Return of the Log (Function)

Ed Hanson writes, after plotting the data:

The graph shows, in general, Minnesota’s increasing gap of per capita income over Wisconsin since at least 1970. It is not just since 2011 that this trend began.

This observation is right in a way — wrong in a deeper, more economically interesting, way. Investigation highlights the usefulness of the log function.

First, let’s graph per capita personal income, as Ed Hanson admonishes me.

Figure 1: Personal income per capita in Minnesota (blue), in Wisconsin (red), in dollars. Source: BEA.

The gap sure seems to be ever widening. But notice what happens if one plots the two series in proportional terms, i.e., on a log scale.

Figure 2: Personal income per capita in Minnesota (blue), in Wisconsin (red), in dollars, both on a log scale. Gray arrows and figures denote growth rates calculated as first log differences, over 1985-2011 and 2011-2017 periods, respectively. Source: BEA, and author’s calculations.

A gap opens up in 1984 due to a short burst of growth in Minnesota relative to Wisconsin income. Then the gap in proportional terms is constant. Until about 2011. Then the growth rate differs from zero, at the 27% msl…

Hopefully, instead of criticizing me like he did the last time I mentioned logs, Ed Hanson will cut me some slack as I have plotted the series on a log scale, rather than logging the variables before plotting.

Bottom line: Think before interpreting a graph of macroeconomic time trends, especially if you’ve plotted on a linear scale.

Update, 7/19 7:30AM Pacific: Ed Hanson writes:

Are you saying FRED is lying? Is the data made up? Or is the data presented in an honest way and presents the data properly? It is honest and the presentation is powerful.

Since Ed appears to only believe data plotted in FRED, here is my Figure 2, from FRED.

I hope Ed Hanson doesn’t think the “deep state” or “black helicopter” guys have got to FRED…

Addendum, 7/19 8:50AM Pacific: Ed Hanson continues to describe the contents of this post as:

… the propaganda as exemplified here by Menzie ….

I am thankful he did not describe me as a “socialist” again. Still, apparently now I am the Herr Goebbels of the socialist power elite. Woe to those who use logs!

58 thoughts on “Return of the Log (Function)

  1. Moses Herzog

    Log function!?!?!?!


    Next you’ll be telling us the Earth is round and the Universe does not revolve around planet Earth!!! Damned Leninist scum!!! And just because all those shellfish in the oceans are dying does not mean there is carbonation and acidification of the oceans!!! Satanic leftist!!!!!

    My log is yuuuuuge. All the ladies tell me it’s a “big log”.

  2. pgl

    “But notice what happens if one plots the two series in proportional terms, i.e., on a log scale.”

    Log scale? Mathematics? Careful there as you made this a wee bit harder, which of source means SOCIALISM!

  3. pgl

    Barkley Rosser explains why the Trump tariffs have actually hurt the share price for Alcoa:

    Interesting read but he never presented the actual share prices. The stock price was $60 a share earlier in the year but now is less than $48 a share. Of course the Usual Suspects will mine the data to present a different picture. Let’s hope they do so by taking the log of the share price -just for fun!

  4. PeakTrader

    A couple of economists explain the differences in income and employment:

    I suspect, Minnesota benefited more when the Information Revolution accelerated after 1982, with faster growth in emerging industries, while Wisconsin remained mostly in old industries. Milwaukee is on the edge of the Rust Belt. There was likely a brain drain in Wisconsin as potentially higher skilled workers moved to Chicago and St Paul-Minneapolis rather than to Milwaukee. Every economic expansion is different and perhaps Minnesota benefited more, since 2009. Wisconsin reducing higher paying government or union jobs when Wisconsin is creating lower paying private or non-union jobs, for example, may reduce income and tax revenue.

      1. PeakTrader

        Pgl, you don’t know what you’re talking about, as usual. Both are economists.

        If you’re ever accepted into a high quality econ course (which I doubt they’d admit you), then you’d realize you’ll get an extensive and rigorous education in fundamentals and methodology in macro, micro, econometrics, mathematical econ, and history of econ thought, along with specializing in two fields.

