Assessing the Stimulus and Its Aftermath

Or, on reading those who can do math, and those who can’t (i.e., yet more from Heritage)

The CEA released its most recent assessment of the impact of the ARRA. Some popular accounts, from the Heritage Foundation, from the Weekly Standard, and from Ted Nugent, argue that those estimates of output and employment effects are outlandish. They also cite incredibly high cost-per-job figures. Here are some thoughts on the those arguments (analyses would be going too far).

The basic findings of the CEA report are recounted in Tables 7 and 8 of the report. Those tables also include comparable estimates from the CBO and private firms. I’ve used data from Table 7 to generate the counterfactual GDP. Figure 1 presents the CEA approaches and the CBO low and high effect estimates, while Figure 2 presents the CEA model approach estimate against the private sector estimates.

Figure 1: Log GDP (blue bold), and implied counterfactual (no stimulus) GDP under CEA model (multiplier) approach (red bold), CEA projection (VAR) approach (light green), CBO low and CBO high estimates (gray), all in Ch.2005$ SAAR. NBER defined recession dates shaded gray. Source: BEA, 2011Q1 3rd release, CEA, NBER, and author’s calculations.

Figure 2: Log GDP (blue bold), and implied counterfactual (no stimulus) GDP under CEA model (multiplier) approach (red bold), Macroeconomic Advisers (chartreuse), IHS-Global Insight (light purple), Goldman Sachs (green), Moody’s (teal), JP Morgan/Chase (orange), all in Ch.2005$ SAAR. NBER defined recession dates shaded gray. Source: BEA, 2011Q1 3rd release, CEA, NBER, and author’s calculations.Two observations

  • The CEA model approach (which incorporates using multipliers) is bracketed by the CBO low and high estimated effects.
  • The CEA model approach yields a counterfactual GDP in 2011Q1 that is virtually indistinguishable from the private sector forecasts.

Once one views these graphs, it is somewhat surprising to see the ridicule heaped upon the CEA estimates, implying that they are outlandish. The Weekly Standard writes:

When the Obama administration releases a report on the Friday before a long weekend, it’s clearly not trying to draw attention to the report’s contents. Sure enough, the “Seventh Quarterly Report” on the economic impact of the “stimulus,” released on Friday, July 1, provides further evidence that President Obama’s economic “stimulus” did very little, if anything, to stimulate the economy, and a whole lot to stimulate the debt.

Figure 2 demonstrates that the CEA estimates are in line with private sector estimates indicating a substantial impact on GDP.

What is truly hysterically funny (and demonstrates the innumeracy so typical of so much writing these days) is the following assertion:

… The council reports that, using “mainstream estimates of economic multipliers for the effects of fiscal stimulus” (which it describes as a “natural way to estimate the effects of” the legislation), the “stimulus” has added or saved just under 2.4 million jobs — whether private or public — at a cost (to date) of $666 billion. That’s a cost to taxpayers of $278,000 per job.

This seemed like a familiar argument, and then I realized Casey Mulligan performed a similarly (incorrect) calculation two years ago, which involved a similar stock-flow mismatch calculation. My rebuttal was here; to quote:

Note that $787 is spent over several years (a flow). 3.5 million jobs is a stock. But wouldn’t we want to incorporate how long those jobs would be around? That suggests we should use job-years instead of jobs, to make the numerator and denominator comparable. The Administration estimated the number at 6.8 million [2]. That works out to a cost per job-year of $116 thousand.

Since innumeracy abounds, here is a reprise, applied to the Weekly Standard calculation. So far, $666.3 billion has been spent over the past two years (a flow). The cited 2.4 million number applies to an instant, 2011Q1 — a stock. In previous quarters, the number of jobs created was higher (and lower). What one wants to do is to compare a flow to a flow. The number of person-years (equal to one job over one year) is 3.911 million (a flow). Doing the math correctly leads to an estimate of $170,366.

To further highlight the stupidity of the Weekly Standard calculation, suppose in 2015, when almost all funds are expended, only one job was still being supported. Then, using their preferred methodology would indicate each job cost $787 billion…

In addition, back in my 2009 critique of Mulligan’s approach (which he implicitly acknowledges as correct in his blog), I observed that one would also want to know what had happened to profits (i.e., returns to both labor and capital matter).

It’s also important to recall that around a third of the ARRA was tax related. Had more been devoted to infrastructure investment and transfers to the states, as I’d suggested [1], then the cost-per-worker-year would have been lower. It was only at the insistence of Republicans that a larger share of the stimulus was devoted to tax cuts. (By the way, where are all those critics who argued the recession would be too brief for infrastructure spending to matter?).

This post originally appeared at Econbrowser and is reproduced here with permission.