George Soros delivered a lecture at the LSE on May 21st, 2008 on his 'reflexivity', credit crisis and others (actually to advertise his book, but still a very interesting talk).
Factor Analysis
I've been trying to learn a bit of factor analysis recently. Here are some readings on the web:
"Dollar Falls as Oil Goes Up"
is a typical financial news headline these days. Bloomberg just ran an article that stated exactly this
This accounting correlation is masking what's going on underneath. There's probably a real but complex causal mechanism between oil, dollar, euro and everything else, but it will not be easily identified by just looking at the simple correlation or multiple plots.
At the very least, if we were to test the hypothesis that an increase in oil price is bad for dollar, then we are looking for a relationship between the oil price in effective terms, and the dollar in effective term (say some trade-weighted index). To the best of my knowledge, such strong and systematic statistical relationship cannot be found, and there's no compelling reason why it should be found. US is the world's biggest importer of oil, yes, but that's an absolute measure, plus the energy use efficiency needs to be taken into account. And should the Asian countries stop subsidising their oil prices (as Stephen Jen at Morgan Stanley recently wrote they might have to soon), no doubt you'll see that US is by no means the most vulnerable to oil price shock.
Incidentally, on exactly the same day, Chicago Tribunal ran the headline "Dollar's Drop Fuels Oil Rise". Know what I'm saying?
The dollar posted its third consecutive weekly decline against the euro as the U.S. housing slump and record oil prices slow growth in the world's biggest economy.First of all, the statistical correlation between euro and oil price implies absolutely nothing about the causality between oil and dollar. Both euro and oil are priced in dollar term, so if the dollar depreciates against everything else (euro, sterling, yen, gold, and oil), you'd precisely expect a positive correlation between euro and oil. In fact, the closer the correlation is to 1, the more likely that we're having an exogenous shock that comes from the dollar factors, and not the oil factors or the european factors.The dollar fell against 13 of the 16 most-traded currencies this week as oil touched a record $135.09 a barrel yesterday on the New York Mercantile Exchange. The U.S. is the world's biggest importer of oil. Oil traded at $131.87 today.
The correlation coefficient between oil prices and the euro dollar exchange rate has been 0.95 for the past year, indicating they have moved in the same direction 95 percent of the time.
This accounting correlation is masking what's going on underneath. There's probably a real but complex causal mechanism between oil, dollar, euro and everything else, but it will not be easily identified by just looking at the simple correlation or multiple plots.
At the very least, if we were to test the hypothesis that an increase in oil price is bad for dollar, then we are looking for a relationship between the oil price in effective terms, and the dollar in effective term (say some trade-weighted index). To the best of my knowledge, such strong and systematic statistical relationship cannot be found, and there's no compelling reason why it should be found. US is the world's biggest importer of oil, yes, but that's an absolute measure, plus the energy use efficiency needs to be taken into account. And should the Asian countries stop subsidising their oil prices (as Stephen Jen at Morgan Stanley recently wrote they might have to soon), no doubt you'll see that US is by no means the most vulnerable to oil price shock.
Incidentally, on exactly the same day, Chicago Tribunal ran the headline "Dollar's Drop Fuels Oil Rise". Know what I'm saying?
Oil Price: Is It a Bubble?
Charles Engel reckons it's a real possibility, and has this to say
Economics is an inexact enough science that we can’t know whether $125, or $60, or $200 is the right price based on fundamentals. I don’t know one way or the other what the right price of oil is, but what I don’t understand is the steady increase in the price of oil. How can an asset such as oil consistently pay such a high return?
One possible explanation is that the market has kept learning about the strength of demand and the weakness of supply over the years. It is consistently being surprised, in other words. That may be right, but it is a shaky argument: why is the market always being surprised in the same direction – that excess demand is greater than we thought?
Another story that I think makes some sense is the one that Jeffrey Frankel and Jim Hamilton have promoted – that Fed monetary policy has played a role. As I noted at the outset, a drop in real interest rates should cause commodity prices to rise. But here again, the decline would also have to be unanticipated to explain the continual increase in the price.
I think there is a lot of truth to the view that markets keep getting surprised in the direction that makes oil prices higher. We have been surprised at the growth in emerging markets, the shortfall in supply from some countries (such as Iraq), and the continuing low real interest rates. On the other hand, it seems to me that rising prices are also typical of frothy markets (like the housing market of late.) In fact, the steep rate of increase could even be a “rational bubble”. The rate of increase of the price is so high, perhaps, because the market is incorporating a probability of the bubble popping and prices falling back down to earth.
In a rational bubble, the oil price is rising, but there is some probability that the bubble will burst. Let r be the real interest rate. Let p(t) be the log of the real price of oil at year t, pfun(t) be the fundamental long-run price (after the bubble pops), and let k be the probability of the bubble popping. To keep it simple, I’ll assume r and k are constant. Then the expected rate of increase in the real price of oil should equal r:r = (1-k)(p(t+1)-p(t)) -k(p(t)-pfun(t)).
