tag:blogger.com,1999:blog-6837159629100463303.post4516969752680021950..comments2023-06-18T01:25:08.748-07:00Comments on Information Transfer Economics: Explicit implicit modelsJason Smithhttp://www.blogger.com/profile/12680061127040420047noreply@blogger.comBlogger30125tag:blogger.com,1999:blog-6837159629100463303.post-89600399949859647372015-08-15T12:05:54.744-07:002015-08-15T12:05:54.744-07:00"Did you perform unit root tests to make sure..."Did you perform unit root tests to make sure differencing them makes them stationary?"<br /><br />Yes.<br /><br />"In applied macroeconomics, interest rates are almost never logged. ... "<br /><br />Of course that makes sense, but there are two reasons to look into the logged versions:<br /><br />1) Interest rates change by a couple orders of magnitude (from ~ 1% to ~ 0.01%) at the onset of QE. They're not just fluctuating around a fixed level.<br /><br />2) There seems to be a pattern across several countries where you can write a function a log MB + b ~ log r<br /><br />US: <a href="https://research.stlouisfed.org/fred2/graph/?g=1DrS" rel="nofollow">Graph on FRED</a><br /><br />Japan: <a href="https://twitter.com/infotranecon/status/632619107397996545" rel="nofollow">Graph on Twitter</a><br /><br />UK: <a href="https://twitter.com/infotranecon/status/628693898580262912" rel="nofollow">Graph on Twitter</a><br /><br />(The UK one is actually a log MB + b log NGDP + c ~ log r, but most of the visible effect is from log MB)<br /><br />And yes the negative interest rates present a problem for taking log r, but negative interest rates represent a separate effect from normal monetary policy (e.g. one explanation is program buying by mutual funds). Therefore negative rates shouldn't be explained by the monetary base. You can see the negative interest rates in the Japan graph as asymptotes to (minus) infinity.<br /><br />[In the information transfer model, r is just bounded by r ≤ (k1 NGDP/MB)^k2 with approximate equality most of the time, so negative rates would just signal that something more complicated is going on, like some kind of market failure.]<br /><br />This is not meant to be conclusive evidence (it's not) -- just an idea to investigate.Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-66206946354867437422015-08-15T10:28:32.028-07:002015-08-15T10:28:32.028-07:00Jason:
"I did everything I did above but with...Jason:<br />"I did everything I did above but with added noise (~ 1%) and it came out the same to the accuracy of the numbers reported above."<br /><br />Did you perform unit root tests to make sure differencing them makes them stationary? It's very likely that they are not integrated of order one.<br /><br />Jason:<br />"Interesting. Are you comparing log MB with log r, or log MB with r (r = interest rate)?"<br /><br />With r, not ln r. <br /><br />In applied macroeconomics, interest rates are almost never logged.<br /><br />In fact, in time series analysis in general, the rule of thumb is to only log those series which are expected to grow exponentially (e.g. NGDP, population etc.) but not those series expected to fluctuate around a fixed level (e.g. unemployment rates, interest rates etc.). <br /><br />And, interest rates can be nonpositive, for which values the log will of course be undefined. <br /><br />Furthermore, some master econometricians argue that the primary benefit of logging a series is that it stabilizes the variance. But if you take the log of an interest rate series near zero in value, variance becomes less stable, not more. So logging interest rates is, if anything, counterproductive.<br /><br />Jason,<br />"Regarding Tom's question..."<br /><br />I already answered Tom's question.Mark A. Sadowskihttps://www.blogger.com/profile/08259309059705236763noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-57161481630205912532015-08-14T17:15:12.969-07:002015-08-14T17:15:12.969-07:00Thanks Jason. You ever check your request box on t...Thanks Jason. You ever check your request box on the right? I think I'll send one.Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-25177250951543040772015-08-14T16:42:12.232-07:002015-08-14T16:42:12.232-07:00This comment has been removed by the author.Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-48304638772579284192015-08-14T16:42:08.051-07:002015-08-14T16:42:08.051-07:00Yes, it would involve looking at a mutli-dimension...Yes, it would involve looking at a mutli-dimensional space containing data set 1 and data set 2 and finding the multi-dimensional linear transformation (a matrix) that best maps one to the other (given some restrictions for causality, i.e. a triangular matrix -- each data point could be caused by all the previous ones, but not following ones).Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-79534440061687179202015-08-14T16:33:08.945-07:002015-08-14T16:33:08.945-07:00Mark,
"By themselves graphs are not sufficie...Mark,<br /><br />"By themselves graphs are not sufficient evidence of anything."<br /><br />I did everything I did above but with added noise (~ 1%) and it came out the same to the accuracy of the numbers reported above. The graph was just a sample because I am lazy and didn't want to just repeat everything. Your argument didn't hold after checking it, so there really isn't any reason to say anything more than that. But I'll post a link to a pdf of the notebook when I get a chance.<br /><br />"No, the p-value is 22.0%."<br /><br />Interesting. Are you comparing log MB with log r, or log MB with r (r = interest rate)?<br /><br />Regarding Tom's question I think you might have messed up the sentence there (I don't think it's a big deal since I understood what you were trying to say). A stochastic process is the probabilistic counterpart to a deterministic process.Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-56310353442959663672015-08-14T16:09:05.087-07:002015-08-14T16:09:05.087-07:00Tom:
"Is that what you meant to write?"
...Tom:<br />"Is that what you meant to write?"<br /><br />Yes.<br /><br />Tom:<br />"Matched filters work best on (correlating) deterministic signals."<br /><br />Matched filters work via cross correlation, and cross correlation refers to the correlation between stochastic signals. Mark A. Sadowskihttps://www.blogger.com/profile/08259309059705236763noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-22703810694516601452015-08-14T16:03:48.016-07:002015-08-14T16:03:48.016-07:00Jason:
"That this is acceptable is backed up ...Jason:<br />"That this is acceptable is backed up by the fact that the results here are unchanged by adding a bit of noise."<br /><br />By themselves graphs are not sufficient evidence of anything.<br /><br />Jason:<br />"If short term interest rates aren't correlated with the economy while the monetary base is correlated with the economy, it stands to reason that there shouldn't be a strong correlation between the monetary base and short term rates."<br /><br />Why? The monetary base is strongly correlated to bank deposits and bank credit and yet there isn't a correlation between bank deposits or bank credit and the economy in the age of ZIRP.<br /><br />Jason:<br />"Question: do 3-month rates Granger-cause the monetary base?"<br /><br />No, the p-value is 22.0%.Mark A. Sadowskihttps://www.blogger.com/profile/08259309059705236763noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-66986132521863120032015-08-14T15:26:01.279-07:002015-08-14T15:26:01.279-07:00Given the Granger test (more specifically the T&am...Given the Granger test (more specifically the <a href="http://davegiles.blogspot.com/2011/04/testing-for-granger-causality.html" rel="nofollow">T&Y procedure</a>, say) determined model parameters and lags, etc, is it possible to more directly use the resultant "bunch of linear models" in a comparison like you do in the above (computing the Spearman rho, etc) rather than a single line approximation? I've been trying to imagine how that would work, but my over-taxed brain can't connect all the dots. Maybe it's a fool's errand. (c:Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-22818106694711191372015-08-14T09:44:04.760-07:002015-08-14T09:44:04.760-07:00Matched filters work best on (correlating) determi...<a href="https://en.wikipedia.org/wiki/Matched_filter" rel="nofollow">Matched filters</a> work best on (correlating) deterministic signals. It's true they are intended to be robust to additive noise, but the less noise there is, the better they work (i.e. the more meaningful is their output).Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-86095026201186183862015-08-13T22:51:13.985-07:002015-08-13T22:51:13.985-07:00Mark, you wrote:
