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.

Depreciation and Income Shares

I would like now to wade briefly into a debate over the gap between growth in productivity and wages by introducing a bit of modeling fun. It seems clear that— in recent decades— although wage income has grown more slowly than GDP there has been little difference between the growth rate of NDP (GDP net of capital depreciation) and the growth rate of total labor compensation.

On the other hand, inequality of compensation has increased quite a bit— driving a large wedge between pay at the top and pay of the ordinary worker. None of this is news. Somewhat less clear is whether net product is more or less appropriate as a comparison. At first blush, workers still have to produce the whole of output no matter how much investment goes to replacing depreciating capital. It might make sense for labor compensation to rise in step with gross production. But...

Spreading Imports Thin Does Not Mean Exchange Rates Do Not Matter

I am in the middle of a Twitter debate with J.W. Mason. The starting point for the debate is an empirical paper suggesting that real currency depreciation does not increase real exports, but a real currency appreciation decreases real exports (pdf). Let us see if I can clarify my position that there is an implication that real currency depreciation leads to lower real imports.

Let us suppose there are 101 countries and everyone imports \$100 worth of goods from each of the 100 different partner countries, so that each country imports a total of \$10,000 worth of goods. Now suppose that my current depreciates, say, 10% so that everyone else’s currency appreciates 1% 0.1%. Suppose further that a 1% 0.1% appreciation reduces exports by 0.05%.

At first blush it seems that this implies a 0.05% reduction in my imports. After all, if every partner country reduces their exports to every other country by 0.05%, then my imports must fall by 0.05%– almost too small to measure.

But this ignores the fact that my partner countries exchange rates did not appreciate with each other. When each partner loses 0.05% of exports, that partner reduces exports to me by \$5 and exports to the rest of the world by \$0. Thus, my total imports from all countries falls by \$500, or 5% of my initial imports.

Which is to say, I do not understand the position that the reduction in real imports due to depreciation is “formally correct but practically and empirically irrelevant.”

Farmer’s Folly: The Sequel

The post below is part of an exchange with Roger Farmer with origins which predate the start of this blog. The ultimate question is should (or even can) the government control asset markets for purposes of managing the rate of inflation. I believe Farmer’s call for such interventions is misguided.

More specifically, Farmer declares that the fall in the stock market in 2008 “caused” the Great Recession. What he seems to mean is that current movements in stock prices can be shown to help predict future movements in unemployment. Unfortunately, there is evidence that the relationship has broken down in recent years. Indeed, Farmer dismisses my concern that his initial model produces poor forecasts by making this very point. Furthermore, it is difficult to distinguish between stock prices as forward-looking, as opposed to forward-causing. Thus, even if the actual association today may be discerned, it is not clear that if, say, the Federal Reserve bought up stocks to keep prices high that such action would actually lead to much reduction in unemployment.

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In a new working paper (PDF) UCLA’s Roger Farmer responds to last year’s investigation into his claim that declines in the stock market caused the Great Recession.(PDF) Farmer apparently failed to grasp the nature of the critique.

In his original paper, Farmer claimed to have found a stable relationship between the movements in S&P 500 and unemployment rates, and that the data “leads me to stress asset market intervention as a potential policy resolution to the problem of high and persistent unemployment.” In other words, the government should deliberately prop up the stock market as a way of boosting the economy. Farmer appealed to the apparent forecasting power of his model to support his policy preference.

In response we countered that his visual evidence of forecasting power was deceptive– playing off the serial correlation in the data to trick the naïve observer. Rather, his model was not in fact powerful, as was demonstrated by the fact that a simpler model that ignored stock prices produced superior forecasts. Our analysis showed that even if Farmer’s model was correct, movements in the stock market fail to explain– let alone cause– the Great Recession. Finally, we pointed out that the intervention necessary to prevent the recession was implausibly large to be considered serious.