(For those who aren’t familiar with logs, p(t+1)-p(t) is approximately the percentage increase in the price of oil, and p(t)-pfun(t) is approximately the amount by which oil is “over-priced” in percentage terms. The “expected rate of growth” of the oil price is simply the weighted average of the growth rate of the price if the bubble persists and the percentage decline expected if the bubble bursts. The weights are given by the probability of the bubble persisting or popping.)
So, as long as the bubble has not popped, you will see
p(t+1)-p(t) = [r+k(p(t)-pfun(t))]/(1-k).
The percentage rate of increase in the price exceeds the real interest rate. Indeed, you can see that the growth rate in oil prices would have to rise as the price rose (as p(t)-pfun(t) gets larger.) That is, the price would accelerate until the bubble burst.In this type of rational bubble, the futures price would indicate an “expected” increase in the price equal to r, the real interest rate. But until the bubble burst, the actual increase in the price would always exceed the real interest rate. So the futures price would always underpredict the actual increase in the price of oil, much like it has in fact over the past four or five years. The payback to speculators betting against oil only comes when the bubble finally bursts.
From the perspective of producers, there is no difference between this and the no-bubble case (assuming that the producers care only about their expected return.) If they “hoard”, they expect the price to rise at the rate r, and if they sell now they can take the proceeds and earn r. They are indifferent between selling now and hoarding. There is no excess supply. Producers pump out of the ground exactly what people will buy at price p(t). The level of the price in this case is determined just as in the no bubble case – the sum of the expected demands in every period equals the amount of oil in the ground.
A bubble in asset prices need not be “rational”. But if the run-up in prices were too rapid, so that the “expected” growth rate of the price exceeded the interest rate, there would be a strong disincentive to sell any oil. Producers would want to keep the oil in the ground, and, as Paul Krugman has argued, speculators would have an incentive to hoard oil. We see very little of that type of behavior going on, as Krugman has noted.
The problem for economists is that the market for oil is so complicated that we cannot very accurately calculate what the price of oil “should be” if there is no bubble. We have to read the entrails to figure out whether the price is really reflecting market fundamentals – demand, supply, real interest rates – or has a bubble component. As I look at the rising price, I wonder which story is most plausible: (1) the markets have been surprised over and over about demand by end users and production capabilities; (2) markets have been surprised over and over about how low real interest rates are; (3) there is a bubble. These stories may go together, in fact. Indeed, it is hard to see how a bubble could get started all by itself, or how it could go on for a long time before it popped. In the previous asset price bubbles I mentioned above, it seems as though fundamental economic causes set off the rise in asset prices. But it looks like the bubble traders were inspired by the price increases to bet on further increases in prices, even when there was little evidence that the price needed to rise more based on fundamentals. It’s as if the fundamental traders normally keep the bubble traders at bay. But a series of shocks to the fundamentals in the same direction seem to undermine the confidence of the fundamental traders and give the bubble traders the upper hand. In any case, if either (2) or (3) are true, we might see oil prices coming down in the future, as real interest rates return to more historic levels, or as the bubble bursts.
Cutting-edge Stuff
Knowledge flows freely in internet age...
- William Sandholm is writing a book on evolutionary game theory (specifically on population game). Get a free copy before it's printed!!!
- What's new in econometrics? A series of lectures in google videos by Imbens and Wooldridge on modern econometrics.
Joze to Tora to Sakana Tachi
Recently I stumbled upon quite a few movies that I like. The title of this post is the name of one, which literally means "Josee, the Tiger and the Fish". A good review can be found here, and below is the trailer...
The basic story revolves around a romance between a young college student and a girl who is handicaped. The narrative is very low-key, and you do not need a box of tissues while watching this, despite the plot that seems to promise tear jerking scenes. Instead, this film is largely a uplifting tale that ultimately breaks your heart from the inside, and will leave you quitetly devastated. It is a honest study of humans, a depiction of the cruelty of reality, and it makes viewers ponder about themselves.
At a shallower level, this movie boasts a cast of top young stars in Japan today. Satoshi Tsumabuki was in the acclaimed "Waterboys", "Dororo", and even "Tokyo Drift" (he's the guy who shouted 'Go', and let the car race begin...remember?). Chizuru Ikewaki was in "Strawberry Cheesecake". It's also interesting to see Juri Ueno in her early years here playing a supporting role. She'd later appear as lead in "Swing Girls" and "Rainbow Song".
The basic story revolves around a romance between a young college student and a girl who is handicaped. The narrative is very low-key, and you do not need a box of tissues while watching this, despite the plot that seems to promise tear jerking scenes. Instead, this film is largely a uplifting tale that ultimately breaks your heart from the inside, and will leave you quitetly devastated. It is a honest study of humans, a depiction of the cruelty of reality, and it makes viewers ponder about themselves.
