PC math errors and Benjamin Zycher's eight-year itch

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The controversy regarding the mathematical errors in the Ontario PCs' "million jobs plan" went viral last week, after a critical mass of economists weighed in to confirm that the party had indeed badly misinterpreted the findings (by as much as eight times over) of their own consultants' studies. This sparked a firestorm of media coverage, inspired the Globe and Mail's Adrian Morrow to rename the Tory campaign bus (now called "The Million Person-Years Express"), and spawned a satiric hashtag (#Hudak8) that trended on Twitter.

The damage to the centrepiece of the Tory platform is serious, although leader Tim Hudak continues to push his vision of fiscal austerity, corporate tax cuts, and anti-union policies as aggressively as ever. And some Tory allies have continued to defend the party's math, despite the odds.

In the Financial Post Terence Corcoran argued that the Conference Board's original estimate of the jobs created by corporate tax cuts was too low. Hence the multiple counting of those jobs in the Tory platform was actually, inadvertently, getting us closer to the "real" number. He cited Jack Mintz to suggest the true job-creation effects of a CIT cut would be at least four times as large as the Conference Board suggested. (Too bad he couldn't find someone who would claim they would be eight times as large -- that would perfectly cancel out the Tories' math mistake!)  In reality, it's questionable whether the Tory plan would produce any new jobs at all: corporations are already hoarding cash (not even re-investing their existing cash flow), and the Tory analysis didn't count the negative effects of cancelling an offsetting amount of government spending (as they promise to do).

Corcoran, at least, cited anonymous Tory staff acknowledging the multiple counting of the Conference Board numbers. Corcoran called it a "technical error." (Exaggerating job estimates up to eight times over is a bit more than a "technical error," I should think.) Adrian Morrow's story in the Globe and Mail also cited an anonymous PC source acknowledging that the platform conflated new jobs with person-years. But these folks obviously missed the memo from Tory HQ, namely: "Stick to your guns." Here is the party's Will Stewart holding firm: "We stand behind our numbers." Tim Hudak's strategy seems to be to imply that economists can't agree on anything, so whether the numbers are right or wrong is ultimately just a matter of opinion. Adam Radwanski's devastating Globe and Mail commentary summarized nicely what that says about Mr. Hudak's leadership style.

Actually, it's not about the "opinions" of economists. Economists could indeed have an honest disagreement over whether Hudak's proposals are good for the economy, or bad. But the fact that his platform multiple-counted job projections published by its own consultants is a matter of clear arithmetic, not opinion.


Benjamin Zycher's defence of the PC math error

In my view, the most disingenuous defence of the Tory numbers has come from Benjamin Zycher, hard-right U.S. economist, long-time advocate of right-to-work laws (including advocating them for Ontario), and author of one of the two consulting papers the Tories cite in support of their job-creation estimates. In Corcoran's column, and then again in a blog by David Reevely (the Ottawa Citizen reporter who first noted the multiple-counting issue), Zycher claims that the numbers in his report are indeed annual new job-creation figures, generated by one-time gains in GDP (which he predicts will result from things like lower corporate taxes, slashing Ontario electricity prices, and emulating the "economic freedom" of U.S. states).

How can a one-time gain in GDP spawn new job-creation year upon year upon year? Because it takes time for an economy to adjust to a structural change, Zycher told Reevely. That's an eminently reasonable suggestion. Especially regarding deep policy changes, economists typically assume it takes many years for an economy to fully adjust. That's precisely why they would usually specify some kind of adjustment process, or estimate what is called a "dynamic model" (projecting growth rates of GDP or employment over time, rather than one-time changes in those variables), to explain how the economy adapts to a policy shift over time. That's exactly what the Conference Board did in its model: even after 10 years, the economy was still experiencing small additional changes from the initial simulated policy change. (The problem was that the Tories misunderstood the running 10-year tally as representing new jobs in each year of that forecast.)

We all agree it takes time for the economy to adjust to a major change. How long? "Two years is clearly too few," Zycher said to Reevely. And "twenty years would probably be too many." How many is just right? You guessed it: eight years is just right! This Goldilocks proposition (not too long, not too short, eight years is perfect) just happens to cancel out the Tory math error.

Here's the problem. There is not a single word in Zycher's original model or results about time lags and adjustment mechanisms of any sort, let alone an adjustment mechanism of precisely eight years. The phrase "eight years" does not appear in Zycher's original paper. Every mention of the jobs created by the Tory policies simulated by Zycher refers only to "jobs" or "employment." Not annual jobs. Not jobs per year. Not growth in employment per year. Not new jobs per year for eight years. Just "jobs" and "employment." Check every place in his paper that describes the employment effects of the simulated policy changes (on p.1, p.2, p.16, p.17, and p.18). There is no mention anywhere of the gain in employment from any of the simulated policy changes being something that occurs year after year at all, let alone for a magical eight years.

