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shipman showing posts with label hodrick prescott show all posts showing posts with label hodrick prescott show all posts monday november 25 2013 how to change the past i ve fiddled with hodrick prescott trend lines a bit and one thing i noticed is that they have a sorry kind of foresight they can predict the future but only in hindsight i did a post a while ago a post named hindsight actually in which i showed this fred graph graph 1 natural log of the inflation adjusted change in total credit market debt owed then i showed the same graph in excel with a hodrick prescott trendline added in graph 2 same as graph 1 with hodrick prescott trend thru 4th quarter 2007 i stopped the trend line at the high point of the blue line and wrote i stopped the hp calc at that point so that the later decline did not drag down the earlier years numbers so that the later decline did not drag down the earlier years numbers the hp calc is entered in excel as an array formula it takes as input a whole series of fred data for graph 2 i fed it data from 4th quarter 1952 to 4th quarter 2007 for graph 3 i fed it data from 4th quarter 1952 to 4th quarter 2012 that s the only difference graph 3 the blue line is the same as on graph 2 but the red line continues to 4th quarter 2012 notice that the red line no longer reaches up to the high blue peak the red line bends down early now around 2004 and begins the plunge while the blue line is still trending up to its high peak the trend line anticipates the future adding data for the years after 2007 to the hodrick prescott calculation changed the results we got for a few years before 2007 if that s not a sorry kind of foresight i don t know what is another example this from a second look at the heteconomist post graph 4 percent change in the non federal portion of tcmdo blue and the h p trend red the red line on graph 4 is a hodrick prescott trend of the debt data through 2007 graph 5 shows the same debt data and the h p trend again but this time the trend is based on all the data through 2012 graph 5 same as graph 4 except the h p trend is figured through 2012 on graph 4 the red line trends upward for the last few years before the 2007 end on graph 5 the red line runs flat until about 2004 when it starts to fall the decline since 2004 on this graph is the result of figuring in data for 2008 2012 look at it from the start of 2008 and it appears that the future changes the past the excel files on google drive nonfederal debt growth xls for the change in non federal debt graph dtcmdo rel gdpdef xls for the log of change in tcmdo graph both files contain kurt annen s vba code for the hodrick prescott calculation posted by the arthurian at 4 00 am 3 comments labels hodrick prescott wednesday july 3 2013 creating malaise graph 1 real gdp growth rate and trend lines look at the range of dates often called the great inflation from the mid 1960s to the early 1980s the red trend line is low then a flatland between 5 hills and 4 hills growth in those years is often said to have been disappointing chris kissell in the 1970s the american economy faced the dual problems of high unemployment and high inflation the origins of this problem began in the late 1960s and the economy was adversely impacted through the early 1980s overall the american economy experienced malaise for almost 15 years u s history org nothing fuels a strong case of malaise like a sputtering economy wikipedia the 1970s were perhaps the worst decade of most industrialized countries economic performance since the great depression although there was no severe economic depression as witnessed in the 1930s economic growth rates were considerably lower than previous decades economic growth rates were considerably lower in the 1970s you can see it on the graph between the mid 1960s peak and the mid 1980s peak but what else do you see i see the federal reserve fighting inflation by slowing growth creating troughs in 1967 and 1970 and 1975 and 1980 and 1982 those troughs did a remarkable job of creating malaise and making growth look bad posted by the arthurian at 4 00 am 3 comments labels hodrick prescott malaise friday april 12 2013 seeing for myself i looked before at the econbrowser guest post the myth of jobless recoveries by laurence ball johns hopkins university daniel leigh imf and prakash loungani imf since then i found kurt annen s visual basic code for calculating hodrick prescott values so now i can try again to duplicate the graphs from the econbrowser post and maybe learn more about them from that post using annual u s data from 1948 to 2011 we find that the okun s law has a coefficient of 0 4 or 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 ...
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