Serial Correlation

The reason why AR1 is particularly pernicious is because of the possibility of serial correlation. AR1 is consistent and unbiased with least squares (but Gauss Markov fails) given uncorrelated disturbances. But with correlated disturbances, then we lose consistency and unbiasedness.

In the preceeding post, we show that the correlation coefficient of AR1 is pretty darn close to its true value of 0.9. Here, we show what happens to the estimate of the correlation coefficient changes when we increase the sample size.

n=100 B=0.9942

n=300 B=0.9935

n-500 B=0.9936

n=1000 B=0.9934

As we can see increasing the sample size does nothing to bring the estimate closer to its true value. In fact, the persistence of the error is 0.9, and it can be shown that the limit of the correlation coefficient is 1 as the persistence term approaches 1.

Without serial correlation, more information should provide more information:

B=0.797

B=.9248

B=0.8951

B=0.9028

…which in fact is what happened.

AR1

Back to basics: lets say you have a time series data set:

Above, we have 700 observations. You suspect that it is a simple Autoregressive process. (In fact it is!, this is how i generated it in Matlab, the errors are random normal around zero with standard deviation of 1). You graph y(t) on a one period lag and see that its highly correlated. in fact, a regression gives a corellation coefficient of 0.8536
. [in fact, its 0.9].

I transfered this ‘data’ to Stata to do a autocorrelation and partial autocorrelation.

.. and as expected, the autocorrelation function smoothly drops to zero and the partial autocorrelation drops to zero after the first lag.

Journalists in the Line of Fire III

DJB has an mp3 file of Cheche Lazaro interviewing Ellen Tordesillas and Maria Rezza. Tough question by cheche, but no followup.

Specifically, Cheche asked: …. (PNP general?) Razon said there was an order to clear out the area to protect people in the Peninsula hotel, and that the journalists were not following a ligitimate order…. Ellen replied that it was not a legit order because of the free press provision. Later Maria said, if you ask journalists there, there was NO order given.

Setting aside legitimacy, was there in fact an order? I wanted Maria to answer the hypothetical: had there been an order, would it be correct for media to file out? A hypothetical to lawyers: If there had been order, would it be correct to call what the journalists did as obstruction (and charge them with such)?

If there was no order, then i side with maria. As she tells it,  journalists weren’t charged — why not? This is important. The fact that they weren’t charged makes the arrest seem like harrassment which is unconscionable. The DOJ should do a better job explaining the protocol of police action during these situations.

Funny Photoshop Video

This is Good News?

If it is, we’re in trouble!

Why can’t we have more movies like Juno?

I saw Juno today and it was very good. The writing was fun and easy. The direction, acting  and music were all great. Its not a movie that costs much. We should have more movies like this. Specifically: 1) an straightforward plot, 2) an engaging hero/heroine, 3) smart writing, 4) an actual character arc. It made me think about the Juno’s journey in understanding what love is between a guy and a girl, and how sex and pregnancy is this complicated thing that makes things better and/or ruins things. The funny scenes are too numerous to mention, but i have two favorite heartwarming scenes. The first is when Vanessa touches Juno’s stomach and says thank you. It teaches Juno that being a mom is this wonderful thing, that while she’s not ready now, one day she might want it for herself. Second is when Juno asks her dad, whether its possible for two people to be happy together forever, and her dad tells her what to look for in a guy. On the face of it, its standard love story stuff. But here, it exists in a context (which i won’t share here for fear of ruining the movie to the three people who read this blog!).

Also, somewhat beside the point i’m making here, they kept using what now is my word of the month -shenanigans. Such a funny word!

I think that the vast majority of Filipino movies rely on fantastic scenarios (i’m looking at you GMA films!), complicated-stereotypical relationships between family, and by-the-numbers romances.

Let me talk about romances a bit more. The movies are only vehicles for love teams, so the story is basically maximizes the romantic interactions between the pair (one might call this: mining the ‘kilig factor’). The Plot is basically variations on the same theme: a couple, then something happens, they drift apart, then they end up together. the end.

