Sunday, 22 December 2013

Income Distribution and the Savings Ratio

Unfortunately, I missed the exchange in the comments section of this Interfluidity post.  It raises some issues on the measurement and interpretation of savings ratios and inequality that I found rather interesting.  I thought it would be useful to go through some of these points

The issue is to do with whether the rich save more than the poor and it should be seen in the context of the question of whether the distribution of income affects overall consumption.  Much of the difficulty arises over whether capital gains should be included in household income when looking at this.

For the purposes of this discussion, I am going to treat gains as being the increase in the value of net assets, regardless of whether or not they are realised.  I am going to use the term disposable income to refer to what is normally treated as disposable income in the NIPA accounts, i.e. wages, benefits, interest, dividends, etc..  I will use the term HS income to refer to Haig Simons income, which is disposable income plus gains.

So first of all I want to assume a simple consumption function based on disposable income and gains.  I am going to assume that households have the same consumption function whatever their income, but that richer households have a greater proportion of their HS income in the form of gains.  So our consumption function is:

Ci = αy . YDi + αa . Ai

where C is consumption, YD is disposable income and A is gains, for each household i.  The difference is that the rich have a greater ratio of A to YD.  What happens if we assume that households do not spend any of their gains (i.e. αa = 0)?  Then, we will find the following:

  • The aggregate savings rate of the economy (being 1 - C / YD ) will be equal be equal to 1 - αy
  • If we measure the savings ratios of rich and poor as for the aggregate (i.e. using disposable income) their savings ratios will both be the same as the aggregate measure, 1 - αy
  • If we measure savings ratios by reference to HS income (i.e. using 1 - C / [ Y + A ] ), then the savings ratio of the rich will be higher than the aggregate savings ratio and higher than that of the poor.
  • Neither a transfer of earned income, nor of gains, from rich to poor will change the aggregate savings ratio of the economy (conventionally measured), nor the level of consumption.

Because the savings ratio is conventionally measured by reference to disposable income, we must do the same (ignoring gains) for individual households if want to get comparable measures.  And in this special case, that is consistent with the result that redistribution of income and gains has no effect on consumption.  However, I think this misses some important points.

So far we have just looked at the household consumption function based on income and gains that accrue directly to households.  But we need to be aware that this is not equivalent to GDP.  In the simplest case (ignoring flows with public and foreign sectors), disposable income will differ from GDP to the extent of earnings retained by firms.  This part of GDP is accruing to the benefit of shareholders, but is not part of their disposable income as it is not paid to them.  It is likely that retained earnings will increase the gains of households owning those shares, but this is certainly not a one-for-one relationship.

However, it is important to take this into account, because it is relevant to the issue of how income distribution is affecting consumption expenditure.  If we find greater profit retention by corporations, we are likely to find less consumption, even though households may still be benefiting in the form of gains.  But it is important to recognise that the effect here shows up as a fall in household disposable income rather than a rise in the savings ratio.  Furthermore, on our original assumed consumption function, it still makes no difference if we transfer income or gains from rich to poor.  The only thing that is making a difference is the earnings retention level.

Given our assumed consumption function, it is true to say that the rich save more, at least if we consider HS income.  However, this is really just a consequence of our assumptions that everybody saves more of their gains than their disposable income and that the rich have more gains.  That is why, on this assumption, re-distribution has no effect.

We might alternatively consider a consumption function where the propensity to spend out of gains is non-zero but that the rich have a lower propensity to spend out of disposable income.  So the rich may be consuming the same amount as with our previous assumption, but based on different inputs.  We could assume different functions for rich and poor, so the function for the rich is:

Cr = αry . YDr + αra . A

and for the poor:

Cp = αpy . YDp + αpa . A

So even with αry < αpy, we might still find that the savings ratio of the rich (measured as 1 - C / YD ) is the same as that of the poor, because they are also spending partly out of gains.  And as before, we have to measure individual savings ratios that way if we want the ratios to be comparable to the aggregate savings ratios, simply because that is the way the aggregate savings ratio is measured.   

