Not all GDP measurement errors are greater than zero!

Bryan Caplan is an optimist. He thinks that economists do many errors in estimating GDP (overall well-being). He is right in the sense that we are missing many dimensions of welfare improvements in the last half-century (see here, here and here). These errors in measurements lead us to hold incorrectly pessimistic views (such as those of Robert Gordon). However, Prof. Caplan seems to argue (I may be wrong) that all measurements problems and errors are greater than zero. In other words, they all cut in favor of omitting things. There are no reasons to believe this. Many measurement problems with GDP  data cut the other way – in favor of adding too much (so that the true figures are lower than the reported ones).

Here are two errors of importance (which are in no way exhaustive): household output and adjustments for household size.

Household Output

From the 1910s to the 1940s, married women began to enter moderately the workforce. This trickle became a deluge thereafter. National GDP statistics are really good at capturing the extra output they were hired to produce. However, national GDP statistics cannot net out the production that was foregone: household output.

A married woman in 1940 did produce something: child-rearing, house chores, cooking, allowing the husband to specialize in his work. That output had a value. Once offered the chance to work, married women thought the utility generated from producing “home outputs” was inferior to the utility generated from “market work”. However, the output that is measured is only related to market work. Women entered the labor force and everything they produced was considered a net addition to GDP. In reality, any economist worth his salt is aware that the true improvement in well-being is equal to the increased market output minus the forsaken house output. Thus, in a transition from a “male-labor force” to a “mixed labor force”, you are bound to overestimate output increases.

How big of an issue is this? Well, consider this paper from 1996 in Feminist Economics. In that paper, Barnet Wagman and Nancy Folbre calculate output in both the “household” and “market” sectors. They find that even very small changes in the relative size of these sectors alter growth rates by substantial margins. Another example, which I discussed in this blog post based on articles in the Review of Income and Wealth, is that when you make the adjustment over four decades of available Canadian data, you can find that one quarter of the increase in living standards is eliminated by the proper netting out of the value of non-market output. These are sizable measurement errors that cut in the opposite direction as the one hypothesized by prof. Caplan (and in favor of people like prof. Gordon).

Household Size

Changes in household sizes also create overestimation problems. Larger households have more economies of scale to exploit than smaller households so that an income of $10,000 per capita in a household of six members is superior in purchasing power than an income of $10,000 per capita in a single-person household. If, over time, you move from large households to small households, you will overestimate economic growth. In an article in the Scottish Journal of Political Economy, I showed that making adjustments for household sizes over time yields important changes in growth rates between 1890 and 2000. Notice, in the table below, that GDP per adult equivalent (i.e. GDP per capita adjusted for household size) is massively different than GDP per capita. Indeed, the adjusted growth rates are reduced by close to two-fifths of their original values over the 1945-2000 period and by a third over the 1890 to 2000 period. This is a massive overestimation of actual improvements in well-being.


A large overestimation

If you assemble these two factors together, I hazard a guess that growth rates would be roughly halved (there is some overlap between the two so that we cannot simply sum them up as errors to correct for – hence my “guess”). This is not negligible. True, there are things that we are not counting as Prof. Caplan notes. We ought to find a way to account for them. However, if they simply wash out the overestimation, the sum of errors may equal zero. If so, those who are pessimistic about the future (and recent past) of economic growth have a pretty sound case. Thus, I find myself unable to share Prof. Caplan’s optimism.

Interwar US inequality data are deeply flawed

For some years now, Phil Magness and myself have been working on improving the existing income inequality for the United States prior to World War II. One of the most important point we make concerns why we, as economists, ought to take data assumptions seriously. One of the most tenacious stylized facts (that we do not exactly dispute) is that income inequality in the United States has followed a U-curve trajectory over the 20th century. Income inequality was high in the early 1920s and descended gradually until the 1960s and then started to pick up again. That stylized fact comes from the work of Thomas Piketty and Emmanuel Saez with their data work (first image illustrated below). However, from the work of Auten and Splinter and Mechling et al. , we know that the increase post-1960 as measured by Piketty is somewhat overstated (see second image illustrated below).  While the criticism suggest a milder post-1960 increase, me and Phil Magness believe that the real action is on the left side of the U-curve (pre-1960).



