# Implied Supply Side Elasticities from the Heritage CDA Simulations

Following up on yesterday’s post on the Heritage Foundation’s assessment of the Ryan plan, I thought it would be useful to see how the labor and capital supply elasticities that are implied in the simulations compare with the literature, for the benefit of my macroeconomics class. Unfortunately, I come up with some really odd numbers, so I must either be making a mistake somewhere, or the simulation is very odd. Update 4/10, 4:50pm Pacific: I added two graphs illustrating exactly how odd these numbers are.

Figure 1: Private nonfarm payroll employment (blue), baseline (dark blue), and simulated under Ryan plan (red). Actual data average of monthly data. Source: BLS via FREDII, and Heritage Foundation, Appendix 3: Simulation Results.

Figure 2: Real equipment investment, bn. Ch.05\$ (blue), baseline (dark blue), and simulated under Ryan plan (red). Source: BEA, and Heritage Foundation, Appendix 3: Simulation Results.

Labor supply elasticities

First consider the labor supply elasticity. 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 average baseline private nonfarm payrolls at 119.9 million, simulated at 121.5 million; the log difference is 0.0132. The average baseline personal tax rate is 0.184, and the simulated is 0.181. The log difference is 0.0025. I don’t have demand side elasticities, but assuming a perfectly elastic demand for labor gives me the minimum figure for the implied supply elasticity. Hence, substituting these figures into the formula leads to:

5.28 = (0.0132/0.0025)

This figure is 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. This disjuncture must mean something else is going on in the model (perhaps capital and labor are complements, or employment differs substantially from hours worked).

For reference, here are the elasticities used by CBO (reported earlier in this post):

Source: CBO, “The Effect of Tax Changes on Labor Supply in CBO’s Microsimulation Tax Model,” Background Paper (April 2007).

Investment response

Now consider the implied behavior of capital investment.

The standard rental cost of capital approach to modeling investment goes back to Dale Jorgenson’s classic 1960’s paper. The key parameter is the elasticity of the investment-to-capital ratio with respect to the rental cost:

ln(I/K) = γ rK

Where the rental cost is given by:

(1-u)rK = (i – πK – d)(1-z)PK

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 0.04972, the alternative 0.04596. 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:

0.07649 = 0.04972/0.65

and under the Ryan plan:

0.06128 = 0.04596/0.75

(I’m assuming a percentage point for percentage point change in the effective corporate tax rate, so there’s some slippage here). So the change in the rental cost of capital is 0.01521.

Now consider the change in equipment investment relative to the capital stock. Under the baseline, average equipment investment is 1.611 trillion Ch.05\$, under the Ryan simulation, it is 1.827 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 change in the investment-to-capital ratio is = 0.0385, the average investment-to-capital ratio over the next ten years is 0.2918 (assuming the net capital stock grows by 1% per year). Solving out for the elasticity yields:

γ = (0.0385/0.2918)/(-0.01521) = -8.67.

This figure is somewhat(!) above (in absolute value terms) the short run elasticity of 0.50 cited by, for instance, Gilchrist and Zakrajsek (2007) (their long run elasticity is about unity).

Now, I know that elasticities are supposed to be essentially partial derivatives, rather than total derivatives. But when the magnitudes are so far off, either I’m making a math mistake, or something really interesting is going on in the Heritage CDA’s combined microsimulation-plus-IHS Global Insight model.

So, if anybody can help me out, I’d be much obliged.

Update, 4/9 8:25am: Some readers might wonder why I spend time on the Heritage analysis. It’s because there are individuals out there who cite the projections from the Ryan plan (validated by the Heritage CDA analysis) as if they were serious, and compare them against CBO baselines. Take for instance Keith Hennessey’s 4/6/2011 post (which provided my first big guffaw of the day). By taking at face value the projections, he is taking at face value these implied elasticities.

Personally, people who have master’s degrees in policy analysis should know better. And that’s what I’m going to teach my students on Monday.

Footnote: I know it’s hard to keep up, but I wonder why Hennessey’s post of 4/6 made no mention of the CBO analysis of the Ryan plan, when it had been circulated on 4/5 (or why he made no update to the post to mention what was arguably an important document).

