. Much of the world enjoys significant quantities of leisure time. Much of the world can carve out decades of their lives for education, skill development and the moral formation and enlightenment that come with it. Growth has enabled this. Let’s keep growing.

No, innovation has enabled this. So let’s keep innovating. The fact that all these welfare-improving innovations contributed to a rise in measured GDP to rise does not mean that causing measured GDP to rise will raise welfare. Innovations can allow us to produce more with the same inputs (raising GDP) or allow us to produce the same amount with fewer inputs (possibly lowering GDP). Strain confuses measured GDP growth with innovation. They are not the same. What we want, as he says, is policies that foster innovations that improve human living standards. Whether they also happen to raise GDP growth rates is a side issue. Think of it this way. If the BEA came out tomorrow and said they had discovered that they had mistakenly understated GDP by \$1 trillion a year since 1948 due to a calculation error, would your living standard be instantly higher? No. But if tomorrow someone announces that they’ve invented a 60% efficient solar panel, that would change your living standards.

Growth facilitates the flourishing life. By creating a dynamic environment characterized by increasing opportunity, growth gives the young the opportunity to dream and to strive. And it gives the rest of us the ability to apply our skills and talents as we see fit, to contribute to society, to provide for our families. A growing economy allows individuals to increase their living standards, facilitating economic and social mobility.

Oh, come on. This is vacuous drivel. Replace every instance of the word “growth” here with the word “liberty”, or “dignity”, or “patriotism”, or “human rights”, or “unicorns” and this paragraph is true. Replace it with “universal free college” and you’ve got Bernie Sanders’ stump speech. This paragraph is the equivalent of Gary Danielson saying “LSU would be helped by a touchdown on this drive.” It’s meaningless.

If we are interested in raising living standards for everyone, which Strain is saying he is for, then we need to promote the introduction and diffusion of innovations. Is there some either/or choice between promoting innovation and progressive social policies? Do we have to sacrifice innovation if we pursue progressive programs? No and no.

What we know about innovation is that it depends on market size and the stock of people who can do innovation. See any of the econosphere’s recent run of posts on Paul Romer’s original work on endogenous growth. By pursuing the progressive policies Strain is so wary of, we can positively affect both market size and the stock of innovators.

First, the policies let relatively poor families access the existing set of innovations, and the diffusion of these welfare-improving innovations accelerates. Think of Whole Foods. Whole Foods is an innovation in access to relatively healthy food. (Yes, some specific items are just overpriced bulls***, and some specific items are not healthier than other brands, but in general Whole Foods and stores like it make a healthier diet more accessible. I’m married to a nutritionist, I’ve had this conversation more than once.) Many poor families eat unhealthy food because it is cheap. Those progressive social programs give these families the purchasing power to access the innovation that is healthier food. Innovations are useless if no one can afford them.

Second, the incentives for innovation are based on the size of the market. Practically, this means that innovation is geared towards producing ideas for people with money. A concentration of income into a small group means innovation is skewed towards that group. Hello, Viagra. If we’re lucky, perhaps the innovations being sold to that small group have some spillovers in producing innovations that are available for the mass of people. But if you expand purchasing power of the mass of people, this raises the incentives to innovate directly for this mass of people. Rather than hoping we get lucky, the market will actively work to produce innovations that improve welfare of most people, not simply the small group with the most purchasing power. Under certain conditions, a concentration of income actively slows down innovation because there simply aren’t enough people with sufficient purchasing power to make it worth innovating (see Murphy, Shleifer, Vishny).

Finally, those progressive social policies that Strain is worried about expand the stock of people who can do innovation. Kids in poor families who receive income support do better in school. Support for vocational school or college raises the supply of people who are capable of innovation. Alleviating income uncertainty through health insurance and income support means that individuals with risky business ideas can pursue them without fearing they won’t be able to take their kids to the doctor.

So it is important to focus on another of the many fruits of economic growth: It provides the money to make targeted spending programs possible. In a nation as rich as ours, no one should fall too far — no one should go hungry, everyone should have a baseline level of education, no one should be bankrupted by a catastrophic medical event. Slow growth impedes progress toward social goals that require targeted spending, both because of the political climate it fosters and because those goals, even only those that are advisable, are expensive.

This, again, presumes that there is an either/or choice between growth and progressive social policies.

Hungry people are less productive. Uneducated people are less productive. People bankrupted by catastrophic medical events are not productive. Reaching those social goals is as much a contributor to growth, as growth is to achieving those social goals. These social goals are not a black hole into which we dump money. They have ramifications – positive ones – on our economy. If Strain wants the U.S. economy to grow faster, then invest in it. Invest in it with better educational opportunities, the elimination of extreme poverty, and the alleviation of the uncertainty associated with medical care. Educated, fed, securely healthy people are productive innovators.

