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Sunday, March 16, 2014

Inequality In Savings Drives Wealth Inequality

Paul Krugman discusses the dynamics of wealth inequality in a recent blog: Notes on Piketty (Wonkish). (Note: The article is behind a New York Times paywall, but you can view a number of their articles free within a month.) In it, he uses the standard Solow model to explain rising inequality. Although I do not have a formal model, my reading of a stock-flow consistent models implies that his analysis is not quite correct. The driving force behind wealth inequality is the differential in savings amongst households, and with a second order effect being that larger portfolios may have greater returns on their assets.

Professor Krugman's article was prompted by Thomas Piketty's new book that discusses long-term trends in inequality, Capital in the Twenty-First Century (affiliate link).

He looks at a model with aggregated capital and labour, and then states:
The answer depends on the relationship between r, the rate of return on assets, and g, the overall rate of economic growth. If r is less than g, dynasties are doomed to erode: even if all income from a very large fortune is devoted to accumulation, the family’s wealth will grow more slowly than the economy, and it will slowly slide into obscurity. But if r is greater than g, dynastic wealth can indeed grow to gigantic size.
I argue that this misses the key point in discussing inequality: if you reduce your analysis to representative agents ("capital" and "labour"), you cannot analyse the inequality amongst households.

The relationship between r (the rate of return on assets), and  g (the economic growth rate) only tells us what is happening to the ratio of the stock of assets to the flow of income. If r is greater than g, then there is a rising tide that could theoretically lift all boats - for example, if workers owned most equities via pension funds, then everyone would be better off. (This is not happening, for many reasons.) And households in modern economies are hybrids between pure "capitalists" and "workers", in that they have at least some financial assets. And if after-tax rates of return are the same, a household with 10 times the savings flow of another, it will always have 10 times more financial assets.

Note that the savings flows can be unequal either as the result of after-tax income inequality, or the savings rates out those after-tax incomes are unequal. There are obviously large income inequalities, but savings rates are also very unequal, even within the same income cohorts.

And of course, if there is a large inequality in wealth, that in return helps create income inequality, since most measures of income include returns from financial assets. Since we have households who aim to replace their working incomes with financial flows living side-by-side with households whose only saving flow is paying down their mortgage, this can create considerable income inequality even when wage incomes are evenly distributed.

To be fair to Paul Krugman, his post was short and he did not directly address inequality - he writes about the "society dominated by great dynastic fortunes". His analysis was really about the analysis of aggregate capital versus aggregate labour, and thus his focus is on the ratio of wealth to incomes. Even so, a rising ratio of the stock of financial assets to the flow of GDP does not have to imply that rentiers in aggregate are more dominant economically [update: fixed typo]. Most financial assets are long duration, and the value of assets will rise as long-term interest rates fall. (Krugman's model has only a single rate of return, which cannot replicate this effect.) The income flow would remain the same, as the greater-valued assets now produce income at the lower yield. This has certainly been one factor behind rising wealth/GDP ratios since the early 1980's.

Return Differentials Probably Favour The Rich


It seems likely that assuming the after-tax rates of return for household with large wealth are the same as poorer households is probably incorrect, even after taking into account progressive taxation. Large fortunes (in North America, at least) are built around holding tax-advantaged equities, which have historically had higher returns than more conservative investments, such as term deposits at banks. Poorer households typically have a greater weight of those more conservative investments in their portfolios.

Additionally, transaction and management fees are stacked against smaller investors. As an extreme example, the Canadian middle class were herded into mutual funds that skimmed 2+% of assets every year. These greater transaction costs may outweigh the tax advantage of having a lower income.

Does This Matter?


This post is a somewhat academic quibble; I am explaining why I dislike Paul Krugman's mode of analysis, but I am not addressing the more important question of whether inequality matters, and what could be done about it.  I will use the same defence as Paul Krugman - this was a theoretical digression, and he is saving his bigger points for a review of Piketty's book. I will do the same, assuming I write a review of the book (I have not yet read it).

Paul Krugman closed with two questions:
1. How much of the decline in r relative to g in the 20th century reflected fast growth, and how much reflected policies that either taxed or in effect confiscated inherited wealth? In other words, how much was destiny, how much wars and political upheaval? Piketty stresses both factors, but never gives us a relative quantitative assessment. 
2. How relevant is this story to what has happened so far? In the United States, as Piketty himself stresses, soaring inequality has to date been largely been driven by labor income – by “supermanagers” (I prefer superexecutives.)

To restate my argument, I do not think the discussion of r and g matter in this context. However, I think you need to add in the rise of mainstream equity investing as being a major driver of inequality. Although  "superexecutive" compensation matters, the really big fortunes were generally the result of ownership of companies that went public (and in some countries, taking advantage of botched privatisations).

