IS-LM and All That

IS-LM is quite the rage this week.  Perhaps I will come back with some further observations another time, IS-LM being a perpetual object of argumentation among monetary theorists and macroeconomists, but here are some of my own, mostly critical, observations about that old standby of Keynesian economics.

Everyone recognizes that, in its original Hicksian form, IS-LM is a static one-period model, which sharply limits its practical application unless it is augmented to give it some dynamic features.  But augmenting it in the standard fashion doesn’t address, much less fix, its basic deficiency.  What is the nature of a static one-period equilibrium in which there is positive investment and saving and a rate of interest?  The model doesn’t have a coherent intuitive economic interpretation even in its one-period form.  Merely adding some dynamics doesn’t address the disconnect between the model and basic economic concepts.

For example, does anyone outside of Cambridge England actually think of the rate of interest as the price of holding money?  In the IS-LM model, the rate of interest is determined by the demand for money and a fixed supply of money (though in more up-to-date versions the interest rate is chosen by monetary authority).  The demand for money depends on income, so investment spending and consumption spending do affect the interest rate by way of their influence on the demand for money.  Now it’s true that there are bonds in the IS-LM model, otherwise there would be no way to measure the cost of holding money, but the presence of bonds doesn’t fix the underlying problem.  Even though a bond market is included, it can be kept in the background out of sight inasmuch as you only have to solve for equilibrium in two of the markets in a three-good system to find the equilibrium for the third market as well (Walras’s Law).

The trouble is that the bond market, reflecting the supply of and the demand for loanable funds, is an epiphenomenon.  There is a mismatch between the money market (demand for and supply of a stock) and the market for loanable funds (demand for and supply of a flow).  In the real world, interest rates are not equilibrating the supply of and demand for loanable funds; interest rates emerge out of the process of evaluating all durable assets, which are nothing but claims to either fixed or variable future cash flows of various durations and risk characteristics.  The structure of interest rates and risk and liquidity factors must adjust to bring about equilibrium between the demand for and the fixed supply of the current stock of physical assets.  The interest rates on the subset of financial assets that we call bonds are determined as part of the process of valuing all durable assets, the valuation of bonds being constrained by the valuations placed on the entire range of durable assets.  One of the good things about Milton Friedman’s 1956 restatement of the quantity theory of money was his explicit recognition that interest rates are determined not in a narrow subset of markets for fixed income financial assets, but in the complete spectrum of interrelated markets for long-lived physical and financial assets.

One way to handle this would have been to make explicit the consumption/investment tradeoff by defining a purchase price (for consumption) and a rental or hire price for current use of the output as an input in producing units of output for the next period.  The rental price over the purchase price represents a real interest rate and allows in an obvious way for both expected inflation and a consistent distinction between the real and the nominal interest rate.  (In the General Theory, Keynes explicitly rejected that distinction, based on reasoning implicitly assuming the existence of a liquidity trap, but in fact, using a comparative-statics approach, you can derive an effect on the interest rate in IS-LM from expected inflation when there is no liquidity trap.  And if you start from full employment equilibrium, the comparative-statics exercise increases the interest rate by as much as expected inflation.  Allyn Cottrell showed this in a paper some years ago, “Keynes and the Keynesians on the Fisher Effect,” Scottish Journal of Political Economy 41:416-33, 1994.

The conditions of factor-market equilibrium and money-market equilibrium can then be used to derive an equilibrium time path for the economy with the Keynesian spending (consumption and investment) functions suppressed instead of a meaningless bond market which can be discarded.  Earl Thompson developed such a model nearly 40 years ago, but never published it.  The 1977 version of his working paper deriving and applying the model is available here.  He also modeled the monetary sector in a way that can be made consistent either with the competitive nature of a modern banking system or with the fixed money-supply approach of the General Theory.

