The purpose of this post is to present IS-LM model and also my own made-up model, just to demonstrate how arbitrary are some assumptions made in economics, and how it obscures the truth. The models like IS-LM and the conclusions drawn from them have their criticism within economic community as well, but the criticism is being no less obscure than the models themselves.
So here's a theoretical physicist's take on IS-LM model. We aim to describe a country with a government, a bunch of banks, businesses and people. Their economic activity is exchange of money and goods/services. It is measured by following well-defined quantities:
CPI - price of a fixed list of goods that are supposedly the most common consumer choices. Is used to adjust for inflation, so all other quantities get the adjective "real": real GDP, real interest rate. We talk about real values without mentioning it from now on.
GDP - every time money is exchanged for goods/services this year, the amount is added to GDP. Buying shares in a company (or stock) is also counted. Taking/paying loan in a bank, and paying taxes are not counted.
r - interest rate. Reflects what kind of loans are available. Is set by either government, or some agreement/competition between banks (depends on a country).
MS - money supply. Counts how much money (how many bills) the government has printed.
I - investment. Part of the GDP that involves buying shares (or stock).
C - consumption. The rest of the GDP. For economists in the room, we ignore export and government spendings.
Then economists write several equations to determine the equilibrium values of these quantities, and also see how they change if some of the internal mechanics of the system changes. First equation follows directly from definitions:
GDP = C + I
Second equation follows from a simple consideration about Investment and interest rate. Supposedly for investors there's a "safe" option to put their money in a savings account that has rate of return that follows the interest rate r. So some of the investment opportunities are not interesting (if their rate of return is smaller than one of savings account). So investment depends on the interest rate with a negative coefficient:
I = Io - a*r
Here Io and a are describing how many investment opportunities are there, They may, and in principle should, depend on what's up in the economy. If people tend to spend more money, there should be bigger investment opportunities, and more profitable ones. But for some reason IS-LM model doesn't consider that, and instead fixes Io and a to be constants.
Consumption, on the other hand, is allowed (in IS-LM model) to depend on how much money people and businesses got. What they got this year is GDP. They probably have paid taxes, so the amount decreased by a bit. Then they have decided which fraction of the rest to spend this year (or possibly overspend and reduce their savings):
C= c0 +c1*GDP
Here c_1<1, or else we can't balance the equation for GDP. If we collect our knowledge so far, we get the IS (investment-savings) part of IS-LM model:
(1-c1)*GDP = c0 + I0 - a*r
it's a line with \ slope on (GDP,r) axis. Note that somewhat in spite its name, IS equation doesn't actually talk about savings. What's going on is that of total amount of money MS some part have been circulating (possibly several times) to count towards GDP, while other part were people's savings. Some people made money, some people lost this year. GDP by itself does not really tell us anything about savings. We can imagine a year when two monkeys are selling a banana to each other ad infinitum for a dollar, while the rest of MS in never used. In this case, GDP may be arbitrary huge, but at the same time MS-1 dollars never left people's savings.
To describe savings, one needs to involve heavier math. Suppose that MS is split between people according to a distribution m(i) - how much money does i'th person/business have. Everyone wants to consume c(i) and invest I(i). Also this year they earn g(i). In case m(i)+g(i)>c(i)+I(i), this particular individual/business can achieve it's goals. In fact, the quantities c(i) and I(i) should probably depend on m(i) +g(i). But we ignore it for now. If there's not enough money, then an individual can take a loan, or decrease its consumption goals. In the end, we get an inequality:
m(i)+g(i) + l(i)>c(i)+I(i)
In fact some individuals also need to pay for older loans, so:
m(i)+g(i) + l(i)>c(i)+I(i)+p(i)
If we sum these inequalities, we don't get anything interesting:
MS+GDP + LOANSissued>GDP+LOANSpayed
Any significant MS will allow this to balance always.
But the breakdown into individual agents has taught us an important lesson: investment and consumption depends on their savings. Economy where people have tons of savings will grow until they start spending most of them every year, but or IS-LM model doesn't capture that.
Finally, the LM ("liquidity preference/money supply") part of the model describes how the interest rate is set. Looking at the above, intuitively more consumption means more loans (because for more people their savings are not enough). As we noted, this cannot be seen in the aggregates, one actually needs to consider a distribution. Roughly half of the agents will not need loans this year. But how big will be LOANSissued really depends on the economic inequality accumulated from the past, this year's salaries and this year's desire to consume. We assume that both salaries and consumption depends linearly on GDP for those who are in debt. So
LOANSissued = a + b*GDP
Here b>0. We then make a simple assumption about bank operation (that is very far from what they actually do). The global interest rate is set by the following procedure: they look how many loans are requested this year, and think: ok, the bigger the demand, the bigger we can set the "price". The "price" of loans is the interest rate:
r = a' + b'*GDP
Here b'>0. This is the LM part of the IS-LM model. Together these equations can be solved, and if we assume that all the used coefficients except one are constant, then we can find the dependencies between different economical indicators. Like, when we change c0, we observe that if the GDP grows, I decreases. Other parameters would lead to other relations, so for instance GDP and I can both increase.
What one can do to check that the above makes sense, is to try other things. For instance, one can fix r=0, and instead develop a relationship between I and people's savings. Unfortunately, as soon as savings are involved, the simple line-crossing economists do is not applicable anymore, instead one needs to run numerical simulations. I have run a simple one and observed the relationship between the supply of shares of a specific company (people willing to sell their shares) and the GDP. It turns out that the supply is bigger when GDP is bigger, which would imply that the corresponding stock price is anticorrelated with the GDP.