Why? Here is our case made simple: the IRS data used to measure inequality up to at least 1943 are deeply flawed. In another paper recently submitted, I made the argument that some of the assumptions made by Piketty and Saez had flaws. This did not question the validity of the data itself. We decided to use state-level income tax data from the IRS to compute the state-level inequality and compare them with state-income tax data (e.g. the IRS in Wisconsin versus Wisconsin’s own personal income tax data). What we found is that the IRS data overstates the level of inequality by appreciable proportions.

Why is that? There are two reasons. The first is that the federal tax system had wide fluctuations in tax rates between 1917 and 1943 which means wide fluctuations in tax compliance. Previous scholars such as Gene Smiley pointed out that when tax rates fell, compliance went up so that measured inequality went up. But measured inequality is not true inequality because “off-the-books” income (which was unmeasured) divorced true inequality from measured inequality.  This is bound to generate false fluctuations in measurement as long as tax compliance was voluntary (which is true until 1943). State income taxes do not face that problem as their tax systems tended to be more stable throughout the period. The same is true with personal exemptions.

The second reason speaks to the manner the federal data is presented. The IRS created wide categories with the numbers of taxpayers according to net taxable income (rather than gross income) in each categories. For example, the categories go from 0$ to 1,000$ per filler and then increase by slice of 1,000$ until 10,000$ and then by slices of 5,000$ etc. This makes it hard to pinpoint where to start each the calculations for each of the fractiles of top earners. This is not true of all state income tax systems. For example, Delaware sliced the data by categories of 100$ and 500$ instead. Thus, we can more easily pinpoint the two. More importantly, most state-income tax systems reported the breakdown both for net taxable and gross income. This is crucial because Piketty and Saez need to adjust the pre-1943 IRS data – which are in net income – to that they can tie properly with the post-1943 IRS data – which are in adjusted gross income. Absent this correction, they would get an artificial increase in inequality in 1943. The problem is that the data for this adjustment is scant and their proposed solution has not been subjected to validation.

What do our data say? We compared them to the work of Mark Frank et al. who used the same methodology and Piketty Saez but at the state-level using the same sources. The image below pretty much sums it up! If the points are above the red line, the IRS data overestimates inequality. If below, the IRS underestimates. Overall, the bias tends towards overestimation. In fact, when we investigated all of the points separately, we found that those below the red line result merely from the way that Delaware’s (DE) was adjusted to convert net income into gross income. When we compared only net income-based measures of inequality, none are below the red line except Delaware from 1929 to 1931 (and by much smaller margins than shown in the figure below).


In our paper, we highlight how the state-level data is conceptually superior to the federal-level data. The problem that we face is that we cannot convert those measures into adjustments for the national level of inequality. All that our data do is suggest which way the bias cuts. While we find this unfortunate, we highlight that this would unavoidably alter the left side of the curve in the first graph of this blog post. The initial level of inequality would be less than it is now. Thus, combining this with the criticisms made for the post-1960 era, we may be in presence of a U-curve that looks more like a shallow tea saucer than the pronounced U-curve generally highlighted.  The U-curve form is not invalidated (i.e. is it a quadratic-looking function of time or not), but the shape of the curve’s tails is dramatically changed.

On Robert Allen’s defense of the High-Wage Economy hypothesis

The high-wage economy thesis is a topic I have blogged about many times before as I think it is an important debate among economists and economic historians (see notably here and here, see also this contribution of mine to the Journal of Interdisciplinary History). For those unfamiliar with this thesis, here is a simple summary of the idea advanced by Robert Allen: high wages relative to capital units was a key force in the industrialization of Britain and thus it explains why the Industrial Revolution was British before if was anything else.

As I have explained in the aforementioned blog posts, I am unsure of where I stand regarding this idea. I tend to be skeptical, but I have stated the evidence needed to convince me of the opposite. In the past year or so, there has been an avalanche of articles on the topic including this article by Humphries and Weisdorf, a follow-up working paper by the same authors, another paper by Judy Stephenson and a working paper by Stephenson (bis). Today, Robert Allen replies to his critics in this working paper.