At a shallower level, this movie boasts a cast of top young stars in Japan today. Satoshi Tsumabuki was in the acclaimed "Waterboys", "Dororo", and even "Tokyo Drift" (he's the guy who shouted 'Go', and let the car race begin...remember?). Chizuru Ikewaki was in "Strawberry Cheesecake". It's also interesting to see Juri Ueno in her early years here playing a supporting role. She'd later appear as lead in "Swing Girls" and "Rainbow Song".
Champions League Afterthoughts
Here's the full story. Congrats to all the Man U fans! 
The game was decided after Nicholas Anelka's penalty was saved by Van de Sar. On this, Alex Ferguson commented..
On second thought, was he double-bluffing?
The game was decided after Nicholas Anelka's penalty was saved by Van de Sar. On this, Alex Ferguson commented..
"That wasn't an accident, his penalty save. We knew exactly where certain players were putting the ball, so great credit to him."If only someone had taught a bit of game theory to Anelka, he would have 'mixed his strategy' properly, and turned the tide for Chelsea.
On second thought, was he double-bluffing?
Bernanke's Top Gun on Bubbles
Full story @ WSJ
Now, the study of financial bubbles is hot.
Its hub is Princeton, 40 miles south of Wall Street, home to a band of young scholars hired by former professor Ben Bernanke, now the nation's chief bubble watcher as Federal Reserve chairman. The group includes Mr. Hong, a Vietnam native raised in Silicon Valley; a Chinese wunderkind who started as a physicist; and a German who'd been groomed to take over the family carpentry business. Among their conclusions:
Bubbles emerge at times when investors profoundly disagree about the significance of a big economic development, such as the birth of the Internet. Because it's so much harder to bet on prices going down than up, the bullish investors dominate.
Once they get going, financial bubbles are marked by huge increases in trading, making them easier to identify.
Manias can persist even though many smart people suspect a bubble, because no one of them has the firepower to successfully attack it. Only when skeptical investors act simultaneously -- a moment impossible to predict -- does the bubble pop.
As a result of all that and more, the Princeton squad argues that the Fed can and should try to restrain bubbles, rather than following former Chairman Alan Greenspan's approach: watchful waiting while prices rise and then cleaning up the mess after a bubble bursts.
Final Words...
So it is finally final exams tomorrow...please don't forget to
1. Answer all questions, and attempt all subsections. Allocate your time proportionately to each question.
2. Never, ever, panic! Use what you know and what you have learned to try to answer the questions as best you can. If you have come to the lectures and have studied, you are qualified to do well, provided you are calm.
3. Don't come in late. Time is better spent in the exams than outside doing last-minute reading. Plus, it's a disturbance to your friends who come early (poor them!).
Lastly, it's been a great pleasure to have taught you all, and I'd like to thank everyone for making this class a fun and stimulating experience! Best of luck tomorrow!
1. Answer all questions, and attempt all subsections. Allocate your time proportionately to each question.
2. Never, ever, panic! Use what you know and what you have learned to try to answer the questions as best you can. If you have come to the lectures and have studied, you are qualified to do well, provided you are calm.
3. Don't come in late. Time is better spent in the exams than outside doing last-minute reading. Plus, it's a disturbance to your friends who come early (poor them!).
Lastly, it's been a great pleasure to have taught you all, and I'd like to thank everyone for making this class a fun and stimulating experience! Best of luck tomorrow!
Questions on Time Inconsistency
Here are some questions:
Firstly, what's the word "time inconsistency" mean in this case?
Suppose you ask the policy maker what inflation and output pair will he prefer ex ante, between (pi-star,y-bar) and (pi-high,y-bar), where pi-high is the Nash equilibrium inflation derived in lectures and is greater than pi-star the inflation target. The policy maker will readily tell you that he prefers (pi-star,y-bar), because in his loss function it gives lower inflation with no output loss. But once you let the public fix their inflation expectations at pi-star, the policy maker will no longer wish to deliver pi-star, as he wants to push output beyond y-bar by increasing inflation. When the time comes and agents decide fix their expectations at pi-star, the policy maker's optimal action is inconsistent with the plan he promises before the expectations are fixed. So ex post, what the policy maker wants to do is inconsistent with what he prefers ex ante. The public foreseeing this will not fix inflation expectations at pi-star in the first place, and we get inflation bias results.
Also in topic 7, we get output-inflation trade off but not in the topic 5. Is it because in topic 5 we consider only 1 time game and we also assume no shock but in topic 7, shock and time dimension are taking into consideration? Could you explain it intuitively?
