It would be great if you could have a look at this on your own. Draw the circular flow diagram on a sheet of paper and labor the initial steady state values of the variables. They are the values taken in the equilibrium that we suppose the economy is in up until the end of period 0. Each period is structured like this. In the 'morning' firms place orders for the goods they will make available in the afternoon. At the time they place their orders they don't know what demand in the afternoon will be. Demand comes in from households, the government and from other firms as a result of their planned investment decisions.
The firm decides how much to order in the morning depending on what happened in the previous period. In the example, they order the amount that they order the amount that they ordered in the previous period, minu any unintended inventory accumulation in the previous period (recall, unintended inventory accumulation can be positive or negative).
Suppose that in period 1, the autonomous component of consumption drops by 2. This happens in the afternoon, after 100 units of output have been produced and have been made available for sale. So, the drop in consumption implies that inventories rise in an unintended way by 2 units. In the national income and product accounts, inventory investment (whether planned or unintended) is included in investment. So, this means that actual investment in period 1 is 17, 2 higher than the 15 that was planned. This increases the financing requirement of firms. They now have to finance not 15 units of output, but 17. When they go to financial markets to get the purchasing power, they find that its there. The reason is that the unintended accumulation of inventories of 2 reflects households' decision to cut back on consumption by 2 units, which corresponds to their decision to increase saving by 2 units.
So, that's the whole story about period 1. Now consider period 2. In the morning, firms look back and see that in the previous day they ordered 100 units, but unintended inventory accumulation was 2. So, they order 98. This is what gets produced in the morning and put up on the shelves of the store. In the afternoon, customers show up to purchase goods. Planned spending by government and business is still the same - 15 units each. Household consumption, however, is not just two units below what it was in the previous equilibrium. In the previous equilibrium it was 70, and in period 0 it was 68. But, it was 68 when income was 100. Income is now 98, and the cut in income by 2 units implies a drop in desired consumption by (3/4)*2. So, in the afternoon of period 2, consumption is 70 - 2 - (3/4)*2. The additional drop in consumption induced by the reduction in output has the consequence that inventories accumulate: this time by (3/4)*2.
In the morning of period 3, firms reduced their orders from what they were in period 2 by the unintended inventory accumulation in period 2. The process goes on and on like this, until eventually it stops when income has fallen to 92. That is output falls by 4 times the initial drop due to the drop in c0.
According to my understanding, the demand for goods, Z, is 1/1-c1 (Co+i+g-c1T). When the economy is at equilibrium, Y equals demand, Z. Is this correct?
answer: no, the demand for goods is Z=c0 + c1*(Y-T) + Ibar + Gbar. In equilibrium, Z=Y, so that the formula for equilibrium Y is Y=(c0-c1*T+Ibar+Gbar)/(1-c1).
I have a question:
- Money supply determines interest rate through the central banks bond market operations.
- Assuming fixed money supply, an Increase in Y ---> Money Demand increase
- Interest rate has to increase in order to negate effect of money demand, and maintain equilibrium.
Thus, if money supply is fixed, how does the interest rate increase?
Who is it that effects this change if money supply remains constant?
If Y increases, then there are more transactions occurring in the economy.
So, people find it useful to hold more of their wealth in the form of money.
But, with the money supply fixed, all the extra desire to hold money does is to
drive up the rate of interest, to the point where people don't mind holding the
existing stock of money.
The rise in the interest rate just described occurs as an outcome of natural market forces. There is no individual person who effects this change. It's just that everyone trying to acquire money by selling bonds drives down the price of bonds and, hence, their yield (i.e., the interest rate) up. The rise in the interest rate occurs as a consequence of the general attempt to sell bonds. No bonds actually change hands because everyone is trying to sell and no one is trying to buy. The price simply rises until people simply quit trying.
Jan. 27, 2004
Questions and answers....
1. We never really graph savings in either the goods market nor in the IS-LM market. But, savings is related to consumption. So, when we are looking at our circular flow diagram (or Keynesian Cross), what happens to savings when co rises or co decreases? Same question with an increase or decrease in taxes.
you can back the desired saving function from the definition, saving = disposable income minus consumption, and our equation for desired consumption. We have graphed the desired saving function in a graph with saving on the vertical axis and income on the horizontal. When c0 rises, the desired saving function shifts down in a parallel way, by the amount of the rise in c0. Taxes also shift the saving function in a parallel way.
2. In class, desired investment = given investment - qi where q is a constant and i is the interest rate. What exactly is q? Is it the accelerator effect? Same with one of the past midterm questions that says desired consumption is a function of disposable income minus gi where i is the interest rate. What happens if g was greater or less than zero?