Earl’s paper is tough to follow in a number of places, which may have something to do with its lack of influence.  His earlier papers were not always written in the most accessible style, as he tended to leave out too many steps in his argument that were obvious to him, but not so obvious to his readers.  To achieve a level of aggregation comparable to IS-LM requires some heroic assumptions, and making them explicit, as Earl did, underscored the unrealistic nature of his model, a characteristic that Hicks’s matter-of-fact presentation of IS-LM tended to obscure in his presentation.  Also carrying out the analysis in terms of spending functions imparts a certain appearance of realism that is lacking from characterizing factor-market equilibrium in terms of a single labor input and the rental rate for using the single output as in input into its own production.  That is probably why IS-LM, for all its faults, remains popular with people with a moderate degree of economic sophistication when trying to get a handle on economic policy.  The fact that, despite its many shortcomings, some recognized some not, so many economists and policy makers are stilling using it is a sad commentary on the deplorable lack of progress made by macroeconomics over the past 40 years than on the virtues of IS-LM, a lack of progress for which both Keynesians and non-Keynesians alike can take the blame in roughly equal shares.

26 Responses to “IS-LM and All That”


  1. 1 Luis H Arroyo October 7, 2011 at 11:34 am

    I think that IS-LM model is a betrayal of keynes, as I´ve learned from Minsky.
    As you say, ther is a big mismatch between interest rate and the price of loanable funds.
    That is one of the lessons that I deducted of your blog.
    In my post
    http://cuadernodearenacom.blogspot.com/2011/10/expectativas-y-tipos-de-interes.html ,
    following you (I expect so) I intend to relate the effect of QE2 on corporate bonds spread through inflation expectations… That is, through real effect.
    Curiously, I observed that when inflation expectations rose in the QE2 period, the stock value rose (as you have said many times) whereas corporate bonds spreads fell… What I see as a sign that the supply of loanable funds increase due the better expectation for corpotrate income.
    So is as I see the relation: a keynesian explanation
    I´ve been very inspired in your blog, so I hope not to have betrayed you so much…

  2. 2 Ritwik October 8, 2011 at 4:38 am

    David

    I did not quite understand what you meant by

    “In the real world, interest rates are not equilibrating the supply of and demand for loanable funds; interest rates emerge out of the process of evaluating all durable assets, which are nothing but claims to either fixed or variable future cash flows of various durations and risk characteristics”

    Do you mean to say that abstracting out of credit risk nullifies the Keynesian analysis of interest rates? Or do you mean to say that interest rates can and do exist independently of any credit at all.

    Can you give an example of the durable asset valuation that you talk about?

  3. 3 David Glasner October 8, 2011 at 10:06 pm

    Luis, That sounds like an interesting correlation that you have found, and I look forward to reading more about it on your blog. In such matters, one can only betray oneself.

    Ritwik, The point I was making is that every real or financial asset can be evaluated as a stream of future cash flows. For a bond the cash flows in nominal terms at least are fixed (though there is default risk) for other assets the cash flows are anticipated, but to arrive at a valuation people have to discount the future cash flows at some rate, so all asset valuations imply some interest rate. Because people can choose among a range of different real and financial assets the prices of those assets are subject to the constraint of the prices of alternative assets, so you can’t say that it is the price of a certain narrow class of assets that is determining what THE interest rate is. Interest rates are determined in the markets for every asset.

  4. 4 Mr_RDES October 9, 2011 at 9:19 am

    IS-LM does have the distinct advantage of at least getting the signs right, which is more than can be said for much of contemporary academic economics. And for policy makers getting the sign right is an important virtue. IS-LM tells us that followers of the Treasury View, along with its modern day RBC and austerian descendants, are getting the signs wrong. Austerity will not increase output. Widespread and persistent unemployment is not due to an exogenous labor/leisure shock to the AS curve. And IS-LM coupled with a twist of Mundell-Fleming comes pretty close to getting things right on the broader international scale.

    It is true that IS-LM is a very static model, but is that a bad thing when the developed part of the global economy is largely in the grip of stasis? The bond and equity markets are mainly moving horizontally. Unemployment is stuck at 9.1% and has been for awhile. Private investment is in the dumper. Even Apple’s much vaunted reputation for ingenuity and dynamism showed us with its iPhone-4S that the economy is static. Intertemporal substitution is a joke when the future looks no better than the recent past. In short, economic variable are not moving at all, so why is a static model such a bad way to describe current reality? IS-LM is a sorry excuse for a model if you’re still living in 1979; but we aren’t living in 1979.