So here's a theoretical physicist's take on IS-LM model. We aim to describe a country with a government, a bunch of banks, businesses and people. Their economic activity is exchange of money and goods/services. It is measured by following well-defined quantities:
CPI - price of a fixed list of goods that are supposedly the most common consumer choices. Is used to adjust for inflation, so all other quantities get the adjective "real": real GDP, real interest rate. We talk about real values without mentioning it from now on.
GDP - every time money is exchanged for goods/services this year, the amount is added to GDP. Buying shares in a company (or stock) is also counted. Taking/paying loan in a bank, and paying taxes are not counted.
r - interest rate. Reflects what kind of loans are available. Is set by either government, or some agreement/competition between banks (depends on a country).
MS - money supply. Counts how much money (how many bills) the government has printed.
I - investment. Part of the GDP that involves buying shares (or stock).
C - consumption. The rest of the GDP. For economists in the room, we ignore export and government spendings.
Then economists write several equations to determine the equilibrium values of these quantities, and also see how they change if some of the internal mechanics of the system changes. First equation follows directly from definitions:
GDP = C + I
Second equation follows from a simple consideration about Investment and interest rate. Supposedly for investors there's a "safe" option to put their money in a savings account that has rate of return that follows the interest rate r. So some of the investment opportunities are not interesting (if their rate of return is smaller than one of savings account). So investment depends on the interest rate with a negative coefficient:
I = Io - a*r
Here Io and a are describing how many investment opportunities are there, They may, and in principle should, depend on what's up in the economy. If people tend to spend more money, there should be bigger investment opportunities, and more profitable ones. But for some reason IS-LM model doesn't consider that, and instead fixes Io and a to be constants.
Consumption, on the other hand, is allowed (in IS-LM model) to depend on how much money people and businesses got. What they got this year is GDP. They probably have paid taxes, so the amount decreased by a bit. Then they have decided which fraction of the rest to spend this year (or possibly overspend and reduce their savings):
C= c0 +c1*GDP
Here c_1<1, or else we can't balance the equation for GDP. If we collect our knowledge so far, we get the IS (investment-savings) part of IS-LM model:
(1-c1)*GDP = c0 + I0 - a*r
it's a line with \ slope on (GDP,r) axis. Note that somewhat in spite its name, IS equation doesn't actually talk about savings. What's going on is that of total amount of money MS some part have been circulating (possibly several times) to count towards GDP, while other part were people's savings. Some people made money, some people lost this year. GDP by itself does not really tell us anything about savings. We can imagine a year when two monkeys are selling a banana to each other ad infinitum for a dollar, while the rest of MS in never used. In this case, GDP may be arbitrary huge, but at the same time MS-1 dollars never left people's savings.
To describe savings, one needs to involve heavier math. Suppose that MS is split between people according to a distribution m(i) - how much money does i'th person/business have. Everyone wants to consume c(i) and invest I(i). Also this year they earn g(i). In case m(i)+g(i)>c(i)+I(i), this particular individual/business can achieve it's goals. In fact, the quantities c(i) and I(i) should probably depend on m(i) +g(i). But we ignore it for now. If there's not enough money, then an individual can take a loan, or decrease its consumption goals. In the end, we get an inequality:
m(i)+g(i) + l(i)>c(i)+I(i)
In fact some individuals also need to pay for older loans, so:
m(i)+g(i) + l(i)>c(i)+I(i)+p(i)
If we sum these inequalities, we don't get anything interesting:
MS+GDP + LOANSissued>GDP+LOANSpayed
Any significant MS will allow this to balance always.
But the breakdown into individual agents has taught us an important lesson: investment and consumption depends on their savings. Economy where people have tons of savings will grow until they start spending most of them every year, but or IS-LM model doesn't capture that.
Finally, the LM ("liquidity preference/money supply") part of the model describes how the interest rate is set. Looking at the above, intuitively more consumption means more loans (because for more people their savings are not enough). As we noted, this cannot be seen in the aggregates, one actually needs to consider a distribution. Roughly half of the agents will not need loans this year. But how big will be LOANSissued really depends on the economic inequality accumulated from the past, this year's salaries and this year's desire to consume. We assume that both salaries and consumption depends linearly on GDP for those who are in debt. So
LOANSissued = a + b*GDP
Here b>0. We then make a simple assumption about bank operation (that is very far from what they actually do). The global interest rate is set by the following procedure: they look how many loans are requested this year, and think: ok, the bigger the demand, the bigger we can set the "price". The "price" of loans is the interest rate:
r = a' + b'*GDP
Here b'>0. This is the LM part of the IS-LM model. Together these equations can be solved, and if we assume that all the used coefficients except one are constant, then we can find the dependencies between different economical indicators. Like, when we change c0, we observe that if the GDP grows, I decreases. Other parameters would lead to other relations, so for instance GDP and I can both increase.
What one can do to check that the above makes sense, is to try other things. For instance, one can fix r=0, and instead develop a relationship between I and people's savings. Unfortunately, as soon as savings are involved, the simple line-crossing economists do is not applicable anymore, instead one needs to run numerical simulations. I have run a simple one and observed the relationship between the supply of shares of a specific company (people willing to sell their shares) and the GDP. It turns out that the supply is bigger when GDP is bigger, which would imply that the corresponding stock price is anticorrelated with the GDP.
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