We haven't defined 'given investment'. We've used an expression, desired investment = I-bar - b*i. The parameter b, which is positive, indicates how quickly projects with a rate of return that warrants investing in them fall off as i increases. The accelerator effect has to do with the impact of output on investment.
3. Is there ever a time when investment is high but interest rates are low? I know this occurred in the 90s where we had high investment and a booming economy as well as a low interest rate. How is that explained through the IS-LM model?
As shown in thursday's class handout, the fed aggressively pushed interest rates down, and that seems to have led to a rebound in investment. So, the last few years is another example. In our investment function, anything that sends the interest rate down (except a fall in I-bar), will drive investment and the interest rate in the opposite direction.
2/16/2004: Question: Please explain the analysis of globalization that you gave in class.
Answer: In class I focused on the fact that globalization hurts the
bargaining power of workers (at least, in the US). To analyze the consequences
of this, we first investigate which curve shifts, (AS or AD?), and then by how
much. It's the AS curve that shifts, because we have nothing like
'globalization' in our goods or financial market. The way to figure out how the
AS curve shifts is to first figure out what happens in the medium run. For this,
construct a graph with the real wage on the horizontal axis and unemployment on
the horizontal. The natural rate of unemployment (equilibrium unemployment in
the medium run when actual and expected prices are the same) is the intersection
of the price-setting equation and the bargaining equation with Pe=P. When the
bargaining equation shifts down in this graph, you see that the natural rate of
unemployment falls. So, the natural rate of output rises in response to this
aspect of globalization.
You can now figure out what happens to the AS curve. It shifts right by the amount of the rise in the natural rate of output. Make sure you understand why this is so.
With all the curves in place, we can now see what happens in the short and medium run. In the short run, Pe is fixed, so you move to the intersection of the AD curve and the new AS curve. In the medium run Pe starts to move down, as people realize the price level has fallen. This shifts the AS curve to the right, until the process stops in the medium run equilibrium where the AD curve intersects with a vertical line drawn above the new natural level of output.
Here is the intuitive story that summarizes the above technical analysis. The reduced bargaining position of the workers has the implication that wages start to fall. Because this drives down costs, the price level falls.
The fall in the price level has the effect of reducing the quantity of money demanded. As people try to reduce their money holdings by purchasing bonds, they drive the price of bonds up and interest rates down.
Businesses with investment opportunities see the fall in the interest rates and initiate new investment projects. The resulting expansion in aggregate demand is experienced as an unintended decline in the inventories by the businesses that produce investment goods. These businesses order more goods, and production starts to increase.
As production increases, income rises. This leads to an increase in consumption, leading to further unintended inventory accumulation. The rise in output accelerates.
The increase in output now triggers forces which work against the rise in output. In particular, it results in an increase in the quantity of money demanded, which places upward pressure on the interest rate, which throws a little cold water on investment. The rise in output produces a fall in unemployment, which leads to stronger wage gains by workers, exerting upward pressure on the price level (or, at least reducing the downward pressure coming from the original globalization shock). By reducing the real value of the money stock, this effect on the price level tends to raise the interest rate too, which tosses a little more cold water on investment. This process continues until equilibrium in all markets is established.
After some time, people notice that the price level has fallen relative to
their expectations. As they revise their expectations, pressure on wages is
reduced and the aggregate price level falls. Through a version of the mechanism
just discussed, the fall in the price level produces an increase in output (this
rise in output that occurs with a fall in the price level corresponds to a move
down the AD curve). This process continues until P=Pe and all markets are in
equilibrium. At this point the system is in the medium run equilibrium.
This whole story can (should!) be filled out by doing the appropriate analysis with IS and LM curves. This story would be essentially impossible to tell without getting yourself hopelessly entangled in verbal knots and mental twists if you didn't have the AD, AS, IS, and LM curves to keep you straight. If you tried to tell it without these curves, you wouldn't know in the end if interest rates ultimately rise or fall, or whether investment rises or falls. You also would have not idea if the system ever does settle down in some equilibrium, for example, if the unemployment rate settles down at the new natural rate. However, as long as you follow the simple rules for pushing around the various curves, you're sure to get the answer right. The intuition is just verbalizing what you see in the graphs.
The natural level of output, Yn, is determined by the natural rate of
unemployment, un, according to the following relationship:
un = 1 - Yn/L,
where L is the labor force. So, if something changes the natural level of unemployment, it will affect the natural rate of output too. To understand the natural rate of output, you need to understand how the natural rate of unemployment is determined.
The natural rate of unemployment is the unemployment rate that is consistent with our assumptions about how prices are set:
P = (1+mu)*W, (1)
and with the bargaining equation in the medium run:
W = Pe*F(u,z),
where in the medium run Pe = P. So, in the medium run
W/P = F(u,z). (2)
Note that W/P is determined by (1) as a function of mu. So, you can substitute out for W/P from (1) into (2), to obtain:
1/(1+mu) = F(u,z).
