Another round on the “elephant curve”

A report from the Resolution Foundation has touched off another round of analysis of Branko Milanovic‘s work on global income growth. Much of what they discuss can be found elsewhere. Including here. But I want to focus for a moment on their claim that

we find that the weak figures for the mature economies as a whole are driven by Japan (reflecting in part its two ‘lost decades’ of growth post-bubble, but primarily due to likely flawed data) and by Eastern European states (with large falls in incomes following the collapse of the Soviet Union after 1988).

Not to suggest that these things did not occur; rather, I find weak the argument that they drive the results. In the figure below, I have estimated the “quasi-nonanonymous” GIC. We see there the growth in real per-capita income among country-deciles sorted by their 1988 income percentiles— with and without China. I have not “reshuffled” incomes when including China, so it is as if Chinese growth had been comparable to its 1988 income peers.

In other words, excess growth in China accounts for nearly all of the fast growth in the 20-70th percentiles. The growth which remains to that half of the world distribution is quite modest— about 1.7 percent per capita annually. True, the more developed 70-99th percentiles seem to have grown somewhat more slowly (1.3 percent per capita annually); even including Japan and Eastern Europe as done here, the severe stagnation which the “elephant” misleadingly suggested does not really exist.

Of course, this latter point was already made clear in Milanovic’s work, as he reminds us.

When we do quasi non-anonymous chart with 1988 country/deciles fixed, we keep 1988 decile populations fixed. Fixed! pic.twitter.com/pdPHcxg6JQ

— Branko Milanovic (@BrankoMilan) September 14, 2016

Ultimately, there are two points:

1. The years 1988-2008 had seen considerable change in what it means to be part of the global middle class.
2. Outside China, the global 10-99th enjoyed only modest growth. To the extent those years saw stagnation among more developed economies, it extended to most of the world. Except China.

Thank Goodness I Did Not Attend GMU

So much Tyler Cowen to criticize here, but I want to focus on one point. The most relevant portion:

At time period zero, a boss hires one hundred workers, who at the time are perceived as being of roughly equal quality and thus are offered the same wage. After a few years on the job, however, some are “keepers,” while others are being paid more than their marginal products.

Because of firing aversion, they are not fired. Because of sticky nominal wages, they also do not take a pay cut. If the economy is imperfectly competitive, and times are good, this nonetheless can be a stable equilibrium.

Now let’s say a negative shock comes along: demand, supply, maybe a bit of both, as is usually the case. At some margin these workers can no longer be carried and the firing aversion of the boss is overcome and they lose their jobs. Then, a few points:

1. They’re not getting those jobs back.
2. They’re not worth a comparable wage elsewhere in many cases.
3. Per hour productivity likely will rise, even adjusting for ex ante measures of changes in worker composition.
4. Companies won’t want to pay higher wages to lure these workers out of leisure, rather they are branded as less productive than average and properly so.

(all emphasis added)

Do you see the problem here? Cowen treats marginal product as a property of the worker, so the worker is “properly” branded as less productive. Yet if all the original hires— “perceived as being of roughy equal quality”— are in fact entirely identical, then the dynamics are the same— if not the explanation. When the demand shock hits, the marginal productivity of all one hundred hires falls. All one hundred are being paid more than “their” marginal productivity. As soon as a few are fired, however, marginal productivity rises so not all one hundred are fired. Presumably, workers are fired in sufficient numbers to bring marginal productivity in line with the sticky wage. The same wage the fired workers are presumably holding out for!

The fired workers— though identical to those retained except in their new (un)employment status— are branded as less worthy just for their bad luck. The fired workers are worth just as much in that they could step in perfectly for any of the retained workers.

By passing off marginal productivity as a property of the worker, Cowen manages to blame workers for their unemployment.

A Little Confusion About Inflation

It may help to clear up a little confusion about inflation. Inflation is basically dimensionless— price over price— and does not have dimension of 1/time as suggested by Nick Rowe. Rather, inflation is an exchange rate. Instead of converting between currencies of different countries (say) at a single moment, inflation (and interest rates!) convert between different times the same nominal currency. That is, one may convert today’s dollars in today’s euros; likewise, one may convert yesterday’s dollars into today’s dollars. An inflation rate of 2 percent over the past year means that what cost \$100 last year today costs \$102. Thus \$100 last year is equivalent to \$102 today.

