Usually, when I look at something longer, I understand more what is going on. In the case of the Heritage CDA simulations of the Ryan plan, it just gets more and more incomprehensible. To illustrate this confusion, consider the following graphs of private employment, equipment investment, nonresidential structures investment and residential investment, under the baseline and as simulated under the Ryan plan.
Figure 1: Private nonfarm payroll employment (blue), baseline (dark b lue) and simulated under Ryan plan (red), in millions. Source: BLS, Heritage CDA, Appendix 3.
Figure 2: Real equipment investment (blue), baseline (dark blue) and simulated under Ryan plan (red), in bn Ch.05$. Source: BEA, Heritage CDA, Appendix 3.
Figure 3: Real nonresidential structures investment (blue), baseline (dark blue) and simulated under Ryan plan (red), in bn Ch.05$. Source: BEA, Heritage CDA, Appendix 3.
Figure 4: Real residential investment (blue), baseline (dark blue) and simulated under Ryan plan (red), in bn Ch.05$. Source: BEA, Heritage CDA, Appendix 3.
Red Flags! Super-High Implied Elasticities
In my previous post, I highlighted the fact that the implied elasticity was too high to be plausible, using the average simulation period values. After reading some of the documentation regarding the IHS-Global model,  in retrospect, I think it might be more appropriate to use the end-of-simulation values, rather than mean, since the elasticity calculations are more relevant in the long run. Essentially, the IHS Global Insight model is a conventional aggregate demand-aggregate supply model with short run price stickiness, but long run Classical characteristics. And so, in order to make the best case for the Heritage CDA simulations, the responses at end of the sample should be more plausible. So, unto the breach once more!
First consider the implied labor supply elasticity, shown in Figure 1. This elasticity is given by the following formula:
η = (∂N/∂ω) × (ω/N)
Where N is labor supply, and ω is the after tax real wage.
From Appendix Table 3 of the Heritage document (as revised 11am 4/6), we have end-of-period (last three years) baseline private nonfarm payrolls at 124.2 million, simulated at 126.5 million; the log difference is 0.0181. The end-of-period baseline personal tax rate is 0.194, and the simulated is 0.186. The log difference in implied real wage is 0.0067. Since I don’t have demand side elasticities, I can assume a perfectly elastic demand for labor to give me the minimum figure for the implied supply elasticity. Hence, substituting these figures into the formula leads to:
2.7 = (0.0186/0.0067)
This figure is still somewhat higher than the authors of the report indicate they are using (a value of 2), which is in turn in the mid-range of the estimates reported by Rogerson and Allenius. 2.7 is smaller than the 5.8 or so I found earlier, using period sample averages, so in that respect, the results are a little less implausible. Nonethelss, as I mentioned before, even this value of 2 is substantially above the CBO’s estimates of labor elasticities (even for second earners).
What about equipment investment. Figure 2 highlights the fact the Heritage CDA simulations imply an incredibly large jump in equipment and software investment. Repeating my analysis using a user-cost of capital analysis. Let log investment-to-capital equal:
ln(I/K) = γ rK
Where the rental cost is given by:
(1-u)rK = (i – πK – d)(1-z)PK
And where u is the corporate tax rate, rK is the rental cost of capital, i is the interest rate on corporate bonds, πK is the inflation rate for capital goods, d is the economic depreciation rate, z is the present discounted value of tax credits and accelerated depreciation allowances, and PK is the price of capital goods. I’ll assume πK, d, and z equals zero (which is okay since they don’t change in the simulation), and the relative price of capital goods at unity. After solving for the rental cost of capital, this leads to:
rK = (i)/(1-u)
The baseline 10 year interest rate is 0.05400 in the last three years of the simulation period, the alternative 0.04661. The current statutory corporate tax rate is 0.35, the rate under the Ryan plan is 0.25. Then the initial rental cost of capital is:
0.08310 = 0.05400/0.65
and under the Ryan plan:
0.06215 = 0.04661/0.75
(I’m assuming a percentage point for percentage point change in the effective corporate tax rate, which is an approximation). So the change in the rental cost of capital is 0.0210.
Now consider the change in equipment investment relative to the capital stock. Under the baseline, average equipment investment is 1.842 trillion Ch.05$, under the Ryan simulation, it is 2.251 trillion Ch.05$. I don’t have numbers for the real capital stock over this period, but for the sake of argument I’ll use the 2009 current cost (nominal) capital stock of 5.611 trillion. (Since the price index for equipment investment goods in 2010Q4 is about 0.975 for 2005=1, this is pretty close to a real magnitude, expressed in Ch.05$.)
Then the log change in the investment-to-capital ratio is = 0.200, (assuming the net capital stock grows by 1% per year in both cases). Solving out for the elasticity yields:
γ = (0.200)/(-0.0210) = -9.52.