Topic 5 uses essentially the Lucas or new classical supply function, so it is impossible to get any extra output beyond potential, unless you are willing to throw away the assumption of rational expectations. But we note that in real life, monetary policy does have real effects (on output gap, say) and it is probably due to nominal rigidities that allow the output-inflation tradeoff to exist at least in the short-run. So to be more realistic, replacing the Lucas supply curve with the New Keynesian supply function seems the most natural thing to do. The introduction of short-run output-inflation tradeoff also makes the question of optimal monetary policy much more interesting...how much short-run output benefit can you get (by active monetary policy), without generating excessive inflation expectations which will be bad for you in the long-run...and so on. So it is the fact that the inflation expectations enter with the particular lag structure according to New Keynesian story which allows us to draw implications as done in the lectures.
Even if topic 5 is extended to multi-period setup, as long as you keep the Lucas supply function, there would not be any interesting role for output stabilisation (i.e. you would not want to respond to aggregate supply shock, but let all the pain falls on output and accept no change in inflation).
In topic 7, we expect different result between rule and discretionary policy while topic 5 seems to offer indifferent result. Is that because in case of topic 5, one time game, when central banker who has similar preference to the society announces that he would commit to some rule, his main strategy is to cheat anyways? As it's the finite game, customer realized this. So output wouldn't be able stimulated, only inflation would be raised. How's this different from the topic 7 ka, why rule and discretion in topic 7 yield the different result?
Under topic 5 model, the only source of inefficiency is the policy maker's wish to target output beyond the potential. His wish to do it generates inefficiently high inflation expectations and hence actual inflation. The solution is to get rid of this vicious cycle somehow. One way is to impose a rule, so that the policy maker cannot cheat, and the inflation expectations can then be credibly controlled. Second solution is to pick someone who doesn't want to cheat (i.e. who targets only the potential output). Another related solution is to pick someone who cares infinitely more about inflation. In short, once you fix the time inconsistency problem, you've restored the efficient outcome.
Under topic 7, it's different. We showed that there is also a time inconsistency problem there, so that makes rule-type commitment valuable for essentially the same reason as in topic 5. But rules add another sort of values as well, which is more subtle. Not only can rules be used to anchor inflation expectations and solve time inconsistency problems, they can also be used to manipulate the future inflation expectations as well. And we showed that, when this is done optimally, the outcome is better than that attained by a discretionary policy maker who may target only zero output gap. The discretionary guy cannot influence future inflation expectations, so he cannot manipulate the output-inflation tradeoff facing him, so he is at a disadvantage for that reason. So the New Keynesian setup of topic 7 offers quite a few interesting implications, despite its simple dynamic form.
I have 2 Questions.For Time Inconsistency,
1. Is it necessary that at Nash equilibrium state, y has to be always y_bar when we plug in the loss function?
Under topic 5 yes...as long as you assume rational expectations. This follows from the Phillips curve alone, if Pi-e=Pi (rational expectations assumption), then we must have y=y-bar.
2. Why don't we have to minnimize our loss function with respect to y? Or Do we concentrate on only inflation?
The Phillips curve says that you face a constraint, so the moment you choose y, pi will already be automatically determined (given inflation expectations). Likewise, once you pick pi, y is already chosen implicitly. This is the same as in any consumption problem where you have a utility function and a budget set. We could minimise our loss with respect to either y or pi, as long as we get the right terms of tradeoff (from Phillips curve) into our first-order conditions.
Could you clearify about the shocks?What is the positive supply shock and negtive supply shock i.e. Ut should be positive or negative (also rise or fall) corresponding with the shocks and output in which case should be rise or fall? Finally, in AD-AS diagram, what direction will AS shift in order to repesent the shock (Ut) i.e. AS will shift to the right or left if there is a positive supply shock?
I think if there is ever a convention, by positive supply shock we normally mean a shock that lowers inflation and/or raise output. In other words, a positive supply shock means AS shifts to the right. So here, a positive supply shock in this language corresponds to u_t being negative (because u_t is the shock that adds to inflation, according to how we write our Phillips curve). But I think of this as a language issue...as long as we are clear whether u_t is moving up or down, there's no confusion.
As u_t goes up, we have higher inflation for any given output (or equivalently, lower output for any given inflation), so AS has to be shifting to the left. And I think it's conventional to call this type of shock a negative supply shock.
Firstly, what's the word "time inconsistency" mean in this case?
Suppose you ask the policy maker what inflation and output pair will he prefer ex ante, between (pi-star,y-bar) and (pi-high,y-bar), where pi-high is the Nash equilibrium inflation derived in lectures and is greater than pi-star the inflation target. The policy maker will readily tell you that he prefers (pi-star,y-bar), because in his loss function it gives lower inflation with no output loss. But once you let the public fix their inflation expectations at pi-star, the policy maker will no longer wish to deliver pi-star, as he wants to push output beyond y-bar by increasing inflation. When the time comes and agents decide fix their expectations at pi-star, the policy maker's optimal action is inconsistent with the plan he promises before the expectations are fixed. So ex post, what the policy maker wants to do is inconsistent with what he prefers ex ante. The public foreseeing this will not fix inflation expectations at pi-star in the first place, and we get inflation bias results.
