Reply to By the numbers: A dispassioned evaluation of Hardy (compared to Deal and Wilson)

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Reply to "By the numbers: A dispassioned evaluation of Hardy (compared to Deal and Wilson)"

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[quote=Anonymous][quote=Anonymous]Op Here.

Thanks. The previous poster is unhinged. I'm not bothered by it. We can ignore her while the adults have a conversation. [/quote]

OP, a few things.

First, thanks again for hanging in there and putting up with the off-topic and downright weird posts.

I think that maybe you should examine some of your assumptions. The first would be, the assumption that you are one of few economists analyzing this, among the DCUM and greater DC parent population. There are many of us with advanced degrees in economics or other quantitative subjects, working in quantitative fields, etc. I have been too lazy to dust off Mas-Colell for this debate (or whatever the kids are reading these days), but I'm no stranger to analyzing data or to game theory and I am sure that goes for many other parents and posters here. So by all means do your best to add to the debate, but please stop assuming that everyone else lives in a data-free or logic-free zone. Discarding this assumption will improve your analysis, because it will force you to accept the assumption of perfect information where it is appropriate, and therefore force you to dig deeper in your theorizing as to why parents avoid Hardy.

Which brings me to the second assumption or related set of assumptions. You have assumed or concluded (I cannot tell which) that there is an information problem here. Specifically, you think that many parents IB for Hardy are unaware that: 1) "white" kids score well wherever they attend; 2) white kids in DC score better than anywhere else in the country (no quotation marks here, as the published data on this one is based on race); 3) when you control for demographics, Hardy's test scores look a lot like Deal's, or Deal's of several years ago; and so on.

I know a lot of people who are white, literally and in the broader sense that you define in your first post. I bet that the vast majority and perhaps every single one of them is aware of the above. The one about white kids in DC scoring the highest in the nation, for example, has been published in the Post and elsewhere, and widely discussed among parents IRL and on DCUM. It's strong proof of your central thesis, which seems to be that if your kid is "white", your kid will do well at Hardy. So, quite the opposite of assuming informational asymmetry, you should assume that everybody knows the above 3 facts, and that everybody knows that everybody knows, etc to infinity. You are not presenting us with anything new in the analysis of test scores in your first post. We all know this, and we know that everyone else knows it too.

So the main problem with your model is that it assumes information problems when in fact we have perfect information ***regarding the likely outcomes of "white" kids***. (BTW if you were more familiar with DCUM, you would use "high-SES" to designate this. This is considered the politically correct way to express this on DCUM. I am not criticizing you, just letting you know FYI.)

Where we lack perfect information, is of course, regarding whether all the other families at the 5th to 6th grade transition will choose Hardy. Here, game theory is appropriate, because we do not have perfect information. This leads to the prisoner's dilemma or coordination problem.

Here I have a smaller quibble with you. You state up-thread that private school is not dominant, and the prisoner's dilemma is inappropriate, but you are over-simplifying. Private is not the only way to avoid Hardy, and for many IB, avoiding Hardy via whatever means is inexpensive relative to family resources. The classic PD matrix is (confess, confess), (confess, deny), (deny, confess), (deny, deny). My best case is (D,D), but my worst case is (D, C), and because my utility function exhibits risk aversion, and because I don't know what you will do, I choose C, and you and I have stable equilibrium at (C,C), the mediocre option.

For the Hardy decision the matrix is (avoid Hardy, avoid Hardy), (avoid Hardy, attend low SES Hardy), (attend low SES Hardy, avoid Hardy), (attend HIGH SES Hardy, attend HIGH SES Hardy). My best case is when we both attend, because I get the benefits of a high performing cohort without paying private tuition or similar expense (high SES Hardy, high SES Hardy), but my worst case is I attend Hardy while you avoid it, i.e. I attend low SES Hardy. So, risk averse and lacking compete info, we are stable with both avoiding Hardy. As with any PD matrix involving costs and benefits, you just subtract the costs (private school tuition eg) from the benefits when inserting the payoff values in the matrix.

I am not saying your use of stag hunt is wrong, but I am saying your quick dismissal of PD is probably wrong. It's hard to generalize this PD to more than 2 actors, like any PD, because there is a big gray area between low SES Hardy and high SES Hardy. There is a similar problem in the original PD: in a game of 100 players, how many confessions are needed to convict all the other players? Unless you assume that even one confession is enough to indict all deniers. This assumption is used in the simplest PD, but relaxed in more complex versions as I am sure you know. This difficulty in generalizing to the entire population does not negate the appropriateness of PD to this situation.

Getting back to the intuition here, my point up thread is, and remains, that across the country and around the world, high-SES families (note use of correct DCUM terminology!) consistently use cohort demographics and cohort academic performance as one of the most important, or the single most important, variable in choosing schools. NOTWITHSTANDING that their high-SES kid will do very well anywhere, they do not want the kid to be surrounded by low performing students. And, this is not irrational, or based on information shortage, or anything of the sort. It's completely rational and backed up by all kinds of research and common sense. So, your analysis of test score data is, frankly, largely irrelevant to the decision for most high SES parents, and for good reasons. The only relevant question is, "how many IB will be at Hardy next year?", which is not surprisingly the title of one of the long running Hardy threads on DCUM. Your game theory analysis (stag vs PD) is very relevant to this question, which is why I raise it again here.

And please note that this is not unique to Hardy or to Washington DC or to the United States of America. We see this in the VA and MD suburbs (if you don't believe me, check the DCUM threads comparing MS and HS options in the suburbs), and across the country and around the world. So if you are truly trying to convince high-SES parents that they should not care about the cohort, and should only care about their own kid's likely performance, then you have a lot of convincing to do, because it is not only many IB Hardy parents who have concluded this, but probably the vast majority of high-SES people anywhere. So, good luck with that.

Finally, because this is the internet, please everyone note that none of what I write is intended to denigrate Hardy or parents IB or OOB who choose to send kids there now, nor am I predicting that Hardy's current situation will continue. On the contrary, I am pretty confident that Hardy is on a clear upward trajectory both in terms of academic performance and IB interest. I am just arguing against those who claim that it is somehow wrong to focus on cohort performance and demographics when choosing schools.

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