This figure is now even more above (in absolute value terms) the short run elasticity of 0.50 cited by Gilchrist and Zakrajsek (2007) (their long run elasticity is about unity). The figure is also much, much larger (in absolute value) than the largest estimate I have found for equipment, of -1.64, obtained by Huntley Schaller (JME, May 2006) using cointegration techniques.
I haven’t worked out the implied elasticities for nonresidential structures, and residential structures, but my guess is similarly bizarre implied elasticities would arise. Figure 4 alone should give pause; it indicates by 2021, real investment in residential structures will be back to near peak levels of 2006.
An Explanation, and Laffer Redux
So, we return to the question of how these very large elasticities come about, when the simulations are from a model that is so conventional. The Heritage Foundation describes the Global Insight model thus:
The Global Insight (GI) short-term US macroeconomic model is a large-scale 10-year (44-quarter) macroeconometric model of the US economy. It is used primarily for commercial forecasting. However, over the years, analysts in The Heritage Foundation’s Center for Data Analysis (CDA) have worked with economists at Global Insight to adapt the GI model to do policy analysis. In simulations, CDA analysts use the GI model to evaluate the effects of policy changes on not just disposable income and consumption in the short run but also the economy’s long-run potential. They can do so because the Global Insight model imposes the long-run structure of a neo-classical growth model but makes short-run fluctuations in aggregate demand a focus of analysis.
Now that I think about the disjuncture between the sheer conventional AD-AS nature of the IHS Global Insight model, and the bizarre output, it seems obvious to me that these paragraphs from the Heritage CDA documentation of the Ryan plan simulations are key to understanding the simulation output:
Labor Participation Rates. Taxes on labor affect labor-market incentives. Aggregate labor elasticity is a measure of the response of aggregate hours to changes
in the after-tax wage rate. These are larger than estimated micro-labor elasticities because they
involve not only the intensive margin (more or fewer hours), but also, and even more so, the
extensive margin (expanding the labor force).
The change in the labor supply variables were adjusted by the macro-labor elasticity of two,
which is a middle estimate of the ranges. The adjustment to the add factors allowed the variable
to continue to be affected both positively and negatively by other indirect effects.
In the final stage of the simulations the add factors were endogenously recalculated in order to
take account of the new estimates of the average tax rates mentioned above.
Private Investment. Economic studies repeatedly find that government debt crowds-out private
investment although the degree to which it does so can be debated.26 The structure of the model
does not allow for this direct feedback between government spending and private investment
variables. Therefore, the add factors on private investment variables were also adjusted to reflect
percentage changes in publicly held debt. This can also put upward pressure on the cost of
capital (thus helping the model balance the demand and supply effects on the cost of capital).
To sum up, it’s clear that while the simulations are in part built on the IHS Global Insight model, the output differs so much from what a conventional macroeconometric model with long run Classical features delivers that one can only conclude that the add factors are critical. (This impression is buttressed by the fact that Heritage CDA re-adjusted the natural or structural rate of unemployment — and hence simulated unemployment — without having any reported impact on any of the other variables changing; any model with a standard Neoclassical long run structure like the IHS Global Insight model will not be able to accommodate such revisions.)
Given that the supply responses are implausible, then the tax revenue results must also be questioned. That is because the positive response of tax revenues to reductions in the effective personal tax rate must be driven by the output response, and this is conditioned by the sensitivity of both labor and capital investment to the relevant after tax factor costs in the long term.
In this context, the simulation result that tax revenues are higher relative to baseline at the end of the sample, despite the fact that the effective personal tax rate is lower (Figure 5) makes perfect sense. It is the ultimate manifestation of the supply-side fantasy.
Figure 5: Difference between effective Federal personal income tax rate under Ryan plan and baseline (blue, left scale), and difference between Federal personal tax receipts, bn$, under Ryan plan and baseline (red, right scale). Source: Heritage CDA, Appendix 3.
Epilog: There have not been any really substantive responses to the various criticisms released directly by Heritage, except for this “pre-sponse” which does not address how the unemployment rate could be adjusted without any of the other forecast series being adjusted in a noticeable fashion. For quotes of William Beach’s responses, see: Slate1, Slate2 FrumForum. Here is a Bloomberg article quoting the (limited and skeptical) remarks of IHS Global Insight’s Nigel Gault who oversees the organization’s macro model, which Heritage CDA partly based their simulations on; similarly skeptical remarks in National Journal. Finally, EPI concludes, like me, that the key to understanding the Heritage CDA projections is to be found in the “add factors”. Chad Stone illustrates the original Heritage unemployment forecast (before they were revised into oblivion).
Update, 8:30am Pacific: Bruce Bartlett points me to a Macroeconomic Advisers analysis which documents their sense of incomprehension of the Heritage CDA assessment.
Update, 2:10pm Pacific: The Economist has its take on Paul Ryan’s intellectual hinterland.