My Dartmouth colleague Michael Herron pointed me to his paper on the recent NH primary and how voting patterns seemed to depend upon whether the vote was counted by hand or by machine. They use some neat but complex statistical methods, and arrive at this conclusion (quoting from their executive summary:
"With respect to Hillary Clinton's surprise victory in the Democratic Primary and the differences across vote tabulation technologies in Clinton's and others' votes, our results are consistent with these differences being due entirely to the fact that New Hampshire wards that use Accuvote optical scan machines have voters with different political preferences than wards that use hand counted paper ballots."
These statistical results may be important, given that it appears some people may not accept the recount results (conspiracy theories run real deep!).
Sunday, January 20, 2008
Harvard's and Yale’s Endowments: A Bias to Quality vs. Quantity in Higher Education?
Some of our leading universities have been criticized lately for hoarding their endowments – accumulating huge warchests and then not spending on appropriate socially valuable causes. Given that the general public supports higher education financially through a variety of mechanisms, the criticism does sting. Yale has the second-largest endowment of all US universities, at $22.5 billion, and Yale just announced that it will increase its yearly take from a little under 4% to at least 4.5%. Bear in mind that a half percentage point means an additional $113 million per year and that Yale’s endowment enjoyed a return last year of 28%! Harvard has the largest endowment -- $34.9 billion. It recently announced a new financial aid policy that will limit how much families pay for tuition: up to $180,000, a family will pay at most 10% in tuition. Yale is considering a similarly generous tuition reduction policy.
What is of interest to me is how little the top universities have grown, especially the private Ivy League colleges (I am going to focus on undergraduates in this, for reasons that will be apparent later). Data on incoming class sizes historically has been hard to find, but for Harvard at least, I know that in 2000, the incoming class size was 1637 and in a faculty report that I located, there was a statement that enrollment had been steady at that level for some time. In fall of 2006, Harvard matriculated 1640 students, basically the same number. Let’s take it for now as a stylized fact that there has been very little expansion.
(Yale’s President Richard Levin has just announced that Yale is considering an increase in its undergraduate student body to 6000, from 5300. This is interesting. Note these are total student body numbers, not incoming freshman only.)
It is somewhat curious to me as an economist that we have an industry with tremendous growth in demand and where the leading firms do not grow. Do we have an increase in demand? Clearly yes: US population has increased, from about 250 million in 1990 to 300 million today, plus we have an increasing number of foreign students applying to US universities. Acceptance rates at the top schools are extremely low – Yale last year took only 9.6 % of its 19,323 total applications for the class of 2011. Plus we observe tuition rising at above the rate of inflation for many years now. That is a strong indicator of increased demand.
Sure, the stylized model of an industry just has more firms enter the industry in response to a demand increase. This is because the existing firms are at optimal scale, so if they grew they would be at a disadvantage relative to others. I think there is some of this story going on in academia, but I don’t think it can completely explain the lack of expansion of existing schools. Among other things, there is already tremendous variation in size of universities, even within the Ivy League, so it is not clear at all what the optimal scale is. I think there is something else going on.
So why don’t schools like Harvard, Yale, Dartmouth and Princeton expand? It is easy for me to make a social case that they should. These schools serve as tremendous gatekeepers for the next step in someone’s career progression. It is not a slam dunk to get into a top law school or business school, or consulting firm or investment bank from HYPS (Harvard, Yale Princeton Stanford) but the probability is certainly higher than if you graduate from….well, let’s say Northern Michigan University. The pyramid with top universities at the top and the world’s undergraduate population at the bottom has gotten much broader at the bottom but it has not expanded at the top. As a result, it is even harder for someone out of the usual social and economic classes to break into the most valuable circles of society. Yes, the top schools do promote diversity, but the focus tends to be racial and ethnic, not economic, and there are just not enough slots available. The top schools do not have to take virtually any risk at all with their incoming class; they routinely turn away students with perfect SAT scores.