Also in topic 7, we get output-inflation trade off but not in the topic 5. Is it because in topic 5 we consider only 1 time game and we also assume no shock but in topic 7, shock and time dimension are taking into consideration? Could you explain it intuitively?
Topic 5 uses essentially the Lucas or new classical supply function, so it is impossible to get any extra output beyond potential, unless you are willing to throw away the assumption of rational expectations. But we note that in real life, monetary policy does have real effects (on output gap, say) and it is probably due to nominal rigidities that allow the output-inflation tradeoff to exist at least in the short-run. So to be more realistic, replacing the Lucas supply curve with the New Keynesian supply function seems the most natural thing to do. The introduction of short-run output-inflation tradeoff also makes the question of optimal monetary policy much more interesting...how much short-run output benefit can you get (by active monetary policy), without generating excessive inflation expectations which will be bad for you in the long-run...and so on. So it is the fact that the inflation expectations enter with the particular lag structure according to New Keynesian story which allows us to draw implications as done in the lectures.
Even if topic 5 is extended to multi-period setup, as long as you keep the Lucas supply function, there would not be any interesting role for output stabilisation (i.e. you would not want to respond to aggregate supply shock, but let all the pain falls on output and accept no change in inflation).
In topic 7, we expect different result between rule and discretionary policy while topic 5 seems to offer indifferent result. Is that because in case of topic 5, one time game, when central banker who has similar preference to the society announces that he would commit to some rule, his main strategy is to cheat anyways? As it's the finite game, customer realized this. So output wouldn't be able stimulated, only inflation would be raised. How's this different from the topic 7 ka, why rule and discretion in topic 7 yield the different result?
Under topic 5 model, the only source of inefficiency is the policy maker's wish to target output beyond the potential. His wish to do it generates inefficiently high inflation expectations and hence actual inflation. The solution is to get rid of this vicious cycle somehow. One way is to impose a rule, so that the policy maker cannot cheat, and the inflation expectations can then be credibly controlled. Second solution is to pick someone who doesn't want to cheat (i.e. who targets only the potential output). Another related solution is to pick someone who cares infinitely more about inflation. In short, once you fix the time inconsistency problem, you've restored the efficient outcome.
Under topic 7, it's different. We showed that there is also a time inconsistency problem there, so that makes rule-type commitment valuable for essentially the same reason as in topic 5. But rules add another sort of values as well, which is more subtle. Not only can rules be used to anchor inflation expectations and solve time inconsistency problems, they can also be used to manipulate the future inflation expectations as well. And we showed that, when this is done optimally, the outcome is better than that attained by a discretionary policy maker who may target only zero output gap. The discretionary guy cannot influence future inflation expectations, so he cannot manipulate the output-inflation tradeoff facing him, so he is at a disadvantage for that reason. So the New Keynesian setup of topic 7 offers quite a few interesting implications, despite its simple dynamic form.
I have 2 Questions.For Time Inconsistency,
1. Is it necessary that at Nash equilibrium state, y has to be always y_bar when we plug in the loss function?
Under topic 5 yes...as long as you assume rational expectations. This follows from the Phillips curve alone, if Pi-e=Pi (rational expectations assumption), then we must have y=y-bar.
2. Why don't we have to minnimize our loss function with respect to y? Or Do we concentrate on only inflation?
The Phillips curve says that you face a constraint, so the moment you choose y, pi will already be automatically determined (given inflation expectations). Likewise, once you pick pi, y is already chosen implicitly. This is the same as in any consumption problem where you have a utility function and a budget set. We could minimise our loss with respect to either y or pi, as long as we get the right terms of tradeoff (from Phillips curve) into our first-order conditions.
Could you clearify about the shocks?What is the positive supply shock and negtive supply shock i.e. Ut should be positive or negative (also rise or fall) corresponding with the shocks and output in which case should be rise or fall? Finally, in AD-AS diagram, what direction will AS shift in order to repesent the shock (Ut) i.e. AS will shift to the right or left if there is a positive supply shock?
I think if there is ever a convention, by positive supply shock we normally mean a shock that lowers inflation and/or raise output. In other words, a positive supply shock means AS shifts to the right. So here, a positive supply shock in this language corresponds to u_t being negative (because u_t is the shock that adds to inflation, according to how we write our Phillips curve). But I think of this as a language issue...as long as we are clear whether u_t is moving up or down, there's no confusion.
As u_t goes up, we have higher inflation for any given output (or equivalently, lower output for any given inflation), so AS has to be shifting to the left. And I think it's conventional to call this type of shock a negative supply shock.
Questions on Transmission Mechanism
I get a few questions regarding the use of VAR in topic 6. Here are some comments.
Exams requirement
As I mentioned in class, I expect you to be able to interpret the VAR results, but I don't require you to understand the econometrics of VAR. So just approach it like an end-user, rather than a developer.
