How is the IS/LM Model supposed to work???

Economics Economics Questions
1

Hi everyone,

I have major problems understanding the logic of Higgs’ IS/LM-Model. I even discussed it with my professor today (who is a devotee of Keynesianism), but she seemed incapable of explaining it to me.

Here’s what I don’t understand: As you propably know, the IS-curve shows all the combinations of output (consumption, investment, net exports and government expenditures) and interest rate, at which the goods markets are in equilibrium. It has a negative slope, because investments go up when interest rates fall and go down when interest rates rise.

But, according to the IS/LM model, investment expenditures can rise without a drop in consumption. In fact, Keynesians even believe that a rise in investment expenditures can cause a further rise in consumptions through supposed multiplier effects. If I were right and every rise in investments would cause a fall in consumption, and vice versa, the IS curve would be vertical, making fiscal policy meaningless.

Similar problems arise with the LM curve: According to the model, the supply of money is fixed and the demand for money rises when the output grows, causing interest rates to rise. However, I find it hard to imagine that people have to borrow money in order to acquire the economy’s growing output (which clearly neglects Say’s law, but I know, we’re still in a Keynesian fantasy world). To me it seems even more unlikely, that output and the interest rate of the model economy have enough time to fluctuate, the price level however is still fixed. But still, that is not the main problem with the LM-curve. Logic and Keynesianism often don’t seem to be really good friends, but when it comes to the fact that money supply and price level are constant in this model, and Monetarist monkey business like velocity of money doesn’t exist in this model - how on earth can a rising interest rate create enough specie to create an equilibrium in the goods market? Remember, output Y has risen by, say 20%, the price level is fixed. In order to buy these additional goods, the supply of money has to increase by 20% as well. How can it do that when it is fixed??? And if a rising interest rate was not capable of increasing the economy’s supply of money, the LM-curve would be entirely flat, making monetary policy incapable of improving economic conditions.

Can anyone explain to me how this model is supposed to work? How would a Keynesian argue? Thank you very much in advance!

2

Thats the $6 trillion question.

3

Is no one here fluent enough in Keynesian theory to eplain the basic meaning of this model to me?

4

The IS curve can be shifted outward by the government taking on greater expenditures through fiscal policy, by borrowing money. Obviously a mere tax increase will be offset by reduced private consumption and investment.

The LM curve can be shifted outward by lowering interest rates through open market operations, i.e. increasing the supply of money.

So, if the government uses solely expansionary fiscal policy by borrowing money, the shifting of the IS curve outwards will raise interest rates in the credit market (crowding out).

If the government uses solely expansionary monetary policy, the interest rate will go down since the credit market is flooded with new money, and this will stimulate consumption and investment.

If on the other hand the government expands both IS and LM simultaneously, i.e. the government creates the money it borrows, then there is no extra drain on the credit market and interest rates will not go up, whereas Y will expand.

Of course, through a greater demand placed upon real goods in the economy, this will still crowd out business, and will still increase prices. But, in the short term, this model does indeed work quite well. Mind you this also depends on confidence. If as now during the recessionary period confidence is/was low, then fiscal and monetary policy has little effect, with both IS and LM curves becoming less elastic, especially the LM curve.

I hope this helps, this is just what I remember off the top of my head from my 2nd year at uni.

5

First off, I think you mean “Hick’s IS-LM model”. :stuck_out_tongue: John Hicks first introduced the model in his paper “Mr Keynes and the Classics”, though it has went through many revisions since.

But, according to the IS/LM model, investment expenditures can rise without a drop in consumption. In fact, Keynesians even believe that a rise in investment expenditures can cause a further rise in consumptions through supposed multiplier effects. If I were right and every rise in investments would cause a fall in consumption, and vice versa, the IS curve would be vertical, making fiscal policy meaningless

Actually it would not.

I think one stumbling block might be that you must remember that IS-LM is just a model of aggregate demand. to have a complete model of output you would need at least some implicit model for aggregate supply. I will do my best to address your question, but I think the best way to better understand IS-LM is to read more textbooks/papers on the subject. Specifically, I would check out Ben Bernanke and Andrew Able’s textbook “Macroeconomics”. I think it is one of the best undergrad textbooks still in publication.

Anyway, the best way answer your question is to describe what the IS curve actually is. Each point on the IS curve represents what, for a given level of income, the interest rate has to be to get the goods market in equilibrium (for now to best address your specific question lets consider an economy where money is only spent on consumption and investment). IOW: the IS curve represents the interest rate that equates spending (because for now let’s just assume we’re dealing with an economy where money is only spent on consumption or investment, no government or exports) with output for a given level of income.

We can summarize this concept mathematically: each point on the IS curve represents a point where this equality holds Y1 = C(Y1) + I(i) (note that consumption is a funciton of income and investment is function of the interest rate).