## 22 thoughts on “Implied Supply Side Elasticities from the Heritage CDA Simulations”

Once upon a time a national government who had an only congressman named Rep. Ryan and a source of tax revenue named the US economy. And all they had to live on was the tax revenue the economy gave every year. But one year the US economy gave very little tax revenue and they didn’t know what to do.
“What shall we do, what shall we do?” said the government, wringing her hands.
“Cheer up, US government, I’ll go and get work somewhere,” said Rep. Ryan.
“We’ve tried that before, and nobody would take you,” said his government; “we must sell the US economy and with the money, start a international lobbying group, or something.”
“All right, US government,” says Rep. Ryan; “it’s market-day today, and I’ll soon sell the US economy, and then we’ll see what we can do.”
So he took the US economy’s halter in his hand, and off he started. He hadn’t gone far when he met a funny-looking old right wing think tank, who said to him: “Good morning, Rep. Ryan.”
“Good morning to you,” said Rep. Ryan, and wondered how he knew his name.
“Well, Rep. Ryan, and where are you off to?” said the right wing think tank.
“I’m going to market to sell our economy here.”
“Oh, you look the proper sort of chap to sell national economies,” said the right wing think tank; “I wonder if you know how many supply elasticities make five.”
“Two in each hand and one in your mouth,” says Rep. Ryan, as sharp as a needle.
“Right you are,” said the right wing think tank, “and here they are, the very supply elasticities themselves,” he went on, pulling out of his pocket a number of strange-looking supply elasticities. “As you are so sharp,” says he, “I don’t mind doing a swop with you — your US economy for these supply elasticities.”
“Jeepers!” says Rep. Ryan; “wouldn’t you like it?”
“Ah! you don’t know what these supply elasticities are,” said the right wing think tank; “if you plant them overnight, by morning they grow right up to the sky.”
“Really?” says Rep. Ryan; “you don’t say so.”
“Yes, that is so, and if it doesn’t turn out to be true you can have your economy back.”
“Right,” says Rep. Ryan, and hands him over the US economy’s halter and pockets the supply elasticities.
Back goes Rep. Ryan to congress, and as he hadn’t gone very far it wasn’t dusk by the time he got to his congressional desk.
“Back already, Paul?” said his government; “I see you haven’t got the US economy, so you’ve sold her. How much did you get for her?”
“You’ll never guess, US government,” says Rep. Ryan.
“No, you don’t say so. Good boy! Five trillion dollars, ten, fifteen, no, it can’t be twenty.”
“I told you you couldn’t guess. What do you say to these supply elasticities; they’re magical, plant them overnight and —”
Well to make a long story short the moral of the story is…
What moral? After all, how can a story about a congressman who is fooled into taking magic supply elasticities, trespasses on someone else’s property, commits burglary, and then kills him offer a “moral lesson”?

2. 2slugbaits

Menzie I’m confused. You said:
Under the baseline, average equipment investment is 1.611 trillion Ch.05\$, under the Ryan simulation, it is 1.827 trillion Ch.05\$.
This can’t be right. That’s pretty close to the total investment component of GDP. The equipment and software piece is ~\$1T, with net investment being even less than that.

3. Menzie Chinn

2slugbaits: I’m just using the numbers from the Heritage CDA study, which I believe are gross flows. In any case, the deviation from baseline should be the number to give pause.

4. Ivars

Current USA debt growth rate has entered the unsustainable superexponential growth part of Sornettes-Johansen log periodic pre-crash oscillations, so crash and correction is inevitable in 2-3 years time, shaving of at least 20% of it (3-5 trillion!) in one year. Here I speculate what are the options, and devaluation with gold standard ( or similar) introduction seems to be the most likely one (as compared to default or pure hyperinflation):
http://saposjoint.net/Forum/viewtopic.php?f=14&t=2626&p=31678#p31678
Politically, such event will de-cooperate the West from emerging nations radically, causing internal political changes ( China, Japan if it still owns USA debt by then) and geopolitical consequences of such de-cooperation will be huge as they slowly emerge. After USA performs its haircutting operation in whatever way in 2013-2014, China will start changing its internal political course, 30 years of Communist New Economic Policy will stop, with all cosequences:
http://en.wikipedia.org/wiki/New_Economic_Policy
NEP ended when Great Depression hit the West. Same here, Great recession in action in the West, Chinese aiming to overcome the West fast.