"A "stationary" s...Mark, you wrote:<br /><br />"A "stationary" series is *stochastic* process. The probabilistic counterpart of a stochastic process is a *deterministic* process."<br /><br />Is that what you meant to write? I would have thought that a stochastic process would be the probabilistic counterpart to a deterministic process.Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-31278687896375634652015-08-13T20:33:55.085-07:002015-08-13T20:33:55.085-07:00Lol... yes, I find I have to put my "speed re...Lol... yes, I find I have to put my "speed reading" to the side when deciphering those sentences.Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-69295111726593310452015-08-13T20:30:42.346-07:002015-08-13T20:30:42.346-07:00This comment has been removed by the author.Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-49463736988713272962015-08-13T19:19:35.375-07:002015-08-13T19:19:35.375-07:00Imagine the limit of a stochastic process with dri...Imagine the limit of a stochastic process with drift as the variance goes to zero.<br /><br />That this is acceptable is backed up by the fact that the results here are unchanged by <a href="https://twitter.com/infotranecon/status/632009763434336257" rel="nofollow">adding a bit of noise</a>.<br /><br />As a physicist everything is the limit of stochastic processes :)<br /><br />If short term interest rates aren't correlated with the economy while the monetary base is correlated with the economy, it stands to reason that there shouldn't be a strong correlation between the monetary base and short term rates. But I guess you show there is in some new calculation?<br /><br />I will stand corrected on that, and will correct the above post.<br /><br />Question: do 3-month rates Granger-cause the monetary base?<br />Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-70564361533019158172015-08-13T18:33:44.139-07:002015-08-13T18:33:44.139-07:00A "stationary" series is *stochastic* pr...A "stationary" series is *stochastic* process. The probabilistic counterpart of a stochastic process is a *deterministic* process.<br /><br />A line is a deterministic process. So is a Fermi-Dirac distribution, which is simply an example of a logistic function. And if you splice three (or more) logistic functions together you still have a deterministic process. <br /><br />Deterministic processes cannot be rendered stochastic by differencing them, so they cannot be made stationary. (And unit root tests will of course produce a "near singular matrix" error message.)<br /><br />Correlation can only be meaningfully computed for stationary series. This is true even if the measure of correlation is Spearman's rho. <br /><br />In other words, every single one of the p-values reported in this post are invalid, since the corresponding Spearman's rho values each involve at least one nonstationary series.<br /><br />Jason:<br />"But remember -- all of these results are model-dependent (linear vs steps)."<br /><br />All of these results are yet more examples of Jason's time series derpometrics.<br /><br />Jason:<br />"You might conclude (as Mark Sadowski does) that short term interest rates and the monetary base don't have a relationship."<br /><br />I've never said any such thing. In fact the monetary Granger causes the three month Treasury-Bill yield at the 5% significance level in the Age of ZIRP. <br /><br />What I said was there is "no credible mechanism by which short term interest rates directly and significantly impact the economy". <br /><br />There is no *short term interest rate channel of monetary transmission* in any monetary textbook, because no such thing exists. <br /><br />P.S. When 3-month T-Bills are added to the baseline VAR, they have no significant effect on output or inflation in any month.Mark A. Sadowskihttps://www.blogger.com/profile/08259309059705236763noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-31618559511440360382015-08-13T17:26:23.255-07:002015-08-13T17:26:23.255-07:00From the Hitchhiker's Guide ...