        It’s not easy to get admitted into a good program, and when they do, many fail, transfer to an easier program, or quit. Just because an economist focuses on one specialty doesn’t mean he or she doesn’t have extensive knowledge in core fields.

        1. Menzie Chinn Post author

          PeakTrader: I took my PhD fields in macro, international, econometrics at UC Berkeley. I do not profess to be an expert in health economics. Nor in IO. And I don’t even profess to be a specialist in econometrics.

          1. PeakTrader

            Menzie Chinn, good for you 🙂

            In the book “The Making of an Economist,” it stated only 600 Ph.Ds and 2,000 MAs in economics are awarded each year in the U.S. (e.g. in the ‘80s or ‘90s), which seems low, although 100,000 MBAs are awarded in comparison (more econ Ph.Ds were awarded in the ‘60s and ‘70s).

            Maybe, that’s why I was told at the University of Colorado I was receiving a junior doctorate rather than an advance bachelors.

        2. pgl

          “It’s not easy to get admitted into a good program”. I was with a full ride scholarship earning my Ph.D. in 1983. Let us know when you graduate from pre-K.

          1. pgl

            “that’s why I was told at the University of Colorado I was receiving a junior doctorate rather than an advance bachelors.”

            When I taught graduate students, we often gave the weaker students M.A.s But junior doctorate? I co-authored a paper on tariffs with someone who taught economics at the University of Colorado. I owe him a call – just for laughs!

          2. PeakTrader

            Pgl, again, you don’t know what you’re talking about.

            I got my BA in Boulder and my MA in Denver, because the program, at the time, was rated higher. I had to take more classes, including seminar classes at the Economics Institute in Boulder.

            It was actually rated high by a magazine like Newsweek, at the time.

          3. pgl

            “I got my BA in Boulder and my MA in Denver, because the program, at the time, was rated higher.”

            Does Peaky know how to read what the University of Colorado websites says about these programs. Note that you cannot get a doctorate from UC-Denver as it is an MA program. So when he says they gave him a “junior doctorate” we know is padding his resume.

            Peaky – we know your job is lying 24/7. Only problem is that you are not very good at lying.

            Resume padding – love it!

    1. pgl

      This is just rich (Phelan’s rant):

      “The EPI report makes some strange choices on which data to use. For example, it uses annual data from the Bureau of Economic Analysis for 2010 to 2016 when quarterly data is available going into 2017. Using quarterly data is better because it allows us to select a more precise base period for our comparison, Q4: 2010, the three months before the two men took office, rather than an average of all of 2010. It also allows us to add another year to our comparison.”

      PeakDishonesty a few days ago credited Trump will increasing nominal Federal tax revenues by 1.3% for the fiscal year ended 9/30/2017 and tried to claim this vindicates the tax cut that occurred only in Dec. of 2017. Beyond confusing nominal v. real, he choice of periods left off the last 2 quarters. When I used BEA quarterly data to show Federal revenues have dramatically declined in the quarter after the tax cut, Peaky’s Minnie Me (CoRev) attacked me for somehow being dishonest.

      The dishonesty of the right wing is so transparent it has become extremely funny.

    2. macroduck

      Seems reasonable to ask: Where does the Center of the American Experiment get its funding? I raise the question because a number of its “researchers” as of September of last year were registered lobbyists:

      That list of registered lobbyists includes Mitch Pearlstein, founder of the center.

      The current director of the Center is John Hinderaker, who also runs Power Line and sits in for Laura Ingraham’s on her show . He pretends the Center is a think tank so that he can get greater press exposure, since Power Line is to obviously a right-wing front organization to get much press coverage.

      Casting doubt on legitimate scientific analysis of public policy issues is the purpose of the “junk science” approach to propaganda. The Center of the American Experiment is in the “junk science” business. Is Ed also in that business, or just a victim?

      1. pgl

        It is a right wing organization. Yes Phelan calls himself an economist but Stephen Moore calls himself an economist as well. Guess who else claims to be an economist? Freshman dropout Donald Luskin. Can ANYONE be an economist? Oh wait – that homeless guy on the subway said he was an economist!

