I Killed Some Brain Cells Today

I ran a regression of ΔY on ΔX and ΔZ, over the 1967Q1-2011Q3 period. I found that the coefficient on ΔX was 0.007, and on ΔZ was -0.080. Neither coefficient was statistically significant at conventional levels, so I concluded that neither affected ΔY.

It turns out ΔY is the GDP deflator inflation rate, ΔX is the growth rate of M1, and ΔZ is the growth rate of real GDP. In other words, I concluded money had no significant impact on inflation.

Well, you might say, that was a silly regression to run. It happens to be exactly analogous to the regressions run by the Phoenix Center for Advanced Legal and Economic Public Policy Studies, in its assessment of the effectiveness of government spending. As the Mises blog published today: “a recent study published by the Phoenix Center looked at the empirical evidence for the US over the last 50 years and found that government spending/stimulus had zero positive impact on private sector job creation.”

To see how the Phoenix Center came to its conclusion, now let ΔY be employment growth, ΔX be investment growth, and ΔZ be government consumption and investment growth, and run the regression over the 1960-2011 period et voilà! Proof positive that multipliers for government spending are zero while those for investment very large. Some additional observations:

  • The authors assert these multipliers are different over high growth and low growth periods (i.e., there are two regimes governing these relationships). Of course footnote 30 indicates that one can’t reject the null that the government spending coefficients are the same.
  • The regressand selection of private employment is not quite standard. The usual interpretation of the multiplier is to relate total employment growth to growth in government consumption and investment, not just private employment.
  • For the life of me, I could not replicate their basic linear model results, even using private employment. If some one can, please tell me.

This is what I get running a regression of log difference of private payroll employment (average of monthly data) on log first difference of real investment and real government consumption and investment (growth rates annualized).

Δn = 0.013 + 0.088 × Δinv + 0.045 × Δgov

Adj.R2 = 0.38, DW = 0.76. Bold Face denotes significance at 10% msl.

Man, oh, man, and I thought the St. Louis money equations were bad; not only does this regression have an extremely restrictive lag structure, it is so restrictive that there are only contemporaneous effects (i.e., no lags — perhaps problematic, given the excruciatingly low DW statistic, but this did not seem to trouble the authors, so I won’t dwell on it besides noting the inappropriate use of conventional standard errors to make statistical inference). Anyway, for those of you wondering why I wasted brain cells on this, apparently some people take these results (and the Phoenix Center) seriously, including these periodicals: [1], reprinted in [2], [3], and [4].

18 thoughts on “I Killed Some Brain Cells Today

  1. Mark A. Sadowski

    I frequently take the time to kill brain cells in the cause of proving a point. I really appreciate it when others do the same.

  2. bmz

    @ Verones: not only does your citation have nothing to do with the post; it doesn’t even support your allegations:
    “Concerns that the government was being too generous reached all the way to President Obama. In an October 2010 memo prepared for the president, Lawrence H. Summers, then his top economic adviser; Carol M. Browner, then his adviser on energy matters; and Ronald A. Klain, then the vice president’s chief of staff, expressed discomfort with the “double dipping” that was starting to take place. They said investors had little “skin in the game.”

  3. Anonymous

    I doubt this brain cell damaging effort adds much value to that provided by ordinary discourse. If the government distributes taxes to a group of private contractors who will expand and improve, for one example, the Boston metro mass transit system, is the net economic effect zero? Of course not, silly boy(s).

  4. cthomson

    Well put, WCV.
    If we didn’t know from painful experience that our government is run by venal, blown dried buffoons, we might believe that Congress is capable of turning the spending pump on and off in some reasonably effective and rational way.
    Since Congress is what it is, we try to keep their ‘help’ to a minimum and our money in our own hands.

  5. 2slugbaits

    Menzie A small quibble. Your first toy regression with money and inflation isn’t quite comparable to the Phoenix Center’s regression with employment and government spending. In your first regression both explanatory variables were insignificant, at least creating the possibility of multicollinearity (assuming M1 and real GDP are correlated). But there’s so much else that’s wrong with the Phoenix Center’s model that no evidence of multicollinearity is small comfort. Gotta love that autocorrelation…you almost have to try to get a DW statistic of .76. Yes, you would have thought that the DW test would have sent up all kinds of red flags regarding the absence of a lag structure or at least an AR term; but what I find even more remarkable is that nowhere does the theory of fiscal multipliers talk about contemporaneous effects, so why would they even model it that way? The multiplier is a limit of an infinite summation, which right off the bat ought to tell you that contemporaneous effects will be near zero and that you need to model a generous lag structure. In other words, forget the bad econometrics for the moment; just the way they structured their model tells us that the authors do not even understand how fiscal multipliers work. The model wasn’t just misspecified in the narrow econometric sense; it was misspecified even in terms of the most rudimentary theory of fiscal multipliers.