  5. 5 Lorenzo from Oz October 9, 2011 at 5:51 pm

    David: that would seem to imply that all expectations of capital gain are anticipations of future income. I am not at all sure that is true, given net wealth effects are not cash flows and, as long as asset prices are rising, it is perfectly possible to profit without matching income flows. Down here in Australia, where the Great Moderation has never stopped, house prices are way outstripping rents, so the issue has particular resonance.

  6. 6 David Glasner October 9, 2011 at 6:40 pm

    Lorenzo, You are introducing a complication that I was trying to avoid by attributing all the value of an asset to an expected future cash flow, but in the case of housing as you point out, the value is associated with an expected future service flow. So the increase in value is associated with an expectation that the future service flow will become more valuable. There may be a question whether such an expectation is plausible or rational, but as long as we are staying within the framework of a rational model of asset valuation, one has to assume that an increased value is attached to either an expectation of an increased future cash flow or an increased future service flow. A lower discount rate would also work, but then it would be difficult to explain why the discount rate would affect only one category of assets and not another.

  7. 7 David Glasner October 9, 2011 at 6:47 pm

    Mr_RDES, Well I don’t subscribe either to RBC or Austrian business cycle theory, but I still don’t care for IS-LM. IS-LM doesn’t always give you the wrong answer, so I don’t reject it out of hand, but you also need to have the right intuition in applying it. Economic policy is as much an art as a science.

  8. 8 Ritwik October 9, 2011 at 9:14 pm

    David

    I’m afraid I still don’t fully understand.

    1) Is there any such real asset apart from housing that would be valued in this way? Are you referring to capex, project financing etc. decisions by firms? These will depend either on opportunity costs (for a cash rich firm) or on financing costs (for a cash constrained firm). The former is not what we are bothered about and the latter is loanable funds, right?

    2) Why do we need knowledge of all interest rates if we have conceptually split them into a ‘the interest rate’ and credit risk? This applies to housing as well.

    Would you be more comfortable if instead of ‘bond market’, the model said ‘bond market & bank lending’?

  9. 9 Lorenzo from Oz October 10, 2011 at 4:46 am

    David: good answer, thank you. Bonds are just congealed cash flows, so they are relatively easy to understand. Other assets provide service flows as well, which complicates. My view on asset bubbles is that they exist, but are only definitively so in retrospect, since if we could reliably pick the turning points, people would not be caught by them, so they would not happen in the first place.

    In the meantime, the rising prices are information feeding into the market. We may well judge that they have outrun plausible values based on income flows but that fails to get market confirmation while prices continue to rise. As long as people can continue to sell to someone who anticipates gain, that is sufficient to sustain the rising trend. Of course, if that anticipation is reversed, then prices may well lose any reason to be more than the value of their income flow: which can be a long way down.

  10. 10 David Glasner October 11, 2011 at 11:23 am

    Lorenzo, Because all asset prices are conditional on expectations, the price of almost every long-lived asset is subject to significant downside risk (in percentage terms), so there is an element of bubble in every asset price because the expectations supporting a given price may turn out to have been incorrect. There are clearly some cases where the expectation is so whacky or fraudulent that we can say that it was clear to anyone with access to the correct information that the price would fall, but i don’t think such cases account for all alleged bubbles.

    Ritwick, Sorry but we don’t seem to be communicating very well. I am talking about houses, apartment buildings, office buildings, factories, machines, gold, as well as stocks and bonds. Every long-lived asset has a value that in principle reflects the expected future net cash flows, plus any associated service flows provided by the asset, discounted to the present by expected future risk-adjusted interest rates. Just as the (risk-adjusted) interest rate is implicit in the valuation of a fixed income security, the (risk-adjusted) interest rate is implicit in the valuation of any long-lived asset, though there are more variables that have to be accounted for in most long-lived assets than there are in fixed-income securities. But the rate of interest is implicated in the valuation of every asset, not just in bonds. I don’t know how to make the point any clearer. I wish I could be more helpful to you.