Where folks get a bit mixed up is, hey, that’s 2 percent per year. Doesn‘t that put time in the denominator? No. All we are saying is that we add 2 percent (compounded) in each period— in this case one year. For example, 10 percent inflation over 5 years is not 10/5=2 percent per year, because if we added to prices 2 percent per year for 10 years, we would wind up with a price level about 10.4 percent higher. ”Per year" describes the frequency of compounding at the specified rate.

But we still divide by time to compute the rate, right? We say $$ 1+\pi=\exp{\frac{\ln{\!\left({P_f}/{P_i}\right)}}{t_f-t_i}} $$ do we not? No, we do not. This is obvious shorthand. (Obvious because the dimensions do not work out.) More carefully, we may write $$ 1+\pi=\exp{\!\left[\Delta\frac{\ln{\!\left({P_f}/{P_i}\right)}}{t_f-t_i}\right]} $$ where $\Delta$ is the period of time between compoundings. Equivalently, $$ 1+\pi=\exp{\frac{\ln{\!\left({P_f}/{P_i}\right)}}{n}} $$ where $n$ is the (dimensionless) number of compoundings. That is, “year” specifies $\Delta$— with units of time.

More on the “elephant curve”

Based on feedback from my previous post, I have started a FAQ.

Moving on, I would like to make a couple points. First, the results are not terribly fragile. Previously, I used the data and code of Lakner and Milanovic to produce GICs with and without China. One interesting quirk of their approach is that quantile populations are not necessarily very even. In 1988, the 20th-25th percentile represents less than 150 million people, while the 40th-45th represents more than 275 million. While this might seem like a big problem, it is not. In Figure 1, I use a different method for binning the data. In particular, I allow country-decile groups to split across quantiles. This helps make much more uniform the population size represented by each percentile.

Figure 1: Growth Incidence With Decile Splitting

Source: Lakner and Milanovic and author’s calculations

Clearly, the story is very much the same. But these “anonymous” GICs are easy to misinterpret. With China included in the data, the incomes associated with the 75th-80th percentiles hardly budged; this does not mean that the incomes of people in the those percentiles failed to rise. Lakner and Milanovic also produce “quasi-nonanonymous” GICs which show the average income growth for the actual country-deciles represented in the 1988 quantiles. (pdf) They estimate that across the board, growth exceeded 20 percent and broke 90 percent in the middle of the income distribution.

That method is laid out in their paper, but I take a more direct approach. First, however, I estimate the 1988 and 2008 population and per-capita income for each country-decile based on the observed growth rates. Then, dividing the country-deciles into global quantiles ranked by 1988 per-capita income, I compute the aggregate per-capita growth from 1988 to 2008 treating the quantile as a single aggregate. $$ G_\mathrm{quantile} = 100\times\frac{\sum_{\in\mathrm{quantile}}{\mathrm{Pop}_{2008}\times\mathrm{Inc}_{2008}}}{\sum_{\in\mathrm{quantile}}{\mathrm{Pop}_{1988}\times\mathrm{Inc}_{1988}}}\times\frac{\sum_{\in\mathrm{quantile}}{\mathrm{Pop}_{1988}}}{\sum_{\in\mathrm{quantile}}{\mathrm{Pop}_{2008}}}-100 $$ Then, keeping the quantile definitions, I re-compute the growth without China. The resulting quasi-nonanonymous GICs are seen in Figure 2. We see that— except for the bottom decile— the results are similar to what Lakner and Milanovic.

Figure 2: Quasi-Nonanonymous Growth Incidence

Source: Lakner and Milanovic and author’s calculations

Without China, growth at the 10th-70th percentiles was quite modest— about 1.7 percent per-capita per year. This agrees with earlier analysis based on very different methods. Excluding the global top percentile, higher-income countries did not grow quite as fast— about 1.3 percent per year. Progress in more developed countries has been uneven, favoring the top incomes there. But we do not see the utter collapse of middle-class incomes a naïve reading of the anonymous GIC would suggest.

The Incredible Story of Developing Country Income Growth: Was it Just China?

To what extent has the age of globalization benefitted developing countries—and what of the poor in those countries? To what extent has such progress been driven by local policy decisions rather than a more global phenomenon? Has such development come alongside stagnation of poor and middle incomes within more developed countries and large benefited the extremely rich?

One way—however incomplete—to begin an investigation would be to look at the global “growth incidence curve” (GIC) of Lakner and Milanovic. They estimate the worldwide distributions of income in both 1988 and 2008, which allows them to answer questions such as “How does median (the 50th percentile) income change between the two years.” The GIC is sometimes referred to as the “elephant curve” for its resemblance to the beast.