However, we now find that a redistribution of disposable income between rich and poor will change that aggregate savings ratio.  This is due to the fact that there is a different propensity to spend out that type of income.  The difference with our previous result is due to the distinction between average and marginal rates.

All I have intended to do here is highlight some of issues involved in measurement and interpretation.  I am not suggesting that actual household behaviour is actually like any of the scenarios I have used here.  On the whole, I believe there is useful truth in the proposition that the rich save more, but I think under-consumption theories are more problematic.  I think growing inequality, particularly wealth inequality is a big problem, but not necessarily for reasons of under-consumption.

It's still something I'm grappling with though, and hope to return to later.

(Ramanan also has a good post on this, put up after I wrote this but before I got round to posting it.)


  1. Nick, I'm really glad you and Ramanan wrote these posts. "Haig Simons income" is a handy term and it is good to know what it should be called.
    The weird thing is that Mark A Sadowski readily acknowledged in the interfluidity comments that if beneficial ownership (and so capital gains) were transferred to poor people then they would dissave and spend much of it. BUT he said it would only be a one-off jolt to the system. He didn't seem to follow at all that it could be a re-cycling of retained earnings back to consumption and so to subsequent sales and profits.
    I really hope that the interfluidity post gets the ping-backs up for your post and Ramanan's post because these posts help to clarify (for me at least). I feel a bit sheepish about having dumped a morass of comments on that interfluidity post that perhaps just end up obscuring.important points.
    To me a big problem with wealth inequality is that it leads to underinvestment. We need to be investing in how we are going to cope with the future. If there is massive wealth inequality then most of the population will be economically excluded to it won't make sense to invest in new technology or sources of power or whatever. If all the money is with a handful of oligarchs, they will just need a few sedan chair carriers and clockwork watch making craftsmen. There will be no point in being able to provide for the penny-less rest of humanity. If everyone has financial power, then we will need the technological innovations that will allow us to get ample food without much freshwater, and energy from the sun and materials that can be endlessly re-cycled etc etc.
    PS Michael Hudson also makes a big point about capital gains being crucial to understanding what is going on in case you are unaware of his stuff and interested..

    1. Hi stone,

      I would have joined in the comments thread on that interfluidity post if I'd seen it at the time, although really the issues being bounced around needed more space to go through properly. I think Sadowski was making some good points, but I also think he was obscuring (whether deliberately or not) some other important points.

      I'll look at the Hudson stuff. As I said, I'm still not working out what I think of all this stuff. Distribution issues are quite tricky, especially if you combine it with life-cycle issues. I appreciate your comments on this and other posts where I have touched on the topic.

  2. Nick,

    Thanks for referring to my post.

    I think - if I am not wrong - one of your points can be summarized as saying that while it may be true that alpha(ry) may be less than alpha(py), it doesn't follow that saving(r)/(disp income) is greater than saving(p)/(disp income).

    Rather the rich may become richer because Wealth(r,-1) - YD(r) - C(r) + CG (r,0) rises faster than the poor.

    I think that may be true for some years but can we say it is true for all years?

    Even if true for all years, it still leaves open the question if income is distributed to the poor (either via primary distribution or secondary distribution), output will be higher or not.

    The two are slightly different questions I think.

    1. On the first point - yes, providing we understand saving as YD - C, not YD + CG - C. (Why did I use the term A rather than CG? - I don't know)

      On the second - not sure I understand that equation. We're saying here though that ( YD + CG - C) / (YD + CG ) is greater for the rich so they accumulate more.

      Is it true for all years? Not necessarily, but I'm not sure why there should definitely be a limit on it. There might if everyone followed some form of C = aYD + bW, but I'm not convinced they do.