https://en.wi...From the Hitchhiker's Guide ...<br /><br /><a href="https://en.wikiquote.org/wiki/The_Hitchhiker%27s_Guide_to_the_Galaxy#Chapter_17" rel="nofollow">https://en.wikiquote.org/wiki/The_Hitchhiker%27s_Guide_to_the_Galaxy#Chapter_17</a><br /><br />Generally, statistics has a way of making its technical language into an unnecessarily confusing chain of double negatives.<br /><br />"the test on X fails to reject the null hypothesis of stationarity"<br /><br />i.e. "X is stationary"<br /><br />"the test on X rejects the null hypothesis of stationarity"<br /><br />i.e. "X is non-stationary"Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-10159258040417160082015-08-13T17:15:33.850-07:002015-08-13T17:15:33.850-07:00tea? ... I'm missing the joke there.tea? ... I'm missing the joke there.Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-17050817816048800982015-08-13T13:12:51.354-07:002015-08-13T13:12:51.354-07:00Yes.Yes.Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-16104568344603171412015-08-13T13:01:42.367-07:002015-08-13T13:01:42.367-07:00"The Granger causality tests implicitly creat..."The Granger causality tests implicitly create a bunch of linear models..."<br /><br />So was your single line fit meant to be an (explicit) approximation of what's implicitly going on in a Granger test?Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-58489910606431396772015-08-13T12:58:13.910-07:002015-08-13T12:58:13.910-07:00Thanks for your answers Jason!Thanks for your answers Jason!Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-56362382958589197432015-08-13T12:19:11.492-07:002015-08-13T12:19:11.492-07:00Seems like a good reference.Seems like a good reference.Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-58956702350365797162015-08-13T12:16:47.155-07:002015-08-13T12:16:47.155-07:00Nothing specific -- it is a QTM country. So devalu...Nothing specific -- it is a QTM country. So devaluing their currency relative to the US means there will be inflation and increased output. Just like normal.Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-50036240200334426492015-08-13T12:02:15.942-07:002015-08-13T12:02:15.942-07:00All of the series are almost but not entirely unli...All of the series are almost but not entirely unlike tea. I mean, fail to reject the null hypothesis of stationarity ...Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-63422021199343183422015-08-13T11:59:14.121-07:002015-08-13T11:59:14.121-07:00Ha!
What's funny is that I actually don't...Ha!<br /><br />What's funny is that I actually don't entirely disagree with the result as I wrote about here:<br /><br /><a href="http://informationtransfereconomics.blogspot.com/2015/07/the-sadowski-theory-of-money.html" rel="nofollow">http://informationtransfereconomics.blogspot.com/2015/07/the-sadowski-theory-of-money.html</a><br /><br />The order of magnitude of the effects Mark finds are consistent with a view that monetary policy became about ten times less effective immediately after the financial crisis. It's consistent with an IT index going from 0.6 to 0.9.Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-42599215282518410712015-08-13T11:53:33.643-07:002015-08-13T11:53:33.643-07:00Hi Tom,
"One thing I don't understand is...Hi Tom,<br /><br />"One thing I don't understand is this sentence ..."<br /><br />I effectively created two 'idealized data sets': a line and some steps (MBline, MBstep). I then compared these two idealized data sets (MBline, MBstep) to the original data (MB). I then used MBline and MBstep to look at MBline vs P and MBstep vs P, etc. I could also compare MBline vs MB and MBstep vs MB. When Mark does his analysis, he doesn't explicitly create a model of MB -- he compared the MB data vs P. <br /><br />If you compare the original data to itself (MB vs MB), it would line right up and you wouldn't learn anything. You can't do the analyses MBline vs MB and MBstep vs MB ... which is the meaning of that sentence.<br /><br />The Granger causality tests implicitly create a bunch of linear models (that are translated in time by the lags). I wanted to show you could get different results if you assumed a single line (explicit implicit model) vs assuming a series of steps (a different explicit implicit model).<br /><br />...<br /><br />I didn't look for lags in the step model (because I was lazy) and the subsequent choice of the locations of the steps weren't constrained to the grid points (monthly data) so they appear off because of the sampling. For the linear model, a single lag is chosen implicitly by the slope/intercept. Take a lag of 1 ...<br /><br />y = m (x - 1) + b = m x + m + b = m x + b'<br /><br />with b' = m + b<br /><br />...<br /><br />The coloring was chosen to go to the axis because in the graph of delta log MB, the curves lined up almost too well to be seen clearly.<br /><br />...<br /><br />I fit the function f(t, {p}) where p are the parameters fit to the log MB data. To fit the interest rate and price level data, I fit <br /><br />a f(t, {p}) + b<br /><br />to the respective data using the fit parameters {p} from the original fit to MB, only fitting a and b.Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.com