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The normative implication in Marxian economics is that "exploitation of labour-power" is a bad thing. I'm hoping to understand quantitatively who are the winners and losers.

Definitions:

Data:

My reasoning:

  1. If there were no corporate profits, there would be 0 return on stocks.
  2. If my savings in stock exceed 4.1 years of my wages, I earn more from stocks than the corporate profits I generate.
    1. can be seen as: I am gaining more from others' labor than others are gaining from my labor
  3. If labor share was 100%, 2-3 would not be possible due to 1, so I would be worse off.

What are the mistakes in my definitions & reasoning, if any?

Follow-up question: My argument 1. applies specifically to 100% labor share. If labor share was 99% it wouldn't apply. Is there any known general relationship between labor share and stock market returns? Some leads:

  • "Despite its importance, there is no systematic empirical evidence on the effect of monetary policy shocks on the share of output allocated to wages. Using data for five developed economies, this column finds that standard models generate the ‘wrong sign’ for the effect when compared to the empirical results, and that the labour share temporarily increases following a positive shock to the interest rate. Using the standard models to analyse the distributional effects of monetary shocks could be misleading." - Cantore, Ferroni, León-Ledesma (2019). The missing link: Monetary policy and the labour share. VoxEU
  • Zombie companies have a lot of debt, and neither have a large labor share nor shareholder profit

Notes:

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    $\begingroup$ A capitalist is an owner of capital, not just a beneficiary of capitalism. Like a concubine of a capitalist benefits from capitalism, but she isn't a capitalist herself. $\endgroup$ Jun 22, 2022 at 12:35
  • $\begingroup$ @user161005 clarified some assumptions $\endgroup$
    – llllvvuu
    Jun 24, 2022 at 8:21
  • $\begingroup$ @Giskard clarified some assumptions $\endgroup$
    – llllvvuu
    Jun 24, 2022 at 8:21
  • $\begingroup$ I don't understand what the actual question is here. $\endgroup$
    – user253751
    Jun 24, 2022 at 10:52

1 Answer 1

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What are the mistakes in my definitions & reasoning, if any?

Problem with Definitions

There are some problems with some of the definitions.

Definition of Capitalist

You claim:

If I work and invest in stocks (e.g. via a tax-advantaged investment account), I am both a capitalist and a laborer.

But this is not completely clear. In fact, under many definitions you would only be counted as a capitalist if a significant proportion of your income comes from capital. For example, according to Hashimzade et al (2005) Oxford Dictionary of Economics 5th edition, a capitalist is:

A person whose income, or a significant proportion thereof, comes from the ownership of capital.

Hence, this is not really clear cut, unless all your income comes from capital it depends on what you consider 'significant proportion'. Here reasonable people might disagree, but it would not make sense to call everyone who earns any insignificant return on capital capitalist. For example, if a self employed painter sells a painting some tiny portion of profit from that sale was return on capital (brushes), but I don't think any serious economist would say that in that case the person is both laborer and capitalist.

Definition of Capital

For example, the modern definition of capital in economics does not include stocks (see for example Mankiw Principles of Economics 5th ed Glossary on pp 505). Capital is:

the equipment and structures used to produce goods and services

This is what Marx in das Kapital calls 'real capital'.

Also, I had look at your reference and the chapter never states that stocks are defined as capital. Maybe I missed the definition somewhere, but as far as I can see there isn't such definition in the chapter you cite. In fact, in chapter 30 Marx states:

Titles of ownership to public works, railways, mines, etc., are indeed, as we have also seen, titles to real capital.

Stock is a title of ownership over a firm. Firm can or may not own capital. If a firm owns capital, then by transitive property you can say that your stock is deed to capital. If the firm owns no capital then owning a stock does not make you owner of capital. For example, if street pantomime would decide to set up his business as a stock company the stock ownership would not turn the pantomime into capital owner since the business has literally no capital.

This being said, usually the main reason why companies issue stock is to purchase some capital to work with, so most of the time if you purchase stock you will indirectly own some capital with it.

Problems with Data

There mistakes in your claim about data. You claim:

The labor share of corp sector net income was 70% as of 2017 (Federal Reserve Bank of Richmond) i.e. the "rate of exploitation" is 3/7

But this claim is not empirically sound even using Marx's definition of exploitation as $(T-T^*)/T$. Not all those profits are empirically created by labor. For example, if only 80% of all profits are created by labor, then the rate of exploitation would be 1/7 not 3/7.