Figure 1 shows the worldwide GIC as produced directly by Lakner and Milanovic’s public data and code.

Figure 1: Lakner and Milanovic Growth Incidence Curve

Source: Lakner and Milanovic

As seen in the figure, the average income representing the world’s 50-55th percentiles rose more rapidly than any other group. Entrance into the upper half of the world distribution required in 2008 some 76 percent more income—adjusted for inflation—than it did in 1988. Likewise, the average income defining the top 1% rose only 65 percent over the same period. Between, however, the distribution become much more compressed. The average income of the world’s 75th-80th percentiles in 2008 was \$3831—up only 1.3 percent from \$3782 in 1988.

Milanovic looks at this “global reshuffle of income” and finds “it would be hard to dismiss the period 1988-2008... as being one of failure.” While two decades of 2.9 percent annual growth would be reasonable enough, this appears to be much less global and much more local—driven by China’s very rapid progress. Doubtless, China’s poor represented a large fraction of the world’s poor, and growth there greatly increased their incomes. Still, it is critical to investigate how much of the reshuffle is specific to China. With a simple edit of line 12 of their code¹ we may re-run with China excluded from the data.

More on Noah Smith’s Low, Low, Standards

To review, Noah Smith asserted that poor countries “incredible progress” in the last 30 years. Challenged, he erroneously tried to make examples of Mexico and Brazil– both of which have suffered pretty substantial growth failures in the period. (He presented data which was not adjusted for inflation which made gains look much, much larger than an honest defense would permit.) He then pointed to the faster growth of 2000s. Indeed, the 2000s were in the last 30 years. But if he meant ten years then why say 30? This makes no sense, especially as growth again slowed over the last five years.

As a consequence of this spat, Smith has tried to peg me as a poverty-decline-denier, writing

[O]n Twitter, David Rosnick strongly challenged the very existence of a rapid recent drop in poverty. At first he declared that the poor-country boom was purely a China phenomenon.

Yes, I first argued that the “poor-country” boom of the last 30 years was largely China. All evidence points to just this. I am hardly the only person to point out that China can bias your thinking about worldwide trends. Branko Milanović wrote of the “ambivalent role of China in global income distribution” several months back.

But I never argued that, say, \$1/day poverty rates have not actually fallen rapidly. Smith knows this very well and is simply trolling (successfully, to judge by my reaction.) The only difference between us is that I am far less convinced that the rapid fall is as “incredible” as Smith insists.

How could I possibly think that Smith is hyperbolic when he writes things like

This is incredible— nothing short of a miracle. Nothing like this has ever happened before in recorded history.

In truth, this is a ridiculous statement. Of course it has never happened before. So long as poor countries grow and that poor people in those countries share in that growth, then it would be inevitable that fewer and fewer people would live below any threshold of absolute poverty. Believe me, I am thrilled that the percentage of people living in such poverty has come down rapidly. But would I call it a miracle? Please.

Are we supposed to be impressed that someone with income of \$0.99 per day one year now has an income of \$1.01 per day? Starvation is not determined by a bright line. Be happy that such poor people are starving a little less than before, but let us not pretend that their situations have so very much improved.

But poverty rates are falling more rapidly these days, right? Yes, the numbers do bear this out. But it is a mistake simply to infer that they are falling more rapidly because of incredible progress among poor countries. If we found incredible shared growth in poor countries (such as China) then the economy will rapidly pull large numbers of people out of poverty. But there is another important factor: if an incredible number of people live just below the poverty line, then little growth will also pull large numbers of people out of poverty. Such progress in poverty reduction would be best described as “credible.”

That is, even if China had not grown so rapidly, the fact that so large a proportion of people there lived near the poverty line meant that large reductions in poverty rates were all but a matter of time. The fact that China grew so fast for so long meant that large numbers quickly approached and then passed the threshold. So which is it? Faster growth or more people happening to live just short of the poverty line? Consider two countries with exactly the same (high) poverty rate, but one country (dark blue) happens to have more of its population near the poverty line as in Figure 1.

Figure 1: Distribution Matters for Poverty Reduction

Holding constant each country’s level of inequality (measured by the Gini), if both countries grow at the same rate, then the more equal country will pull about 75 percent more people across the poverty line. Put another way, if the more equal country grows at 2 percent, the less-equal country must grow at 3.5 percent in order to keep its poverty rate from rising above that of its neighbor. The important point here is that it takes a lot of growth to make up for not having a population already near the poverty line.