  11. 11 Ritwik October 11, 2011 at 11:46 am

    Thanks, I do get it. Just not very sure if I’m able to grasp why it would be so important. In risk neutral valuation, you would discount every asset, physical or financial, at the risk free rate. So your point basically is credit risk + (maybe) heterogeneous capital? I tend to think that that still leaves the risk free rate (whatever that is) as something that can be analyzed separately. And isn’t that ‘the interest rate’ of the IS/LM model?

    Perhaps I need to think about this a lot harder, or just differently. But thanks anyway!

  12. 12 Ritwik October 11, 2011 at 11:52 am

    Let me rephrase that “so important, in the aggregate, if not for default”.

    One last thing – is your concern subsumed/answered by Tobin’s q?

  13. 13 JP Koning October 11, 2011 at 1:50 pm

    “The interest rates on the subset of financial assets that we call bonds are determined as part of the process of valuing all durable assets, the valuation of bonds being constrained by the valuations placed on the entire range of durable assets. One of the good things about Milton Friedman’s 1956 restatement of the quantity theory of money was his explicit recognition that interest rates are determined not in a narrow subset of markets for fixed income financial assets, but in the complete spectrum of interrelated markets for long-lived physical and financial assets.”

    At what point does something qualify as being long-lived or durable? I’d assume my pencil would qualify as a long-lived physical asset, but as I use it up to a mere stub, at what point has it ceased to be long-lived?

  14. 14 David Glasner October 11, 2011 at 8:46 pm

    Ritwik, My point is that because all long-lived assets are substitutable in some degree for one another, it doesn’t make sense to think of THE interest rate as being determined in the bond market any more than it makes sense to think of THE price of crude oil as being determined in Cushing Oklahoma for West Texas Intermediate. All crudes prices are interrelated and they are jointly determined and you can’t single out the market for one particular crude as the market in which crude oil prices are determined. About Tobin’s q, I think it fits in with my general point, but it’s not exactly what I am thinking of, but maybe if I think about it some more I’ll get a better handle on it.

    JP, It’s a continuum. A pencil has so little value that it only makes sense to sell it in packages when they are brand new. There’s no second hand market for pencils.

  15. 15 Mitch October 11, 2011 at 10:25 pm

    I am confused along with Ritwik. So what if the bond market doesn’t “determine” the interest rate? Yes, all those other, separate markets to which you refer also *reflect* the underlying interest rate, and decisions about the desirability of those long-lived assets are important in setting the interest rate in the economy. Nonetheless, the point is that the risk free interest rate, which can be measured in the bond market, among other places, represents the cost of holding money rather than a risk-free asset.

    When the fed, having the ability to influence the zero-risk interest rate, sets a particular value for it, it will also affect all those other long-lived asset markets. That is, the zero-risk interest rate isn’t separate in the different kinds of asset markets. Thus, when interest rates go down, prices of houses go up. That’s not because the houses became more desirable, it’s because their prices are connected to interest rates.

  16. 16 JP Koning October 12, 2011 at 9:49 am

    “Nonetheless, the point is that the risk free interest rate, which can be measured in the bond market, among other places, represents the cost of holding money rather than a risk-free asset.”

    So what is this rate? IOR, LIBOR, GC repo, three month bills, the federal funds rate? They are all yielding varying amounts starting from around -0.1% to 0.49%. Which one represents the cost of holding money?

  17. 17 Mitch October 12, 2011 at 10:08 pm

    Now you’re quibbling. These rates differ because they represents different terms, durations, currencies, and risks. Or, let me flip it around: why do *you* think that these are different? If they’re really all just identical zero-risk rates, why aren’t you getting rich on the arbitrage?

    The point that David was making was that you have to consider all asset classes instead of just the bond market. Fine, do so. It won’t render IS-LM is “not coherent”. You just made a much more complex “bond market” than IS-LM considers, without gaining much conceptual insight.

  18. 18 JP Koning October 13, 2011 at 6:39 am

    I’m genuinely curious and hope I am not merely quibbling. What is the observed risk-free rate of interest that goes into IS-LM? I gave a short list, but I don’t claim to know. One can’t choose just any of those numbers since they all differ. If the risk-free rate is just a hypothetical number in a model that is another issue.