  6. ppcm

    How many stimuli shall governments account for, how many lags in time series,when may we conclude that multiplier theory(ies) have a long lasting impact on employments?
    In a NBER paper few quantitative answers are available, the outcome is not straightforward when looking at the jobs perenity of ERRA.
    James Feyrer Bruce Sacerdote Working Paper 16759
    “In Table 3 we present our baseline results at the state level. In column (1) we regress the change in employment per capita (from 2/09 to 10/10) on stimulus spending per capita in hundreds of thousands of dollars. We find a coefficient of 0.54 which suggests that each $100,000 spent
    created 0.54 jobs. If we control for the log of population, the coefficient rises to 0.59 (column 2).”
    The implied multiplier was more favorable for low income as a 100.000 usd would drive a multiplier of 1.96,overall the margin of uncertainty is high
    between 0.5 and 2.
    In a paper titled “The Financial Crisis and the Policy Responses:An Empirical Analysis of What Went Wrong” professor John B. Taylor supplies enough evidences on the causes of the ERRA,enough evidences to drive caution when it comes to dogmatic conclusion on policies.
    ERRA may have been in existence under different titles as the graphics of Fed St Louis may suggest
    Federal Government: Current Expenditures (FGEXPND)
    In summary gratitude should always be granted to brains burning cells for collective well being purpose,but not all brains should be cloned.

  7. dwb

    well, it makes a huge difference for these policy papers whether you regresson on “government spending” for military or other types of spending. military spending always has a very positive significant multiplier while other types do not.
    yes, that was sarcasm.

  8. Brian

    Maybe we should all chip in and send them a copy of Jim’s time-series book. At least then they could learn about VARs and testing for cointegration.

  9. Philip Rothman

    Perhaps someone should inform the Phoenix Center’s researchers that, close to 40 years ago, recent Nobel Prize winner Chris Sims published a paper showing how one can avoid pitfalls so as to save the world from silliness of this sort.

  10. W.C. Varones

    Actually, my citation had everything to do with the post. Government spending is political allocation of capital.
    And the New York Times article, even with the NYT’s well-known ideological and partisan bias, completely supported my allegations.
    But if you need another example of political allocation of capital leading to corrupt and sub-optimal outcomes, here you go.

  11. kharris

    Note that the [1] link is to the PR news wire. The PR wire is what the name suggests – a public relations outlet. For other news outlets to pick up a PR release as if it were straight news is just another form of journalistic malpractice.

  12. bmz

    @ Verones: You are kidding aren’t you? You could gather together every right wing diatribe and you couldn’t cumulate 1/10 of 1% of the federal budget. I can give you a single example of a Republicon “free market””sub optimal” outcome that produces 1000 times more economic waste than those: healthcare. The socialized healthcare systems of other technologically advanced countries cost less than half of ours yet produce better outcomes and greater patient satisfaction. Even our own socialized healthcare: the VA is 40% more efficient than our current “free market” healthcare as well as producing better outcomes and greater patient satisfaction:http://www.time.com/time/magazine/article/0,9171,1376238,00.html. Now that is real money($1 trillion per year).

  13. kharris

    The NYT’s left-wing bias is “well-known” to those with a right-wing bias. Otherwise, it’s generally understood to have an allegiance to power, just like other major news outlets.
    However, even if the NYT actually was biased toward the left, it is also pretty well known that the facts have a left-wing bias. If the NYT were biased toward the facts, that would be OK with me.

  14. jult52

    I probably shouldn’t get in the middle of this, but I have to ask kharris whether she wrote this:
    “However, even if the NYT actually was biased toward the left, it is also pretty well known that the facts have a left-wing bias.”
    with a straight face.

  15. Pickett

    Applying classical OLS regression techniques to summarize time series data sets (almost) always produces results that are invalid. The exceptions are few and far between.
    The correct statistical technique is time series analysis. Estimating a transfer function (sometimes referred to as a dynamic regression) is the correct technique. Even after applying transfer function techniques, evidence of feedback among the variables may call for using multiple time series techniques.

  16. dshing

    @kharris VA and efficient in the same sentence? Surely you jest. In my experience, they are anything but efficient, at least from a patient care basis.

  17. Anonymous

    @ dshing it was me, not KHarris, who stated that the VA is the country’s most efficient healthcare system. But, my statement is not based on my opinion; but rather extensive nonpartisan surveys and analysis: http://www.time.com/time/magazine/article/0,9171,1376238,00.html. I am sorry that your experience has been the exception; but that is often the case with individual experiences. What KHarris stated was the rather well-known phenomenon that the facts have a left-wing bias; which can be also easily verified by reviewing the various non-partisan fact check organizations.

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