I am working towards a theory of bias towards quality in higher education. Perhaps this has already been done, so don’t be shy in letting me know of prior work.
Any decision to expand a school will be made by the faculty, so we need to think of their incentives. Since a university is not owned by anyone, the incentives are more similar to those of partners in a partnership than shareholders in a for-profit firm. Specifically, the existing professors are going to disapprove of any expansion that worsens their own situation. This can play out in a variety of ways in a university setting. The main mechanism, I think, is as follows. Suppose that tuition covers 50% of the total current cost of the university, with the rest being covered by endowment spending (these are not far from truth). Then the “profitability” of additional students depends upon how the endowment will change with an additional student versus the incremental cost of additional students. If we are dealing with a significant increase in students, the incremental cost will be closer to the current average costs, for the university will have to increase all the fixed assets to serve additional students (dorms, classrooms, professors, labs, etc.) However, it is doubtful that the increase in future endowments (through anticipated gifts by the new students) will equal the average endowment per student currently enjoyed (I could expand on this assumption, and it is important). Therefore, increasing students will reduce the “surplus” of the university, and the existing professors could rightly infer that an expansion will make them worse off. It will also make the existing students worse off, so they are likely to oppose it as well. Even alumni might infer that their degrees will be worth less, if the average student in the future will have fewer resources and therefore receive a lower quality education.
So we will get opposition to expansions that in some sense reduce the “average” quality of the institution. But nothing in the above story implies that the addition of the new students is not worthwhile from a pure cost-benefit calculus. The current situation could be one where the “surplus” from the existing endowment is being spent to make the lives of the current students and faculty of higher quality – but that quality is more than is necessary, in some sense. This is the bias towards quality: the existing beneficiaries of the top schools’ wealth are unwilling to lower the average quality. And indeed, this sounds very respectable: who can stand up and say that we should expand and accept lower quality in any sense?
I think this theory could be built up formally, and it is potentially testable. Schools that cover a lower percentage of their costs from tuition, and a higher percentage from an endowment, ceteris paribus should be less likely to expand. I think this prediction might help explain why business schools have generally been more responsive to demand and increased their class sizes – generally they fund more of their operations from tuition.
What is of interest to me is how little the top universities have grown, especially the private Ivy League colleges (I am going to focus on undergraduates in this, for reasons that will be apparent later). Data on incoming class sizes historically has been hard to find, but for Harvard at least, I know that in 2000, the incoming class size was 1637 and in a faculty report that I located, there was a statement that enrollment had been steady at that level for some time. In fall of 2006, Harvard matriculated 1640 students, basically the same number. Let’s take it for now as a stylized fact that there has been very little expansion.
(Yale’s President Richard Levin has just announced that Yale is considering an increase in its undergraduate student body to 6000, from 5300. This is interesting. Note these are total student body numbers, not incoming freshman only.)
It is somewhat curious to me as an economist that we have an industry with tremendous growth in demand and where the leading firms do not grow. Do we have an increase in demand? Clearly yes: US population has increased, from about 250 million in 1990 to 300 million today, plus we have an increasing number of foreign students applying to US universities. Acceptance rates at the top schools are extremely low – Yale last year took only 9.6 % of its 19,323 total applications for the class of 2011. Plus we observe tuition rising at above the rate of inflation for many years now. That is a strong indicator of increased demand.
Sure, the stylized model of an industry just has more firms enter the industry in response to a demand increase. This is because the existing firms are at optimal scale, so if they grew they would be at a disadvantage relative to others. I think there is some of this story going on in academia, but I don’t think it can completely explain the lack of expansion of existing schools. Among other things, there is already tremendous variation in size of universities, even within the Ivy League, so it is not clear at all what the optimal scale is. I think there is something else going on.