      2. Alan Goldhammer

        Of the few Board members that I looked at on the CAE website, they all had links to the Republican Party. Among the issues that several of them work on was ‘school choice’ a favorite of our current Secretary of Education. One cannot get a a read of the funding of the organization since as with many 501(c)(3) organizations they are not obligated to disclose sources of funding. Unlike 501(c)(4) organizations, the Center of the American Experiment can lobby government. 501(c)(4) organization are ‘social welfare’ organizations according to the IRS regulations. There are numerous such organizations on all sides of the political spectrum

        1. pgl

          Great research guys. Look – we all know PeakDishonesty is blatantly dishonest here but he is also persistent. He hates it when we check his sources as it exposes his dishonesty.

          But be careful as he will next call you uninformed or stupid. Notice how he claims I could not get admitted to an economics program even after I noted I have a Ph.D., have taught graduate courses, and published. Then again CoRev and Ed are questioning our host’s integrity as well as his teaching ability. This is Team Trump at its finest!

  5. Ed Hanson


    Are you saying FRED is lying? Is the data made up? Or is the data presented in an honest way and presents the data properly? It is honest and the presentation is powerful.

    Go right ahead and interpret the data anyway you want, but the fact of the matter, in general, the gap between Wisconsin and Minnesota has been growing and has been for a lot longer than since 1984. One of the neat things about FRED is they have the software to make many of their graphs interactive. You can quickly and easily get the raw numbers by placing the cursive to a date you like. Going back to “Max” time period on the FRED graph and moving the cursor,it can be easily seen that until 1960, Wisconsin and Minnesota were quite even in PCI growth though 1960. But then things change and Minnesota began its improvement, faster than Wisconsin, first narrowing the gap and then actually overtaking Wisconsin in PCI, The gap between the two states, in general, widen from then on.

    Does that mean every single year the gap widens, no. Does that mean that there may be a period of several years that the gap does not grow, yes? Does that mean in particular years Minnesota is economically hit harder than Wisconsin, yes? But is it meaningful or misleading to choose a time horizon by picking and end date of a bad period for Minnesota and then go back a number of years (cherry picking) to make the average look the way you wish it looks? The answer is misleading.

    The power of a graphic presentation is the way it can visually present the data. The FRED graph is powerful and refutes your suggested hypothesis that the period since 2011 is unusual. It is not.


    1. pgl

      ‘Are you saying FRED is lying?’

      Here we go again. FRED does present reliable data but as Menzie notes – you have no clue what the data is showing. Please stop embarrassing yourself.

    2. 2slugbaits

      Ed Hanson The power of a graphic presentation is the way it can visually present the data.

      The danger is that an ocular analysis is not the same as a formal analysis. If you want to use FRED (and you should), then you might want to learn how to use it properly. For example, instead of showing levels, why not select the option that shows percent change over the previous year? That’s (virtually) equivalent to Menzie’s use of log differences. What you’ll see is that there were two big spikes in Minnesota’s growth rate, one in 1975 and another in 1984. Those two large spikes get translated into permanent level shifts, but not permanent changes in the growth rates. That means there will be a permanent widening of the levels gap even if the growth rates are the same. When you graph levels rather than first log differences or percent changes the cumulative effect of past shocks gets perpetuated through time. If you want to know how to do a proper econometric analysis, then lesson one is to learn the difference between levels and rates. It’s almost as important as learning the difference between stock variables and flow variables.

      Here’s some free advice. Take a break from posting and spend a few months reading some basic econometric textbooks. I promise that you won’t find any image of a hammer-and-sickle impressed on the front cover. No socialist realist artwork alongside graphs and tables. Touching the pages won’t turn your skin pink.

      1. pgl

        “I promise that you won’t find any image of a hammer-and-sickle impressed on the front cover.”

        The gentleman who taught me econometrics was from Taiwan. Not exactly a socialist nation but his sense of humor was outstanding.

  6. Bruce Hall

    When one looks at Minnesota’s employers, it is heavily skewed toward healthcare (think ACA since 2009 and inflation in healthcare) and government.

    When one looks at Wisconsin employers, it is more heavily skewed toward retail and manufacturing (which has taken a hit from the recession in 2009 and Asian competition).