Given any reasonable distribution of world income, an unprecedented share of people would approach the poverty line. And in fact this is exactly what happened in the late 1980s.

(source: Our World In Data)

Of course, fast-growing China pulled its poor across the line much faster than other countries. No matter what Smith thinks about India’s rate of growth, there is a vast chasm between China’s reduction in its poverty rate and what India managed in the same period.

(source: Our World In Data)

So the “miracle” of accelerated poverty reduction is the result of a combination of fast-growing China and the non-China world’s modal income happening to lie close to the poverty line. If Noah Smith wants to sell it as a miracle, I guess that is fine so long as he understands it took China to turn the coincidence into a miracle. Coincidence might be the kind of stuff he considers heady, but not me.

Noah Smith has very low standards

Noah Smith made a ridiculous claim and insists that he is correct. But he does not stop there. For some reason, he chooses to blow it all up by exaggerating the differences in our positions.

To review, Smith asserted “incredible progress in poor countries” over last 30 years. Doubtless, there has been progress over the last three decades. After all, countries do generally grow. But incredible? Progress was generally more slow in comparison to, say, the 1960s and 70s. To be sure, some countries have done well. India– a Smith favorite— grew at an average annualized rate of 4.6 percent per capita between 1985 and 2015. And sure, there are a lot of poor people in India. But I do not consider this “incredibly” fast growth in comparison to 1960-80. The Penn World Tables show countries growing at least 4.6 percent per-capita per year between 1960 and 1980: Spain, Malawi, Tunisia, Portugal, Malaysia, Brazil, Greece, Thailand, Cyprus, Korea, Hong Kong, Japan, Gabon, Taiwan, Singapore, Malta, Botswana, and Romania.

Maybe every single one of these countries simply caught up following a period of poor growth yet no such claim may be made regarding India. Maybe I just have higher standards for incredulity. I find Botswana growing 8 percent per year a bit more impressive.

Smith did look at papers I suggested— which indicates that since 1980 there has slowdown in many indicators of progress across all income levels. But then he moves the goalposts, writing about per-capita GDP growth

By [CEPR’s] measure, the 2000-2010 decade exceeds or ties the supposed golden age of the 60s and 70s, for all but the top income quintile.
...
[T]he graph clearly shows that Rosnick is wrong, and the recent unprecedented progress of global poor countries is not just a China story. Case closed.

No doubt, growth has resumed for a period. And had Smith originally asserted that poor countries enjoyed a decade of growth close to that of middle-income countries in the 1960s and 1970s, I could hardly argue. But again, we are looking for “incredible” growth over three decades— not one. Twenty years of growth one percentage point below is not made-up for by a decade half a percentage point of growth above. Hardly “unprecedented” is growth in recent decades.

I argued that truly “incredible” growth over the last few decades comes from China, rather than “poor countries” in general. Yes, China has a large share of the world’s poor, but it is still not kosher to attribute to “poor countries” what may be specific to one country. Haiti’s poor can take little comfort in China’s success. Still, between 1985 and 2015, China sustained 8.6 percent per-capita growth and now produce 12 times per person than 30 years ago. Assuming the poor in China benefitted anywhere near as well as per-capita output might suggest, we are talking about tremendous gains to very large numbers of people with who had precious little. I will return to the question of poverty later.

First, however, I would like to address Smith’s complaint that CEPR’s several reports are deficient because they averaged countries rather than people. We use countries because that is the unit of observation, and we do not want to say countries generally improved performance if Chinese policymakers did something right while the IMF pushed terrible policies on the most vulnerable. Even Smith used “countries” and not “people.” Perhaps this was just a miscommunication on his part. Twitter is not always the clearest of communication channels.

But I am willing to humor Smith on this point. What happens if we weight real per-capita GDP growth by population and create a worldwide index?

Figure 1: World Growth in per-capita GDP

Sources: Penn World Tables (1950-2011), IMF World Economic Outlook (2011-) including IMF projections

Indeed! Population-weighted growth has accelerated rather than declined. However, my argument is that this is driven by growth in China, which obviously does weight strongly. Has population-weighted growth outside China accelerated?

Figure 2: World (less China) Growth in per-capita GDP

Sources: Penn World Tables (1950-2011), IMF World Economic Outlook (2011-) including IMF projections

Oops. No evidence for “incredible” growth here.