So why don’t schools like Harvard, Yale, Dartmouth and Princeton expand? It is easy for me to make a social case that they should. These schools serve as tremendous gatekeepers for the next step in someone’s career progression. It is not a slam dunk to get into a top law school or business school, or consulting firm or investment bank from HYPS (Harvard, Yale Princeton Stanford) but the probability is certainly higher than if you graduate from….well, let’s say Northern Michigan University. The pyramid with top universities at the top and the world’s undergraduate population at the bottom has gotten much broader at the bottom but it has not expanded at the top. As a result, it is even harder for someone out of the usual social and economic classes to break into the most valuable circles of society. Yes, the top schools do promote diversity, but the focus tends to be racial and ethnic, not economic, and there are just not enough slots available. The top schools do not have to take virtually any risk at all with their incoming class; they routinely turn away students with perfect SAT scores.
I am working towards a theory of bias towards quality in higher education. Perhaps this has already been done, so don’t be shy in letting me know of prior work.
Any decision to expand a school will be made by the faculty, so we need to think of their incentives. Since a university is not owned by anyone, the incentives are more similar to those of partners in a partnership than shareholders in a for-profit firm. Specifically, the existing professors are going to disapprove of any expansion that worsens their own situation. This can play out in a variety of ways in a university setting. The main mechanism, I think, is as follows. Suppose that tuition covers 50% of the total current cost of the university, with the rest being covered by endowment spending (these are not far from truth). Then the “profitability” of additional students depends upon how the endowment will change with an additional student versus the incremental cost of additional students. If we are dealing with a significant increase in students, the incremental cost will be closer to the current average costs, for the university will have to increase all the fixed assets to serve additional students (dorms, classrooms, professors, labs, etc.) However, it is doubtful that the increase in future endowments (through anticipated gifts by the new students) will equal the average endowment per student currently enjoyed (I could expand on this assumption, and it is important). Therefore, increasing students will reduce the “surplus” of the university, and the existing professors could rightly infer that an expansion will make them worse off. It will also make the existing students worse off, so they are likely to oppose it as well. Even alumni might infer that their degrees will be worth less, if the average student in the future will have fewer resources and therefore receive a lower quality education.
So we will get opposition to expansions that in some sense reduce the “average” quality of the institution. But nothing in the above story implies that the addition of the new students is not worthwhile from a pure cost-benefit calculus. The current situation could be one where the “surplus” from the existing endowment is being spent to make the lives of the current students and faculty of higher quality – but that quality is more than is necessary, in some sense. This is the bias towards quality: the existing beneficiaries of the top schools’ wealth are unwilling to lower the average quality. And indeed, this sounds very respectable: who can stand up and say that we should expand and accept lower quality in any sense?
I think this theory could be built up formally, and it is potentially testable. Schools that cover a lower percentage of their costs from tuition, and a higher percentage from an endowment, ceteris paribus should be less likely to expand. I think this prediction might help explain why business schools have generally been more responsive to demand and increased their class sizes – generally they fund more of their operations from tuition.
More on the National Security Levy
US Senate candidate Jay Buckey was kind enough to comment on my posts below.
Here is the paper that he cites as a reference for the hidden cost of oil, particularly those costs related to national defense. The link brings you to the National Defense Council Foundation, a think tank focused on national security. Look around and you will find the paper.
In principle, as I said in my original post, I agree that some military spending is related to our oil consumption and therefore should be reflected in the price we pay. The questions are of magnitude, how we will impose the tax, and what we will do with the proceeds.
The paper cited by Mr. Buckey has annual oil-related costs of defense of $137.8 billion, which would result in a levy of $18 per barrel given our US consumption of roughly 21 million barrels per day. That is a significant number. There are of course a lot of things to question in the analysis. The biggest issue I have is the idea that we are in the Middle East to protect our oil consumption interests. Unfortunately, the Middle East has the world's cheapest oil reserves, and they are going to be bought by somebody -- if not us, then someone else. Those purchases will result in revenues to governments that are not always friendly to us.
Here is the paper that he cites as a reference for the hidden cost of oil, particularly those costs related to national defense. The link brings you to the National Defense Council Foundation, a think tank focused on national security. Look around and you will find the paper.