I find that some of the points are convincing, however I must take issue with a particular point that falls into my ballpark as Allen mentions my work on wages in France (the aforementioned article in Journal of Interdisciplinary History). In my research, I pointed out that Allen’s computations underestimated wages outside Paris. With the correct computations, the rest of France does not appear as poor relative to England as Allen suggests. Allen concedes this point but then goes to state the following:

Geloso (2018) has pointed out that the Strasbourg unskilled wage series for 1702-64 is low in comparison to that of comparable towns, and workers may have received food, which has not been taken into account.  This is a perceptive point, but its implications are limited. The most important use I make of the Strasbourg evidence is in calculating the ratio of the wage to the user cost of capital. If the Strasbourg wage in this calculation is raised to that of neighbouring towns, the wage-capital cost ratio does rise but only by a small degree. The reason for this somewhat surprising result is that the wage is also an argument in the formula for the user cost of capital–building workers have to build the machines and the mills that house them–so the denominator of the ratio increases as well as the numerator, although to a lesser extend.

This is a incorrect characterization of my argument. First, I did not state that wages in Strasbourg did not account for in-kind payment. I stated that in-kind payment was evidence that the wages did not pertain to Strasbourg! The wages from the primary sources were for a city some 70 km away from Strasbourg, they did not concern unskilled workers and they included large in-kind compensation. To correct for this problem, I compared agricultural wages in England with those around Strasbourg that had been collected by Auguste Hanauer. What I found was the the lowest wages in farming were equal to 74% of farm wages in Southern England (as opposed to 64% with Allen’s stated wages). While I did not report this in the article because I had doubts, it is worth pointing out that the high bound of farm wages in Strasbourg is above the level reported for Southern England (which acts a proxy for England – see table 2 in my paper). As Strasbourg is a proxy for living standards outside Paris, my finding suggests a much smaller gap in living standards. It also entails a much more important change in the cost of capital to labor (wages are in the range of 50% above those suggested by Allen and sometimes they are higher by more than 100% which would mean a halving of the relative cost of capital! These are not peanuts to be thrown on the sidewalk!

Second, I ought to point out the nature of my argument. I was not trying to prove/disprove the high-wage hypothesis. My point was much more modest. The mirror of the question as to why the industrial revolution was British is why it was not French. France had a large population offering large returns to scale (in both economic and political organizations) and an array of navigable rivers that facilitated internal trade. It also key pockets of Lancashire-like industrialization such as Normandy (for textile) and Mulhouse (the French Manchester). As such, it is an entirely reasonable endeavor to try to situate living standards in France relative to Britain. If France was massively poorer than England, then Allen has a greater likelihood of being correct. If it was closer to an equal footing (I do not believe that anyone places France above England in circa 1750), then Allen’s critics have a greater likelihood of being correct.* However, regardless of the answer, the data does not infirm/confirm the high-wage hypothesis. It merely situates relative likelihood. As I point out that wages were quite above those postulated by Allen, I am merely stating the extent of the reasonableness of being skeptical of the high-wage hypothesis.

Finally, it is worth pointing out that the work of Leonardo Ridolfi is absent from Allen’s reply. The latter’s work is very important as it echoes (in a much richer manner) my point that wages outside Paris were not as low as cited by Allen.**

*As I assume a greater equality of capital returns across both countries, the smaller the wage gap, the smaller the relative differences in capital/labor costs ratios.
** Ridolfi shows France had incomes equal to 64% of English incomes circa 1700. However, I am skeptical of this figure. This is because, while I trust the index produced by Ridolfi, I am unconvinced about the benchmark year to convert the index into international dollars.

The minimum wage induced spur of technological innovation ought not be praised

In a recent article at Reason.comChristian Britschgi argues that “Government-mandated price hikes do a lot of things. Spurring technological innovation is not one of them”. This is in response to the self-serve kiosks in fast-food restaurants that seem to have appeared everywhere following increases in the minimum wage.