VAR faqs
Disclaimer: My worst nightmare would be for you to skip all journal readings and just relying on my comments below. Below I intend only to clarify certain issues, and answer questions that were raised, so it is not comprehensive in any way. Also, in no way does the following aim to provide any hint about what's coming in exams!!!
What is VAR?
VAR or vector autoregression is a statistical model, which attempts to capture interdependence between various variables over time. It is purely statistical, so if you put in all the variables that really matter (and have not omitted anything important), then your model would be 'true', and would capture how these variables really co-move over time
VAR analysis returns an output in the form of many estimated coefficients, e.g. the response of inflation to interest rate 1 period ago, 2 periods ago, and so on. Because there are simply too many numbers, it is not very useful for us. One way to illustrate the implications of VAR is to ask..."what would be the impact of a one-time shock to variable x on variables z1, z2, z3 and so on, over time?". By one-time shock, we mean we let x go up or down by more than the model predicts by one period, and then return things to normal thereafter. The responses of other variables will take place over a number of periods, as the rich interactions between variables work through over time. If you plot these responses over time, you get the impulse-response analysis graphs, which I show on the last slide (these graphs were taken from a very good introductory paper by Stock and Watson (2001), "Vector Autoregressions", Journal of Economic Perspectives...a highly recommended read) . So all the changes of the various variables shown on each graph are due to that single one-time shock to one variable.
Impulse-Response Analysis: Interpretation
As an example, we can look at the last row of the Stock-Watson diagram. This is the result of impulse response analysis of a one-time positive shock to the interest rate. We see that this single one-time shock has no impact on inflation until after 4 quarters, after which the inflation will start to contract. Unemployment responds slowly also, with maximum impact felt after 8 quarters. The last graph shows that the model predicts the interest rate will gradually come down from the level at which it was shocked. Thus this type of analysis can help us quantify the time-lag involved after the policy variable changes, and also for us to check if the data really confirm our economic understanding that inflation should come down after interest rate is increased.
Why does unemployment come down eventually? Well, having done half a term of Friedman-Lucas-New Keynesian, this should not come as a surprise to us. We have pretty much reached a sure conclusion that monetary policy cannot affect real variables in the long-run. Once prices are allowed to adjust eventually, it does not matter if there's more money being printed, the unemployment should go back to its natural rate, and output should return to trend. VAR analysis gives us theorists confidence that our understanding is in line with the data.
How do I know from this graph, which transmission channel is more important?
Well we can't figure this out from this graph alone, because VAR here only includes interest rate, inflation and unemployment. For example, if you want to know how credit plays a part in the transmission mechanism, you simply add the credit variables into the VAR, and then see what kind of result the impulse-response analysis generates. If theory suggests interest rate shock should hit bank loans, and then shrinking loans hit the investment, and then investment hits GDP, then all these linkages can be checked within VAR framework. Dr.Piti's paper is an example of how this is done (page 14 onwards). For an end-user like us, life is very easy...we can readily infer from graphs what's going on.
What if there are many shocks at the same time?
We'd basically have to work that out in our head, as impulse-response only give us the marginal impact of each variable's one-time shock. The VAR developer can compute the net effect exactly in a special impulse-response exercise, but it would only be useful under special cases. Knowing marginal impact and the time lags involved tells us almost everything we need to know.
Other issues
What's 'Variance Decomposition' (e.g. Dr. Piti's paper, p.8)?
The impulse-response tells us how a shock to variable x affects variables z1, z2, z3... Variance decomposition tells us how variable x is responding to a shock to each of the other variables z1, z2, z3. E.g. does inflation respond more strongly to a shock to interest rate or a shock to unemployment? Variance decomposition basically gives you information on the other side of the coin.
What are stylised facts?
Stylised facts mean well-documented empirical facts, which can be taken as true beyond doubt. So any good theory should be able to at least replicate results that are in line with stylised facts. These are represented in short 'bullet-point' form, hence the term stylised. Recall earlier during the term, we noted that the traditional Keynesian model fails to explain the stylised fact that real wage, if anything, is weakly procyclical.
Exams requirement
As I mentioned in class, I expect you to be able to interpret the VAR results, but I don't require you to understand the econometrics of VAR. So just approach it like an end-user, rather than a developer.
VAR faqs
Disclaimer: My worst nightmare would be for you to skip all journal readings and just relying on my comments below. Below I intend only to clarify certain issues, and answer questions that were raised, so it is not comprehensive in any way. Also, in no way does the following aim to provide any hint about what's coming in exams!!!
What is VAR?