In principle, as I said in my original post, I agree that some military spending is related to our oil consumption and therefore should be reflected in the price we pay. The questions are of magnitude, how we will impose the tax, and what we will do with the proceeds.
The paper cited by Mr. Buckey has annual oil-related costs of defense of $137.8 billion, which would result in a levy of $18 per barrel given our US consumption of roughly 21 million barrels per day. That is a significant number. There are of course a lot of things to question in the analysis. The biggest issue I have is the idea that we are in the Middle East to protect our oil consumption interests. Unfortunately, the Middle East has the world's cheapest oil reserves, and they are going to be bought by somebody -- if not us, then someone else. Those purchases will result in revenues to governments that are not always friendly to us.
Saturday, January 19, 2008
More on Jay Buckey's National Security Levy
It gets worse. See my posting below on the supposedly major plank -- a "national security levy" -- in Jay Buckey's campaign for US Senator from New Hampshire.
I had neglected to mention that the proceeds from this levy will not be dedicated to lowering marginal tax rates or something benign, but will instead finance an "Apollo program for energy dependence, which would develop new technologies and stimulate the economy." Remember, now, that Mr. Buckey was an astronaut.
Here we go again with naive Democratic views of economic engineering. Let's put a tax here, a subsidy there, give out some tax credits and incentives here, put some price floors over here and some wage controls over there....Presto! The economy is whirring along like a Stirling engine.
It is an engineering view of the economy. Engineers can look at something like an engine and improve its operation through mechanics. Why not an economy too?
Just one little thought on the law of unintended consequences, which usually stops economic engineering experiments dead in their tracks: If we tax OIL, what will we do with natural gas? What kind of stimulus to natural gas production and importation will a tax on oil yield? What about that big liquid natural gas terminal proposed for the East coast, to import LNG from....guess where...the Middle East?
I had neglected to mention that the proceeds from this levy will not be dedicated to lowering marginal tax rates or something benign, but will instead finance an "Apollo program for energy dependence, which would develop new technologies and stimulate the economy." Remember, now, that Mr. Buckey was an astronaut.
Here we go again with naive Democratic views of economic engineering. Let's put a tax here, a subsidy there, give out some tax credits and incentives here, put some price floors over here and some wage controls over there....Presto! The economy is whirring along like a Stirling engine.
It is an engineering view of the economy. Engineers can look at something like an engine and improve its operation through mechanics. Why not an economy too?
Just one little thought on the law of unintended consequences, which usually stops economic engineering experiments dead in their tracks: If we tax OIL, what will we do with natural gas? What kind of stimulus to natural gas production and importation will a tax on oil yield? What about that big liquid natural gas terminal proposed for the East coast, to import LNG from....guess where...the Middle East?
Friday, January 18, 2008
US Senate Candidate Jay Buckey
I met a Democratic candidate for US Senate from NH last night, Jay Buckey. I was at a reception for a Tuck event and a colleague made sure to bring Mr. Buckey over to see me. My colleague was bored I guess and wanted to see some excitement. I don't think I disappointed him. I only wish I had had a little chance to prepare, but I have not been following the Senate race.
Buckey has a good resume and seems to be a nice and sincere person.
As the reception was for Matt Simmons, the leading proponent of the "Peak Oil" idea, Mr. Buckey and I naturally gravitated to discussion of oil economics. Mr. Buckey has a proposal, available here. It is a tax on all oil consumed in the US, with the tax being variable on the basis of world oil prices: if world oil prices rise, the tax falls, and if the price falls, the tax increases. Well, maybe I am being generous: The actual wording of the proposal is that if the price of oil falls, the levy WILL be increased, but if the price of oil "spikes" then the levy "could be suspended." Ah, you have to love that kind of language.
Now as an economist, I have said many times, I do support the concept of internalizing externalities. Consumption of oil does impose externalities, so there is a case for some taxes. My first question for Mr. Buckey is how he knows that the current taxes, as well as a possible monopoly rent built in, do not already do the optimal compensation for externalities.