  19. 19 Mitch October 13, 2011 at 8:40 pm

    I am by no means an expert on this subject. My impression is that in that you imagine that there is a risk-free interest rate that represents the cost of holding cash. How you abstract this from the very much more complicated real world is beyond the scope of the model. However, you can try to look at the various interest rates you listed and see where the risks are, and, if you can assess a market value for risk, remove those effects and see if you can find a zero-risk interest rate.

    My objection to David’s post is that he’s making it seem that because the world is more complex than IS-LM attempts to capture, that it is “incoherent”. My takeaway is simply that in IS-LM, “bonds” represent all long-term assets from which you can deduce a zero risk rate.

  20. 20 David Glasner October 16, 2011 at 8:47 pm

    Mitch, I have no problem looking at the bond market to get an estimate of the risk free interest rate that represents the cost of holding money. My problem is with the interpretation of the equilibrium in the bond market as being determined by the supply of and the demand for loanable funds. That is the equilibrium that determines the interest rate is not a flow equilibrium between current savings and current investment, but a stock equilibrium that in which asset prices and interest rates are such that the stock of capital assets is willingly held. There is a huge difference between those two conceptions of equilibrium. The flow concept leads to the obviously incorrect proposition that the budget deficit is positively correlated with the level of interests, a proposition lacking any empirical support, but consistently maintained by both economists and non-economists alike as if it were a natural law.

    The Fed can affect the short-term interest rate, but it is not at all so clear that it can affect the entire yield curve. The notion that operation twist will have any affect on long-term rates is highly doubtful and if it does affect long-term rates it is probably not through its interventions in the market for bonds, but by somehow altering expectations about its future policy stance.

    IS-LM implicitly assumes that there is a uniform interest rate and a flat yield curve. But that’s not my main issue. My main issue is that using the bond market to model the interest rate tosses out the entire structure of Fisherian capital theory that is one of the great achievements of neoclassical economics. Even though Keynes was critical of Fisher in the GT, his discussion of the marginal efficiency of capital, some of the most insightful parts of the GT, was in many respects very close to Fisher’s work and none of that is really reflected in IS-LM, which is why a lot of the Cambridge Keynesians and post-Keynesians are unhappy with IS-LM as well.

  21. 21 Luis H Arroyo October 17, 2011 at 12:39 am

    David, just what I tried to say in my previous comment…. And the figure that I quoted was an example of the huge gap between public and private bonds – these out of control of the FED.

  22. 22 Mitch October 17, 2011 at 7:08 pm

    You are doubtless more expert on these matters than I. My understanding is that the idea of IS-LM is that it applies only in the short term. I am much more ready to believe that the money market rates of interest are set by the short-term supply and demand for loanable funds. People are very unlikely to rush to sell their houses because the short-term interest rate moves around.

    At any rate, my understanding s certainly what is claimed on the Wikipedia page:

    http://en.wikipedia.org/wiki/IS-LM

    A better criticism it seems to me is that the GDP cannot respond in the way claimed on the short term timescales implied.

    Nonetheless, the question is whether IS-LM gets things qualitatively right even though the arguments for it are (as admitted by the inventors) simplistic.

  23. 23 David Glasner October 17, 2011 at 8:47 pm

    Mitch, I am not a fan of IS-LM, but that doesn’t mean it is never useful. And you seem to have a good grasp of what it is all about.

    Luis, Sorry, I still haven’t looked at your post. I have been very busy, but I will try to do so.


  1. 1 Economist's View: links for 2011-10-08 Trackback on October 8, 2011 at 12:22 am
  2. 2 The big IS/LM debate – DeLong comes under heavy shelling « The Market Monetarist Trackback on October 8, 2011 at 10:43 am
  3. 3 Who needs a macroeconomic model? « azmytheconomics Trackback on November 4, 2011 at 11:15 am

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About Me

David Glasner
Washington, DC

I am an economist in the Washington DC area. My research and writing has been mostly on monetary economics and policy and the history of economics. In my book Free Banking and Monetary Reform, I argued for a non-Monetarist non-Keynesian approach to monetary policy, based on a theory of a competitive supply of money. Over the years, I have become increasingly impressed by the similarities between my approach and that of R. G. Hawtrey and hope to bring Hawtrey's unduly neglected contributions to the attention of a wider audience.

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