# Perfect Competition is Bad for Growth

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You have to be careful in confusing “free markets” with “perfect competition”. By “free markets”, I think we mean free entry for new firms and/or products into the market. We don’t want restrictions on innovators from bringing their ideas to the market. We typically *assume* that free entry exists in economic models, but one thing that holds back development may be the absence of this free entry (think red tape and bad institutions).

But we don’t want “perfect competition” even if we do want “free markets”. One of the counter-intuitive things that comes up in growth courses is that perfect competition is not conducive to rapid growth. The story here involves a few steps

• Growth is ultimately driven by innovation
• People will innovate if they have incentives to innovate
• The incentive to innovate comes from economic profits
• Profits only exist when the innovator or firm has some market power

Innovators and/or firms need to charge a price greater than marginal cost to earn profits, otherwise there will be no incentive to innovate, and ultimately no growth. If you allow competitors to copy innovations they will drive the price down to marginal cost, eliminating profits and incentives for innovation. We want free entry of new firms with market power, but not free entry of imitators who produce perfect competition.

But perfect competition does maximize the combined consumer and producer surplus from a given product. So there is a tension here. Perfect competition maximizes the output of *existing* products, but minimizes the output from *potential* products. Think of it this way, if we decided that we had all the types of goods and services that we could ever want, then we’d want to enforce perfect competition. We would nullify every patent, and let competition take over to maximize the output of those existing goods and services. Nullifying patents (or any other kind of intellectual property) would crush the incentives to innovate, and we’d never get any new products.

This means that it is not obvious what the right policy is for intellectual property rights and/or competition in general. It depends on your long-run perspective. You can trade off long-run growth for a higher level of current output by canceling intellectual property rights. Or you can trade off current output for a higher long-run growth rate by enforcing property rights strictly, and probably instituting even stronger ones.

There is no *right* answer here, because it depends on your time preferences. But extreme answers are probably unlikely to be optimal for anyone. Strict perfect competition – allowing imitators to ensure P=MC – isn’t good because it prevents us from getting new products. Super strong market power – limiting each good to being produced by a perpetual monopolist, say – would shrink the availability of every existing product, even if it makes the incentive to innovate huge.

# Measuring Misallocation across Firms

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One of the most active area of research in macro development (let’s not call it growth economics, I guess) is on misallocations. This is the concept that a major explanation for why some countries are rich, while others are poor, is that rich countries do a good job of allocating factors of production in an efficient manner across firms (or sectors, if you like). Poor countries do a bad job of this, so that unproductive firms use a lot of labor and capital up, while high productivity firms are too small.

One of the baseline papers in this area is by Diego Restuccia and Richard Rogerson, who showed that you could theoretically generate big losses to aggregate measures of productivity if you introduced firm-level distortions that acted like subsidies to unproductive firms and taxes on produtive firms. This demonstrated the possible effects of misallocation. A paper by Hsieh and Klenow (HK) took this idea seriously, and applied the basic logic to data on firms from China, India and the U.S. to see how big of an effect misallocations actually have.

We just went over this paper in my grad class this week, and so I took some time to get more deeply into the paper. The one flaw in the paper, from my perspective, was that it ran backwards. That is, HK start with a detailed model of firm-level activity and then roll this up to find the aggregate implications. Except that I think you can get the intuition of their paper much more easily by thinking about how you measure the aggregate implications, and then asking yourself how you can get the requisite firm-level data to make the aggregate calculation. So let me give you my take on the HK paper, and how to understand what they are doing. If you’re seriously interested in studying growth and development, this is a paper you’ll need to think about at some point, and perhaps this will help you out.

This is dense with math and quite long. You were warned.

What do HK want to do? They want to compare the actual measured level of TFP in sector ${s}$, ${TFP_s}$, to a hypothetical level of TFP in sector ${s}$, ${TFP^{\ast}_s}$, that we would measure if we allocated all factors efficiently between firms.

Let’s start by asking how we can measure ${TFP_s}$ given observable data on firms. This is

$\displaystyle TFP_s = \frac{Y_s}{K_s^{\alpha}L_s^{1-\alpha}}, \ \ \ \ \ (1)$

which is just measuring ${TFP_s}$ for a sector as a Solow residual. ${TFP_s}$ is not a pure measure of “technology”, it is a measure of residual productivity, capturing everything that influences how much output (${Y_s}$) we can get from a given bundle of inputs (${K_s^{\alpha}L_s^{1-\alpha}}$). It includes not just the physical productivity of individual firms in this sector, but also the efficiency of the distribution of the factors across those firms.

