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0 5 with an r 2 in the neighborhood of 0 8 chart 1 illustrates the fit of the estimated okun s law by plotting the unemployment gap the gap between unemployment and the natural rate against the output gap output relative to potential the relationship is very tight no year is a major outlier in the graphs chart 1 united states okun s law 1948 2011 annual data natural rates based on hodrick prescott hp filter with λ 100 note in the econbrowser article the text reads a coefficient of 0 4 or 0 5 with an in the neighborhood of 0 8 something is obviously missing between the words an and in i tracked down laurence ball at ideas clicked the imf link to paper opened the pdf okun s law fit at 50 and searched it for the phrase coefficient of 0 4 yup what s missing is r squared given in the pdf as capital r with an overbar followed by a superscript 2 so i inserted that into the econbrowser excerpt i went to fred for annual data on unemployment and output retrieved the seasonally adjusted civilian unemployment rate unrate and seasonally adjusted real gross domestic product gdpc1 for both i selected annual data and the default aggregation method average used excel to calculate the hodrick prescott values and figure the gaps the differences between the fred values and the hp values created a scatterplot showing gap versus gap graph 2 well i ll be darned the chart s a good match i got my axes the wrong way around from chart 1 but the data points are definitely grouped along the trend line and i even got an r 2 comparable to the 0 8 reported in the econbrowser post and no major outliers huh okay what i m looking at is the difference of output values from their trend versus the difference of unemployment values from their trend i have to think about it a while two points 1 on my graph the unemployment gap values range roughly from 2 to 2 or a difference of four percentage points and the output gap values range roughly from 4 to 4 a difference of 8 percentage points roughly the change in output is twice the change in unemployment this agrees with okun s law 2 the output gap for this exercise is assumed to be the difference between inflation adjusted output and the trend of that output in other applications the output gap is taken to be the difference between inflation adjusted output and potential output which is not the same as the trend of realized output according to cbo s a summary of alternative methods for estimating potential gdp pdf statistical filters such as centered moving averages bandpass filters the hodrick prescott filter and the kalman filter are often used to extract the trend from gdp directly these methods do not generally use okun s law having actually used the hp filter now two or three times having seen it for myself i understand this better and i see it applies to the work of laurence ball et al ball s work is not circular because he uses an alternative to cbo s calculation one that does not use okun s law and yet as the cbo paper states there are many ways to estimate the trend in gdp and other economic data as well as to compute the economy s productive potential some methods rely on purely statistical techniques others such as cbo s method rely on models guided by economic theory many methods used to compute potential output do not benchmark their trends to inflation or any independent measure of capacity and therefore cannot be interpreted as estimating the level of maximum sustainable output that is they provide a measure of trend output but not potential output if we laurence ball and i are not measuring the output gap as the difference from potential output then we are likely understating the size of the gap if there is a long term trend of decline in realized gdp as i believe then there may be a long term increase in the size of the output gap that we are understating thought about it given the actual unemployment we ve had over the years it is reasonable to draw a trend line that minimizes the actual variations and helps us picture the general trend likewise output and then is is interesting to compare the differences from trend of unemployment against the differences from trend of output this is what we see in the above graphs there is nothing circular in the arithmetic that i can see and the correlation appears to be strong regarding the second graph in the econbrowser post we read our finding of a stable okun s law is robust to various methods of measuring short run movements in output and unemployment we try alternatives to the hodrick prescott hp filter we also estimate the relationship in changes that is between the change in the unemployment rate and the change in log output which does not require using the hp or any other filter the relationship holds for quarterly as well as annual data chart 2 shows the tight fit between actual unemployment and the estimate based on okun s law some residuals are evident during the early years of the great recession for which ferrara and mignon provide some conjectures chart 2 united states actual and fitted unemployment rate 1948q2 2011q4 notes figure reports fitted unemployment rate from okun specification estimated on quarterly data in levels with two lags and natural rates based on hodrick prescott filter with λ 100 trying to get clear on what they re saying this part is easy chart 2 shows the tight fit between actual unemployment and the estimate based on okun s law in this case they definitely are using okun s law to determine fitted unemployment the note below the graph refers to levels with two lags which must be some specific detail of the calculation but the meaning escapes me the note below also refers to natural rates based on hodrick prescott rates plural so i think they figured hp trends for both output and unemployment and used these somehow in their calculation then okun s law comes into play working it backwards they use the output gap to estimate unemployment they call this estimate fitted unemployment and they compare it to actual unemployment in their graph okay i think i figured out a way to estimate unemployment numbers using okun s law and the hp trends in my post linked at the top i wrote to figure potential output the congressional budget office uses the unemployment gap they take that gap and stretch it to fit over actual output that gives them the output gap the output gap looks like the unemployment gap by design i ll do the same thing now but reverse the direction first i ll figure the hp trends for unemployment and gdp then i ll take the difference of gdp and its trend shrink it by half that s the okun s law part and add it to the unemployment trend then use the result for my estimated unemployment numbers now it s simple graph 4 holy crap it s a really good match okay again take the discrepancy between rgdp and its hp trend shrink it by half per okun s law and add it to the unemployment hp trend that s the red line the blue line is fred s unrate what i ve learned 1 the hp trend calc is a really good trend calc 2 laurence ball s output gap is the difference between rgdp and its trend without regard for inflation or the phillips curve which play a role in the cbo calc ball s output gap is based on the trend of realized rgdp not on potential output this is a significant difference but i now think not relevant to ball s econbrowser post 3 laurence ball s calc is not circular and it is interesting on graph 4 the blue line is above the red line when actual unemployment is higher