    Not sure that could be changed significantly since Walker came in office. Overall, Wisconsin is doing well despite the focus on lower-paying retail and blue-collar manufacturing jobs.

    1. pgl

      So folks shop in Wisconsin but go to the doctor in Minnesota? Let’s hope gasoline is cheap!

        1. pgl

          I live in New York City. I guess I’m required to write only about Kansas or whatever. Dr. Hamilton teaches at UCSD. If he ever decides to write about California – I presume you will attack him for doing so?

          Professors write about their local economies all the time. I bet the University of Wisconsin appreciates Dr. Chinn’s efforts. Now if you are willing to pay his salary – maybe you can have him write more about Kansas.

          1. Bruce Hall


            Pointing out factual differences in the basis of the Minnesota and Wisconsin economies is hardly “attacking”.

            I’ve not disputed the fact that Minnesota’s economy is better, in general, than Wisconsin’s. But Minnesota has benefited from expansive ACA and Medicaid spending through it’s very large healthcare systems (such as the Mayo Clinic) medical products corporations (Medtronic and 3M to a lesser extent). Wisconsin has had to deal with the erosion of old-line manufacturing (Harley-Davidson, Rockwell, Johnson Controls) and lack of new tech/high tech industries. Nevertheless, Wisconsin has done considerably better than its neighbor to the south and across the lake. I have family in Wisconsin and they seem satisfied with present conditions.

            I can understand why you might be upset with New York City/state leadership given economic performance there (higher than U.S. average unemployment, labor force and number of employed dropping), but you do get to pay very high taxes so that’s a plus. On the bright side, you might have a young, female, socialist representing you in Congress. . She is so insightful. Mexico should push right past the U.S., economically now that it has someone like Oscario-Cortez.

            Regardless, I don’t really care much about Kansas; who does except the people who live there? California? I enjoy visiting Sonoma. The redwoods near Marin are quite lovely. Unfortunately, Francisco is becoming a shithole … literally. LA? Well that’s a large prison where the inmates are kept in cars on freeways. However, there are some areas that are great for making S’mores.

          2. Menzie Chinn Post author

            Bruce Hall: Wisconsin benefitted from EPIC and Madison as high tech hub. If only Governor Walker hadn’t been busily cutting government spending in order to give tax breaks that brought little investment, and had agreed to Medicaid expansion, think of what could’ve been. Econometric analysis suggests that one might have seen faster Wisconsin growth…

          3. Bruce Hall


            I was referring to the links I had provided originally regarding largest employers in both states. I’m sure Wisconsin did see some benefit from the ACA spending, but not nearly to the extent that the large Minnesota corporations in the health care and health care products industries did. Large universities do provide a technology “hub” for many states, but that doesn’t always translate into a “technology economy” such as “Automation Alley” with the University of Michigan and large corporations in the Detroit Metropolitan area. UW Madison has the unfortunate geographic separation from Milwaukee that is unlike the University of Michigan from metropolitan Detroit or the University of Minnesota from the Twin Cities which makes corporate collaboration a little more difficult.

            But I agree, UW is a top-notch university:—Madison.html
            as is UMich:
            and UMinn:

            Interestingly, the latter two are rated higher in economics/business… 12 and 11 respectively. That may be from the greater economic collaboration with area businesses.

  7. Ed Hanson


    Wisconsin needed a change according to its voters. They liked the changes Walker promised, so voted him in the first time. They disliked the temper tantrum of the dems during the early part of the first term and gave Walker a big win after the recall and then confirmed their feelings by keeping the repubs in power in the legislature. Then they liked what Walker did during the first term so reelected him for a second.

    It is fortunate that the voters see through the propaganda as exemplified here by Menzie and direct the state to better path. There are times voters get it wrong but it is fortunate that our republic allows the voters the choice.


    1. pgl

      “It is fortunate that the voters see through the propaganda as exemplified here by Menzie”.

      Facts and accurate analysis are now propaganda? Enough with this intellectual garbage – address Menzie’s latest point.