Now, the issue is that we cannot measure ${Y_s}$ directly. For a sector, this is some kind of measure of real output (e.g. units of goods), but there is no data on that. The data we have is on revenues of firms within the sector (e.g. dollars of goods sold). So what HK are going to do is use this revenue data, and then make some assumptions about how firms set prices to try and back out the real output measure. It’s actually easier to see in the math. First, just write ${TFP_s}$ as

$\displaystyle TFP_s =\frac{P_s Y_s}{K_s^{\alpha}L_s^{1-\alpha}}\frac{1}{P_s} = \overline{TFPR}_s \frac{1}{P_s} \ \ \ \ \ (2)$

which just multiplies and divides by the price index for sector ${s}$. The first fraction is revenue productivity, or ${\overline{TFPR}_s}$, of sector ${s}$. This is a residual measure as well, but measures how produtive sector ${s}$ is at producing dollars, rather than at producing units of goods. The good thing about ${TFPR_s}$ is that we can calculate this from the data. Take the revenues of all the firms in sector ${s}$, and that is equal to total revenues ${P_s Y_s}$. We can add up the reported capital stocks across all firms, and labor forces across all firms, and get ${K_s}$ and ${L_s}$, respectively. We can find a value for ${\alpha}$ based on the size of wage payments relative revenues (which should be close to ${1-\alpha}$). So all this is conceptually measurable.

The second fraction is one over the price index ${P_s}$. We do not have data on this price index, because we don’t know the individual prices of each firms output. So here is where the assumptions regarding firm behavior come in. HK assume a monopolistically competitive structure for firms within each sector. This means that each firm has monopoly power over producing its own brand of good, but people are willing to substitute between those different brands. As long as the brands aren’t perfectly substitutable, then each firm can charge a price a little over the marginal cost of production. We’re going to leave aside the micro-economics of that structure for the time being. For now, just trust me that if these firms are monopolistically competitive, then the price index can be written as

$\displaystyle P_s = \left(\sum_i P_i^{1-\sigma} \right)^{1/(1-\sigma)} \ \ \ \ \ (3)$

where ${P_i}$ are the individual prices from each firm, and ${\sigma}$ is the elasticity of substitution between different firms goods.

Didn’t I just say that we do not observe those individual firm prices? Yes, I did. But we don’t need to observe them. For any individual firm, we can also think of revenue productivity as opposed to their physical productivity, denoted ${A_i}$. That is, we can write

$\displaystyle TFPR_i = P_i A_i. \ \ \ \ \ (4)$

The firms productivity at producing dollars (${TFPR_i}$) is the price they can charge (${P_i}$) times their physical productivity (${A_i}$). We can re-arrange this to be

$\displaystyle P_i = \frac{TFPR_i}{A_i}. \ \ \ \ \ (5)$

Put this expression for firm-level prices into the price index ${P_s}$ we found above. You get

$\displaystyle P_s = \left(\sum_i \left[\frac{TFPR_i}{A_i}\right]^{1-\sigma} \right)^{1/(1-\sigma)} \ \ \ \ \ (6)$

which depends only on firm-level measure of ${TFPR_i}$ and physical productivity ${A_i}$. We no longer need prices.

For the sector level ${TFP_s}$, we now have

$\displaystyle TFP_s = \overline{TFPR}_s \frac{1}{P_s} = \frac{\overline{TFPR}_s}{\left(\sum_i \left[\frac{TFPR_i}{A_i}\right]^{1-\sigma} \right)^{1/(1-\sigma)}}. \ \ \ \ \ (7)$

At this point, there is just some slog of algebra to get to the following

$\displaystyle TFP_s = \left(\sum_i \left[A_i \frac{\overline{TFPR}_s}{TFPR_i}\right]^{\sigma-1} \right)^{1/(\sigma-1)}. \ \ \ \ \ (8)$

If you’re following along at home, just note that the exponents involving ${\sigma}$ flipped sign, and that can hang you up on the algebra if you’re not careful.

Okay, so now I have this description of how to measure ${TFP_s}$. I need information on four things. (1) Firm-level physical productivities, ${A_i}$, (2) sector-level revenue productivity, ${\overline{TFPR}_s}$, (3) firm-level revenue productivities, ${TFPR_i}$, and (4) a value for ${\sigma}$. Of these, we can appeal to the literature and assume a value of ${\sigma}$, say something like a value of 5, which implies goods are fairly substitutable. We can measure sector-level and firm-level revenue productivities directly from the firm-level data we have. The one big piece of information we don’t have is ${A_i}$, the physical productivity of each firm.

