----- Original Message ----- From: "Erik Reuter" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Thursday, February 06, 2003 10:17 PM Subject: Re: Plus the NY Times Re: The Washington Post Editorial on Iraq
> On Thu, Feb 06, 2003 at 02:47:12PM -0600, Dan Minette wrote: > > > The simulation I did was for the change in the GDP from 1929 to 2002. > > During that time period, the Democrats have been in office 40 years, > > and the Republicans 34. I took as my base sample, the change in the > > GDP from one year to the next. This provided me an array of values > > ranging from -13.1% to + 18.4% for the yearly change. > > Thanks for posting this. I'm assuming those are real GDP changes (rather > than nominal) judging from the max and min you quote there. > The are the real changes in inflation adjusted GDP,. > > For each case, I calculated the product y1*y2*y3...yn for the > > Democrats (n=40) and the Republicans(n=34). I randomly selected the > > past 74 years to obtain the answer for both the Democrats and the > > Republicans. > > I'm not sure I follow your method. Do you mean that you randomly > permuted the entries in the "base sample" array (with each entry being > 1+percentage/100) for each iteration and then calculated the ratio > > A[1]*A[2]*...*A[40] / A[41]*A[42]*...*A[74] > > which would represent a random trial of cumulative Democratic > performance over cumulative Republican performance? > > Or, alternatively, do you mean that you looped 74 times, each time > choosing a random integer between 1 and 74, and the first 40 iterations > multiplied together represent the Democratic GDP increases and the next > 34 represent Republican, and you take that ratio? The latter. > I don't think it would make much difference (one is sampling with > replacement, one without), but I just want to make sure I understand > what you did. It would have minimal effect. It would, I think, increase the sd and kurtosis of the distribution, I think. For example, it would be possible for the maximum growth or shrinkage to be sampled 40 times in a row with my methodology. > > On average, one would have expected the ecconomic growth during > > the Democratic years to be 35% higher than the growth during the > > Republican years...simply because there are 40 years to grow under > > Democrats and 34 under Republicans. > > I don't understand the 35% higher figure. Could you explain how you > calculated it? Sure. I randomly sampled 40 times for the Democrats and 34 times for the Repubicans. Since most of the multiplicative factors are >1, the averge of that ratio is > 1. (Also, I took the arithmatic instead of the geometric mean, which made that number higher.) BTW, I did catch a mistake on this. The Republicans had only 33 years in power for which a comparison could be made. 1929 was the base year, so it can't be counted. This changes the results. Instead of an average ratio of 1.35, it is really 1.395. Instead of a 0.24% chance that it happens randomly, there is a 0.32% chance. > If x represents the average annualized compounding factor for GDP over > that time period (x is about 1.034), then if Democrats and Republicans > were equal we should expect the cumulative Democratic value to be x^40, > and x^34 for Republicans, so the ratio is x^6 or about 1.22, which means > the Democrats would be expected to have a cumulative GDP increase of > about 22% more than the Republicans if everything else were equal. If it were not random, sure. In reality, I guess you are pointing out that I should have used the geometric mean. When I do, I get a number that is 1.28....the average improvement is 1.24%, so I'll have to think about why random sampling would give a different result. I did check my random number generator before I did the work, so I don't think that's it. Dan M. _______________________________________________ http://www.mccmedia.com/mailman/listinfo/brin-l