      1. 2slugbaits

        He can’t. Ed Hanson has pulled this stunt before. When he can’t address the actual economics or the math, then he always falls back on some ramblings about the supposed political wisdom of the most clueless and economically illiterate voters. The topic might be how to interpret logarithms and growth rates, but you can be sure that it will always come back to socialist elites. This is what happens when someone’s interest level in economics exceeds his formal training. It’s an even bigger problem with older folks because having to admit that they don’t actually know anything means they also have to admit that they’ve been wrong about economics for most of their adult life. It’s easier to just engage in gaslighting and maintain the fiction of having some kind of deeper knowledge that escapes academics.

    2. 2slugbaits

      it is fortunate that our republic allows the voters the choice.

      Except when it comes to Presidential elections. Then you prefer affirmative action for rural Republicans, otherwise known as the Electoral College.

      1. Bruce Hall

        2slug, I may not agree with many of your opinions (but I do some), but your comment regarding the Electoral College reflects either 1) ignorance or 2) disdain, and I don’t believe you are an ignorant person. Nevertheless, a history lesson: we are a republic, not a democracy. We have a representative form of government, not a poll of voters. This was by design:

        It is not often that the popular vote and the Electoral College vote oppose each other, but in the case of the last election they did. Now before you cite “one man; one vote”, let’s be clear that applies to individuals. States, on the other hand have a slightly different arrangement with the federal government. There was a concern that the larger, more populous states would run roughshod over smaller or less populous states; hence, each state gets two senators. That doesn’t fit in with the direct democracy narrative either. States like California and New York have a tendency to for more government. I personally attribute that to the large cities with more a sense of anonymity than community where people feel the need for a government support system rather than a community support system (not that government is rejected by smaller states, but that people are more active as a community in pursuing goals rather than delegating everything to the government). End of digression… smaller population groups/states seem less inclined to seek a large, overlord government system. So, Trump appealed to this distrust of “Big Brother” and won the majority of the smaller states… some with slim margins, but won them anyway. It’s the states that decide how to divvy up their “electoral votes”. Some choose “winner takes all” while others split close to the actual vote lines. It’s the states that decide how the leader of “Big Brother” gets elected… after the people of those states make their voices heard at the polls.

        You may not like the lack of “individual direct democracy”, but it is by design and deeper than the Electoral College.

        The Republicans got the prize this time; maybe next time it’s the Democrats or Socialists. But it’s the “direct democracy” of the states, not the voters of those states. Read the link; it’s not that long.

        1. 2slugbaits

          Bruce Hall Yes, yes. I’ve heard all that garbage many times before. Bad history at the service of bad arguments.

          Hamilton and the other founders believed that the electors would be able to insure that only a qualified person becomes President.

          Howz that working out? It reads to me like an unforced error. Even George Will, who is one of the biggest defenders of the EC you’re ever going to find, agrees that this time the EC gave us “an embarrassing, wreck of a man.” It’s failed many times. It didn’t just give us Trump; it also gave us Bush #43 in 2000. It gave us Benjamin Harrison. And in 1876 it not only gave us Rutherford B. Hayes, but it also did so because of personally corrupt Electors at the EC. So much for Hamilton’s men of wisdom and integrity And the 1824 election was a misfire. So out of 45 Presidents, the EC has failed 5 times and twice in 16 years. Not my idea of a rare event.

          part of the structure of the government that gave extra power to the smaller states.
          and this
          Obviously this creates an unfair advantage to voters in the small states whose votes actually count more then those people living in medium and large states.

          Even if you support the EC, you’d have to concede that those two comments are almost the perfect examples of affirmative action as understood by today’s conservatives. The part that you don’t like is actually calling it an “affirmative action” program, even though that’s exactly what it is. But the fact that you don’t like the term doesn’t mean it isn’t spot on.

          but it is by design and deeper than the Electoral College.

          You should try reading some of the actual notes from the Convention; and not just Madison’s notes. The EC, like Article II itself, was an afterthought that was given almost no serious consideration at all. It was a bribe given to small states to keep their delegates from leaving Philadelphia (which many did anyway). Federalist #68 was an op-ed piece in the newspapers that Hamilton wrote to try and persuade the New York state convention to ratify the Constitution. He anticipated that alert convention voters would notice the obvious; i.e., that the EC would hurt large states like New York. So he tried to head off that argument by denying the obvious and offering up some lame excuses to try and convince New York voters to vote against their interests by pretending that the EC would not really hurt New York. As in a lot of other Federalist Papers, Hamilton engaged in a little bit of intellectual dissembling in order to win votes for ratification. Hamilton wasn’t an enthusiastic supporter of the Constitution, but he thought it should be ratified because it was better than the Articles of Confederation. He also believed that the flawed Constitution could be cleaned up later once it was ratified.