Before describing how we’re going to find ${A_i}$, just consider this measurement of ${TFP_s}$ for a moment. What this equation says is that ${TFP_s}$ is a weighted sum of the individual firm level physical productivity terms, ${A_i}$. That makes some sense. Physical productivity of a sector must depend on the productivity of the firms in that sector.

Mechanically, ${TFP_s}$ is a concave function of all the stuff in the parentheses, given that ${1/(\sigma-1)}$ is less than one. Meaning that ${TFP_s}$ goes up as the values in the summation rise, but at a decreasing rate. More importantly, for what HK are doing, this implies that the greater the variation in the individual firm-level terms of the summation, the lower is ${TFP_s}$. That is, you’d rather have two firms that have similar productivity levels than one firm with a really big productivity level and one firm with a really small one. Why? Because we have imperfect substitution between the output of the firms. Which means that we’d like to consume goods in somewhat rigid proportions (think Leontief perfect complements). For example, I really like to consume one pair of pants and one shirt at the same time. If the pants factory is really, really productive, then I can lots of pants for really cheap. If the shirt factory is really un-productivie, I can only get a few shirts for a high price. To consume pants/shirts in the desired 1:1 ratio I will end up having to shift factors away from the pants factor and towards the shirt factory. This lowers my sector level productivity.

There is nothing that HK can or will do about variation in ${A_i}$ across firms. That is taken as a given. Some firms are more productive than others. But what they are interested in is the variation driven by the ${TFPR_i}$ terms. Here, we just have the extra funkiness that the summation depends on these inversely. So a firm with a really high ${TFPR_i}$ is like having a really physically unproductive firm. Why? Think in terms of the prices that firms charge for their goods. A high ${TFPR_i}$ means that firms are charging a relatively high price compared to the rest of the sector. Similarly, a firm with a really low ${A_i}$ (like our shirt factory above) would also be charging a relatively high price compared to the rest of the sector. So having variation in ${TFPR_i}$ across firms is like having variation in ${A_i}$, and this variation lowers ${TFP_s}$.

However, as HK point out, if markets are operating efficiently then there should be no variation in ${TFPR_i}$ across firms. While a high ${TFPR_i}$ is similar to a low ${A_i}$ in its effect on ${TFP_s}$, the high ${TFPR_i}$ arises for a fundamentally different reason. The only reason a firm would have a high ${TFPR_i}$ compared to the rest of the sector is if it faced higher input costs and/or higher taxes on revenues than other firms. In other words, firms would only be charging more than expected if they had higher costs than expected or were able to keep less of their revenue.

In the absence of different input costs and/or different taxes on revenues, then we’d expect all firms in the sector to have identical ${TFPR_i}$. Because if they didn’t, then firms with high ${TFPR_i}$ could bid away factors of production from low ${TFPR_i}$ firms. But as high ${TFPR_i}$ firms get bigger and produce more, the price they can charge will get driven down (and vice versa for low ${TFPR_i}$ firms), and eventually the ${TFPR_i}$ terms should all equate.

For HK, then, the level of ${TFP_s}$ that you could get if all factors were allocated efficiently (meaning that firms didn’t face differential input costs or revenue taxes) is one where ${TFPR_i = \overline{TFPR}_s}$ for all firms. Meaning that

$\displaystyle TFP^{\ast}_s = \left(\sum_i A_i^{\sigma-1} \right)^{1/(\sigma-1)}. \ \ \ \ \ (9)$

So what HK do is calculate both ${TFP^{\ast}_s}$ and ${TFP_s}$ (as above), and compare.

To do this, I already mentioned that the one piece of data we are missing is the ${A_i}$ terms. We need to know the actual physical productivity of firms. How do we get that, since we cannot measure physical output at the firm level? HK’s assumption about market structure will allow us to figure that out. So hold on to the results of ${TFP_s}$ and ${TFP^{\ast}_s}$ for a moment, and let’s talk about firms. For those of you comfortable with monopolistic competition models using CES aggregators, this is just textbook stuff. I’m going to present it without lots of derivations, but you can check my work if you want.

For each firm, we assume the production function is

$\displaystyle Y_i = A_i K_i^{\alpha}L_i^{1-\alpha} \ \ \ \ \ (10)$

and we’d like to back out ${A_i}$ as

$\displaystyle A_i = \frac{Y_i}{K_i^{\alpha}L_i^{1-\alpha}} \ \ \ \ \ (11)$

but we don’t know the value of ${Y_i}$. So we’ll back it out from revenue data.