But I have two bigger concerns. The first is the purpose of the variability. The goal here, according to Mr. Buckey, is to create a floor for oil prices so to give alternative energy sources in the US the assurance they need to be developed. Isn't that great? How many producers would like the assurance that their main competitor will never charge a price lower than $x? It sounds great, but it is nothing more than your typical Democratic meddling in markets. Bear in mind that the real price of oil today is still less than its peak in 1980. If we had implemented this price floor back in 1980, we would have foregone 28 years of cheap energy. Let's leave it to market forces to decide which source of energy should be developed.
Also, the externality case for a tax on oil does not have that tax varying according to the price of oil, only according to the marginal damage caused by burning the oil.
If new energy sources cannot attract capital given the historic volatility of oil prices, it is prima facie evidence that those sources of energy are uneconomic. You can argue with me about adding a premium for avoiding the externalities associated with oil, but we will have to do that analysis carefully, accounting for the taxes already on oil.
I think my biggest objection to Buckey's idea is that he calls it the National Security Levy. In my talk with him, he was adamant that we are militarily engaged in the Middle East to protect our oil interests, and therefore we should have a tax on oil to represent that cost. While I agree in principle with this argument, in this case the magnitude of my agreement is quite slight. Mr. Buckey kept saying that there are other unstable parts of the world where we are not engaged, hence it must be the oil of the Middle East. First, what about Afghanistan? We were attacked by terrorists from Afghanistan, and there is no oil production there. So that part of the defense budget should not be attributed to oil. And I think Israel would be rather taken aback if they learned that we are only in the Middle East to protect our oil interests.
I think the link between oil in the Middle East and our military involvement there is not due to a desire to protect our CONSUMPTION of oil, but because the presence of oil reserves in the Middle East gives countries there a huge revenue source with which to create trouble. If we stopped buying oil from the Middle East, China and India would welcome our absence. The oil suppliers would still have billions of dollars annually to spend on weapons and disruption. If we value our freedom and that of other countries, I contend that we would still be militarily engaged.
So to say that we are in the Middle East for oil is not precise. We are there because of oil, but more precisely, because the oil reserves of that area give additional strength to any enemies located in that region. I would put forth that our engagement as a customer gives us some political power that we would forsake if Buckey's National Defense Levy succeeded in getting us to buy less Middle Eastern oil.
I tried to get Mr. Buckey to buy into my ideas for the Democratic party of being socially libertarian, fiscally conservative, reasonably strong on national defense, and leaving economics to market forces, but I don't think he bit.
Buckey has a good resume and seems to be a nice and sincere person.
As the reception was for Matt Simmons, the leading proponent of the "Peak Oil" idea, Mr. Buckey and I naturally gravitated to discussion of oil economics. Mr. Buckey has a proposal, available here. It is a tax on all oil consumed in the US, with the tax being variable on the basis of world oil prices: if world oil prices rise, the tax falls, and if the price falls, the tax increases. Well, maybe I am being generous: The actual wording of the proposal is that if the price of oil falls, the levy WILL be increased, but if the price of oil "spikes" then the levy "could be suspended." Ah, you have to love that kind of language.
Now as an economist, I have said many times, I do support the concept of internalizing externalities. Consumption of oil does impose externalities, so there is a case for some taxes. My first question for Mr. Buckey is how he knows that the current taxes, as well as a possible monopoly rent built in, do not already do the optimal compensation for externalities.
But I have two bigger concerns. The first is the purpose of the variability. The goal here, according to Mr. Buckey, is to create a floor for oil prices so to give alternative energy sources in the US the assurance they need to be developed. Isn't that great? How many producers would like the assurance that their main competitor will never charge a price lower than $x? It sounds great, but it is nothing more than your typical Democratic meddling in markets. Bear in mind that the real price of oil today is still less than its peak in 1980. If we had implemented this price floor back in 1980, we would have foregone 28 years of cheap energy. Let's leave it to market forces to decide which source of energy should be developed.