If we re-arrange the terms of this equality we can see another way of thinking about IS (one which is actually the way Hicks originally formulated it and the way Bernanke presents it):

(Y1)-C(Y1)=I

since money can only spent on investment and consumption, (Y1)-(C1) must represent saving. So each point on the IS curve represents a different equilibrium between saving and investmet or

S(Y1) = I(i)

This is why Hicks actually called it the I-S curve, it presented equilibrium between saving and investment for different levels of income.

So how does making this substitution help us? Well, thinking about it in terms of saving and investment try to explain why the IS curve would slope downward. Why would the interest rate fall as income/output increased?

Answer: Because savings are a function of income and as income increases so does saving! And this increase in savings is what places downward pressure on the interest rate (see figure)

This is why there is no conflict with what you are saying. You are saying that for a given level of income, you can’t spend one more dollar on investment without spending one less dollar on consumption. If you want to make that assumption that is fine. But you missed the point that the IS curve is talking about the consequences of *increasing income.

Now you may ask, “Well I really do believe that output is fixed and that you can never spend more money on both consumption and investment, doesn’t IS-LM model as a whole conflict with that belief if not in the way I originally described???”

Not at all. The assumption that income is fixed is a supply-side assumption and IS-LM is a model of aggregate demand. The two are easily combined. In fact, I’m surprised that your textbook doesn’t describe how one can combine the assumption of a fixed level of output with IS-LM. Try re-reading it and if it isn’t in there, check out Bernanke’s textbook.

I don’t have time to get to yuour second quesiton but you might be able to figure out for yourself now. I’ll be back later though.

6

Similar problems arise with the LM curve: According to the model, the supply of money is fixed and the demand for money rises when the output grows, causing interest rates to rise. However, I find it hard to imagine that people have to borrow money in order to acquire the economy’s growing output (which clearly neglects Say’s law, but I know, we’re still in a Keynesian fantasy world).

that isn’t really why the interest rate is rising.

in the lm portion of the model we are saying that people can only allocate their savings into 2 verhicles: a fixed supply of money and a fixed supply of bonds. this assumption allows us to look solely at the money market because determining equilibrium in the money market determines equilibrium in the bond market.

as you note, increasing income => increasing demand for money

but increasing demand for money => decreasing demand for bonds (as noted we have only 2 fixed assets) => downward pressure on bond prices => increase the yield/interest rate achieved by those bonds (http://personal.fidelity.com/products/fixedincome/price.shtml#determining)

That is why interest rates rise as income increases.

Here is a good way to think about IS-LM: It is all about figuring out the interest rate, which is the ultimate price signal for allocating resources in the economy. Specifically, the interest rate is determined by two different decisions that are captured in the model–the savings decision and the portfolio decision. The saving decision is how much of our income we want to allocate to investment for a given level of income (IS curve). The portfolio decision is how we want to allocat our savings across assets for a given level of income (LM curve). And for the interest rate to be determined, these two decisions must be consistent (IS=LM).

7

From an Austrian perspective, the concept “level of output”, such that there exists an equilibrium output Y for every interest rate i, is not very meaningful, since capital and consumer goods are heterogeneous, thus cannot be properly aggregated.

That said, the closest approximation of the Austrian theory within the IS-LM model would be a vertical IS, in the sense the “level of output” is irrelevant to the rate of interest. If the increase rate increases, investment in the higher order goods decreases, while investment in the lower order goods increases.

If the interest rate decreases, investment in the lower order goods decreases, while investment in the higher order goods increases. No matter what the interest rate is, expansion of one sector would most likely offset a contraction in another sector, until the most appropriate output mix is allocated.

Even in the absence of an aggregate output level, an unhampered market would most likely produce at its optimum for any given savings-consumer preference (interest rate). In neoclassical terms, such an economy would be operating nearest the boundary of its production possibility frontier (PPF).

Here is the reason why in Keynesian theory the IS curve is downward sloping, with lower interest rates corresponding to higher investment.

Every point on the IS curve corresponds to an equilibrium where supposedly “savings” is equal to “investment.”

But what the textbook does not clarify is that by “savings”, it really means incremental savings S, and by “investment” it really means incremental investment I.

For example, C + S = Y = C + I, where S and I are incremental savings and investment, respectively.

For every period of time, the income produced contributes incremental savings to increase the total stock of savings within an economy. However, some of those savings are “horded”, instead of invested, and as such accumulate as real cash balances.

Because of these real cash balances, the total stock of savings can be greater than the total stock of investment. Too much savings, and not enough investment, contributes to excess capacity within the economy, and thus a lower level of output Y.

Normally, too much real cash balances should not matter, since the cash is not spent, the price of all other goods should adjust downward, until the proper price relations within the economy is restored, and everything is back to full employment output.

However, because the prices in the IS-LM model are fixed, such that the prices are downwardly sticky, too much excess capacity exists.

To increase the level of output Y, the real cash balances must be spent down, so that incremental investment is greater than incremental savings, bringing the total stock of savings equal to the total stock of investment. This can be done by increasing the money supply, and thus lowering the interest rate.