Even if you are interested just in normative (moral) analysis you can't ignore positive economics (facts). Otherwise, you can just make up any number you want regardless of statistics.

I think that you probably assume here that all that profits are derived from labor (i.e. you assume Smith's and Ricardo's Labor Theory of Value that Marx adapted in his work). Under LTV it would be reasonable to assume that all profits are derived from labor. However, empirically that theory turned out to be incorrect and was already disproven long time ago (e.g. see West 1983; Samuelson 1971; Grant & Brue History of Economic Thought 7th ed pp186 and sources cited therein). Hence, you cant make that claim without first showing that in 2017 it happened to be that whole profit was fully derived by labor with some additional assumptions. For example, one of those additional assumptions would be no entrepreneurial labor as well. If an owner actually also does some work within business then the profit would not be all due to laborers even if LTV would be correct.

Now, the fact that not all value derives from labor doesn't break Marx definition of exploitation, as indeed firms could still appropriate some quasi-rents from workers. Also, labor markets are not always perfect so workers can be paid less than their total contribution etc. However, revenue of all firms does not depend just on labor so this is something that would have to be researched further.

Problems with Reasoning

If there were no corporate profits, there would be 0 return on stocks.

This claim is not correct either theoretically or empirically. Even theoretically firm can achieve positive returns reinvesting profits and growing because stock gives you ownership over part of a company as long as the company grows even if its not profitable yet its value can increase. There are also other reasons why that might happen such as due to speculation etc. I won't discuss this more deeply as this answer is already very long.

Second, empirically you can clearly see this isn't true. Consider Dropbox Inc. According to the Market Watch Dropbox not only did not had any profit but it actually had loss in 2020. Yet on 29/12/2019 (last trading day of 2019) stock price was \$18 and on 27/12/2020 (last trading day of 2020) the stock price \$22.19. They did not paid any dividends but stock return depends also on change in prices, this means that the stock return was $r=\frac{P_{t+1}- P_t}{P_t} = \frac{22.19- 18}{18 } = 0.2327 $. Hence the stock still delivered return of 23.27% despite of firm not just having no profit, but actually experiencing loss. That doesn't mean its good idea to buy stock of unprofitable company, especially if you save for retirement, but empirically its possible to have positive return even with zero profit.

If my savings in stock exceed 4.1 years of my wages, I earn more from stocks than the corporate profits I generate

I honestly can't understand how did you calculated that. This can't be generally true. The profits you generate for the company are $\pi(d=1) - \pi(d=0)$ where $\pi$ is profit and $d$ is a dummy variable that is 1 if you are somehow involved in the company and 0 if you aren't.

Profit of a price taker company employing both labor and capital will be given by:

$$ \pi = p q− wL − rK \text{ s.t. } q=f(L,K)$$

Here $\pi$ is profits, $p$ is price of product, $q$ is quantity of product, $w$ wage of laborers, $L$ quantity of labor, $r$ price of capital and $K$ units of capital. Both wage and price capital are positive ($r>0$, $w>0$).  Product $q$ is produced using production function $q=f(L,K)$. We can assume Cobb-Douglas technology given by $q=L^{0.5}K^{0.5}$.

$$ \pi = p(L^{0.5} K^{0.5})− wL − rK $$

Now suppose $L$ is measured by number of employees who all work same hours per year, so $w$ is yearly wage, lets assume that this company uses all money from stocks to get capital so $K$ will be number of stocks and $r$ value of those stocks where we implicitly assume that price of every unit of machine is also $r$ so for every stock company gets they can buy one extra machine. Suppose the yearly wage is equal to $w= 1$, price of capital is also $r=1$, company employs 10 workers including you and and it uses 10 units of capital from some other people and 4.1 units of capital from you (so together $K=14.1$). Hence value of your capital is exactly equal to 4.1 times your yearly wage. Assume prices are equal to 5. Assume dividend payout ratio is 0.1.

In the case you are part of the company:

$$\pi(d=1) = 5(10^{0.5}\cdot 14.1^{0.5})− 1 \cdot 10 − 1 \cdot 14.1 \approx 35.27$$

The money you earn from yearly wage are 1, now your capital investment of 4.1 entitles to 0.291 share of dividends since we assumed K corresponds to stocks and 4.1/14.1 means you own 29.1% of company so you also get 29.1% of dividends. Since we assumed dividend payout ratio of 0.1, the total dividends are 3.527 and you are entitled to 29.1% of these dividends meaning that your dividend earnings are about 1.03.