5. CoRev

Ivars, I certainly wish you had not brought up the possibility that we MIGHT be just around the corner from a fiscal crash. Why should anyone even consider the bigger picture, when focusing on minutiae is so much less frightening.
Menzie, why have we not seen the same level of review over the Obama Budget Request?

6. Menzie Chinn

CoRev: The OMB (like the CBO) scoring did not include feedback effects. That is, neither allowed for tax cuts to affect output, and so economic effects were not being implied in those instances. So what would I say? Keynesian and supply side effects are zero’d out in the projections? Well, that only took one sentence, which hardly constitutes enough for a blogpost (and is in any case obvious to anybody who had been following Econbrowser posts on CBO and OMB scoring).

7. Ivars

Interesting citation from Keynes:
“John Maynard Keynes, perhaps the single most influential economist of the 20th century, said that, “by a continuing process of inflation, governments can confiscate, secretly and unobserved, an important part of the wealth of their citizens.” ”

8. Ivars

CoRev, this just came as an OBVIOUS realization as I slowly figure out how things work in the world, and the role of the USA in post war boom.:)
It (the USA debt downwards correction by about 20% in few years) kind of fits together with other things happening after 2008 crash. Things does not happen linearly, but are still predictable. But are they avoidable? Human nature needs to be reeducated to avoid them. That has not happened anytime as it requires really long term thinking for mortals. A contradiction.
Predicting fat tail events and taking them into account in their early development phase, when something still can be done.
I added few more thoughts and got a bit confused who will be involved in the haircut mostly. My perhaps wrong conclusion was participants of M2 and M3 money base. M0 and M1 may come out almost clean, no devaluation.
http://saposjoint.net/Forum/viewtopic.php?f=14&t=2626&p=31683#p31683
Does that sound right?

9. Ivars

I did some more predictions on USA crashing its debt by returning to gold standard. The value of gold, if this is done in 2014, came out around 5400-6000 USD/ounce.
I was wondering who will get the haircut. It seems it will be those mony instruments that form M2 and M3 above M1 and M0. Is that feasible? That would be a major upset as it involves domestic deposits as well as foreign and domestic short term debt.
http://saposjoint.net/Forum/viewtopic.php?f=14&t=2626&start=100#p31683
I may have got a bit confused, but definitely debt holders will suffer. Short or long term, or both?
But it will happen in some form, the correction ( reduction) of USA debt no later than in 2014.

10. CoRev

Ivars, I’m not sure how Money will be affected by a fiscal tipping point. I am fairly certain that we are headed for that tipping point, either due to inability to borrow in the amounts needed, or a deeper recession caused by inflation (but not hyper) triggered by a move away from the dollar standard.
I also see us approaching a tipping point toward WWIII. No, I am not a Glen Beck fan, but I have not seen the world with this much unrest in politically volatile and armed parts of the world.

11. 2slugbaits

CoRev why have we not seen the same level of review over the Obama Budget Request?
I take the real thrust of your question to be why hasn’t Obama put forward a deficit reduction plan. Well, he did have the deficit commission, but thankfully he appears to have had the good sense to ignore much of their recommendations. Still, sooner or later at least one of the political parties is going to have to present a serious deficit reduction plan. On the other hand, the overall outline of a viable deficit reduction plan is not all that hard to devine. We need to increase tax revenues and that means allowing the Bush tax cuts to expire plus some kind of VAT (say 2%). We need to cut spending on DoD & ag subsidies. And we need to address Medicare and Medicaid, which are the big problems. All else pales in comparison. But you don’t fix Medicare and Medicaid by just cutting the government’s share of the costs…that just shifts the costs. Cost shifting is not cost reduction. So all of those interests that are getting fat on growing medical costs will have to start a diet. This includes doctors, hospitals, medical labs, and Big Pharma. It also means Medicare should only pay for effective procedures. If seniors want to pay for ineffective procedures, then let them do so using their own money. And we need to remind the very old that they won’t live forever. A lot of medical costs are generated in the last few months of life. Medicare recipients should not expect the taxpayer to fund heroic efforts to squeeze out one more day of drug induced unconcious life on a respirator. Again, none of this should be a surprise to anyone. We just need to get past smoke screens like Ryan’s Roadmap.