  3. I'm interested from the Winterspeak post that Winterspeak and JKH thought that Mark A Sadowski was spot on and so I guess that I was blathering.
    To me the crucial point is that of firms doing the saving on behalf of their shareholders. You also make that point. I really don't understand why Winterspeak and JKH and Mark A Sadowski say that that is irrelevant and can not be viewed as saving by the wealthy.

    1. Liked some of your comments at Interfluidity.

      You may be interested in this review article by Marc Lavoie and Engelbert Stockhammer

    2. I think it's a question of definitions. The point is it does not count as saving and does not factor into the savings ratio. As I said, what is measured as taking place is a fall in household income, rather than a rise in savings. That doesn't mean though that important things aren't going on.

    3. Ramanan, thanks for the link, I'll check it out and thanks for the reassurance that I wasn't entirely wasting everyone's time with ignorant blather.

      Nick, so am I right in understanding that possibly it needs to be explicitly said that the underconsumption phenomenon manifests as reduced total household income due to less dissaving by the wealthy as they get capital gains?

    4. Perhaps I'd put it by saying that there may be a process, under which national income is accruing to the wealthy by building up in corporations rather than being distributed, thereby reducing household income and consumption, but still adding to their wealth.

    5. Stone,

      Yeah in particular Sadowski says "In particular, there is no such thing per se as corporate savings." which is quite wrong because it does have a definitive meaning and is the undistributed profits of corporations.

    6. What to me is the even more mysterious phenomenon is how this spills over into inflating the value of irreproducible assets of all types. It could be rights to collect parking charges in Detroit, or artworks, or land or pharma patents or whatever.
      The richest UK citizen, the Duke of Westminster is a landowner. His wealth increases due to other people bidding up the value of land in central London etc. They are the ones doing the saving, paying off mortgages or whatever but if he were to sell up, land would be cheaper and they wouldn't be saving so much. The basic thesis of Steve R Waldman's original post is still supported by that phenomenon though isn't it.

    7. Ramanan - that's a good point and another way of thinking of this is to say that the corporations are doing the saving on behalf of their shareholders.

      stone - this is where we have to be a bit careful because those gains are definitely not national income, so the fact that they're not being spent may not be relevant to underconsumption. It is still possible though that it has an impact on people's propensity to spend out of other income.

    8. Nick, when you say, "It is still possible though that it has an impact on people's propensity to spend out of other income." - that is exactly what I'm trying to get at.

      I think Mark A Sadowski had a point that income and saving need to be precisely defined and I guess I was being exasperatingly woolly about that but I also think he was failing to see a real phenomenon that is occurring.

      I think we really need to get a good definition of the underconsumption hypothesis that encompasses what we mean.

      To me the underconsumption hypothesis means that that there is less production and consumption than there would be if global wealth were equally divided up amongst all seven billion people on earth. The crazy thing is that Mark A Sadowski actually said that he agreed that that would cause more consumption at least in the short run. Perhaps the real argument is simply about what is meant by the term, "underconsumption hypothesis".

      To be honest, I'd be delighted with everyone agreeing that some "classic underconsumption hypothesis" (that I'm unfamiliar with) is bogus whilst the "newfangled underconsumption hypothesis" (as defined above) is a real phenomenon holding us back.

      IMO Mark A Sadowski was doing more than policing sloppy definitions. My impression was that he was challenging the whole idea that inequality is causing a less productive economy. He was basically trying to make the case that inequality is only a problem to the extent that it is "unfair" rather than it being something that will decide whether the economy evolves over coming decades to provide for future advancement and food, water and energy security etc. To me that is the crucial issue.

    9. Right.

      Sadowski is presenting it as if high income earners are able to eat the pie not afforded by low income earners instead of talking of having a bigger pie but I don't believe him in the former as well as - although he doesn't mention it - has some Say's Law kind of logic.

      As Marc Lavoie says in his book Introduction to Post-Keynesian Economics:
      "The Kaleckian model, as presented,... shows that cooperation between workers and entrepreneurs can have beneficial effects for the overall economy. Wage increases lead to increased profits. Accumulation is wage-led."

