tag:blogger.com,1999:blog-6837159629100463303.post4511556552390411054..comments2023-06-18T01:25:08.748-07:00Comments on Information Transfer Economics: Fiscal austerity logic failJason Smithhttp://www.blogger.com/profile/12680061127040420047noreply@blogger.comBlogger15125tag:blogger.com,1999:blog-6837159629100463303.post-82383886458363196182015-06-20T00:35:57.980-07:002015-06-20T00:35:57.980-07:00"His assumption that all the data points have..."His assumption that all the data points have independent central banks means that any country engaging in austerity can't experience contraction". This is wildly dishonest. By you.Robert Simmonsnoreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-35208217275159157172015-06-19T15:02:54.167-07:002015-06-19T15:02:54.167-07:00As for the Eurozone, first, it is not a country, a...As for the Eurozone, first, it is not a country, and it has no fiscal authority, so A is neither true nor not true for it. IIUC, each Eurozone country has both an independent central bank and a fiscal authority, but the ECB controls monetary policy for the whole Eurozone. That is like the gold standard, so I guess that the Eurozone countries should not be considered to have a central bank.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-61328486578107163422015-06-19T13:32:07.896-07:002015-06-19T13:32:07.896-07:00I completely agree, but the thing is that the Euro...I completely agree, but the thing is that the Eurozone already shows this. But the MM answer is that the Eurozone <b>wants</b> low growth. This is the "no true scotsman" logical fallacy:<br /><br /><a href="https://en.wikipedia.org/wiki/No_true_Scotsman" rel="nofollow">https://en.wikipedia.org/wiki/No_true_Scotsman</a><br /><br />Basically, the ECB isn't a true scotsman (a proper central bank) so the austerity does have an impact on growth.<br /><br />The reason is that they use NGDP as an indicator of what monetary policy is -- if NGDP is bad, it's because the central bank wants bad NGDP; if NGDP is good, it's because the central bank wants good NGDP.<br /><br />It's not falsifiable since whatever the data is, it is an indicator of what it's supposed to be testing!Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-33818386573489172312015-06-19T13:10:06.449-07:002015-06-19T13:10:06.449-07:00Oops! I miscopied 2.
It should be this.
1 true, ...Oops! I miscopied 2.<br /><br />It should be this.<br /><br />1 true, 2 false: (A . Z -> C) . -(A . -B -> C) , or<br />(-A v -Z v C) . ( A . -B . -C) , or<br />A . -C . -B . -Z<br /><br />Likewise, 1 false, 2 true: A . -C . B . Z<br /><br />And therefore this:<br /><br />IOW, we look for countries that have engaged in fiscal austerity without experiencing contraction. If that country did not have an independent central bank and was not at the zero lower bound, then Keynesian theory trumps money marketist theory. But if that country did have an independent central bank and was at the zero lower bound, then money marketist theory trumps Keynesian theory.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-89445109767969042612015-06-19T13:02:40.780-07:002015-06-19T13:02:40.780-07:00Here is Sumner:
"let’s review the two compet...Here is Sumner:<br /><br />"let’s review the two competing theories:<br /><br />"1. Keynesian: Fiscal austerity is contractionary at the zero bound regardless of whether you have an independent central bank.<br /><br />"2. Market monetarist: Fiscal austerity is contractionary if you lack an independent central bank."<br /><br />OK. Let A = fiscal austerity, B = independent central bank, C = contraction, Z = zero lower bound. That gives us this.<br /><br />1. Keynesian theory: A . Z -> C<br />2. Market monetarist theory: A . -B -> C<br /><br />To test these theories against each other we are interested in instances where 1 is false but 2 is true, and vice versa.<br /><br />1 true, 2 false: (A . Z -> C) . -(A . B -> C) , or<br />(-A v -Z v C) . ( A . B . -C) , or<br />A . -C . B . -Z<br /><br />Likewise, 1 false, 2 true: A . -C . -B . Z<br /><br />IOW, we look for countries that have engaged in fiscal austerity without experiencing contraction. If that country had an independent central bank but was not at the zero lower bound, then Keynesian theory trumps money marketist theory. But if that country did not have an independent central bank but was at the zero lower bound, then money marketist theory trumps Keynesian theory.<br /><br />Logic is sometimes useful. :)Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-79943700515192979422015-06-19T02:12:54.788-07:002015-06-19T02:12:54.788-07:00BTW, Sumner's proposition,