In order to avoid the huge windfalls that accrue to owners of companies going public, it seems that it would be necessary to replace the entire set of portfolio managers, and burn all the academic finance work that highlighted the advantages of equity investing. This does not seem like a particularly plausible policy. Attempting to use tax policy to address inequality would probably just result in those taxes being built into the price of Initial Public Offerings. Any attempt to redress inequality without a restructuring of the mixed economy would be difficult, even if we assume the political will to do so exists.

Final Administrative Note: E-mail subscribers received an extra message Sunday morning containing an older article. This was the unexpected result of a setting change on my feed, and should be a one-time occurrence (I will not make that change again...). 

(c) Brian Romanchuk 2014

5 comments:

  1. Brian,

    You say:

    "I argue that this misses the key point in discussing inequality: if you reduce your analysis to representative agents ('capital' and 'labour'), you cannot analyse the inequality amongst households."

    You are right on that, of course. If one analyses the problem of distribution in terms of these two variables only (namely, r, the rate of return on assets, and g, the overall rate of economic growth) clearly one "cannot analyse the inequality amongst households", as you say.

    However, why should inequality amongst households be the key point? Personally, I can't see any reason why functional wealth distribution needs to be less important than household inequality.

    In fact, if you go back to Paul Krugman's article, this is how he understands Piketty's work:

    "Piketty’s big idea is that we are in the early stages of returning to a society dominated by great dynastic fortunes, by inherited wealth."

    Piketty is not studying the whole wealth distribution. His aim is much more limited: to study what happens with that top portion of the wealth distribution, not to each and every household's.

    And, if you think about it, with the data available, that's the only thing that can be done.

    Just my two cents, anyway.

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  2. Incidentally, I don't quite understand why you say the analysis was reduced to "representative agents".

    But the main problem I see is this:

    "And households in modern economies are hybrids between pure 'capitalists' and 'workers', in that they have at least some financial assets. And if after-tax rates of return are the same, a household with 10 times the savings flow of another, it will always have 10 times more financial assets."

    It's true that households have some financial assets. But the thing is that wealth is even more unequally distributed than incomes and, on top, most of the net wealth households have (with a few exceptions, like Japan) at least in developed countries, is in housing, not financial wealth.

    So, as approximations go, I don't think the approximation used is excessive.

    ReplyDelete
    Replies
    1. (I am attempting to respond to your two comments here.)

      I will once again underline that I am making a fairly academic point about Krugman's model, and not attempting to cover the bigger issues. It's "Wonkish", as Krugman originally labelled it.

      "Piketty is not studying the whole wealth distribution. His aim is much more limited: to study what happens with that top portion of the wealth distribution, not to each and every household's."
      Firstly, I did not read the book, so I withhold judgement on what he said. All I have read is Paul Krugman's interpretation of it, and it is possible that his summary misses key points. But even if we look at just the top households, Krugman's model of the rate of return will not work. Poorer households have considerable tax advantages over the rich, and so higher pre-tax returns would flatten the wealth distribution - if we assume that holdings have the same mix. As I discuss above, that is not true. But if the portfolio weightings are unequal, we cannot conclude anything about how the wealth distribution is changing based on aggregate returns of all assets.

      " It's true that households have some financial assets. But the thing is that wealth is even more unequally distributed than incomes and, on top, most of the net wealth households have (with a few exceptions, like Japan) at least in developed countries, is in housing, not financial wealth."

      Your statement seems to be similar to what I am saying. However, ignoring housing wealth completely is also questionable. Housing wealth is tax advantaged, and does provide a real benefit to home owners. I think it was a policy error to encourage high house prices. But dropping housing out of the wealth measure artificially skews the measured inequality.

      Should I be outraged that I have a household that owns a $500,000 house, but with no financial assets, living next door to a renter with $500,000 in financial assets? My understanding of the Canadian wealth data has been spectacularly skewed by this housing preference.

      I have not looked at Piketty's data, so I cannot really comment on the public policy implications. I have not been able to draw any conclusions based on the income/wealth distribution data that I have glanced at. But it my defence, that was not exactly a high priority research topic for an interest rate analyst, which was my day job until I resigned a few months ago.

      Delete
  3. The point about housing wealth (which Piketty did not drop out, btw) is that it does not generate income. Housing being the bulk of the wealth owned by the so-called middle-class, it means that middle-class households get mainly labour compensation, plus whatever profits included in mixed income (as per system of national accounts).

    Top incomes, by comparison, get labour compensation and profits (as the middle class do), **and** financial incomes, generated by their wealth, which (unlike that of the middle class), is largely invested in financial assets.

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    Replies
    1. I would note that I had already made similar comments about housing here: ( http://www.bondeconomics.com/2013/10/houses-and-portfolio-allocation.html). Since I had repeatedly linked that housing discussion in recent articles, I did not want to repeat it yet again in this article.

      Delete

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