For the IS-LM model, increase investment can also increase savings, and as well as increase consumption, because the real cash balances are large enough to finance both an increase in savings and consumption.

The moment the economy reaches a full employment output Y*, investment reaches a maximum, and any increase in saving must correspond to a decrease in consumption, and vice versa, In other words, the classical supply side condition appears.

8

But what the textbook does not clarify is that by “savings”, it really means incremental savings S, and by “investment” it really means incremental investment I…

Because of these real cash balances, the total stock of savings can be greater than the total stock of investment.

I would say that textbooks do not say this because it doesn’t accurately represent the IS-LM model. Saving and investment are not considered stocks (like money and bonds in the model), they are considered “flows”. You can think about income as a river and that river will branch off into different spending categories (consumption, investment, etc). If you want to describe the amount of water flowing to a particular branch, you wouldn’t talk about the “stock” of water, you would talk about the amount of water flowing to the branch over a given interval of time (e.g. 1,000 gallons per hour)

By contrast, in the IS-LM model we assume that the supply of money and bonds are fixed. So you would indeed call these stock variables (as a side note, combining stocks and flows in this fashion is one confusing and intellectual weak point of the model and it is one reason more modern treatments for undergrads are dumbing the LM curve all together and replace it with a sort of taylor rule curve–it is closer to how more advanced econ models work, it avoids the stock-flow confusion, and it explicitly pulls monetary policy into the model as it is currently percieved).

9

But, according to the IS/LM model, investment expenditures can rise without a drop in consumption.

Tobbog,

I meant to mention this is in my first post but didn’t have time. I just want to make it clear that most Austrians would have no problem with the “keynesian” notion that consumption and investment expenditures can rise at the same time as a result of nominal shocks (like an increase in the money supply). In fact, it is kind of central to modern ABCT.
http://www.auburn.edu/~garriro/b3beyond.htm

I can see why you may have the opposite impression though. Like I mentioned in another thread, there are older but still popular expositons of the ABCT that leave this notion out (like rothbard’s in america’s great depression). but it really is quite essential. if you really think that an increase in investment must imply a decrease in consumption, then ABCT becomes logically inconsistant as Bryan Caplan and Paul Krugman have correctly noted (krugman’s comments are more concise and readable and can be found here:
http://www.slate.com/id/9593/)

10

I acknowledge the text books do no state this. Here is my thinking though. Investment I must mean a contribution to a pre-existing stock of Capital K such that:

It = Kt - Kt-1

Else where is the output Y going to come from? For example, someone may invest a big investment I in a factory, which produces an output Y.

Furthermore an investment I can increase the planned investment in inventories, such that total inventories can accumulate.

If the total stock of Capital K is kept constant in the model, then investment I must equal depreciation, such that investment is equal to the rate that capital must be replaced.

From the water flow analogy, the water flows must accumulate somewhere, such as a tank or a reservoir, else there would be no savings or investment. The problem, how I see it is, is when leakages is not equal to injections, per the circular flow model, such that the total amount of water is not conserved.

I detect there is an inconsistency between the IS and LM side, such that on the LM side the total stock of real financial wealth WN / P is allocated between real cash balances L and real bond holdings DB.

However, on the IS side there is no mention for a pre-existing capital stock K where capital is allocated among various investments.

That said, real financial wealth stock WN / P should counterbalance the capital stock K in the model.

11

ahh i see what you’re saying. it is an interesting thought, but i still don’t think it gels with IS-LM. here is how i’m thinking about it.

IS-LM is a static model - you’re right that investment today => expansion of capital stock and output potential tomorrow. but IS-LM is an expresly static model. so it does not account for the consequences of investment on economic growth. this is why just because the existing capital stock is assumed to be fixed in the model that doesn’t mean investment cannot exceed depreciation. think about it this way. if investment exceeds depreciation today that implies that the capital stock and the output potential of the economy will be greater tomorrow. but the is-lm model is only interested in today so it does not consider that impact (though that isn’t to say you can’t build a dynamic is-lm model, i am just speaking to as how the model is typically taught to undergrads).

as far as your last comment, you are right that there is a major inconsistency between IS and LM because one deals with flows and the other deals with stocks. but that is the least of its problems really. for example, why does it split the decision between how much to save and how to save it? in the model, an increase money holdings can only be met by a decrease in bond holdings. in reality, it could be also met by a decrease in consumption. and hey, why are there only two investment vehicles anyways? what about stocks or commodities?

it has problems but what you gonna do? as a undergrad teaching tool, it is hard to find a better model than IS-LM for providing a formalized introduction to thinking about general equilibrium in a monetary economy.

PS* If anyone is really interested, I think the New School History of Economic Thought Website has good info on the IS-LM model and its flaws.

Here is a good summary of the model itself:
http://homepage.newschool.edu/het//essays/keynes/hickshansen.htm

Here is a good summary of monetarist criticisms.
http://homepage.newschool.edu/het/essays/monetarism/monetransmission.htm