Given that the elasticity of substitution across firms goods is ${\sigma}$, and all firms goods are weighted the same in the utility function (or final goods production function), then the demand curve facing each firm is

$\displaystyle P_i = Y_i^{(\sigma-1)/\sigma - 1} X_s \ \ \ \ \ (12)$

where ${X_s}$ is a demand shifter that depends on the amount of the other goods consumed/produced. We going to end up carrying this term around with us, but it’s exact derivation isn’t necessary for anything. Total revenues of the firm are just

$\displaystyle (P_i Y_i) = Y_i^{(\sigma-1)/\sigma} X_s. \ \ \ \ \ (13)$

Solve this for ${Y_i}$, leaving ${(P_i Y_i)}$ together as revenues. This gives you

$\displaystyle Y_i = \left(\frac{P_i Y_i}{X_s}\right)^{\sigma/(\sigma-1)}. \ \ \ \ \ (14)$

Plug this in our equation for ${A_i}$ to get

$\displaystyle A_i = \frac{1}{X_s^{\sigma/(\sigma-1)}}\frac{\left(P_i Y_i\right)^{\sigma/(\sigma-1)}}{K_i^{\alpha}L_i^{1-\alpha}}. \ \ \ \ \ (15)$

This last expression gives us a way to back out ${A_i}$ from observable data. We know revenues, ${P_i Y_i}$, capital, ${K_i}$, and labor, ${L_i}$. The only issue is this ${X_s}$ thing. But ${X_s}$ is identical for each firm – it’s a sector-wide demand term – so we don’t need to know it. It just scales up or down all the firms in a sector. Both ${TFP_s}$ and ${TFP^{\ast}_s}$ will be proportional to ${X_s}$, so when comparing them ${X_s}$ will just cancel out. We don’t need to measure it.

What is our ${A_i}$ measure picking up? Well, under the assumption that firms in fact face a demand curve like we described, then ${A_i}$ is picking up their physical productivity. If physical ouput, ${Y_i}$, goes up then so will revenues, ${P_i Y_i}$. But not proportionally, as with more output the firm will charge a lower price. Remember, the pants factory has to get people to buy all those extra pants, even though they kind of don’t want them because there aren’t many shirts around. So the price falls. Taking revenues to the ${\sigma/(\sigma-1)}$ power captures that effect.

Where are we? We now have a firm-level measure of ${A_i}$, and we can measure it from observable data on revenues, capital stocks, and labor forces at the firm level. This allows us to measure both actual ${TFP_s}$, and the hypothetical ${TFP^{\ast}_s}$ when each firm faces identical factor costs and revenues taxes. HK compare these two measures of TFP, and find that in China ${TFP^{\ast}_s}$ is about 86-115% higher than ${TFP_s}$, or that output would nearly double if firms all faced the same factor costs and revenue taxes. In India, the gain is on the order of 100-120%, and for the U.S. the gain is something like 30-43%. So substantial increases all the way around, but much larger in the developing countries. Hence HK conclude that misallocations – meaning firms facing different costs and/or taxes and hence having different ${TFPR_i}$ – could be an important explanation for why some places are rich and some are poor. Poor countries presumably do a poor job (perhaps through explicit policies or implicit frictions) in allocating resources efficiently between firms, and low-productivity firms use too many inputs.

* A note on wedges * For those of you who know this paper, you’ll notice I haven’t said a word about “wedges”, which are the things that generate differences in factor costs or revenues for firms. That’s because from a purely computational standpoint, you don’t need to introduce them to get HK’s results. It’s sufficient just to measure the ${TFPR_i}$ levels. If you wanted to play around with removing just the factor cost wedges or just the revenue wedges, you would then need to incorporate those explicitly. That would require you to follow through on the firms profit maximization problem and solve for an explicit expression for ${TFPR_i}$. In short, that will give you this:

$\displaystyle TFPR_i = \frac{\sigma}{\sigma-1} MC_s \frac{(1+\tau_{Ki})^{\alpha}}{1-\tau_{Yi}}. \ \ \ \ \ (16)$

The first fraction, ${\sigma/(\sigma-1)}$, is the markup charged over marginal cost by the firm. As the elasticity of substitution is assumed to be constant, this markup is identical for each firm, so generates no variation in ${TFPR_i}$. The second term, ${MC_s}$, is the marginal cost of a bundle of inputs (capital and labor). The final fraction are the “wedges”. ${(1+\tau_{Ki})}$ captures the additional cost (or subsidy if ${\tau_{Ki}<0}$) of a unit of capital to the firm relative to other firms. ${(1-\tau_{Yi})}$ captures the revenue wedge (think of a sales tax or subsidy) for a firm relative to other firms. If either of those ${\tau}$ terms are not equal to zero, then ${TFPR_i}$ will deviate from the efficient level.