In essence, his argument is that minimum wages do not induce technological innovation. That is an empirical question. I am willing to consider that this is not the most significant of adjustment margins to large changes in the minimum wage. The work of Andrew Seltzer on the minimum wage during the Great Depression in the United States suggests that at the very least it ought not be discarded.  Britschgi does not provide such evidence, he merely cites anecdotal pieces of support. Not that anecdotes are bad, but those that are cited come from the kiosk industry – hardly a neutral source.

That being said, this is not what makes me contentious towards the article. It is the implicit presupposition contained within: that technological innovation is good.

No, technological innovation is not necessarily good. Firms can use two inputs (capital and labor) and, given prices and return rates, there is an optimal allocation of both. If you change the relative prices of each, you change the optimal allocation. However, absent the regulated price change, the production decisions are optimal. With the regulated price change, the production decisions are the best available under the constraint of working within a suboptimal framework. Thus, you are inducing a rate of technological innovation which is too fast relative to the optimal rate.

You may think that this is a little luddite of me to say, but it is not. It is a complement to the idea that there are “skill-biased” technological change (See notably this article of Daron Acemoglu and this one by Bekman et al.). If the regulated wage change affects a particular segment of the labor (say the unskilled portions – e.g. those working in fast food restaurants), it changes the optimal quantity of that labor to hire. Sure, it bumps up demand for certain types of workers (e.g. machine designers and repairmen) but it is still suboptimal. One should not presuppose that ipso facto, technological change is good. What matters is the “optimal” rate of change. In this case, one can argue that the minimum wage (if pushed up too high) induces a rate of technological change that is too fast and will act in disfavor of unskilled workers.

As such, yes, the artificial spurring of technological change should not be deemed desirable!

On “strawmanning” some people and inequality

For some years now, I have been interested in the topic of inequality. One of the angles that I have pursued is a purely empirical one in which I attempt to improvement measurements. This angle has yielded two papers (one of which is still in progress while the other is still in want of a home) that reconsider the shape of the U-curve of income inequality in the United States since circa 1900.

The other angle that I have pursued is more theoretical and is a spawn of the work of Gordon Tullock on income redistribution. That line of research makes a simple point: there are some inequalities that are, in normative terms, worrisome while others are not. The income inequality stemming from the career choices of a benedictine monk and a hedge fund banker are not worrisome. The income inequality stemming from being a prisoner of one’s birth or from rent-seekers shaping rules in their favor is worrisome.  Moreover, some interventions meant to remedy inequalities might actually make things worse in the long-run (some articles even find that taxing income for the sake of redistribution may increase inequality if certain conditions are present – see here).  I have two articles on this (one forthcoming, the other already published) and a paper still in progress (with Rosolino Candela), but they are merely an extension of the aforementioned Gordon Tullock and some other economists like Randall Holcombe, William Watson and Vito Tanzi. After all, the point that a “first, do no harm” policy to inequality might be more productive is not novel (all that it needs is a deep exploration and a robust exposition).

Notice that there is an implicit assumption in this line of research: inequality is a topic worth studying. This is why I am annoyed by statements like those that Gabriel Zucman made to ProMarket. When asked if he was getting pushback for his research on inequality (which is novel and very important), Zucman answers the following:

Of course, yes. I get pushback, let’s say not as much on the substance oftentimes as on the approach. Some people in economics feel that economics should be only about efficiency, and that talking about distributional issues and inequality is not what economists should be doing, that it’s something that politicians should be doing.

This is “strawmanning“. There is no economist who thinks inequality is not a worthwhile topic. Literally none. True, economists may have waned in their interest towards the topic for some years but it never became a secondary topic. Major articles were published in major journals throughout the 1990s (which is often identified as a low point in the literature) – most of them groundbreaking enough to propel the topic forward a mere decade later. This should not be surprising given the heavy ideological and normative ramifications of studying inequality. The topic is so important to all social sciences that no one disregards it. As such, who are these “some people” that Zucman alludes too?