Farmer now:

• Asserts as fact certain properties of his data shown to be consistent with, but unsupported by his analysis.
• Argues that the asserted properties require the use of a particular type of model.
• Suggests that despite using the proper kind of model, his model was “seriously mispecified” by failing to account for a structural break.
• Reasserts that despite this structural break the observed relationship is somehow “structurally stable.”
• Abandons the “correct way to model” and employs pre-break data in an effort to support the uncontroversial position that stock market data may help forecast unemployment.

We agree that his model may have failed due to structural breaks. In fact, post-2008 data may be completely different in structure than data prior, and therefore any model based on previous data is liable to produce forecasts only spuriously related to the post-2008 economy. In any case, we believe this undermines both his assertion that stock prices caused the Great Recession and his proposed policy solution.

Is It Really Time for the Fed to Worry About Inflation?

Ylan Mui at The Washington Post’s Wonkblog had a piece Thursday titled “This is why the Fed should start worrying about inflation again.” The main bit of evidence is a graph attributed to Kevin Logan showing a negative relationship between the unemployment rate and increasing rates of inflation. But this graph actually says far less than Mui says.

Indeed there is a relationship between unemployment and inflation. The Federal Reserve is tasked with balancing inflation and unemployment, and when the Fed fears inflation, it raises interest rates with the intent of slowing the economy and creating unemployment. To some extent, then, the relationship is the Fed’s doing.

Let us put that aside, however, and take the observed relationship at face value. First, it is far from obvious that 6.5 percent unemployment represents a threshold below which inflation is as likely to rise as fall– particularly given the small sample size. In Figure 1, I was unable to reproduce exactly Logan’s figure, but according to data available at the Fed, four of the five years with the highest unemployment rates under 6.5 percent are associated with decreasing inflation.

Figure 1: Unemployment and Changes in Inflation

Source: FRED, series JCXFE and UNRATE and author’s calculations

Rather than cherry picking, we may regress changes in inflation against the unemployment rate. As it turns out, the relationship is statistically weak. The expected change in inflation switches between positive and negative somewhere between 2.5 and 7 percent. Likewise, this suggests that the 50/50 point lies closer to 5 percent than 6.5.

Table 1: Regression results

		(1)	(2)	(3)
$\beta_0$	constant	0.52 (0.37)	0.52 (0.43)	0.52 (0.39)
$\beta_1$	unemployment rate	-0.11 (0.06)#	-0.11 (0.07)	-0.11 (0.06)#
variance/covariance estimator		OLS	jackknife	bootstrap
$-\beta_0/\beta_1$		2.6-7.1	2.9-6.8	3.0-6.7

Standard errors in parenthesis
# Significant at 10% level
Source: FRED, series JCXFE and UNRATE and author’s calculations

In Figure 2, we see the probability that inflation will be higher in 2014 than it was in 2013– assuming various year-round average unemployment rates for 2014. At 6.5 percent unemployment, the probability is closer to one in three than one in two.

Figure 2: Probability of Increased Inflation in 2014

Note: The widest (lightest) confidence band covers 95 percent of outcomes and the most narrow (darkest) band covers 50 percent.
Source: FRED, series JCXFE and UNRATE and author’s calculations

More importantly, increasing inflation is the wrong consideration. The Fed has tolerated inflation below 2.0 percent ever since 2007, and in 2013 core inflation ran only 1.2 percent. If the Fed must target some rate of inflation, it should target a higher rate of inflation. Yet, even if the relationship is meaningful then there is less than a 5 percent chance that 2014 inflation will run even as high as 2.0 percent.

Figure 3: Probability of At Least 2% Inflation in 2014

Note: The widest (lightest) confidence band covers 95 percent of outcomes and the most narrow (darkest) band covers 50 percent.
Source: FRED, series JCXFE and UNRATE and author’s calculations

To the extent that the relationship is both meaningful and a result of Fed activity, then, this suggests that meeting a 2% inflation target would require the Fed to be less hawkish than would be normal for the rate of unemployment. It may yet be some time before the Fed raises interest rates.

(This post originally appeared on the CEPR blog.)