VAR or vector autoregression is a statistical model, which attempts to capture interdependence between various variables over time. It is purely statistical, so if you put in all the variables that really matter (and have not omitted anything important), then your model would be 'true', and would capture how these variables really co-move over time
VAR analysis returns an output in the form of many estimated coefficients, e.g. the response of inflation to interest rate 1 period ago, 2 periods ago, and so on. Because there are simply too many numbers, it is not very useful for us. One way to illustrate the implications of VAR is to ask..."what would be the impact of a one-time shock to variable x on variables z1, z2, z3 and so on, over time?". By one-time shock, we mean we let x go up or down by more than the model predicts by one period, and then return things to normal thereafter. The responses of other variables will take place over a number of periods, as the rich interactions between variables work through over time. If you plot these responses over time, you get the impulse-response analysis graphs, which I show on the last slide (these graphs were taken from a very good introductory paper by Stock and Watson (2001), "Vector Autoregressions", Journal of Economic Perspectives...a highly recommended read) . So all the changes of the various variables shown on each graph are due to that single one-time shock to one variable.
Impulse-Response Analysis: Interpretation
As an example, we can look at the last row of the Stock-Watson diagram. This is the result of impulse response analysis of a one-time positive shock to the interest rate. We see that this single one-time shock has no impact on inflation until after 4 quarters, after which the inflation will start to contract. Unemployment responds slowly also, with maximum impact felt after 8 quarters. The last graph shows that the model predicts the interest rate will gradually come down from the level at which it was shocked. Thus this type of analysis can help us quantify the time-lag involved after the policy variable changes, and also for us to check if the data really confirm our economic understanding that inflation should come down after interest rate is increased.
Why does unemployment come down eventually? Well, having done half a term of Friedman-Lucas-New Keynesian, this should not come as a surprise to us. We have pretty much reached a sure conclusion that monetary policy cannot affect real variables in the long-run. Once prices are allowed to adjust eventually, it does not matter if there's more money being printed, the unemployment should go back to its natural rate, and output should return to trend. VAR analysis gives us theorists confidence that our understanding is in line with the data.
How do I know from this graph, which transmission channel is more important?
Well we can't figure this out from this graph alone, because VAR here only includes interest rate, inflation and unemployment. For example, if you want to know how credit plays a part in the transmission mechanism, you simply add the credit variables into the VAR, and then see what kind of result the impulse-response analysis generates. If theory suggests interest rate shock should hit bank loans, and then shrinking loans hit the investment, and then investment hits GDP, then all these linkages can be checked within VAR framework. Dr.Piti's paper is an example of how this is done (page 14 onwards). For an end-user like us, life is very easy...we can readily infer from graphs what's going on.
What if there are many shocks at the same time?
We'd basically have to work that out in our head, as impulse-response only give us the marginal impact of each variable's one-time shock. The VAR developer can compute the net effect exactly in a special impulse-response exercise, but it would only be useful under special cases. Knowing marginal impact and the time lags involved tells us almost everything we need to know.
Other issues
What's 'Variance Decomposition' (e.g. Dr. Piti's paper, p.8)?
The impulse-response tells us how a shock to variable x affects variables z1, z2, z3... Variance decomposition tells us how variable x is responding to a shock to each of the other variables z1, z2, z3. E.g. does inflation respond more strongly to a shock to interest rate or a shock to unemployment? Variance decomposition basically gives you information on the other side of the coin.
What are stylised facts?
Stylised facts mean well-documented empirical facts, which can be taken as true beyond doubt. So any good theory should be able to at least replicate results that are in line with stylised facts. These are represented in short 'bullet-point' form, hence the term stylised. Recall earlier during the term, we noted that the traditional Keynesian model fails to explain the stylised fact that real wage, if anything, is weakly procyclical.
Is EE432 pretty much useless?
Here's a question from a student...
I question that all of the topics that we covered in the class are really applied in today banks or BOT, something like plug in the data in model and use its outcome to predict the economy? or they are just the model to form the idea for each topic, something like if you are inflation-bias type, the economy gonna be like blah blah blah without any need to use any data to plug in?
The main reason for my question is to answer myself that I know how useful of what I have learned for the whole semester because now I’m blanked with the practical uses of this course (may be it may takes time for me to use it in the future some day) and also if my friend ask me why they have to study this course, I still have no idea.
It's a very important and perfectly legitimate question. Here are my thoughts...
A lot of economics that's taught today is still pretty much a 'pure' rather than an 'applied' science. The sad fact is, there's still a lot about the economy or human behaviour that we economists have not fully understood, so we're pretty much in the stage of developing our understanding. So it would be wrong to approach economics like an applied science, like medicine or engineering, where after you finish a course, you expect to be able to build a bridge or cure a certain disease. Learning formal models does not promise you a complete recipe to solve all economic problems on earth. But it gives you an invaluable habit of a scientist...i.e. to approach a problem in a systematic way. To be able to differentiate key factors from trivial ones, and to come to conclusions that are free from emotions, personal bias, or political orientation. That's what makes properly trained economists different from economic commentators.
I hope our course will have illustrated to you how each conclusion we reach is based on solid formulation, so that if there is any disagreement, we can always go back to check which step in our model or our assumption we disagree about. This provides a framework on which we can progressively learn something about the economy, and not just circling around the same issue over and over without knowing really what's right and what's wrong and why.