A recent example is One more Chance. The premise was a promising one — a couple that has been together for ages splits up to ‘find themselves’. Even the first scene was golden — john lloyd’s character is so insecure, that it takes a gastric event (wink!) from Bea Alonzo to allay his fears.

Great start — but the characters don’t grow. At the end of the movie, we just know that they MUST: 1) be different somehow, 2) split up from their respective partners, 3) get back together. But we don’t know HOW they get to this point. The film makers don’t want to tell a STORY. All they want, is a beginning/premise, and then an ending. The most interesting part (potentially) of the movie — the middle — is never shown on film!

Not all pinoy movies are like this. I recall, Kasal, Kasali, Kasalo wanted/tried to tell a middle part. Alot of the movie is how real couples get their act together and make mistakes along  the way. Indeed, i came out of that movie thinking: when is it okay to forgive your husband for his infidelity? Ultimately, how they resolved this issue was unsatisfying to me;  but at least it made me think.  

New Photo

Thanks, K. Nice Picture.

Trade Analogies part II

From Cafe Hayek:

Don argues in the book and in the podcast that to point to an American steel worker put out of work by imports of Brazilian steel and say that he is “harmed by trade” is to misunderstand the nature of trade and its winners and losers. He says it’s like saying that a man whose wife leaves him for another man is harmed by love. After all, the man married because of love. The man is the product of his parents who were touched by love. So it is with the steel worker. His steel job exists because of trade. His whole life is supported by trade of various kinds. So in what sense is he “harmed by trade?”

To this i clarify:

If a wife leaves her husband for another, WE DO say he was harmed by love. Its true that love helped him, for all the reasons you mentioned. But its also possible to be harmed by love. Hence the term heart broken. I think the analogy is incomplete. You should instead argue, even during times when love hurts us, does that mean we should NOT fall in love? to anyone with a broken heart, do we say: “you are right, love sucks. kill yourself” ? Of course not. Similarly, for trade, sometimes people get hurt by it, but this doesn’t mean we should retreat from potentially profitable/enjoyable relationships.

Optimal product launch strategy

There is a paper in our seminar schedule about the monopolist’s product launch strategy in multiple markets. Its highly stylized, but heck, its a start.There are N > 1 markets in which the monopolist can launch her product. The monopolists decision is to decide how many markets in which to launch. She can launch in all, in some, or none of these markets. For some reason, (unexplained, but i assume for simplicity), price p is fixed, at say 1/2. The good is either high quality, and its value v is 1, or low quality, where in its v is 0. The monopolist doesn’t know the quality of the good, which explains why we have non-discriminatory pricing. If the monopolist knew about her products quality, she would set two different prices and there would be a separating equilibrium. [Which raises an interesting question: how can a monopolist not know the quality of the product?]

The consumers belief about the value (lambda) takes values from (0,1). The consumer buys v-p>0 [This is confusing, it should be lambda-p>0? Is lambda the distribution of consumer's unit demands? I think the author wants to say that lambda is the same for each consumer in a market, which means its just like assuming one consumer per market, not terribly interesting].

Whats interesting is the updating method. Imagine you are in a market, and you observe a ’signal’ (she doesn’t explain what this signal might be, but this is a random signal) from another market where the product is launched. This signal can either be good or bad. A good signal may mean that the value of the good is 1 (the highest possible). A bad signal is defined similarly. A signal is independently and identically distributed across markets and time.

However, like many signals in life, signals are noisy. Let q = Prob(signal=1|v=1) =Prob(signal=0|v=0). That is, q is the probability that the signal is correct.We assume here that signals are more likely to be correct than not: q>1-q. [note: if this isn't true, then the graph i present below will switch].

The updating of beliefs on the product’s value is of interest to the monopolist. The monopolist would prefer to launch sequentially, IF she can manipulate willingness to pay in markets where she has not launched yet. In terms of the signal, if the signal is good, this implies, by Bayesian updating, those who see this signal would revise their beliefs/lambdas upward which raises demand.