1. A ∧I ∧ Z → C
2...BTW, Sumner's proposition,<br /><br />1. A ∧I ∧ Z → C<br />2. A ∧¬I ∧ Z → C<br /><br />simplifies to<br /><br />A ∧ Z → C<br /><br />To disprove that, all he needs to do is to find a counterexample. Throwing out countries without an independent central bank ties one hand behind his back. <br /><br />There is also a question about the meaning of A, since "austerity" was not a technical term in economics as of a few years ago, and, as far as I know, does not have a consensus definition yet. It obviously means more than running a government surplus, but what? (It may also mean attempting to run a government surplus, even if the result is a deficit.) <br />Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-12680691120789816282015-06-18T23:30:57.899-07:002015-06-18T23:30:57.899-07:00Also, in the last plot Mark did include "Euro...Also, in the last plot Mark did include "Euro Area" so I guess that might be the "EU" point you were referring to? I asked him what his last plot would look like if he also removed the countries which were not at the zero bound.Tom Brownhttp://www.google.comnoreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-61108736220601534942015-06-18T22:29:42.286-07:002015-06-18T22:29:42.286-07:00Thanks Jason: much appreciated. I knew about → bei...Thanks Jason: much appreciated. I knew about → being "implies" but I was trying to force a reading along the lines of set theory. You decoder ring is a big help.Tom Brownhttp://www.google.comnoreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-77579162266888588362015-06-18T22:16:24.260-07:002015-06-18T22:16:24.260-07:00Also the right arrow means "implies" or ...Also the right arrow means "implies" or for p → q:<br /><br />"p implies q"<br /><br />or <br /><br />"if p then q"<br /><br />Also important to the logic is that<br /><br />False → True<br />False → False<br /><br />are true statements. "If black is white, then all ants can talk." But black isn't white, so it doesn't matter what the rest of the statement is.Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-26299396167645351452015-06-18T22:06:53.238-07:002015-06-18T22:06:53.238-07:00And yes, the overall picture is that the EU engage...And yes, the overall picture is that the EU engaged in austerity and experienced contraction, therefore there exists a country that has an independent central bank but no monetary offset.<br /><br />Sumner adds the bit about "expected to" but that just turns the statement into the wishy-washy "austerity may or may not result in contraction in a country with an independent central bank".<br /><br />If we allow the wishy-washy statement, then monetarism becomes a tautology on the dataset as well -- both Keynesianism and monetarism are true!<br /><br />In the next post, I show that Sumner's characterizations of monetarism and Keynesianism do in fact say the same thing! Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-50782629985316987192015-06-18T22:01:02.297-07:002015-06-18T22:01:02.297-07:00The Z = F0, which should actually be Z(X), is the ...The Z = F0, which should actually be Z(X), is the statement that for every element in X, that country is at the zero lower bound. This isn't true (there are countries that aren't at the ZLB in X), so Z(X) is false, or:<br /><br />Z(X) = F0Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-21098146678316704552015-06-18T21:58:48.958-07:002015-06-18T21:58:48.958-07:00The x becomes lowercase when it is about an elemen...The x becomes lowercase when it is about an element of the set X. A(x) means A is true of x, A(X) means A is true for all x in X.<br /><br />I also made the corrections I mentioned above.<br /><br />EU refers to the Eurozone so the element EU is just one element of X, i.e. X = {EU, US, ... (other countries on Sumner's graph) }.<br /><br /><br />Also, the F0 and T0 are universal false (falsehood, always false) and universal true (tautology, always true). In set theory they are the empty set and the "universe".Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-38905462057700570322015-06-18T21:50:53.465-07:002015-06-18T21:50:53.465-07:00Also, for these two lines:
∃ x ∈ X, ¬A(x)
and
∴...Also, for these two lines:<br /><br />∃ x ∈ X, ¬A(x)<br /><br />and<br /><br />∴ ∃ x ∈ X | ¬A(x)<br /><br />Why is it "A(x)?" In other words, why did the "X" become an "x" (lower case)?<br />Tom Brownhttp://www.google.comnoreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-86044395823719320922015-06-18T21:50:09.152-07:002015-06-18T21:50:09.152-07:00Some quick answers first ...