      (with qualifications of course). I think this is a subject on its own even complications due to open economy issues also being important for analysis.

    10. Ramanan, that is why I tried to make the case that the real damage from inequality is not so much via causing unsold inventory but rather by causing the inventory to never get made in the first place.

      If I understand Mark A Sadowski right, he was saying that current production getting sold is all that matters. I'm saying that that is no good if current production is far below what it should be..

      I totally agree that its crucial to see how this ties in with how each country sits in the global economy. To me the "evil genius" of Thatcherism was its dexterity with using asset price inflation to draw in capital flows so that the UK could get a free ride on the global economy. It necessitated beating down labour with high unemployment so that asset price inflation took the place of wage inflation. Inflating asset markets then lured in capital flows from other countries. I tried to get my head around that in the post:

    11. Will look.

      I'll say it matters even more in the case of open economies because wage-restraint is a strategy to keep exports competitive and it is deflationary to the whole world.

    12. Ramanan, I read that Lavoire link you gave, thanks. I must admit though that I do have a preference for solutions that can be conducted by a single country with an open economy without needing a sort of one-world-government. I know that is a tall order though. The Lavoire idea does seem to require a lot of international coordination. As a general principle I think it is very important that each country can do its own thing in its own way. We don't want all of humanities eggs to be in one basket.

      Could the solution be to have much more profit sharing and employee ownership so that it didn't matter whether there was a big wage share or a big profit share because everyone was both getting wages AND profits?

      I also would have liked to have seen more examination of the 1970s collapse of the post war "golden age". Understanding that is crucial IMO. It is always blamed on OPEC but isn't it true that ALL commodities and not just oil were becoming very expensive in the USA and UK? I wonder whether it was more a case of currency exchange rate slippage relative to the developing world rather than being a genuine pure "oil price shock" as is claimed.

      Also in the UK, there was crippling industrial unrest in the 1970s. It wasn't just strikes, it was also massive disruption and ineffectual working practices. Again I think profit share / employee ownership is needed if there is to be genuine full employment (not NAIRU supposed "full employment"). Otherwise we get back to a 1970s scenario where any profit at all is viewed as tantamount to theft by the workforce and unrest means that much of the time workers spend at work is wasted anyway.

    13. Yeah international coordination is a dream because even the badly needed coordination of fiscal policy seems politically unachievable in recent times - after the G20 London meet in 2009.

      The reason is that for each country, it is important for it to maintain international competitiveness because domestic demand cannot be expanded if exports do not rise sufficiently. So for a single nation, not only will rise in wages take away some international competitiveness, but also lead to a higher domestic demand causing a deterioration in trade.

      Cooperation can be achieved between workers and owners but what I read from the work of Marglin and Bhaduri is cooperation can give way to conflict. It cuts both ways - wages are important for aggregate demand but a fast rise can also lead to a fast price rise.

      Btw, in Winterspeak's thread, he sort of seems to think that fiscal policy can take up the slack due to underconsumption - I guess that's one of the pitfalls of looking at things purely from a demand-viewpoint. I think there's something called the Webb-effect according to which rising wages lead to rise in productivity, improving the supply side.

    14. Ramanan, to me the ideal is when the workers actually are also the owners as in this UK example
      Off course many small businesses are also like that too but it is currently rare for very large businesses such as John Lewis Partnership.

      When the workers are the owners there really isn't any scope for conflict. More profits and less wages or vice verse makes no difference because either way the same people get the same money. In the 1970s in the UK, the unions were so powerful that they basically could have taken ownership of much of the UK economy and set up John Lewis Partnership type structures if they had wanted. BUT in the UK the left is just as wedded to "class struggle" nonsense as the right is if not more so. Both sides see the "class war" as something that needs to be fought rather than be resolved. What we basically had in the 1970s was industries going bankrupt, being taken over by the state then being shut down or sold off once Thatcher came in. What I find sobering is that neoliberalism only swept to power because things were in a mess in the 1970s. It would never have got a foothold if things had been working well.