* A note on multiple sectors * HK do this for all manufacturing sectors. That’s not a big change. Do what I said for each separate sector. Assume that each sector has a constant share of total expenditure (as in a Cobb-Douglas utility function). Then

$\displaystyle \frac{TFP^{\ast}_{all}}{TFP_{all}} = \left(\frac{TFP^{\ast}_1}{TFP_1}\right)^{\theta_1} \times \left(\frac{TFP^{\ast}_2}{TFP_2}\right)^{\theta_2} \times ... \ \ \ \ \ (17)$

where ${\theta_s}$ is the expenditure share of sector ${s}$.

# Economic Dynamism and Productivity Growth

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There’s a paper out in the latest Journal of Economic Perspectives by Decker, Haltiwanger, Jarmin, and Miranda (DHJM) on “The Role of Entrepreneurship in US Job Creation and Economic Dynamism“. They document, in more detail than an earlier Brookings report I talked about recently, that the proportion of firms that are “young” has declined over the last 30 years.

DHJM use the number of young firms – those less than 5 years old – as a proxy for entrepreneurship. And therefore the conclusion is that entrepreneurship has declined over the last 30 years. You can see this in their figure 4, below. In 1982, for example, roughly 50 percent of all firms were less than 5 years old, while by 2011 only about 35 percent of firms were under 5 years old. Similarly, the share of total employment in young firms fell from about 18 percent in 1982 to about 13 percent in 2011.

Perhaps most important, the share of job creation from young firms has declined over the same period. In the early 1980’s, young firms were responsible for about 40 percent of all new jobs, while by 2011 this was down to about 33 percent. In sum, there are fewer young firms, they employ fewer people, and they create fewer jobs today than they did 30 years ago.

Where is this decline coming from? DHJM show in their figure 5 that for manufacturing, the share of employment in young firms has declined very slightly over the same period, and was never very large to begin with. In contrast, in the service sector the proportion of jobs in young firms was over 25 percent in 1982, and now is around 15 percent. The shift of economic activity from manufacturing to service firms both raised the share of employment in young firms (because of the higher rate in services) and lowered the share of employment in young firms (because of the downward trend within services). On net, the downward trent in services won out, and overall the proportion of jobs in young firms has dropped.

There’s nothing to dispute in these numbers, and I don’t think DHJM have done anything to misrepresent what is going on. But the big question is: did this decline in the proportion of young firms lower productivity growth? The short answer is, I don’t see any evidence that it did. [Update 8/1/14: Just to be clear, DHJM are not claiming that it does lower productivity growth. This is a question I have given their data.]

Consider the figure from Fernald’s (2014) recent paper on productivity. It shows the trend of labor productivity from the late 70’s until today. There is no secular slowdown in productivity growth between 1982 and 2011. Productivity growth from 2003-2011 is just as fast as it was in the pre-1995 period. As Fernald points out, 1995-2003 is an outlier, probably associated with the IT revolution. Therefore, if the decline in the number of young firms is bad for productivity, it hasn’t been so bad that it shows up in any aggregate numbers over the last 30 years.

So what does the decline in young firms mean? One plausible explanation is mentioned by DHJM, which is the advance of “big box” or national stores relative to mom-and-pop operations. In 1982, if you saw a niche for a coffee shop in your town, you would open up a coffee shop. Now, a Starbucks was there three years ago. National retailers have gotten very good at identifying lucrative retail locations, and are able to move more quickly than individuals.

Note that this doesn’t imply that national retailers are any more productive than mom-and-pop stores (although they do pay higher wages than small retail establishments). If they were, then we should have seen some kind of long-run boost to productivity from 1982-2011. We don’t. My guess is that it just means national retailers have a distinct advantage in identifying and opening lucrative retail locations compared to individuals.

Of course, it could be that the loss of productivity from the drop in young firms is offset almost perfectly by the increase in productivity from having national firms more readily identify and take advantage of new retail opportunities. If so, okay. From a productivity standpoint, though, it’s a wash, and does not necessarily have any implications for future productivity growth.

Does it imply anything about employment? Well, as DHJM document in their figure 3, there has been a decline in the job creation and job destruction rates from 1980-2011 (don’t get too worked up about the big dip in the trend line for job creation – HP filters are sensitive to the end points you use). Both rates are declining, meaning that there is less worker churn in the economy, which is consistent with less churn in firms, which is what fewer young firms implies. Again, note that the trend of decline in job creation and destruction occurs over the 80’s, 90’s, and 2000’s consistently, which covers periods in which the employment to population ratio rose pretty consistently before leveling off in the last decade.