# Chad Jones on Paul Romer’s Contribution to Growth Theory

NOTE: The Growth Economics Blog has moved sites. Click here to find this post at the new site.

I’m very pleased to host a guest post by Chad Jones celebrating the 25th anniversary of Romer (1990). Enjoy!

If you add one computer, you make one worker more productive. If you add a new idea — think of the the computer code for the first spreadsheet or word processor or even the internet itself — you can make any number of workers more productive.

The essential contribution of Romer (1990) is its clear understanding of the economics of ideas and how the discovery of new ideas lies at the heart of economic growth. The history behind that paper is fascinating. Romer had been working on growth for around a decade. The words in his 1983 dissertation and in Romer (1986) grapple with the topic and suggest that knowledge and ideas are important to growth. And of course at some level, everyone knew that this must be true (and there is an earlier literature containing these words). However, what Romer didn’t yet have — and what no research had yet fully appreciated — was the precise nature of how this statement comes to be true. By 1990, though, Romer had it, and it is truly beautiful. One piece of evidence that he at last understood growth deeply is that the first two sections of the 1990 paper are written very clearly, almost entirely in text and with the minimum required math serving as the light switch that illuminates a previously dark room.

Here is the key insight: ideas are different from essentially every other good in that they are nonrival. Standard goods in classical economics are rivalrous: my use of a pencil or a seat on an airplane or an accountant means that you cannot use that pencil, airplane seat, or accountant at the same time. This rivalry underlies the scarcity that is at the heart of most of economics and gives rise to the Fundamental Welfare Theorems of Economics.

Ideas, in contrast, are nonrival: my use of the Pythagorean theorem does not in any way mean there is less of the theorem available for you to use simultaneously. Ideas are not depleted by use, and it is technologically feasible for any number of people to use an idea simultaneously once it has been invented.

As an example, consider oral rehydration therapy, one of Romer’s favorite examples. Until recently, millions of children died of diarrhea in developing countries. Part of the problem is that parents, seeing a child with diarrhea, would withdraw fluids. Dehydration would set in, and the child would die. Oral rehydration therapy is an idea: dissolving a few minerals, salts, and a little sugar in water in just the right proportions produces a life-saving solution that rehydrates children and saves their lives. Once this idea was discovered, it could be used to save any number of children every year — the idea (the chemical formula) does not become increasingly scarce as more people use it.

How does the nonrivalry of ideas explain economic growth? The key is that nonrivalry gives rise to increasing returns to scale. The standard replication argument is a fundamental justification for constant returns to scale in production. If we wish to double the production of computers from a factory, one feasible way to do it is to build an equivalent factory across the street and populate it with equivalent workers, materials, and so on. That is, we replicate the factory exactly. This means that production with rivalrous goods is, at least as a useful benchmark, a constant returns process.

What Romer appreciated and stressed is that the nonrivalry of ideas is an integral part of this replication argument: firms do not need to reinvent the idea for a computer each time a new computer factory is built. Instead, the same idea — the detailed set of instructions for how to make a computer — can be used in the new factory, or indeed in any number of factories, because it is nonrivalrous. Since there are constant returns to scale in the rivalrous inputs (the factory, workers, and materials), there are therefore increasing returns to the rivalrous inputs and ideas taken together: if you double the rivalrous inputs and the quality or quantity of the ideas, you will more than double total production.

Once you’ve got increasing returns, growth follows naturally. Output per person then depends on the total stock of knowledge; the stock doesn’t need to be divided up among all the people in the economy. Contrast this with capital in a Solow model. If you add one computer, you make one worker more productive. If you add a new idea — think of the the computer code for the first spreadsheet or word processor or even the internet itself — you can make any number of workers more productive. With nonrivalry, growth in income per person is tied to growth in the total stock of ideas — an aggregate — not to growth in ideas per person.

It is very easy to get growth in an aggregate in any model, even in Solow, because of population growth. More autoworkers mean that more cars are produced. In Solow, this cannot sustain per capita growth because we need growth in cars per autoworker. But in Romer, this is not the case: more researchers produce more ideas, which makes everyone better off because of nonrivalry. Over long periods of recent history — twenty-five years, one hundred years, or even one thousand years — the world is characterized by enormous growth in the total stock of ideas and by enormous growth in the number of people making them. According to Romer’s insight, this is what sustains exponential growth in the long run.