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readsheet with some made up numbers for debt gdp and a price index in columns on the left i made up 30 years of data test 1 the yellow cells are numbers i might want to change the other cells are calculated from the yellow cells or from calculations that depend on them the graph is generated by the numbers in the rightmost column the nn rr column as the third row of yellow cells shows i started with a price index value of 100 an initial gdp of 100 and an initial debt of 50 half the size of gdp the latter two numbers are somewhat arbitrary i had to pick numbers to get started the initial price index value of 100 is not arbitrary by convention or on principle or for reasons unknown the base year of a price index is always given the value 100 it s probably to simplify matters whatever since i m using 100 as my first year s price index value you should be able to guess that i am using the first year as the base year for my calculations didn t have to be but it is economists tend not to do that but i m not an economist and i m free to put the base year any where i want besides it just makes sense when i think about the economy i like to set things up start the action and see what happens it s just natural that where i start is the beginning so the graph test 1 above figures 2 inflation each year 4 annual gdp growth that s nominal gdp by the way and an 8 annual increase of outstanding debt how that works for inflation i take each year s value and multiply it by 1 02 to get the next year s value the new value turns out to be 2 bigger than the value i started with for gdp multiplying by 1 04 makes each new value 4 bigger than the one before for debt multiplying by 1 08 makes each new number 8 bigger the numbers i use to set my growth rates 1 02 1 04 and 1 08 appear in the yellow cells on the first two lines of the test 1 spreadsheet image i use the numbers on the top row in the calcs for the first 15 years for the left half of the blue line on the graph i use the numbers from the second row for the next 15 years the right half of the blue line in test 1 the blue line is a nice smooth curve because the numbers on row one and the numbers on row two are the same now i can change one of the growth rates on the second row and maybe we ll see a kink show up right in the middle of the blue line test 2 nope the line looks just the same i kept the value 1 04 an annual growth rate of four percent for the first 15 years but changed the number to 1 40 for years 16 to 30 that s forty percent annual gdp growth that s way more than china was getting it s a ridiculous number ridiculously big still there is no change in the blue line no kink there in the middle making a huge change in the growth rate of gdp and leaving the inflation rate and the debt growth rate unchanged made absolutely no difference in this graph i thought that was pretty weird and hey maybe i have something wrong it wouldn t be the first time but i can t find it if there is so anyway i figured let me get even more extreme with the change in gdp growth rates so i used 0 01 for the first 15 years and then 100 0 for the next fifteen still no change in the blue line test 3 in test 3 some of the numbers below the graph are now so big that i got nothing but cross hatches hash marks i guess they re called now or hash tags whatever but the blue line for test 3 looks just the same as it did for test 1 and 2 even the numbers in the vertical axis are the same they run from 75 to 105 and that s it what this is telling me is the growth rate of gdp has no bearing on the rate of erosion of debt i still think that s odd and like i said i could have mistakes in the spreadsheet but that s what it s telling me so i set the gdp growth numbers back to 1 04 so the second period matches the first so we are starting from the test 1 picture again and then i increased inflation the annual rate of inflation from 2 to 8 on the second line that gave me a kink in the graph test 4 for test 4 we have 2 inflation for the first 15 years and then 8 inflation for the next 15 years and you can see that the blue line starts dropping faster as soon as the higher inflation rate enters the calculation so test 4 tells me that the blue line is falling because of inflation remember now the blue line is a model of saturday s graph which showed the value remaining after inflation as a percent of the total value borrowed the value after inflation as a percent of the value at the time the money was borrowed so test 4 says 2 inflation makes debt erode slowly and 8 inflation makes debt erode rapidly pretty interesting to see that on a graph i think okay so changing the gdp growth rate has no effect but changing the inflation rate does have an effect what about debt what happens if we start at test 1 again and then double the rate of debt growth from 8 to 16 annual test 5 whoa now it looks like the saturday graph for the first 15 years the blue line goes down as inflation erodes debt then debt growth doubles and now debt is growing so fast that the line goes up despite the 2 inflation the saturday graph again for comparison to test 5 test 5 shows a much smoother line than the saturday graph because growth rates on the spreadsheet change once in 30 years not every year like the real world but you can see from these tests that inflation erodes debt that more inflation erodes debt more and that if debt is growing fast enough the burden of debt increases regardless of inflation here s a link to the google drive template and the excel xlsx file posted by the arthurian at 4 00 am 17 comments saturday august 15 2015 gdp the gdp deflator federal debt and time inflation erodes the real value of debt paul krugman a few days ago i showed a graph of federal debt relative to gdp showed the ratio of nominals and also the ratio of reals the two are not the same because the calculation of reals for debt differs from the calculation of reals for gdp because debt is a stock and gdp is a flow this graph graph 1 ratio of nominals blue and ratio of reals red in a comment on that post jazzbumpa reacted i find the whole concept of inflation adjusting debt to be deeply troubling you end up with a real debt gdp value that is greater than the real i e currently factual value what does that even mean what does it mean it means inflation erodes debt the inflation adjusted or real value is greater than the inflated value because inflation erodes debt the gap between the red and blue lines shows the extent of the erosion come to think of it we can look at the one line relative to the other we can look at the blue line relative to the red the inflated values as a percent of the inflation adjusted values on this new graph a value of 100 will indicate zero erosion of debt due to inflation a value of 80 will indicate that 20 of the value borrowed has been lost to inflation and 60 indicates that 40 has been lost to inflation or that to pay off the debt would require only 60 of the total value borrowed graph 2 the blue line from graph 1 as a percent of the red line from graph 1 the only variables we re using here are gdp the gdp deflator federal debt and time so it can only be these that influence the pattern shown on the graph i m having a hard time imagining how changes in the data would be related to the changes visible on the graph i ll have to look into that this excel file contains the above graphs and the source data posted by the arthurian at 4 00 am 0 comments friday august 14 2015 social