than the estimate the blue line is lower when actual unemployment is lower than the estimate we like low unemployment we like the blue line low looking at graph 4 i see two periods where the blue line is clearly below the red line for more than a very brief period those periods are 1960 1964 approximately and 1994 2000 approximately those were both periods of exceptionally good economic growth so we should expect the unemployment to be relatively low in those times we should expect the blue line to be relatively low in those times i decided to look at the discrepancy between the two lines i subtracted the blue line from the red this gives me the error of the unemployment estimate relative to realized unemployment graph 5 for the most part the error is within plus or minus half a percentage point not bad the excel file containing my graphs and calcs is available for download from google drive note that the file contains kurt annen s hodrick prescott filter in visual basic code and also some routines i use for formatting my graphs if your security settings are reasonable when you open the file excel will warn you of a potential problem because the file contains vb code excel doesn t know there s a problem it only knows there could be a problem excel lets you disable the code and open the file but with the code disabled the h p filter calcs won t work and the whole thing will probably be garbage so maybe you don t care to mess with it but anyway the file is available if you want posted by the arthurian at 4 00 am 0 comments labels hodrick prescott thursday april 11 2013 hindsight change in tcmdo corrected for inflation log of that so that a constant rate of growth looks like a straight line graph 1 natural log of the inflation adjusted change in total credit market debt owed same graph in excel with a hodrick prescott trendline graph 2 ditto plus trend straight lines indeed the red line is flat briefly before 1958 straight line uphill 1958 1986 straight line downhill 1986 1992 and straight line uphill 1992 to the crisis i stopped the hp calc at that point so that the later decline did not drag down the earlier years numbers the media would tell you debt is a problem over there on the right where the blue line is broken and there is no red line most people would tell you debt was a problem in the 2000s where the red line goes above the 3 5 level or maybe where it goes above 3 lots of people would tell you debt went up during the reagan years for some reason most people don t seem to know about the great slowdown of debt growth 1986 1992 too many media stories maybe apart from that downtrend i would say the only time the graph does not show a problem is in the early years the early 1950s that s the only time the trend does not show increase looking at this graph you could have known by 1961 that debt was going to be a problem posted by the arthurian at 4 00 am 0 comments labels hodrick prescott monday april 8 2013 a second look at the heteconomist post the other day i looked briefly at peterc s why neoliberals pretend private debt doesn t matter and public debt does time for a second look consider the opening sentence of the post peterc writes the neoliberal policy approach in the decades leading up to the crisis basically amounted to enticing or pushing people into increasing levels of private debt what is neoliberal wikipedia doesn t help bill mitchell writes of the early 1980s as the neo liberal onslaught began in earnest the early 1980s then since reagan basically same as my k r shift and actually in his post peterc writes the neoliberal attack on workers pay and conditions from the early 1980s onwards was highly orchestrated the early 1980s it is so reconsider peter s opening thought revised the policy approach since the early 1980s and up to the crisis basically amounted to enticing or pushing people into increasing levels of private debt is it true it must be true right i mean how else did we end up with all this debt yeah but take a look at the rate of debt growth since the 1950s graph 2 percent change in the non federal portion of tcmdo blue if i did it right the red line is a hodrick prescott trend of the debt data the first thing that happened after the early 1980s was a slowdown in debt growth a slowdown beginning in the mid 1980s immediately after the early 1980s there was a major downtrend in the growth of debt but by the late 1990s the growth rate of debt was back to normal back to 10 annual give or take back where it was before the neoliberals took over back where it was in the keynesian years what s different is that in the keynesian years excessive debt growth led to inflation in the neoliberal years excessive debt growth led to unemployment that s the main difference the problem is the excessive debt growth the excessive reliance on credit the excessive cost of circulating money excessive finance excessive accumulated savings excessive accumulated debt all the same thing it s a cost push problem the liberal solution to the cost push problem is inflation the conservative solution is unemployment the arthurian solution is to reduce financial costs by reducing the size of finance providing more money to balance against less debt using policy to limit the amount of creditmoney that can be generated from a dollar of money the arthurian solution is to reduce the factor cost of money posted by the arthurian at 4 00 am 0 comments labels hodrick prescott sunday april 7 2013 de trending it was easy i couldn t even remember the name hodrick so i googled prescott filter excel jackpot there is a how to use pdf short says you give it a range of cells and a number a constant the long version select a range of cells for your results type hp select the range of cells containing the data to be filtered type in a comma type in the constant and close the parentheses but don t hit enter instead hold down ctrl and shift and then press enter that s it then you can make a graph or whatever from the results holding down ctrl and shift while you press enter is standard excel stuff they call it array formulas which sounds pretty complicated but all you have to do is hold down ctrl and shift while pressing enter how complicated is that none of that works though if you don t have the hodrick prescott filter installed no problem among the search results is a link to kurt annen s hp filter excel add in at ideas there are three separate files you can download 1 an xla file an excel add in which adds the hp function to the built in excel functions 2 the visual basic source code for the hp function 3 an example for most people the simple thing would be to install the add in the pdf linked above tells how for me the simple thing was to copy the visual basic source code and paste it into a code module that way i got to look the code over a bit it looks like a very complicated arithmetically version of a moving average calculation or something comparable that s a crude description i didn t work through all the arithmetic but the result you get from the hp filter serves the same sort of purpose as the result you get from the moving average calc anyway after it s installed one way or the other it s as easy to use as sum or any other excel function i expect to explore it and to use it what number do you use for the constant for the lambda as they call it at the eviews user forum trubador explains rule of thumb is lambda 100 number of periods in a year 2 in this respect for annual d...
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