Also, the externality case for a tax on oil does not have that tax varying according to the price of oil, only according to the marginal damage caused by burning the oil.
If new energy sources cannot attract capital given the historic volatility of oil prices, it is prima facie evidence that those sources of energy are uneconomic. You can argue with me about adding a premium for avoiding the externalities associated with oil, but we will have to do that analysis carefully, accounting for the taxes already on oil.
I think my biggest objection to Buckey's idea is that he calls it the National Security Levy. In my talk with him, he was adamant that we are militarily engaged in the Middle East to protect our oil interests, and therefore we should have a tax on oil to represent that cost. While I agree in principle with this argument, in this case the magnitude of my agreement is quite slight. Mr. Buckey kept saying that there are other unstable parts of the world where we are not engaged, hence it must be the oil of the Middle East. First, what about Afghanistan? We were attacked by terrorists from Afghanistan, and there is no oil production there. So that part of the defense budget should not be attributed to oil. And I think Israel would be rather taken aback if they learned that we are only in the Middle East to protect our oil interests.
I think the link between oil in the Middle East and our military involvement there is not due to a desire to protect our CONSUMPTION of oil, but because the presence of oil reserves in the Middle East gives countries there a huge revenue source with which to create trouble. If we stopped buying oil from the Middle East, China and India would welcome our absence. The oil suppliers would still have billions of dollars annually to spend on weapons and disruption. If we value our freedom and that of other countries, I contend that we would still be militarily engaged.
So to say that we are in the Middle East for oil is not precise. We are there because of oil, but more precisely, because the oil reserves of that area give additional strength to any enemies located in that region. I would put forth that our engagement as a customer gives us some political power that we would forsake if Buckey's National Defense Levy succeeded in getting us to buy less Middle Eastern oil.
I tried to get Mr. Buckey to buy into my ideas for the Democratic party of being socially libertarian, fiscally conservative, reasonably strong on national defense, and leaving economics to market forces, but I don't think he bit.
Saturday, January 12, 2008
Joe Kennedy's Heating Oil Ads
Has anyone seen the ads on TV done by former US Representative Joe Kennedy on behalf of the nonprofit Citizen Energy's program to provide discount heating oil to the needy? Here is one. I wish I could link to the one I saw last night that was even more over the top in a blatantly shameless use of poor folks' misery to promote one's own cause.
I am less concerned about the free publicity that Kennedy is giving to our good friend Hugo Chavez down in Venezuela. It just makes me sick to see the situations of the unfortunate used for political purposes.
Joe, how about stopping the ads and kicking the saved dollars in for buying oil for some of the people you are using?
I am less concerned about the free publicity that Kennedy is giving to our good friend Hugo Chavez down in Venezuela. It just makes me sick to see the situations of the unfortunate used for political purposes.
Joe, how about stopping the ads and kicking the saved dollars in for buying oil for some of the people you are using?
New Hampshire Recount
A good article appeared this morning on the discrepancy between hand counted and machine counted votes in New Hampshire. The author, Beverley Wang, does a decent job of covering the statistical issues involved. The gist of the story is exactly what my post below discusses, that the use of machines to count votes is not a random event but is in fact correlated with underlying demographics that themselves determine the vote.
My colleage John R. Lott Jr. has a paper, joint with Kevin Hassett, titled "Voting Technology and Voter Fraud: A Test Using Exit Poll Data." In this paper, the authors use exit polling data to show that exit polls had a similar pattern between machine counts and hand counts, using national 2004 election data. Since the technology to count final votes could not have influenced exit polls, this is pretty conclusive statistical evidence that the counting technology was not behind voting patterns.
I still would like to see if additional demographic variables in my vote prediction model would reduce the significance of the machine count variable. If I can get the data, I will run the models and report them.
Of course, since there will be a recount, any claims of irregularities will be quickly dispensed with.