The fact that the proportion of young firms in the U.S. is declining doesn’t seem to be anything to get worked up about, and it doesn’t imply that U.S. productivity or employment are doomed to stagnate in the future. If there is some “optimal” amount of young firms to have, we have no idea what it is, and we could as easily be over that amount as under it. For now, I’m mentally filing the decline in young firms alongside the secular shift away from manufacturing and towards services. It’s one of those structural changes that occur as economies grow. But evidence from either (a) longer time periods in the U.S., or (b) across countries, could easily change my mind.

# David, Hopenhayn, and Venkateswaran on Misallocation

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Next installment of the NBER growth session recap. The second paper was by Joel David (USC), Hugo Hopenhayn (USC), and Venky Venkateswaran (NYU Stern). Their jumping off point is the apparent mis-allocation of factors of production across firms. The standard of comparison here is Hsieh and Klenow (2009), who find that mis-allocation of factors is lowering output by something like 50% in China and India.

So why are factors mis-allocated? David, Hopenhayn, and Venkateswaran propose that this is partly due to informational issues. That is, firms themselves do not know ex-ante (when they are deciding on how much capital or labor to hire) exactly what their productivity will be ex-post. Hence they make mistakes, and part of what we observe in the ex-post data are these mistakes. So rather than explicit taxes, subsidies, or other frictions, poor information about future productivity drives mis-allocation.

To get some quantitative feel for how important this is, they focus on listed companies. These have the advantage of an extra source of information on future prospects, the stock price. There is a neat little information extraction problem they show solves nicely that allows them to use the observed productivity of firms and the stock prices to back out the degree of uncertainty firms have ex-ante. With this, they suggest that in the U.S. roughly 40% of variation in productivity firms is a surprise to firms. In India, about 80% of variation in productivity is a surprise. Because of the poorer information, Indian firms make bigger mistakes on average, and so there is more ex-post mis-allocation.

It’s a clever explanation for mis-allocation, and is one of those stories that in some sense has to be true to some extent. There is no way firms have perfect information on future productivity (or demand, which is essentially the same thing in these models). The question is how big of an effect it is, and they suggest it’s pretty sizable.

One question that came up in my head afterwards was whether the degree of uncertainty is related to the level of returns. That is, Indian firms have a lot of uncertainty (risk) in their productivity draws, apparently. Is that high risk associated with higher rewards? If it is, then we can’t really say that this is mis-allocation, per se. Firms are making optimal decisions ex-ante, and there happens to be a willingness to tolerate risk in the economy. If, on the other hand, high risk is associated with low rewards, then there really is a mis-allocation in the sense that they are making uninformed decisions.

# Should Developing Countries Try to Create a Business Elite?

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La Porta and Shleifer released a working paper recently on the informal economy (which I believe is a draft for a future issue of the Journal of Economic Perspectives, but I could be wrong). They give an overview of what we currently know about the size and characteristics of informal firms.

The thing that stuck out most after reading this was the strong evidence that big, formal firms do not grow out of small, informal ones. In other words, small informal firms tend to stay small and informal. Big formal firms are created as formal firms, and while they may start relatively small, they generally start out bigger than most informal firms will ever be. While institutions/regulations may make incent some people to run informal firms, these regulations are not preventing informal firms from becoming formal. There is essentially no transition in any country of informal firms into formal ones.

This is important because big formal firms are much, much more productive (per worker, or in terms of total factor productivity) than small informal ones. So big formal firms are the source of nearly all the significant gains in aggregate productivity within countries. You don’t see any highly developed nations dominated by small, informal firms. And fostering the growth of big formal firms is different (according the La Porta and Shleifer) from fostering the growth of small informal ones.

A similar sentiment can be found in a recent column by Daniel Altman, titled “Please Don’t Teach this Woman to Fish“. As the tag line to the article says: poor countries have too many entrepreneurs and too few factory workers. Promoting small (almost universally informal) firms can improve living standards slightly, but does not lead to the massive productivity gains that generate big gains in GDP per capita.

So what does it take to promote big formal firm growth? La Porta and Shleifer suggest that a big constraint is highly trained managers and/or entrepreneurs that can handle running a large firm. Improving the average level of education is less important, in this case, than extending the tail of the education distribution. Nearly all big formal firms are run by college-educated managers, so developing countries need to generate more of those kind of people. Getting everyone to go from 6 to 7 years of education won’t do it – it would be better to leave nearly everyone at 6 years, but add a few extra people with 16 years or 18 years of education.

Yes, you also need an institutional/regulatory structure that makes it low-cost for those college-educated managers to open and operate firms, obviously. But apparently having a good regulatory structure won’t buy you anything without the stable of potential managers.