More math problems

It's not just his words that give him away, it's his math. The paper specifies two econometric equations that he estimated, on the basis of a pooled time-series cross-sectional data set of all Canadian provinces from 1985 through 2012. One equation estimated the level of GDP, on the basis of the lagged GDP level, the current year's GDP growth rate, and several other variables including the policy levers which Zycher wanted to analyze (taxes, electricity prices, and "regulation" -- by which Zycher actually means "economic freedom" as defined by the Fraser Institute). The other estimated the level of employment based on GDP and several other variables.  Zycher followed a two-step process. First he estimated how much a policy change would increase GDP (once and for all), based on his first equation. Then he estimated how many new jobs would be created by that one-time GDP growth (based on his second equation). The result was an estimate of how many jobs could be traced back to the policy change.

There are many questions and concerns that could be raised with his model. McMaster University's Mike Veall has pointed out that regressing current GDP on lagged GDP and the GDP growth rate should have caused the regression to collapse (since those two variables alone precisely determine current GDP by an identity, which should have corresponded to a singular matrix which could not be solved in the regression calculation); it is only because Zycher oddly linearized this relationship that he could get any results at all from his regression. One professor commenting on Veall's blog post suggested he would use Zycher's paper in future as a textbook case study in "spurious regression": that is, formulating a regression equation that seems to show strong results, on the basis of no actual correlation.

But never mind these methodological issues. Even if you accepted Zycher's approach, how should you interpret the findings? A one-time GDP gain (claimed to result from tax cuts, lower electricity prices, or more "economic freedom") translates into a one-time employment gain. Zycher is clearly treating the GDP gain as one-time (as he must): he did not use the coefficient on GDP growth from his employment equation, he used the coefficient on the level of GDP. The resulting job gain can only be interpreted as a one-time employment gain.

Yes, it is certainly true that an employment boost from a one-time boost to GDP might be experienced over several years. But in "comparative static" analysis of the sort Zycher is performing, the results always show the effect after an assumed full adjustment. Unless you specify a dynamic adjustment path, you cannot describe the path that is taken toward that end result (nor how long it will take). There are no lagged terms in the employment equation; there is no reference at all in the employment equation to an adjustment period (let alone a perfect eight-year adjustment period); there is no credible way to interpret his employment predictions as anything other than a one-time effect (attained after some undescribed adjustment period).

Retroactive interpretations

Remember, Zycher's paper was written before he had even seen the Ontario PC platform (it is dated March 2014). The policy changes he is simulating do not generally reflect what the Tories are actually proposing in this campaign (particularly with respect to electricity prices and economic freedom). Importantly, he could not have known that the Tories would present their job-creation promise in the form of an eight-year timetable (which is unusual, considering they are campaigning for a maximum 5-year term of office). There is no reference to eight years anywhere in his paper. (He claims in the Reevely article that he left it to the Tories to decide how long the full adjustment might take. So if the Tories had opted for 100 years, and hence generated 100 times as many jobs, that would have been just fine -- and the total effect would still somehow be consistent with his model. You can't make up stuff this incredible.) All this is just more evidence that Zycher's claim this week (that the numbers in his paper should be interpreted as annual gains that last for exactly eight years) is simply a retroactive fabrication.

Mr. Zycher can say anything he wants today about what he meant to be doing. But what he wrote, and the equations he estimated, in that March paper are now a matter of public record. There is nothing in that paper consistent with his claim that the employment gains he predicted should be interpreted as annual in nature, occurring every year for precisely eight years or any other number of years. The terms "8 years" or "eight years" do not appear anywhere in his report. I challenge any economist at any Canadian university to show how the results of the model described in Zycher's March paper could be interpreted as describing annual job gains that continue for eight years. Mr. Zycher's effort to retroactively attach an eight-year adjustment period to results that he has already published are desperate and dishonest.

This controversy is now about much more than just a math error made by some eager backroom Tories trying hard to get to a million jobs. It is now more about the character of the Ontario PC leadership. Confronted with uncomfortable facts, they are determined to charge ahead -- motivated more by ideology than evidence. That's not a recipe for good government.

im Stanford is an economist with Unifor.

Photo: Laurel L. Russwurm/flickr

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