The natural rate of unemployment is the level of unemployment that satisfies this equation. Typically, we have expressed this equality as the crossing between a curve defined by 1/(1+mu) and F(u,z), with W/P on the vertical axis and u on the horizontal. So, un is the value of u such that:
1/(1+mu) = F(un,z). (3)
From this, you can see that anything that affects the bargaining power of workers (i.e., stuff that appears in z) and anything that affects the monopoly power of firms, or their non-labor costs, mu, affects un. By the reasoning above, these things therefore affect Yn.
A shock to something like Ibar, or c0 has no impact on anything in the relation in (3). So, they have no impact on Yn. However, globalization, which affects z, or oild shocks, which affect mu, do have an impact on Yn.
Working through the implications of our disequilibrium dynamics, it is easy to verify that any shock drives the economy, in the medium run, to the natural rate of output, whether the shock shifted it or not.
Question and answer are mixed up together.....
I have a couple of questions on the lectures.
When we were doing AS shifts, we learned that a rise in P trigger an
The rise in P raises the quantity of money demanded. This leads people to sell their bonds in an effort to have more money. Assuming there is no response by the Fed, the amount of money cannot change, so people in fact cannot get more. All they'll succeed in doing is reducing the price of bonds (everyone selling, no one wanting to buy, leads to a fall in price). The fall in the price of bonds corresponds to a rise in the interest rate. So, the rise in P leads to a rise in i even without any Fed response.
increase in interest rate (because goods are more expensive and Md
increases so the Fed increases interest rate to curtail the increased Md
so that it equals Money supply) I know that this leads to an increase in
The higher interest rate leads to a fall in investment. With the higher interest rate, firms must be more selective about which projects they invest in, because return on the project must be able to cover a now higher interest rate.
Investment. How come this doesn't show up in a shift in the IS curve? Is
The price level does not enter the IS curve, so the shift in the price level does not shift the IS curve. The move in the interest rate and output that occurs after the rise in P is a change in the value of the variables on the axes of the graph in which the IS curve is drawn. For this reason, the shift in P triggers a move along the IS curve, not a shift in the IS curve.
this because we are only using the IS-LM model to understand the AD and
The AD curve is constructed from the IS-LM curve. The AD curve is the P and Y combinations where goods market equilibrium holds (the IS curve) and financial market equilibrium holds (the LM curve).
thus we only care about the effects of an increase in P?
Also, when learning about the AD shocks (specifically a decrease in I) I
am confused as to when we were mapping out the effects of I over time.
When we talk about shocks, they are always to exogenous variables. I is an endogenous variable. You are probably referring to a change in Ibar, which is an exogenous variable. It is the constant term in the desired investment equation. If Ibar falls, then the nominal interest rate will fall. It shifts the IS curve left. It shifts the AD curve left. From the AD curve, you see that a fall in output and the price level results in the sr run. In the medium run output returns to the natural rate, where we assume it started. At this point the price level is lower. To see what happens to the interest rate you look at the IS-LM curves and watch what they are doing as the economy moves around in the P,Y diagram. The IS curve shifts left. As the interest rate falls and output falls, the fall in the price level fall causes the LM curve to shift down. The economy in sr ends up at a point to the right of where we would have ended up in the IS-LM model, but to the left of where we started, in terms of output.
In the mr, the price level falls even more, and the interest rate continues to fall. In the mr, we end up at the same level of output as before, a lower price level, the same level of consumption and government spending. We also have the same level of investment. What's happened with investment is that although Ibar fell - thus discouraging investment - the fall in the interest rate has entirely made up for that.
It says interest rate decreases in the sr and even more in the lr. Is
the initial decrease in I simply due to the shock (and then it increases
in the MR as a result of the decrease in interest rate?)
This last sentence is exactly right.
2/17/2004 Question and answer mixed together:
I was wondering about the format of the second midterm... is it going to
be like the first midterm, or the old midterms? Is the length going to
like old midterms....
be as long as the first midterm? Will there be questions concerning the
i don't want the midterm to be too long. the first one was a little long....
articles you post online? Sorry for bombarding you with so many
articles posted online before last thursday - focus on my commentary on the articles - will be covered
question, but I'd appreciate any help you can give me. Thanks a lot!!
I assume you mean rho in the UIP, when I talked about how people a situation in which traders suddenly develop an aversion to US financial assets.
The idea is that to be happy holding US assets under these conditions, they must get a higher return on them than they can get on foreign assets. That is, i must be such that
i > istar + (Ee-E)/E.
US assets must generate a higher return than foreign assets. rho measures how much higher.....that's because
i = istar + (Ee-E)/E + rho.
rho = i - istar - (Ee-E)/E
it's the excess return on US assets over what you can expect to get on foreign assets.