mechanisms allowing scientists with different scientific viewpoints an opportunity to make themselves heard david glasner in romer v lucas arrow had no answer to the question but offered the suggestion that out of equilibrium agents are not price takers but price searchers possessing some measure of market power to set price in the transition between the old and new equilibrium but the upshot of arrow s discussion was that the problem and the paradox awaited solution almost sixty years on some of us are still waiting but for lucas and the lucasians there is neither problem nor paradox because the actual price is the equilibrium price and the equilibrium price is always the rationally expected price if the social functions of science were being efficiently discharged this rather obvious replacement of problem solving by question begging would not have escaped effective challenge and opposition posted by the arthurian at 6 15 am 0 comments thursday august 13 2015 debt is built in many layers each with its own price level format it like a sentence and the title of nathan tankus s recent post looks like a reply to something somebody said no inflation doesn t erode the burden of debts his opening sentence makes his topic clear it is commonly argued that inflation erodes debts his next sentence makes his position clear however the usual defenses amount to little more than circular logic then he provided an example from paul krugman in short the burden of debt has been aggravated by falling inflation and now we know to whom nathan tankus was replying in his title tankus explains the problem the source of the confusion here is that it is popular to divide key economic variables by abstract measures of the prices across the economy such as the consumer price index this makes sense sometimes but in other situations become nonsensical debt is one such example the source of confusion he says is the common practice of calculating the inflation adjusted or real value of debt the calculation he says divides debt by a price measure such as the consumer price index i picked up on that right away not only is that calculation common it is also wrong tankus lays out the mathematical relation for us and identifies ways the burden of debt can be reduced in the united states most people have debts denominated in u s dollars a useful proxy for the burden of debt is the ratio between an individual s or sector s nominal debt to its nominal income the burden of this debt falls when they can refinance at a lower nominal interest rate their nominal income rises or they default it s not just a proxy i d call the debt to income ratio a way to actually measure the burden of debt but nathan tankus and i are in the same ballpark his next sentence i m not sure about in most discussions the real value of the debt is discussed while still talking about nominal income or at least being unclear about the measurement of income could be i ve seen people divide a nominal quantity by an inflation adjusted quantity and use it as evidence that labor costs drive inflation i ve seen milton friedman divide a nominal quantity by an inflation adjusted quantity and draw the conclusion that printing money is the cause of inflation that s the way that calculation works whatever nominal thing you divide by an inflation adjusted quantity you can make a specious argument that your nominal thing is the cause of inflation so i am highly sympathetic when tankus says he doesn t trust ratios that use both real and nominal values then he says it is basic math that dealing with such a ratio you have to divide the numerator and the denominator from the price level to stay consistent however from that point of view it becomes clear the exercise is nonsense after that he loses me in the next sentence following the word nonsense nathan is suddenly talking of falling productivity and oil so instead of reading more i went back to the part that made sense i agree when he says you have to divide both the numerator and the denominator by the price level to be consistent yes otherwise you re just factoring the price level into your results but nathan says it is okay to use the consistent calculation with debt i disagree debt is almost always an accumulation of multiple borrowings from multiple years the consistent calculation divides each year s debt number by only one year s price level there is no thought given to multiple year accumulations of debt my debt today includes money i borrowed last year to buy a car and money i borrowed several years back when i bought a house to figure my real debt correctly i would have to divide part of my debt by last year s price level and part of it by the price level when i bought the house the common calculation does not do that not even the consistent version the common calc divides this year s total outstanding debt by this year s price level it divides last year s total outstanding debt by last year s price level it divides any one year s total outstanding debt number by that year s price level there is no allowance for multi year accumulations of debt the common calculation converts from any one year to a base year and that s it in addition to the problem of dividing nominals by reals which nathan tankus points out there is the problem that the common calculation does not allow for multiple year accumulations in plain english when you use the common calculation to inflation adjust debt you get the wrong answer posted by the arthurian at 4 00 am 14 comments wednesday august 12 2015 ceteris paribus descartes the man who is wont to attend to many things at the same time by means of a single act of thought is confused in mind people who do not allow their thought to be distracted by various objects at the same time but always concentrate it in attending to the simplest and easiest particulars are clear headed posted by the arthurian at 7 18 am 0 comments tuesday august 11 2015 the inflation adjustment of debt a partial re post from 4 august in response to nathan tankus let me take the federal debt numbers as noah does and look at them a little more carefully than he does i want to look at the year to year change in the federal debt i want to look at each year s increase that s like looking at the deficits just as noah wanted i want to remove the inflation from each year s deficit and then add up all the deficits to see the inflation adjusted debt this is a necessary step as noah s explosion occurs just as the great inflation is coming to an end how can we know whether the explosion noah sees was the result of policy or an accident of inflationary numbers we have to look graph 5 noah s numbers blue and my numbers red the blue line on graph 5 shows a sudden increase beginning in the early 1980s just as noah smith showed the red line shows the increase beginning around 1974 after a decline that ends around 1966 does it matter it might it wouldn t be right to say the u s federal deficit began to trend upward beginning around 1980 real numbers provide the better measure of growth if you are looking at the growth of deficits explosive or otherwise you want to use the red line not the blue line most people will tell you that the red line should be identical to the blue line because a ratio of reals comes out the same as a ratio of nominals it depends how you do the math here s how i did the math 1 take the annual change in gross federal debt fred s fygfd as a measure of federal deficits 2 convert t...
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