Put in simply, this is kinda like viral marketing. Launch a product for a small group first. They tell the world that the product is good once they consume it and know its good. The rest of the world sees the signal and says, hey, windows vista is better than i thought… so they revise their valuations upward based on this signal. Similarly, if the signal is bad, they revise their values downward.

A consumer in a market where the good has not been launched has two pieces of information. The performance in the first market(s) in which it has been launched, as well as the random signal defined earlier.

Below you find a graph depicting the bayesian updating of beliefs:

Given that the price is 1/2, if lambda=lambdalow or less, then the succeeding markets will never buy the good, no matter what the realization of the signal. Hence you will never launch the good. We say that the consumer here is extremely pessimistic.

If lambdalow<lambda<p=1/2, then something interesting happens. Here, we say the consumer is pessimistic — the prior belief is that the good is ‘overpriced’.

Assume for simplicity two markets, and we consider a sequential launch which simply means launching one market at a time. Lets say the good was succesful (which means it received a good signal) in the first market; this leads to an updating upwards for the second market. But there is also a random signal A good random signal leads people to buy, a bad random signal lowers their lambda further. So,if the signal in market one is good and the signal is market two is good, there is no difference between sequential and simultaneous launch. Both markets buy anyway. If the signal in market one is good, and the random private signal in market 2 is bad, then the two signals cancel each other out, leading to lower total sales (good sales in market 1, no sales in market 2) — an inferior outcome which is came from the fact that the product was launched sequntially. If the signal if the first market is bad, and the second is bad, no one buys — but this would be true in a simultaneous launch too.

So the dominant strategy is to simultaneously launch.

[Note: its important here that you have representative, identical consumers in each market to get this result. If you abandon these, the analysis becomes more involved, but still follows the general line of reasoning outlined above]

If p=1/2>lambda<lambda high, something interesting happens. This time, the consumer is optimistic. Here, if you have simultaneous launch, each market will receive a random signal of s, which causes some to buy, others not.

If the launch is sequential, there are two signals for the later market: success/failure in the first and a private random signal in the second market.

The reasoning is similar to the preceeding case. If the signals are opposing, then they cancel out — but thats fine because the lambda>p and they (the second market) still buys. If the signals are the same, clearly both markets buy the good. We see why sequential benefits the monopolist — its a form of random signal hedging. A sequential launch allows opposing signals to cancel outwhich leads to higher total sales, while in a simultaneous launch, opposing signals mean random successes which is inferior.

Finally, if lambda>lambdahigh>1/2, then no matter what the realization of the signal, each market buys the product. so sequential is the same as simultaneous.

This is nice model that allows us to see how sequential launches help a monopolist when there is information assymmetry both for the seller and the buyer. They way the author explains the mechanism and demand was confusing at first. Also, the next step would be to endogenize the signal as a function of market variables, like sales and quantity and price. I also don’t like that latter markets have two signals. I’d rather model it as one signal, and then each market is heterogenous along a certain dimension. In this way, we might be able to get the result that if a sequential launch is implemented, then the first market must have the larger market size, or higher profit potential. This is much more realistic.

Walk for Life 2008

I attended this year’s Walk for Life West Coast.

Deeper thoughts about this to follow. But i do want to say that it was a learning experience for me. I was able to speak with intelligent, middle class americans about faith, reason and the value of life.

Roughly, most people would argue that abortion is a bad. The fetus is alive, and unfortunately for it, unable to defend itself. I’m pretty sure people from both sides can agree on that. The problem is people from both sides see abortion as part of a larger play. Pro-lifers tie abortion to birth control and the family (more on this next), while pro-choicers tie a choice against abortion as a vote for fascism and a blow to gay rights.

Some pro-lifers (at least one, a radio commentator on Sirius Radio’s Catholic radio) realize that issue tying is the wrong strategy, if we/they are to defeat the tide against abortion. Abortion is something we can all be against.

I got to walk in the middle of embarcadero street during the day, which is very cool. The photo above was taken right on the intersection of embarcadero and washington.