I assume that “some people” are strawmen substitutes for those who, while agreeing that inequality is an important topic, disagree with the policy prescriptions and the normative implications that Zucman draws from his work. The group most “hostile” to the arguments of Zucman (and others such as Piketty, Saez, Atkinson and Stiglitz) is the one that stems from the public choice tradition. Yet, economists in the public-choice tradition probably give distributional issues a more central role in their research than Zucman does. They care about institutional arrangements and the rules of the game in determining outcomes. The very concept of rent-seeking, so essential to public choice theory, relates to how distributional coalitions can emerge to shape the rules of the game in a way that redistribute wealth from X to Y in ways that are socially counterproductive. As such, rent-seeking is essentially a concept that relates to distributional issues in a way that is intimately related to efficiency.

The argument by Zucman to bolster his own claim is one of the reason why I am cynical towards the times we live in. It denotes a certain tribalism that demonizes the “other side” in order to avoid engaging in them. That tribalism, I believe (but I may be wrong), is more prevalent than in the not-so-distant past. Strawmanning only makes the problem worse.

On Household Size and Economic Convergence

A few days ago, one of my papers was accepted for publication at the Scottish Journal of Political Economy (working paper version here). Co-authored with Vadim Kufenko and Klaus Prettner, this paper makes a simple point which I think should be heeded by economists: household size matter. To be fair, economists are aware of this when they study inequality or poverty. After all, the point is pretty straightforward: larger households command economies of scale so that each dollar goes further than in smaller households. As such, adjustments are necessary to make households comparable.

Yet, economists seem to forget it when times come to consider paths of economic growth and convergence across countries. In the paper, we try to remedy this flaw. We do so because there was a wide heterogeneity of household size throughout history – even within more homogeneous clubs such as the countries composing the OECD.  If we admit, as the economists who study poverty and inequality do, that income per person adjusted for household size is preferable to income per person, then we must recognize that our figures of income per capita will misstate the actual differences between countries. In addition, if households grew homogeneously smaller over a long period of time, figures of income per capita will overstate the actual improvements in living standards. As such, we argue there is value in modifying the figures to reflect changing household sizes.

For OECD countries, we find that the adjusted income figures increased a third less than the unadjusted per capita figures (see table below). This suggests a more modest growth trend. In addition, we also find that up to the structural break in variations between countries (NDLR: divergence between OECD countries increased to around 1950) there was more divergence with the adjusted figures than with the unadjusted figures (see figure below). We also find that since the break point, there has been less convergence than previously estimated.

While the paper is presented as a note, the point is simple and suggests that those who study convergence between regions or countries should consider the role of demography more carefully in their work.



Fogel on economics and ideology

Many, upon reading the conclusions of economists, believe that economics has an ideological bent. I often respond that this is not the case. True, the “window” of political opinions in economics is narrower but that is largely because the adhesion of economists to methodological individualism precludes certain ideological views that rest on holistic approaches or concepts. However, when you consider more complex situations than “party affiliation”, you will find economists all over the place. They will often cross ideological lines or even have a foot in two antagonistic camps.

Recently, I was reading Robert Fogel’s lectures on the “Slavery debates” which retells the intellectual history of American slavery from U.B. Phillips to … well … Fogel himself. One must remember that Fogel was, and remained from what I can tell, a quite strongly left-leaning economist for most of his life (see here). As such, it is hard to consider Fogel as an ideologue preaching for free market economics. Yet, in the lectures, Fogel (p.19) makes a point that supports the contention that I often make regarding economists and ideology that I believe must be shared:

The ability to view Phillips (NDLR: the dominant interpretation of slavery pre-1960) in a new light was facilitated by the sudden intrusion of a large corps of economists into the slavery debates during the 1960s. This intrusion was welcomed by neither the defenders of the Phillips tradition nor the neoabolitionist school led by Stampp (NDLR: Kenneth Stampp, author of The Peculiar Institution). The cliometricians, as they were called, refused to be bound by the established rules of engagement, and they blithely crossed ideological wires in a manner that perplexed and exasperated traditional historians on both sides of the ideological divide.

Given that the source of this quotation is Fogel, I admit that I am particularly fond of this passage. Maybe the distrust towards economists is because economists can be both friend and foes to established interlocutors in a given discussion.