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ral bank policy depends on a negative correlation between interest rates and economic growth it doesn t work that way he says if you plot the nominal gdp growth rate against nominal interest rates say a scatter plot you will find a positive correlation a positive correlation he says not negative if werner is right this is a major conceptual shift i watched a werner interview two weeks ago and did some reading every day since i ve been drawing his scatterplot it fascinates me i ve started writing about it half a dozen times until now my response has died every time it is a difficult response to write due to both the major conceptual shift and the if werner is right for starters werner s choice of data troubles me if you plot the nominal gdp growth rate and nominal interest rates you see both going high during the great inflation because of the great inflation you see both going low after the financial crisis because of the financial crisis nominal gdp grew rapidly during the great inflation because of inflation at the same time policy and creditors pushed interest rates up to very high levels because of inflation inflation caused both growth and interest rates to rise to high levels and then to fall when inflation receded movement in the same direction that s a positive correlation more recently a different set of special circumstances arose the financial crisis and the great recession drove economic growth to unusually low levels in response our central bank dropped interest rates to the floor again unusual circumstances created a positive correlation this time low growth and low rates these positive correlations arise from sources other than the relation between economic growth and interest rates if you mix such times with normal times in a single picture of the economy you distort the norm and create a hotbed of doubtful gdp interest rate correlations to add an overall trend line to such a mix of data would be absurd to be sure i don t see richard werner showing trend lines on his scatterplots but i do see him proclaim the scatter plots on the left hand side of the graph show a distinct positive correlation i do see him proclaim the positive correlation of both curves is obvious and i do see him proclaim instead of the proclaimed negative correlation interest rates and economic growth are positively correlated werner doesn t need to show a trend line the positive correlation is obvious he says he doesn t need to show the trend line to see it but he does not by his power of vision manage to escape the absurd me yeah i show the trendlines does a positive correlation exist in the normal economy perhaps but if we re going to look into it we should exclude the data since the financial crisis and we ought to strip inflation out of the numbers we will be looking at for starters now you know what we re doing today i thought i might be confused about what werner is saying so i checked he is not speaking of what people in general think about central bank operations he refers explicitly to the views expressed and the actions taken by central bankers recently central banks have been lowering rates while proclaiming that this is a measure to stimulate the economy he disputes their story to the contrary empirical evidence shows that interest rates and economic growth are positively correlated werner uses a scatterplot to show correlation oddly however his scatterplot of u s data does not use the short term interest rate that our central bank uses to influence the economy werner uses a long term rate in his scatter to test the idea that central banks influence growth by changing rates it seems to me the scatterplot should use the same short term rate that is used by the fed granted the scatterplot might show a positive correlation for any interest rate you pick but if you re going to challenge the federal reserve on interest rate policy shouldn t you use the same interest rate that the federal reserve uses for my scatterplot data then i will use real gdp and the inflation adjusted fedfunds rate my inflation adjusted fedfunds calculation is similar to bill mcbride s from a dozen years back i ll use the effective federal funds rate less percent change from year ago of the cpi graph 1 fedfunds blue and inflation adjusted fedfunds red quarterly data the area between the red and blue lines that s all inflation these days the fed prefers pce to cpi but i ll be cutting these days off the chart and the fed only switched from the cpi to the pce in 2000 my scatter data goes back to the 1950s i m sticking with cpi for this calculation here then is the source data for my scatter plot graph 2 quarterly growth of rgdp blue and the inflation adjusted federal funds rate red the graph runs from 1953 before the fedfunds data starts to the end of 2008 i ll trim it down a little more in excel when i can see the data on second thought i ll grab all of the data for download in case i have a use for it to see the path of the data but eliminate the jiggies i m figuring hodrick prescott values for the two data sets my objective is to preserve the shape of the data but make that shape more readable so my smoothing constants are low non standard values here are the smoothed data red and the original values gray graph 3 smoothing the real fedfunds data graph 3 shows the interest rate the source data is gray the smoothed data is red the value of the smoothing constant is 4 as the legend indicates the same details apply to graph 4 graph 4 smoothing the rgdp data i put the two smoothed series together in a scatterplot with gdp on the horizontal and interest on the vertical tried to make the dots pretty connected them with thin gray lines and added a linear trend line in black here is the result graph 5 rgdp and the real fedfunds rate with a linear trend line smoothed data the rgdp values shown on the horizontal axis are for quarterly data the center of the dot cluster call it the average growth rate appears to be somewhere between 0 5 and 1 0 it s a low number because it is a quarterly rate annual rates would be ballpark four times bigger that would give an average real growth rate between 2 and 4 per year which sounds about right the straight black trend line tilts upward to the right doesn t look like much but it probably slopes more than you think the trendline formula says the slope is 0 4876 that s almost 0 5 if the slope was 0 5 y would go up by half of x and the trend line would go up six inches for each foot it goes to the right that s almost as steep as a flight of stairs steeper than it looks for some reason whenever i see a trend line on a scatterplot the trend line is straight a glance at the scattered dots should tell you there s no chance the trend is a straight line but straight line trends are commonly used on scatterplots maybe that has to do with the way economists think i made a copy of graph 5 and changed the trend line to something other than a straight line just to see how it looks it looks like poirot s moustache graph 6 rgdp and the real fedfunds rate with a polynomial trend line the trend line is in the same place and it still slopes up to the right but along the way it curves up and down i can t tell you much of what those curves might mean but i can tell you the trend is not a straight line i wanted a better look at changes in the scatterplot trend i thought i might split the cluster down the middle and get a trendline for each half then i got bold and decided to split economic