Figure 3: Without China, A Shortfall in World Growth Relative to Trend

Sources: Penn World Tables (1950-2011), IMF World Economic Outlook (2011-) including IMF projections

Yes, we see some catch-up in the 2010s– catch-up which has not as of yet continued past the period examined in CEPR’s paper on the subject. Of course, this mixes higher and lower-income countries. So maybe this is a golden age of poor-country development. Or not. But it is clear that population weights matter because of China rather than because of poor people. Which is nothing new.

It seems to me that not only is Smith willing to stand by data which in no way supports his case but he is easily impressed as well. More on that in the next post.

Noah Smith Shuts His Ears and Cries “La La La”

Recently, Noah Smith made reference to “the incredible progress in poor countries in the last 30 years.” Clearly, Noah has a low bar for incredulity. Based on a variety of measures, countries generally progressed more slowly in recent decades than they had previously. (pdf) (pdf) I challenged Noah on this point, suggesting that he was unduly influenced by China‘s truly extraordinary growth. For example, average annual per-capita GDP growth in Latin America over 2000-10 was little more than half that of 1960-80– clearly better than the 1980’s, which saw growth one-tenth that of the previous two decades.

Nor did growth accelerate in the last five years— averaging 1.1 percent. Progress, to be sure, but the last 30 years saw 1.2 percent annual average growth in per-capita GDP. Smith’s reference to 30 years of incredible growth certainly does not apply there.

So it was extra provocative when Smith cited Mexico and Brazil as examples of places where “living standards have improved a lot.” Mexico grew 38 percent per-capita in the 30 years between 1985 and 2015— a whopping 1.1 percent per year. Brazil grew even more slowly at 0.8 percent per year. When called on it, Smith wrote

@ViscidKonrad @DeanBaker13 Heyyy, look at this, Mexico is almost twice as rich as in 2000! https://t.co/4RJM6mI9fu pic.twitter.com/GjOgv7NEsv

— Noah Smith (@Noahpinion) May 29, 2016

Doubled! Now, the data here shows 85 percent growth from 1999-2013, which seemingly would have resulted in a 16-year doubling from 1999 to 2015 if the trend in this data continued.

How can we reconcile Mexico‘s slow growth 1985-2015 and much more rapid growth between 1999-2013? Does Smith believe Mexico collapsed by a quarter between 1985 and 1999? Actual growth was 6.6 percent— slow, but not that bad. The answer was pretty obvious to those of us who have looked at the data in any depth. Smith’s numbers are in current dollars. Adjusting for inflation, Mexico grew 28 percent from 2000-15. That is a far, far cry from Smith’s 100 percent.

Worse, Smith cited Mexico in support of progress over 30 years— not 15. Over the previous 15, Mexico grew all of 8 percent— a mere half of one percent per year. Brazil grew even more slowly, averaging only 0.8 percent per year from 1985-2015. Smith simply does not know what he is talking about yet insists he did not err.

@ViscidKonrad I probably make a lot of errors in life, but I haven't in this discussion! :-)

— Noah Smith (@Noahpinion) May 29, 2016

What is it called when one reiterates a wrong position once confronted with the facts? Derp, perhaps?

Accounting Identities are Useful

Nick Rowe directs us today to an eyebrow-raiser. Economist Ankit Mital writes

In the current system of cross-border bookkeeping, unilateral transfers are recorded in the current account (income from trade and foreign business interests) and not the capital account (financial transactions that end up balancing the current account deficit or surplus) side of the transactions.

This is really interesting to those of us who mind our accounting identities. In its simplest form, the balance of payments identity states that the current (CA) and capital account (KA) balances sum to zero. That is, any transaction which increases the CA balance must also decrease the KA balance. If you see the CA balance changing with no corresponding change in the KA balance then you are failing to correctly record the transaction.

So what is Mital missing? First, the KA balance is defined to be the change in foreign ownership of domestic assets less the change in domestic ownership of foreign assets. So if you— residing in the UK— send me £1, then the UK sees foreign ownership of domestic assets rise. That is, the KA rises by £1– exactly balancing the £1 fall in the CA.

It does not matter exactly how the transfer takes place. If you send me \$1.40 instead, then the UK sees domestic ownership of foreign assets fall by \$1.40, raising the KA by \$1.40 and exactly balancing the \$1.40 fall in the CA. If in my name you hand a £1 coin to a London bank to open a deposit account, then again the UK sees foreign ownership of domestic assets rise. (The relevant asset being the deposit and not the coin which moves only between UK actors.)

And there lies the value in minding accounting identities. They force one to think carefully about what else changes.