At 01:05 PM 3/15/2004, you wrote:
Hi, I have one more question - I'm sorry.
I am confused about what rho is - I know it is the risk factor but I do
not understand how its effects happen. Can you please explain this to
Hi: the equations determining the natural rate of output, Yn, and the natural
rate of unemployment, un, are:
(1) 1/(1+mu) = F(un,z)
(2) un = 1 - Yn/L.
These two equations are used to pin down the two unknowns, un and Yn. Note, however, that the two equations have a special structure. In particular, un is the ONLY unknown that enters (1). So, (1) is one equation in one unknown, un. It pins down un all by itself. Then, the second equation is used to pin down Yn.
I hope this helps.
At 04:26 PM 3/12/2004, you wrote:
Hi Prof. Christiano,
I have a question about the second problem in the second midterm for the intermediate macro class (311). In your solution, you said Labor force (L) doesn't enter the wage or price setting equations and thus, natural rate of unemployment doesn't change. But I don't really understand. u = 1- (N/L). As u is in the wage-setting equation, L should also be in the equation too. Why is it that u doesn't change but Yn changes but not u changes but Yn doesn't change?
question and answer....
Hi Prof Christiano,
Was wondering if you could answer these questions for me
1) Whats the differnet between capital account and current account
See pages 384-385 in the book for details. Briefly, the current account is the place where all the goods and services traded between countries are recorded. The capital account is the 'flip' side of the current account, and registers the associated financial flows.
Here's an example. When a good is exported to Europe, in the first instance the foreigner pays in Euros. Then, the American uses the Euros to acquire an interest-bearing asset in Europe. The net effect is that the American is holding European assets, and the European is holding goods. The shipment of goods is recorded in the Current Account, while the change in asset holdings is recorded in the capital account.
2) You gave an example in class about a car manufacturer to illustrate
exchange rates. Is it possible to put this example into words, looking
over my notes I was a bit unsure as to what te example illustrated
I think I had an example of a Japanese manufacturer of automobiles, who set its price in US dollars. The fluctuations in the Japanese/US exchange rate are so large that they generate huge uncertainty about what a US dollar price will be worth in terms of Yen. This is important to the manufacturer because their obligations are denominated in Yen. (The forward market can, to some extent, be used to mitigate this sort of risk, but in practice this is expensive.)
3) How does Current account help young countries grow? What does this
have to do with savings and why does it not help developed countries grow
You can see the answer to this question by rewriting the national income identity: C+I+G+CA=Y, or
S - CA = I,
where S=Y-T-C + T - G, is national saving...saving by households and government. This relation says that investment is financed in part by saving generated domestically, and in part by saving by foreigners (the excess of what they sell to us over what they buy). The domestic saving, S, corresponds to increased holdings by households of claims on business. The saving by foreigners, -CA, corresponds to increased holdings by them of financial claims on the domestic economy.
A developing country is poor. This often means two things. First, the country has a hard time producing a large value of S. Second, it probably does not have much plant and equipment, and so the return on it may be high....that is, it is desirable to have I high. In a closed economy, you've got a problem: I just has to be small if S is small. In the open economy there is another option, -CA can be large. I showed data in class that showed how many countries grew initially by having large -CA's, 'capital inflows'.
4) Also out of curiosity is there a set format to the final?
it will look a lot like the second midterm.
Why is it that when M goes up the impact on current accounts is
ambiguous while it is unambiguous when there is a raise in G?
A rise in M reduces the interest rate and there results in a depreciation in the currency. This raises net exports. The rise in domestic output reduces net exports. Whether net exports goes up or down depends on which effect is stronger.
1. What is the UIP curse?
UIP: i = istar + (Ee-E)/E
Under a fixed exchange rate, Ee-E=0, so the term to the right of the plus sign is gone. Sometimes, however, traders get it into their heads that the government will depreciate soon, and raise Ee. When this happen, they typically think the government will depreciate something like 10 percent sometime over the next month. Thus, (Ee-Ef)/Ef = 10 percent per month, where Ef is the exchange rate target set by the government. The problem, or curse, is that now the government that does not want to depreciate its currency must set the domestic interest rate 10 percent, PER MONTH, higher. They must do this until traders stop thinking the government will depreciate. Such a large rise in the interest rate could be very destructive to the economy, and will seem to a central banker like a curse.
2. What happens to the multiplier in an open economy?
It goes down. When Ibar rises, this pushes up the interest rate. In the closed economy, this softens the positive output effect of the rise in Ibar by bringing countervailing pressure on investment. In the open economy the output effect is further reduced. The rise in the interest rate leads to an appreciation of the currency, which hurts exports and offsets the output effect of the rise in Ibar.