    15. The difficulty with wage led growth as in the Lavoire link, is that if one country has wage led growth and another has neoliberal growth based on increasing indebtedness, then the neoliberal country could provide a higher return for owners. So there will be capital flows to the neoliberal country and away from the high wage country. Those capital flows will cause exchange rate shifts that will further amplify the benefit to those owners who shifted to the neoliberal country. It will also make internationally traded commodities etc more affordable in the neoliberal country. If the neoliberal country doesn’t much bother with exporting manufactured goods and instead just has a FIRE economy there will be no restraining effect from the exchange rate shift; it will actually help a FIRE sector boom. The fact that it is not indefinitely sustainable won’t worry owners because they can just pull money out before the bubble pops or so they hope.

    16. Ramanan, what you're saying about the Webb effect reminded me of this interfluidity post:
      K is not capital, L is not labor

      "In empirical fact, “human capital” and its more sociable, incorporeal twin “institutional capital” seem to be much more important predictors of the growth path of an economy than physical capital. Europe and Japan bounce back quickly after war devastates their infrastructure. But imagine that a Rapture clears the Earth and pre-agrarian nomads take possession of perfect gleaming factories. I think you will agree that production does not recover so fast. Human and institutional capital dominate physical capital. [3]

      Like physical capital, and unlike hours of the day, the collective stock of human capital grows over time, without obvious bound. Yet, at least under existing arrangements, we have no means of distinguishing between “returns to human capital” and “wages”. “Capital taxation”, in conventional use, refers to levies on capital gains, dividends, and interest. As a political matter, results like Chamley-Judd are often used to support setting these to zero. But eliminating conventional capital taxes shifts the cost of government to wages, which include returns to human capital. If human capital accumulation is as or more important than other forms of capital accumulation, and if the quality of effort that people devote to building human capital is wage-sensitive, then taxing wages in preference to financial capital may be quite perverse. Further, while physical capital grows by virtue of nonconsumption, it seems plausible that human capital development is proportionate to its use, which would render a tax penalty on “wages” particularly destructive. Fundamentally, Chamley-Judd logic suggests that we should tax least the factor most capable of expanding to engender economic growth. You don’t have to be a new-age nut to believe that human and institutional development, which yield return in the form of wages, may well be that factor."

    17. Ashwin has a post making the case that today there is actually a lot of scope for having lots of worker/owner small scale firms due to modern technology etc:
      Perhaps that really offers hope.

  4. Nick, this is an example of something from Michael Hudson that focuses on capital gains:

    To be honest I wonder whether there might be a bit of a gap in that he seems to grapple with the big issues (that to me seem crucial) but he doesn't distill things down to precise, concise, points in quite the way that you have succeeded in doing in this blog. I get the impression that JKH for instance avoids reading Michael Hudson's stuff for just that reason (sorry if I've got that wrong).

  5. Stone,

    I have to come clean.

    When I said "tour de force", I was referring only to his observations concerning macro accounting.

    I thought they were good, clean, and quite rare in that way.

    I wasn't referring to anything else - not from intention - but for lack of time due to personal circumstances in perusing the full substance of the discussion, quite frankly.

    Perhaps not very productive on my part.

    I still don't have a good feel for precisely how the issue being discussed should be framed, or how to understand what the debate should be about, but that's probably my fault for the same reason. Sorry.

  6. JKH, I'm totally with you on the need to be clear and precise. I agree that Mark A Sadowski was being clear and precise. I just worry he clearly and precisely restricted the "underconsumption hypothesis" down to a straw man that he could then dismiss. In reality I think there is a very real phenomenon that doesn't fall within his narrow:

    "In underconsumption theory recessions and stagnation arise due to inadequate consumer demand relative to the production of new goods and services. "

    Is there a valid reason for setting the benchmark as being "relative to the production of new goods and services" rather than being relative to POTENTIAL production of new goods and services? If we don't accept current production as a bench mark, then things are totally different aren't they? It is basically the difference between unsold inventory versus inventory that never gets made in the first place.