So here’s a question(s) related to education policy in developing countries. Would they be better off spending their budget providing scholarships for students to got to college (perhaps abroad) and/or paying for high-achieving students to intern or work abroad at large firms for a while. If you could get GE to hire 100 students into their managerial program, would that ultimately be better for development than achieving universal secondary schooling? Is it worth it to the whole country to create an elite cadre of managers who own/run large formal firms?

# (Mis)Allocation and Growth Reading List

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Back with another set of readings for my grad class this fall. As before, a PDF and BibTeX file of the papers I teach in this area are located under the Papers page.

One of the more active areas in growth right now is studying the allocation of factors of production. Think of productivity growth being decomposed into two sources: “within” productivity growth as each individual firm becomes more efficient, and “between” productivity growth as we shift factors of production from low-productivity firms into high-productivity ones.

A first question is: how much observed growth comes from “within” versus “between” sources? This requires looking at productivity at the firm-level data. That is not easy, because it is not something one can count like workers or machines. We have to back it out from estimations of firm’s production functions. So a lot of growth economists now find themselves hanging around the offices of their industrial organization colleagues, trying to look cool, and hoping to bum some data or get some help with Wooldridge’s (2009) technique for estimating firm-level production functions. Once you’ve got these estimates, doing the “within” and “between” calculations is relatively straightforward.

A different question is: how much potential for “between” productivity growth is there? In other words, how much higher would productivity be if I could rearrange factors of production until the marginal revenue product was equal across all firms? To answer these kinds of questions, you have to actually provide some kind of model of firm behavior so you can figure out how output will respond at each different firm when you start messing around.

For a really simple example, let a firms production be ${Y = A L}$, where ${A}$ is productivity and ${L}$ is labor. The firm has some market power, and the inverse demand curve is ${P = Y^{-\epsilon}}$, which says that if the firm produces more ${Y}$, the price it can charge for that output must fall. ${\epsilon}$ is a measure of how much market power the firm has. If ${\epsilon = 0}$, the ${P = 1}$, and the firm is a price-taker. As ${\epsilon}$ goes to one, their market power gets stronger. The firm hires workers at the wage ${w}$.

Growth economists favorite salad: the wedge

Profits for the firm are ${\pi = (1+\tau)P Y - wL}$. This extra term ${\tau}$ is often called a wedge. It’s like a subsidy (if ${\tau>0}$) or tax (if ${\tau<0}$) facing the firm, although in most applications the wedge is not specifically associated with any tax or subsidy. It just is a stand-in for any kind of additional markup (or markdown) a firm can charge for its product. If I maximize profits for this firm, and solve for their choice of labor to use, I get

$\displaystyle L^{\ast} = \left(\frac{(1+\tau)(1-\epsilon)A^{1-\epsilon}}{w} \right)^{1/\epsilon}. \ \ \ \ \ (1)$

As you’d expect, if productivity ${A}$ goes up, the firm will be larger. However, note that if the wedge is positive, then this expands the firm relative to how big it would be if ${\tau = 0}$. The wedge is acting like a shift up in the demand curve, and so the firm produces more, which requires it to hire more workers. If the wedge is negative, then this is like a shift down in the demand curve, and the firm will be smaller. The wedge means that firms can be large even if they are not productive, or small even if they are productive.

What papers then do is to remove the wedge from each firm, and recalculate the level of ${L^{\ast}}$ for each firm. Once you know that, roll up the output produced across all firms to find out aggregate production without the wedges. Compare this to the observed output level (i.e. with wedges). This tells you how much higher output could be if these wedges didn’t exist. This is the potential “between” productivity growth in a country. And this potential between productivity growth is intriguing, because it doesn’t necessarily mean I have to adopt a new technology or acquire new capital or workers, I just need to reshuffle the capital and workers I have to more efficient firms.

Looking at these calculations across countries, you can talk about whether India is poor relative to the U.S. because it has bigger “wedges” than the U.S., for example. The implication of most of the papers on the reading list is that yes, the wedges in poor countries are bigger/worse. That is, in India and other poor countries, there are lots of frictions keep the marginal revenue product of labor (or capital) from being equal in different firms, and so lots of scope for “between” productivity growth. Those frictions cost India a lot of foregone output. In the U.S., the frictions are smaller (but certainly still exist).

A newer wave of research in this area involves more serious investigations of what these wedges actually represent. One possibility is that high-productivity firms would like to expand, but are limited in their ability to do so by an inability to find financing. In this case, financial sector sophistication is a key to improving allocations. Another likely suspect is the regulatory regime: entry costs, exit costs, and size-dependent rules for firms, for example. A nice concept for future research (hint, hint grad students) is to measure the impact of particular reforms on the measure of potential “between” growth. If the reform effectively opens up entry, or allows easier exit, or eliminates state-owned firms, etc.. etc… then the scope for “between” growth should fall over time as the economy gets more efficient and the wedges get smaller.