growth into four overlapping subsets so i could see four overlapping trend lines i inserted four new columns into the spreadsheet alongside the smoothed data i used formulas to put values into these columns based on growth rate limits i picked for each subset this gave me the values in chronological order with blank cells where the values were outside the limits then i made a scatterplot and it was garbage excel doesn t do what i expect when there are blank cells intermixed with the values but i didn t know that yet so i tried again this time i subsetted the interest rate data instead of the growth rates this time all the blank cells were interpreted as zero values i got a whole lot of dots at the zero level and i couldn t get rid of them that s when i figured out the blank cells must be the problem the question then was how to convert one column of numbers into four columns based on specified value limits without having blank cells mixed in with the data the answer of course was vba i wrote a routine to arrange the data in a way that satisfied both excel and myself and at last i got a look at the trends of the subsetted data graph 7 the scatter data split out as low growth high growth and intermediate levels i got four overlapping trend lines these lines occupy the same general location as the overall trend line shown on graph 5 the trend lines taken together show a positive correlation similar to the overall trend lower on the left higher on the right however three of these four trend lines are downsloping they show negative correlation they contradict the overall trend and they contradict richard werner after a pointless argument with myself that lasted much too long i decided to write more vba to subset the scatter data on interest rate values this time rather than growth rate values the code writer complained that he already did the work and why should he have to do it again the econ hobbyist pointed out that the central bank changes the interest rate on purpose so the interest rate subsets must be more informative than the growth rate subsets and the code writer should have known which data to subset the first time around the code writer gave us the finger but he eventually admitted that his outrage was no more than a way to postpone the inevitable the matter was finally settled when the blogger pointed out that he had to stop blogging so that the code writing could commence i looked at graph 7 and divided up the vertical axis to make four overlapping groups then i copied the code i used to make graph 7 and tweaked it for 8 the code revision took less time than the argument here s what i got graph 8 the scatter data split out as low high and two intermediate interest rate ranges this time three of the four subsets show positive correlation one shows negative i don t know though take the high and low trendlines on graph 8 and throw them away keep the two in the middle they point up the space between these two trendlines appears to be the same space where we find all four trendlines of graph 7 but three of those four trendlines are pointing down it looks like you could get any result you want if you pick the right dots something is wrong here the trend is what it is we must be doing something wrong if we can make the trend slope this way and that we must be doing something very wrong i think i know what the problem is the trends we ve created here are long run trends they reduce more than half a century to only up or down the correlation is positive not negative werner says yes we cut off the data at the crisis yes we stripped away the inflation but too much variation remains in our fifty plus years of dots and data too much for one trend line we still have the golden age early on and though we removed inflation we still have the multiple recessions that occurred at the time of the great inflation then we have the changes in policy that began around 1980 and the change in the trend of interest rates from uphill to downhill and we have the gradual but persistent slowing of economic growth for the full extent of our fifty plus years these factors and others throw monkey wrenches at our scatterplot trend i think we need shorter trends we need to evaluate shorter time periods to answer the obvious questions how short where shall we start them and stop them how can we justify our choices consider the data we are evaluating it is economic growth and the interest rates which may or may not affect that growth it makes sense i think to base our time periods on the business cycle no you know what between one recession and the next there is sometimes a low point of growth sometimes more than one low point to shorten and simplify trend segments in the scatter our subsets can stop at every low point so let s not say business cycles let s say growth cycles instead or not even cycles but loops growth loops that s it growth loops i dug up an old spreadsheet and plugged in the data we ve been developing here changed a few graph titles and some range names put xs in the mingrowth column at the low points of growth and clicked a couple buttons to get some graphs here is the first one graph 9 the business cycle of 1957 1960 against a background showing the whole scatterplot the graph highlights the data points of the period identified in the subtitle line the first dot of the series is green and the rest are red red lines connect the highlighted dots in chronological order the black trend line for the highlighted dots shows a positive correlation higher on the right as richard werner says but oddly what happens with the dots seems to contradict werner after the first three dots green red red the dots start to go higher meaning the interest rate was rising the horizontal distance between the dots gets smaller meaning increases in the growth rate are getting smaller then after the rightmost red dot the rgdp growth rate falls as the dots step to the left based on the data values shown here interest rate increases after the third quarter of 1958 appear to have caused economic growth to slow the story these dots tell matches the central bank narrative that richard werner rejects the trend line displays the positive correlation that werner points out but the dots behave as the central bank describes the dots are saying that werner s positive correlation is not relevant by the way the same rgdp and the same real interest rate for the same dates we see on graph 9 but without the smoothing the hp calculation provides looks like this graph 10 same data as graph 9 but without the smoothing a growth loop of sorts is still visible here in red but it s not the same the smoothed data definitely makes the shape more visible but if you want to say that i have not preserved the shape of the unsmoothed data i refer you to graphs 3 and 4 the trend line for this unsmoothed data is high on the right as for the smoothed data what the dots have to say is less clear but at low interest rates growth is increasing rising rates put a halt to the increase and high interest rates leave us with reduced growth the dots reiterate the central bank narrative despite the positive correlation shown by the trend line not every smoothed growth loop has a trend line that agrees and dots that disagree with werner as the first one does many of them show small clusters or tight groups and are difficult to read at all some of these might make better sense if combined with an adjacent growth loop i didn t look int...
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