Now if you are not part of a company the company the profit is:

$$\pi(d=0) = 5(9^{0.5}\cdot 10^{0.5})− 1 \cdot 9 − 1 \cdot 10 \approx 28.43 $$

So your contribution to profit is $\pi(d=1)-\pi(d=0) = 6.84$, yet you only earn on stock 1.03, so your claim is clearly false in the case above.

Now of course you might be able to find some particular $p$, $w$, $r$ and $q(L,K)$ and pay out ratio for which the statement will be true (e.g. if payout ratio above would be 0.9 your statement would be correct). However, you cant just state it as true statement as the counterexample above shows (you cant claim all swans are white if I show you one black swan). You would have to empirically investigate whether this holds on case by case basis.

If labor share was 100%, 2-3 would not be possible due to 1, so I would be worse off.

Not necessarily because 1 does not hold generally.

Answer to Followup Question

Follow-up question: My argument 1. applies specifically to 100% labor share. If labor share was 99% it wouldn't apply. Is there any known general relationship between labor share and stock market returns?

First the paper you cite is about monetary policy so that's irrelevant to your question. So that lead is dead end.

Second, quick google scholar search did not reveal any paper directly talking about this but there are some papers such as Eiling1 et al 2019 that discuss it indirectly.

However it is possible to have quick look at the relationship using data on average stock prices provided by Fed which I use to calculate quarterly average stock returns and date on the labor share provided by BLS (which is also the data cited in the report you cite).

Calculating correlation in r using cor.test(mydf$ls,mydf$return) we get:

Pearson's product-moment correlation

data:  mydf$ls and mydf$return
t = -0.69099, df = 224, p-value = 0.4903
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 -0.17556326  0.08489185
sample estimates:
       cor 
-0.0461195 

The estimate for correlation is -0.046 which would indicate very weak but negative relationship if significant, but this estimate is not statistically significant at $\alpha=0.05$ so we cannot reject null that the actual correlation is zero.

I also plotted the two variables against each other below. There is no discernible relationship.

Maybe some more rigorous analysis could find some significant relationship but looking at the data it would likely be very weak, if there is any at all.

enter image description here

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  • $\begingroup$ thanks for spelling this out. for the example, what i was imagining was more like L=10, K =14.1 in both cases, but in one case w=1 and in the other case w is such that π=0 (i.e. w~=4.527). as far as the dividend payout ratio being 0.1, i assume the other 0.9 is not going to buybacks or taxes, and r is the depreciation (and not the rental cost, since K is equity-financed), so would it be going towards shareholder value? so i gain more than 1.03. i see the point stands though (that it could be any arbitrary number) $\endgroup$
    – llllvvuu
    Jun 25, 2022 at 17:28
  • $\begingroup$ i'm trying to imagine the "ideal" "Marxian" counterfactual but not sure what it would actually look like other than increasing w; "worker-owned" sounds like "proprietorship" to me, but as the Cobb-Douglas example illustrates, the worker probably does not earn 6.84 as a proprietor 🤔 $\endgroup$
    – llllvvuu
    Jun 25, 2022 at 17:34
  • $\begingroup$ @llllvvuu 1. well as you say you are just picking arbitrary numbers 2. Also those numbers are not consistent if $\pi=0$ then you get 0 regardless of payout rate. Also w should not depend on whether you are involved or not. 3. Also no r is not depreciation in the model above but cost of purchasing unit of capital, depreciation would be some decay of that capital over time K_t+1=(1-\delta)K_t. K are units of capital not value so for example K=1 would be 1 printer if the above is some book printing company. The model above is only 1 period so there is no point in depreciation. $\endgroup$
    – 1muflon1
    Jun 25, 2022 at 17:40
  • $\begingroup$ @llllvvuu 5. firm could choose payout rate of 1 but IRL that would be irrational. In that case the firm would not be able to progress and over time would actually deteriorate precisely because of depreciation that’s not captured in that single period example. The point of that example above is just to show statement 1 is not true statement generally $\endgroup$
    – 1muflon1
    Jun 25, 2022 at 17:47
  • $\begingroup$ sounds good, thanks. re: where i initially got the 4.1 number from, it was based on the (what i now understand to be flawed) idea that if we lived in a corporation-free "utopia" we'd be earning 42.8% more (3/7) and it'd be preferable to make \$70k/yr and hold \$287k in stocks in our current world than make \$100k/yr in the "utopia". but it seems like said "utopia" is undefinable, among other issues $\endgroup$
    – llllvvuu
    Jun 25, 2022 at 17:52

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