My colleage John R. Lott Jr. has a paper, joint with Kevin Hassett, titled "Voting Technology and Voter Fraud: A Test Using Exit Poll Data." In this paper, the authors use exit polling data to show that exit polls had a similar pattern between machine counts and hand counts, using national 2004 election data. Since the technology to count final votes could not have influenced exit polls, this is pretty conclusive statistical evidence that the counting technology was not behind voting patterns.
I still would like to see if additional demographic variables in my vote prediction model would reduce the significance of the machine count variable. If I can get the data, I will run the models and report them.
Of course, since there will be a recount, any claims of irregularities will be quickly dispensed with.
Thursday, January 10, 2008
New Hampshire Machine Count Bias?
There has been some discussion about the difference in Hillary Clinton's vote in New Hampshire with machine counted votes versus hand counted votes -- see here. Overall, Hillary got 39.0% of the NH vote. But she received 40.1% of the machine counted vote and only 34.7% of the hand counted vote.
When my son first showed me this, I jumped to the obvious conclusion that towns in NH that have machines counting the votes are different from town that count by hand. A classic statistical problem: correlation does not prove causation, and the old omitted variables problem. Hillary probably does better with voters who live in towns that count votes by machine. If you look at the data, it appears that "machine count" is the variable determining the Hillary vote, when in fact it is an underlying variable -- wealth, race, educational levels -- that really determines the vote difference, and that we are not measuring. So "machine count" is simply "picking up" the effect of the variable(s) omitted from the analysis.
Ah, the wonders of technology. My son showed me a website that did some analysis by town size. Sure enough, Hillary does better in large towns, and large towns tend to do more machine counting. So, it appears that the relationship between Hillary's vote and METHOD (the vote counting method) is just picking up the underlying relationship between Hillary's vote and TOWN SIZE. TOWN SIZE itself is a proxy for things such as wealth, education, etc.
Even more wonders of technology. I had my son collect the voting data on the 220 towns of NH. Using PERL, he downloaded the data to Excel for me to use in about 15 minutes. So I had four variables on each town in NH: TOTAL VOTE (a measure of town size), CLINTON PERCENT, OBAMA PERCENT, and METHOD (1 for MACHINE COUNT, 0 for HAND COUNT).
I quickly ran a univariate regression of CLINTON PERCENT on METHOD: Sure enough, the regression equation is
CLINTON PERCENT = 33.68 + 5.64 METHOD
with a standard error of 1.01 on METHOD (t-statistic of 5.58).
That fits with the univariate analysis of the data as presented earlier. Sure enough, Hillary seems to do better when the vote is counted by machine!
I was sure that when I added TOTAL VOTE to the regression, the coefficient on METHOD would drop in size and in statistical significance. This does not HAVE to happen with correlated variables such as METHOD and TOTAL VOTE, but I was pretty sure it would.
Here are the multiple regression results:
CLINTON PERCENT = 33.56 +5.08 METHOD + .00028 TOTAL VOTE
with a standard error on METHOD of 1.12 and on TOTAL VOTE of .00024.
Amazing! METHOD continues to be the variable carrying the weight of the data. Town size is statistically insignificant and the method of counting accounts for most of the variation in Clinton's vote difference.
Hmmm.....developing....
UPDATE: I highly suspect, still, that METHOD is simply correlated with some underlying real determinant of the Clinton vote. If I can get more data by town, I will run those models. It is even possible that my variable TOTAL VOTE is not a good measure of town size, as it involves voter turnout as well. What would be really good is if I had exit polling data by town in NH. If I added that variable to the equation, I would think that METHOD will lose significance.
UPDATE2: I got town population data, estimated for 2006. Using that instead of TOTAL VOTE reduces the size of the METHOD variable but not by much and it is still significant. I also calculated a new variable, total vote divided by population, which is an attempt to get at a few things related to turnout and other demographics. Using this new variable in addition to popluation reduces the size of the METHOD variable a bit more, but it is still highly significant. This new variable of vote divided by population seems to be important. I think if I got better demographic data -- age and gender, income, turnout -- the METHOD variable would lose more of its significance. It must be picking up something. If somebody has good NH town data in Excel or easily parsed, let me know the source.