    I floundered around but I'm left with the impression that Mark was good at arguing but nevertheless not grasping the real issue :)

    1. I think he's just making the point that you need to look at consumption relative to GDP, not relative to (GDP + net gains for the national economy). This is a fair point, as unspent national gains shouldn't matter. The important point though is that household gains and national gains are not the same.

    2. I'm still not getting it when you say "unspent national gains shouldn't matter".

      If they were spent, then wouldn't that create more jobs etc?

      Assets as a whole can be inflated can't they? The real value of land in the UK is massively more than it was in 1980 isn't it? Deflating that down to the 1980 level by a generalized sell off to fund consumption would boost the economy a lot wouldn't it?

    3. Yes, I'm at risk of being a bit misleading making throwaway comments like that. That's sort of why I wrote the post - it needs space to explain it properly. I meant something like this. Say you measure the savings ratio by reference to income + gains. No assume there is an increase in gains, say from appreciation in land value. Your savings ratio has now risen, but that should not in itself lead to a recession. However, what you say is also correct.

    4. Thanks for the clarification. I think more and more that this all boils down to my personal "minds eye view" of the "underconsumption hypothesis" being perhaps a bit more wide ranging than what Mark A Sadowski had in mind.

      To my mind pinning things to the reference point of recessions and current GDP is a sort of circular argument. Real GDP could be only 10% of potential and possibly each recession might individually be induced by shocks not connected to the underconsumption phenomenon that nevertheless was causing the GDP to be at 10% of potential rather than being at 95% of potential.

      Its dawning on me that the way to frame the underconsumption hypothesis might be in terms of real GDP being below what it would be if no one had any financial constraints at all. I think Mark A Sadowski sort of eluded to that when he brought in the whole NAIRU constraint subject. BUT as I think he conceeded, NAIRU is totally dependent on distribution. If all of the money is with a handful of oligarchs who only have need for staff amounting to 1% of the population but have very select needs (eg multilingual expert butlers, clockwork watch craftsmen etc) then the NAIRU could be >90% and GDP could be <10% of potential even with unemployment being less than the NAIRU.

    5. Could the underconsumption hypothesis even be condensed right down to being just :

      'The NAIRU is higher when wealth inequality is greater' ?

    6. Thinking about this, it is possible to imagine a scenario where "underconsumption due to inequality" never causes a recession. It just causes booms to be manifested as land price inflation rather than booms inducing invention of robots etc. The overall consequence however is that we end up with expensive land, no robots and few jobs and consequently GDP at only 10% of what it could have been.

    7. I'm not sure. These are issues I'm still thinking about. As I suggested in the post, I'm not so sure how useful the under-consumption idea is as a way of framing the issue anyway.

    8. The thing is that Steve R Waldman never actually mentioned under-consumption once in his post. I've just used the search function to double check that. Mark A Sadowski however said that Steve's overall thesis about inequality limiting growth was rubbish because the under-consumption hypothesis was disproved by the facts. It is sort of a double straw man.

      I think the case needs to be made that the phenomenon of inequality limiting growth is not contingent on the Mark A Sadowski style under-consumption hypothesis where under-consumption is a cause of recessions.

  7. Framing underconsumption in terms of saving rate or in terms of consumption to GDP ratio is wrong-headed. Underconsumption and other stagnationist ideas revolve around capacity utilization. In that sense, the US has suffered from chronic overcapacity. If you look at current costs capital stock to GDP ratio it has trended persistently down since 1980. (many people look at real capital stock to real GDP--I think this is wrong-headed). Moreover, the overcapacity story is borne out by persistently high vacancy rates in office space and industrial space, low capacity utilization across a range of industries.