Are formal theories ever used in real life? A central banker does not differentiate their loss function before they arrive at a decision, that's certain. But you'd be surprised, for example, that not long ago countries with hyperinflation fail to understand this very basic truth that we take for granted in lectures...that you cannot push output beyond potential and hope nothing happens to inflation. In fact, you don't have to actually do the output expansion...once you reveal your intention to do it, inflation will be there almost immediately. Nowadays any properly trained economist in any central bank has this understanding engraved in his head. So global inflation has come down in recent years not because of pure luck, but it comes from our better understanding of economics. And it comes originally from models and theory, from discussions in classroom and universities.
In any given day at the central bank, we don;t go over maths and models. It is assumed that you have learned it in school. We study data and use econometrics a lot, in order to check if the working of the economy as appear in the data is in line with our understanding. But without any theoretical understanding, your econometric skills won't help much, as you will be lost about what to look for. Just like a surgeon who doesn't understand the anatomy...he may be good at cutting, but he will not be able to save lives!
Personally, I can definitely testify that, without my previous econ training, the quality of my work at the bank today will be far inferior. I can't pin point exactly what I have learned that makes such a huge difference...but it's unlikely to be Kiyotaki-Moore equation 3.4 or whatever. I'd say it's a combination of the ability to think critically, the tendency to think analytically (instead of looking for cheap explanation), confidence to tackle problems of quantitative/mathematical nature, ability to recognise the right solutions when you see them, habit of keeping up with recent research etc. These things, I think, are acquired slowly over time. I hope ee432, and other courses you take at TU, give you a good start!
Comments welcomed!
There are other 'exam' questions from other students, and I will post them here too...soon!
I question that all of the topics that we covered in the class are really applied in today banks or BOT, something like plug in the data in model and use its outcome to predict the economy? or they are just the model to form the idea for each topic, something like if you are inflation-bias type, the economy gonna be like blah blah blah without any need to use any data to plug in?
The main reason for my question is to answer myself that I know how useful of what I have learned for the whole semester because now I’m blanked with the practical uses of this course (may be it may takes time for me to use it in the future some day) and also if my friend ask me why they have to study this course, I still have no idea.
It's a very important and perfectly legitimate question. Here are my thoughts...
A lot of economics that's taught today is still pretty much a 'pure' rather than an 'applied' science. The sad fact is, there's still a lot about the economy or human behaviour that we economists have not fully understood, so we're pretty much in the stage of developing our understanding. So it would be wrong to approach economics like an applied science, like medicine or engineering, where after you finish a course, you expect to be able to build a bridge or cure a certain disease. Learning formal models does not promise you a complete recipe to solve all economic problems on earth. But it gives you an invaluable habit of a scientist...i.e. to approach a problem in a systematic way. To be able to differentiate key factors from trivial ones, and to come to conclusions that are free from emotions, personal bias, or political orientation. That's what makes properly trained economists different from economic commentators.
I hope our course will have illustrated to you how each conclusion we reach is based on solid formulation, so that if there is any disagreement, we can always go back to check which step in our model or our assumption we disagree about. This provides a framework on which we can progressively learn something about the economy, and not just circling around the same issue over and over without knowing really what's right and what's wrong and why.
Are formal theories ever used in real life? A central banker does not differentiate their loss function before they arrive at a decision, that's certain. But you'd be surprised, for example, that not long ago countries with hyperinflation fail to understand this very basic truth that we take for granted in lectures...that you cannot push output beyond potential and hope nothing happens to inflation. In fact, you don't have to actually do the output expansion...once you reveal your intention to do it, inflation will be there almost immediately. Nowadays any properly trained economist in any central bank has this understanding engraved in his head. So global inflation has come down in recent years not because of pure luck, but it comes from our better understanding of economics. And it comes originally from models and theory, from discussions in classroom and universities.
In any given day at the central bank, we don;t go over maths and models. It is assumed that you have learned it in school. We study data and use econometrics a lot, in order to check if the working of the economy as appear in the data is in line with our understanding. But without any theoretical understanding, your econometric skills won't help much, as you will be lost about what to look for. Just like a surgeon who doesn't understand the anatomy...he may be good at cutting, but he will not be able to save lives!
Personally, I can definitely testify that, without my previous econ training, the quality of my work at the bank today will be far inferior. I can't pin point exactly what I have learned that makes such a huge difference...but it's unlikely to be Kiyotaki-Moore equation 3.4 or whatever. I'd say it's a combination of the ability to think critically, the tendency to think analytically (instead of looking for cheap explanation), confidence to tackle problems of quantitative/mathematical nature, ability to recognise the right solutions when you see them, habit of keeping up with recent research etc. These things, I think, are acquired slowly over time. I hope ee432, and other courses you take at TU, give you a good start!
Comments welcomed!
There are other 'exam' questions from other students, and I will post them here too...soon!
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