# Declining U.S. Dynamism?

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

There’s a research report from Brookings that’s making it’s way around the inter-tubes. The title is “Declining Business Dynamism in the Untied States“, by Ian Hathaway and Robert Litan. The upshot is that business dynamism is declining. The firm entry rate (i.e. the number of firms less than one year old as a proportion of all firms) was about 15% in 1978, was about 11% in 2006, and is currently less than 8%. This trend is taken as a troubling sign of reduced dynamism. What dynamism exactly is supposed to mean isn’t clear, but on the assumption that it is synonymous with firm entry, then it is declining. There is some hand-waving about how this portends lower growth in the future.

But it isn’t immediately obvious that the declining rate of entry is a problem. I’m suspect that this is a measure that seems like it would be better if it went up, but that isn’t necessarily true. Imagine if the entry rate went to 100%; would it be good that literally every firm in the U.S. was less than 1 year old?

Their appendix figure A1 shows the actual number of firm entries per year. This held at roughly 500,000 new firms per year from 1978 to 2007, and then there is a deep plunge to 400,000 by 2010 before recovering slightly in 2011. So it is not that the U.S. is coming up with fewer new companies. Even in the midst of the worst economic downturn since the Great Depression (or 1981 depending on what rows your boat) the U.S. added 400,000 new companies. At the same time, the absolute number of exits has increased from about 300,000 a year in the early 1980’s to about 450,000 over the last few years. Because we have more firms now (remember all those entries?), this means the exit rate has held steady at about 9% of firms exiting each year.

So, does this imply some kind of loss of dynamism in the U.S. economy? As I said, it’s not obvious. One of the things I think is a pretty robust empirical fact is that productivity (labor productivity or total factor productivity) varies by a lot across firms in the U.S. and other countries (see Syverson, 2011). The stylized fact I have in my head is that the 90th percentile manufacturing firm in the U.S. is roughly 2 times more productive than the 10th percentile firm. A large portion of productivity growth comes from reallocation of inputs from low-productivity firms to high-productivity firms. Some of this reallocation takes place by having low-productivity firms exit and having high-productivity firms enter. But I don’t know that the research is conclusive that entry is the primary source of this reallocation – shifting inputs to existing high-productivity firms is a big part of productivity gains.

Foster, Haltiwanger, and Syverson (2008) is one of the best studies I know of these reallocation effects because they are able to distinguish physical productivity (number of widgets produced) from revenue productivity (number of dollars produced). What they find is that entry alone accounts for 14% of revenue productivity growth from 1977 to 1997. Entry accounts for 24% of physical productivity growth in the same period. A sizeable portion, but reallocation between existing firms and productivity growth within existing firms account for the remaining productivity growth observed.

However, FHS are looking only at very specific industries: coffee, boxes, bread, gasoline, sugar, plywood, and a few others. Basically, industries with very homogenous outputs that can be measured easily (e.g. gallons of gasoline). Their results may under- or over-state the true effect of entry on overall productivity growth in the U.S.. As they note, though, their study actually shows much higher effects of entry on productivity than prior work because of their separate data on revenue physical productivity. Their firms also have entry and exit rates (22% and 19%, respectively) well above the average for the U.S. as a whole, and if entry is very important for dynamism, then shouldn’t these industries show the strongest possible role of entry?

Even if entry does account for a sizeable portion of productivity growth, the Brookings report isn’t saying that entry has fallen to zero. If the entry and exit rate flatten out at, say, 9% each, then this means that every year 9% of all firms go out of business, and that number is exactly replaced by a entirely new group of firms. The total number of firms will remain constant, but each firm would have an average lifespan of about 11-12 years. Do we care if the total number of firms stays constant, so long as there is turnover?

There isn’t any reason to believe that a growing number of firms is necessarily good, especially as we move more and more to producing goods and services that scale easily. To be more clear, it makes sense to believe that the number of cement firms or bakeries increases proportionately with population, as these goods don’t transport well and so meeting demand requires new locations (and possibly new firms). But just because we have more people doesn’t mean we need another Microsoft (you could argue we don’t need the one we have already). So the fact that the growth rate of the number of firms is slowing down doesn’t necessarily bother me. It may just indicate a change in the nature of products we produce, or represent better screening by lenders/backers/VC firms.

I could of course be horribly wrong, and we’ll all be living in the woods in three years. I, at this point, am not planning on buying extra canned goods.