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