Stocks, Flows and Loanable Funds

Economics is the science of confusing stocks with flows.

Michal Kalecki

What is the market of loanable funds? It is supposed to be the market that equilibrates the demand for savings with the demand for investment. But if such a market existed, it would be a market for flows, not stocks.

However the bond market is a market of stocks. The capital market is a market for stocks. Both bonds and capital persist across periods and can be re-sold. Everyone who owns a bond (or who owns capital) is a potential supplier of bonds or capital at some rate. Everyone is also a potential demander of bonds or capital at some rate.

As the interest rate changes, some suppliers become demanders, so that at equilibrium, supply (of the stock) is equal to the demand (for the stock).  This is the equilibrating process for stocks that can be re-sold by their current owner in any period.

But lending and investment are the derivatives of these quantities with respect to time — they are flows.

Can the interest rate equilibrate both flows and stocks?

A flow of investment — say capital goods producing firms or borrowing —  leaves the current period stock of capital or bonds unchanged, but the growth rate of these stocks changes. In future periods, there will be a greater stock of capital or bonds as a result of an increase in the flow of investment or borrowing.  And we can imagine that there might be a demand for a flow of savings or a demand for a flow of lending.

As a simple example, suppose that all bonds are consols — to avoid issues with changes to the quantity of bonds due to bond repayment. The equivalent assumption for capital would be no depreciation.

In that case, let Q(t) be the total quantity of bonds or capital. Then the growth rate of bonds or capital will be dQ/dt = F.

If the rate, r is such that the quantity of bonds demanded is the quantity of bonds supplied:

Q_d(r^*) = Q_s(r^*)

So that

\frac{r}{Q_d}\frac{dQ_d}{dt} =\frac{r}{Q_d}\frac{dQ_d}{dr}\frac{dr}{dt}

or

\frac{r}{Q_d}F_d =E_d(t)\frac{dr}{dt}

Similarly,

\frac{r}{Q_s}F_s =E_s(t)\frac{dr}{dt}

Where E_s\text{ and } E_d are the interest-elasticities of supply and demand (for the stock).

At the market clearing rate, we have Q_d(r^*) = Q_s(r^*), so dividing both equations yields:

F_d(r^*) E_s(r^*)= F_s(r^*) E_d(r^*)

Therefore the interest rate that equilibrates stocks will only equilibrate flows in one of three special cases:

  1. Supply and demand for flows is zero (F_s(r^*) = F_d(r^*) = 0)
  2. The interest-elasticities are zero (E_d = E_s = 0)
  3. Flows are stocks. I.e. all capital depreciates to zero instantly and all bonds are repaid instantly.

None of these assumptions hold in any economy. Nor is plausible to believe that they should hold in simple models.

Therefore the interest rate can only equilibrate the level (stock) of bonds or capital so that at that rate, agents are just as likely to buy the capital from someone else as they are to sell it to someone else. But interest rates cannot clear flows — they cannot clear lending and borrowing, savings and investment.

The flows will be whatever is profitable at the rate, which may not be what is demanded at that rate.

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Stocks, Flows and Loanable Funds

9 thoughts on “Stocks, Flows and Loanable Funds

  1. Sergei says:

    I used to think that loanable funds is applicable only in real terms and only at full employment economy and only in one direction. In that case one clearly has a market of finite and limited resources which have to be shared between consumption and investments with investments being able to crowd out consumption (this is the direction).

    I still tend to think that this is true. But then how does it reconcile with your 3 special cases? Investment demand is not zero by definition. Interest elasticity is not zero due to crowding out. And capital does not depreciate instantly.

    Should there be another special inter-temporal case?

    1. Sergei,

      My argument is about stocks versus flows.

      Demand for capital is a demand for a stock. Supply of capital is the amount of capital currently in existence.

      Production of new capital is a flow. It takes time for a change in a flow to cause a change in a stock.

      At that (later) time, there will be a new set of price vectors, a new auction, and a new demand for the stock, etc.

      But in the current period, a change in the flow of production of new capital cannot clear demand for the stock. Only a change in price of the existing installed capital will clear a demand for the stock of capital in the current period.

      At that (new) price, the flow of production of new capital will increase or decrease, which will affect the supply and price of capital in subsequent periods. But in those subsequent periods, there will be new auctions, new demands, with new equilibrium price vectors.

      So in each period, the causality goes as:

      change in demand for capital + Current quantity of capital –> change in price of capital –> change in (flow) of new capital supply == change in (flow) of savings.

      But across periods — across different auctions — savings and investment will feedback into this process, as an increase in savings will cause the amount of capital in the subsequent period to go up. It may affect the future price of capital goods, but not the current price of capital goods.

      I don’t see how issues like full employment or inflation effect the argument at all.

      1. Sergei says:

        The logic behind loanable funds is about *available* funds. While there is never a fixed volume of available financial funds, there is always a fixed or limited volume of available real funds which one has to share between consumption and investment. Obviously one can not get beyond full employment regardless of anything and interest rate clears conflicting consumption/investment demands. But this is effectively only at full employment. Until we get to this point the conflict between demands is not hard. But whatever…

        Loanable funds specifies the clearing mechanism with interest rate being the tool. Interest rate changes affect the market price of existing capital stock. Do you argue that increasing interest rates lead to increasing demand for capital? It sounds very counter-intuitive to me and the opposite makes much more sense. It seems that in your interpretation you would need to get to the reasons of interest rate changes if you want to avoid the chicken-egg problem. This issue does not bother the standard formulation.