You could interpret...Some quick answers first ... <br /><br />You could interpret the logical statements in terms of set theory, but it's better to use the language of logic where ∧ is "and" and the ∨ is "or". The vertical line | is read "such that" so:<br /><br />X = {x | I(x)}<br /><br />means "X is the set of objects x such that I is true for x" ... i.e. X is the set of countries in the data set that have independent central banks.<br /><br />The predicate A(x)<br /><br />A(X) = ∀x ∈ X, x has engaged in fiscal austerity<br /><br />Says: "A is true of X if for all x in X, x has engaged in fiscal austerity".<br /><br />And:<br /><br />∴ ∃ x ∈ X | ¬A(x)<br /><br />should be read: "therefore there exists x in the set X such that A is not true of x".<br /><br />But in reading that I realized there is an error that I will fix. It should be a combination of A and C.Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-11382086386543607532015-06-18T21:40:12.991-07:002015-06-18T21:40:12.991-07:00Jason, thanks for posting. I'm not good at dec...Jason, thanks for posting. I'm not good at deciphering the symbols so bear with me. Let me take the first line:<br /><br />A(X) = ∀x ∈ X, x has engaged in fiscal austerity<br /><br />So A is then a selector on the set X. It produces a subset of X of countries that have engaged in austerity. True? Etc for the other lines similar to this (I, Z and C). <br /><br />A ∧I ∧ Z → C<br /><br />I read this as "The intersection of subsets A, I and Z is a subset of subset C." Is that correct?<br /><br />A ∧¬I ∧ Z → C<br /><br />The intersection of subsets A not-I and Z is also a subset of C. We could combine the two and say the intersection of A and Z is a subset of C, but you keep them separate for your following development.<br /><br />X = {x | I(x)}<br /><br />I read this as "redefine the set X to be only those elements that are in subset I." I'm curious, how do you read the vertical bar "|" in English? As "given" like in conditional probabilities (e.g. P(A | B))? <br /><br />OK, moving on:<br /><br />Z = F₀<br /><br />What is F₀? I'm not sure if I should read that as "false" or an empty set. Z I'm assuming is a subset, so since there's an equal sign I'm inclined to think that F₀ must be a subset as well. Likewise for T₀ except that it's either "true" or ... what? Everything?<br /><br />"EU" is clearly this (being consistent with your previous notation):<br /><br />EU(X) = ∀x ∈ X, x is a member of the European Union.<br /><br />True? Or is "EU" simply a single element of X?<br /><br />OK, let me back up slightly because this whole bit confuses me:<br /><br />"This means that for all countries exhibiting austerity, there should be no contractionary economic effect. That is:<br /><br />∀x ∈ X, A(X)"<br /><br />I'm not getting how your English words map to those symbols. You write about "contractionary" in English, but the symbol C doesn't show up. How should that line of symbols be read? I read it as "For all x an element of X, subset A." I must be wrong. What does the comma (",") operator do there?<br /><br />Which means that to show monetarism is false, all you need to show is there is one point in the data set that engaged in austerity and experienced contraction, i.e.<br /><br />∃ x ∈ X, ¬A(x)"<br /><br />OK, now for this bit:<br /><br />"Which means that to show monetarism is false, all you need to show is there is one point in the data set that engaged in austerity and experienced contraction, i.e.<br /><br />∃ x ∈ X, ¬A(x)"<br /><br />Again, how do I read those symbols. I'm seeing "There exists x an element of X, not A." Again, I'm not sure how to read the comma.<br /><br />And finally:<br /><br />"∴ ∃ x ∈ X | ¬A(x)"<br /><br />I read that as "Therefore there exists x an element of X" but what do I do with the vertical bar "|?" "Given" doesn't seem to work for that.<br /><br />Oddly enough, I *think* I see what you're saying overall. You're saying that we only need to demonstrate that one element of the set of X has experienced both austerity and a contraction and we've disproved monetarism. That element (or subset?) is "EU." But I'm getting tripped up on the notation here which I want to learn, because I love the idea of translating these sentences into symbols.<br /><br />In fact before I read this tonight I was going to post a question on Sumner's post to Sadowski asking him if we can consider the entire EU to be a single country (in a weighted average, weighted by population or size of their economies). So I think I was getting at your point here.<br /><br /><br /><br /><br /><br /><br /><br />Tom Brownhttp://www.google.comnoreply@blogger.com