The other thing to note is that in the data on votes by machine vs. hand, Romney also has big differences. That would, I think, support the "underlying demographics" theory.
UPDATE3: And just for the record, I do not believe whatsoever that anything untoward or suspicious happened in the NH election. This is simply a great exercise in statistical analysis, a great example of the problem that omitted variables cause in regression analysis.
When my son first showed me this, I jumped to the obvious conclusion that towns in NH that have machines counting the votes are different from town that count by hand. A classic statistical problem: correlation does not prove causation, and the old omitted variables problem. Hillary probably does better with voters who live in towns that count votes by machine. If you look at the data, it appears that "machine count" is the variable determining the Hillary vote, when in fact it is an underlying variable -- wealth, race, educational levels -- that really determines the vote difference, and that we are not measuring. So "machine count" is simply "picking up" the effect of the variable(s) omitted from the analysis.
Ah, the wonders of technology. My son showed me a website that did some analysis by town size. Sure enough, Hillary does better in large towns, and large towns tend to do more machine counting. So, it appears that the relationship between Hillary's vote and METHOD (the vote counting method) is just picking up the underlying relationship between Hillary's vote and TOWN SIZE. TOWN SIZE itself is a proxy for things such as wealth, education, etc.
Even more wonders of technology. I had my son collect the voting data on the 220 towns of NH. Using PERL, he downloaded the data to Excel for me to use in about 15 minutes. So I had four variables on each town in NH: TOTAL VOTE (a measure of town size), CLINTON PERCENT, OBAMA PERCENT, and METHOD (1 for MACHINE COUNT, 0 for HAND COUNT).
I quickly ran a univariate regression of CLINTON PERCENT on METHOD: Sure enough, the regression equation is
CLINTON PERCENT = 33.68 + 5.64 METHOD
with a standard error of 1.01 on METHOD (t-statistic of 5.58).
That fits with the univariate analysis of the data as presented earlier. Sure enough, Hillary seems to do better when the vote is counted by machine!
I was sure that when I added TOTAL VOTE to the regression, the coefficient on METHOD would drop in size and in statistical significance. This does not HAVE to happen with correlated variables such as METHOD and TOTAL VOTE, but I was pretty sure it would.
Here are the multiple regression results:
CLINTON PERCENT = 33.56 +5.08 METHOD + .00028 TOTAL VOTE
with a standard error on METHOD of 1.12 and on TOTAL VOTE of .00024.
Amazing! METHOD continues to be the variable carrying the weight of the data. Town size is statistically insignificant and the method of counting accounts for most of the variation in Clinton's vote difference.
Hmmm.....developing....
UPDATE: I highly suspect, still, that METHOD is simply correlated with some underlying real determinant of the Clinton vote. If I can get more data by town, I will run those models. It is even possible that my variable TOTAL VOTE is not a good measure of town size, as it involves voter turnout as well. What would be really good is if I had exit polling data by town in NH. If I added that variable to the equation, I would think that METHOD will lose significance.
UPDATE2: I got town population data, estimated for 2006. Using that instead of TOTAL VOTE reduces the size of the METHOD variable but not by much and it is still significant. I also calculated a new variable, total vote divided by population, which is an attempt to get at a few things related to turnout and other demographics. Using this new variable in addition to popluation reduces the size of the METHOD variable a bit more, but it is still highly significant. This new variable of vote divided by population seems to be important. I think if I got better demographic data -- age and gender, income, turnout -- the METHOD variable would lose more of its significance. It must be picking up something. If somebody has good NH town data in Excel or easily parsed, let me know the source.
The other thing to note is that in the data on votes by machine vs. hand, Romney also has big differences. That would, I think, support the "underlying demographics" theory.
UPDATE3: And just for the record, I do not believe whatsoever that anything untoward or suspicious happened in the NH election. This is simply a great exercise in statistical analysis, a great example of the problem that omitted variables cause in regression analysis.
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