  2. No, Sergei, I’m not arguing that higher interest rates lead to increased demand for capital.

    But look at what you are arguing for — which is a typical error, IMO:

    1. There must be a trade-off between allocating resources towards investment and consumption (TRUE)

    2. Ergo there must exist a market that equilibrates this trade-off (FALSE).

    Just because there is a trade-off does not mean that the interest rates determine this trade-off.

    They can’t.

    Because for each household, there is *no* trade-off between investment and consumption, as there is no individual demand for investment. The demand for capital is a demand for a stock. Saying that there is a demand for investment would be like saying there is a demand for new bond issues.

    There is no such demand.

    There is only a demand for bonds, not new issues. There is no market in which only new issues are sold, determining the interest rate.

    Which is why, in the general case, there are excess savings desires above and beyond the equilibrium interest rates, even though the bond market continuously clears. It clears, but it doesn’t clear flows, it clears stocks. The flows will be whatever they happen to be at the indifference level determined by the stocks.

    1. Sergei says:

      I think I understand what you say. There is no market for *real* loanable funds simply because it does not and can not exist. So we are left with the financial loanable funds market.

      The financial market operates with stocks. The changing preferences (and so on) affect the todays price level of this stock. These changes to todays prices bring forward changes to flows which will only appear in tomorrows stock when the new price level will be defined and new flows derived for the period thereafter. Is it correct?

      Doesn’t it mean that in general there is no connection between interest rate of stocks and interest rates of flows? The market prices of todays stock can be whatever and we can derive the implied interest rate from it. However flows are influenced by the future interest rates. At the very least the stock is valued with one extra period which also has the largest impact due to discounting. It also sounds like an argument (I think Nick Rowe likes to say it) that MMT claims that I and S do not depend on interest rates.

      1. “Doesn’t it mean that in general there is no connection between interest rate of stocks and interest rates of flows? The market prices of todays stock can be whatever and we can derive the implied interest rate from it. However flows are influenced by the future interest rates. ”

        I don’t understand what you mean by the “interest rate of flows”. There is no such rate.

        It’s easier to think in terms of prices. Does the current price of the stock of capital affect the rate of production of new capital? Clearly it does. At a higher price, producers will produce capital at a faster rate. Therefore at a higher price, the flow of investment will be greater, and therefore the flow of savings will be greater.

        Another feedback in the other direction is that present investment makes the existing stock of capital more profitable.

      2. Sergei says:

        I find it difficult to think in terms of prices of investments. What I meant is that flows clear regardless of anything. I.e. whatever the central bank decides all flows will clear and this is what the market is for.

        The flows are the logical derivative of changes to the market value of stock. My first intuition was that when the market value of stock drops it causes an increase in the flow which will add to the stock and replenish it to some stable value or share of GDP. I am NOT sure that this intuition is absolutely wrong. It is typical that investment increases coincide with rate increases. But then it contradicts what you say, ie. that increases in prices cause changes to flows but in opposite direction. This sounds logical from a price perspective but not so logical from stock perspective relative to GDP. Maybe you have empirical data on this?

      3. What do you mean by “flows clear”? Markets clear.

        Now in terms of stocks, there is a bond market and a capital market. You can sell bonds and buy capital or vice versa. Together, both of these markets clear.

        In terms of flows, there is a consumption goods market and a labor market. Together, both of those markets also clear.

        But you cannot sum excess demands for both stocks and flows to get zero. You need to sum excess demands for stocks together, and do *another* sum of the excess demands for flows. It is two sums — it’s a vector, with each component equal to zero — and a consistency criteria (across time) between the two components of the excess demand vector.

        There is no “savings market”, nor is there an “investment market”. So in what sense do these non-existent markets clear?

      4. Sergei says:

        There is a connection between the stock of capital and the flow of (dis)-investment. What I am trying to understand is this connection.

        You say that when market prices of the existing stock increase this causes a new flow of positive net investment, i.e. future additions to the stock which will provide price arbitrage opportunities in the future. However I struggle to understand why price increases should have the effect on flows which you suggest. And what exactly can drive such price increases. My intuition is that prices increase when interest rates fall and interest rates fall when economic activity drops. So we can get to an over-supply of capital in terms of market values which can depress the flow of new investment. (There might be risk-premiums involved in valuation methodology but then it means that monetary policy should be more aggressive. I would ignore this risk at the moment).

        As I wrote above I tend to think of the stock of capital, probably in the Marxian way, as a, say, share of GDP. As technology progresses the capital intensity of the economy increases. And when we get, for instance, a structural technological break which devalues the existing stock of capital, it also causes a new flow of investment to replenish the market value of the stock back to its Marxian trend line. But this is exactly the opposite of what you suggest. So I wonder whether it is a different time perspective (short or long term) or there is more to it or my view of completely wrong.

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