          The Framers were mere mortals with limited knowledge of political science and even less knowledge of serious history. There’s no need for Framer worship. They made lots of bad mistakes and the EC was one of them. The EC failed almost right out of the box and had to be amended. In fact, it’s failed many times, contrary to what you said. Too bad our middle schools teach the kind of history-for-toddlers crapola in your link.

          1. Bruce Hall

            2slug, I think this may be what you had in mind for the U.S.:

            One doesn’t need to believe those who wrote and signed the Constitution were perfect. But it has served our country well and continues to do so by forcing a balance between popular sentiment of the day and long-term interests of the states. We haven’t had a Hugo Chavez trodding of the Constitution and destruction of a nation. The glib-talking socialism of Obama was considered a danger by many who then selected a crude-talking successor rather than Obama’s anointed successor. I’m sure the pendulum will swing back and forth and I’m fine with that rather than see the nation careen off a cliff of pied piper popularity.

            Ultimately, until shown otherwise, the framers of the Constitution were smarter than the preponderance of their successors and have protected the rights of the citizens from the power-hungry and special interest or identity politics denizens of present day Washington D.C.

      2. ilsm


        Get over it.

        I respect the oath I took in the 60’s to support and defend the ‘electoral college’. It prevented the crook becoming president.

        It has been 20 months! We still get indictments for “conspiracy”………… supported by “possible collusion”.

        It was not Putin, Assange, Brazile or the fact the US is run as a representative republic a bit more modern than in 1787.

    3. Menzie Chinn Post author

      Ed Hanson: No response to the addendum? Or have you concluded that St. Louis Fed has been coopted by the DeepState? Communists? Masons? Illuminati (I know, for some the last two are the same)? Maybe “pods” a la “Invasion of the Body Snatchers”?

  8. pgl

    Trump is having his LBJ 1966 moment. Back in late 1965, the Council of Economic Advisers told the President that fiscal policy had gotten too stimulative in light of how strong the economy was. We had the 1964 tax cut, the Great Society programs, and the Vietnam War build-up. LBJ was not going to abandon the Great Society programs and he was not yet ready to wind down Vietnam. He was somewhat willing to ask for a tax increase by Wilbur Mills ruled tax policy and Norman Ture (the original supply-sider) basically lied to Mills so we did not get the tax increase. So as the CEA predicted, the FED had to raise interest rates to avoid higher inflation.

    52 years later just today Trump blasted the FED for raising interest rates just as LBJ did in 1966. We know what happened back then – the FED complied with politics and inflation rose. Of course supply-siders do not blame Ture but rather the CEA. Supply-siders were back then as they are now – blatant liars.

    Today we have a tax cut for rich people and a President who wants to increase defense spending. But I guess Team Trump thinks this is OK and it is OK to bash the FED. Of course Trump has economic illiterates as his economic advisers. What could go wrong?

  9. pgl

    The other day PeakDishonesty went on a fact free rant about how the U.S. economy was booming during the early Reagan years (forgetting about that massive 1982 recession) and how private investment demand rose by 50% (actually it plummeted during the first two years). He also said R&D was roaring but provided no source.

    J. John Wu published the following excellent discussion of R&D in the U.S. with lots of charts of the actual data:

    It seems we were spending more on R&D as a share of GDP under Obama than we were during the 1980’s. So one has to wonder what Peaky took at the University of Colorado-Denver. Oh yea – Bogus Writing 101. He got an A in that class.

  10. pgl

    OK – those socialist reporters at MSNBC are mad that Trump is saying he wants a weaker dollar. Get real – we need higher net exports. So yea – I’d be with Trump on this one. But take a look – the dollar has appreciated about 5% since the beginning of the year.

    Does Trump have any clue? Of course that was a rhetorical question!

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