12. Ivars

CoRev:
On WWIII I have so far made conclusions (based on Sornette’s work about population crash point) and the fact it deco-operation takes much longer this time than after recessions prior to WWI or WWII, also some other conclusions from graph pattern studies that WWIII will commence when Chinese military capabilities will match that of the combined NATO and Russia, which comes out around 2040-2060.
In global information age, things just happen slower, as people have difficulties to conceal their actions, so they act after longer deliberations. That also requires regime and mentality changes ( in the West- towards new form of fascism =real middle class rule (results over process) , in China- towards militarization and their model export), and that much takes longer time than in 1930 ties…
So that is quite far away, however, the first skirmishes are already on their way. However, these are by no means comparable to Japanese occupation of Manchuria in July 1931 or Russian- Japanese war in 1905 which were the first huge military conflicts after stock market/financial crashes.
I think we will see actions of similar scale, involving big countries directly on both sides, difficult to say where, in about 6-10 years from now. This time Japanese may be on the receiving end…
Problem is not that these clashes and WWIII is close or distant though, but the inevitability of them once it has started its small almost invisible GLOBAL log-periodic buildup of acceptable aggression levels which leads to their outlet in a crash – WWIII. How to change it early, NOW ( again, longterm thinking vs. human nature)
As it coincides in timing with predicted Global population correction (crash event), WWIII in 2040-2080 (or combined with some natural disasters) will reduce then existing global population by about 20% in first rapid reduction, which would be about 2-4 billion depending on population at that time. The length of WWIII will be also extended, about 30 years instead of WWII 6-7 years.
Are we so slaves to Nature that these things are inevitable or can they be dispersed by NOT ACTING like usual in early stages especially (NOW) ? Stop population growth, stop GDP growth?
Have a look at world population crash table in this paper Sornette Johanshttp://arxiv.org/abs/cond-mat/0002075 to see when WWIII may start, page 28 , table 2. The whole paper is a treat, and unique. It gives food for some thinking. And graph 36 of DJIA on page 26. . However, instead of DJIA one would need global stock index. But GLOBAL economic correction are at the same time as population, within errors of model and data.
Excuse me for such a long post. I hope it gets accepted, since I tried to give an answer to Your worrisome but true assessment of increasing aggression levels around the world and their potential consequences.

13. CoRev

2slugs, your plan may be as good as anyone’s. Have you done the math to see how much is needed in each category and how long before we balance a budget? Strangely, this is a relatively simple math problem, if we could just keep the politics out of it. ;-)) BTW, the Tea party members realize that.
Furthermore, you let your ideology override a relatively simple math exercise with this: “And we need to address Medicare and Medicaid, which are the big problems. All else pales in comparison. But you don’t fix Medicare and Medicaid by just cutting the government’s share of the costs…that just shifts the costs. Cost shifting is not cost reduction. So all of those interests that are getting fat on growing medical costs will have to start a diet.” Any cut will result in cost shifting. Cut them and pay for the remainder via taxes. Done! Lowering Healthcare costs without destroying the system or significantly lowering quality of care is a different, but related, problem.
Obamacare tries to do all in one bill while winning a political battle. It has failed in all three areas. Consider the logic of adding another huge, partially paid entitlement, to future budgets where unpaid entitlement spending is, by your own admission: “And we need to address Medicare and Medicaid, which are the big problems. All else pales in comparison.”
For all the times you have accused me of being unconcerned for the young because I am older, then you say this: “And we need to remind the very old that they won’t live forever.” Now, that’s funny. Anyway, it appears that you do not have experience in this area. If you had, the fallacy of this statement would be obvious. It is seldom the elder individual that makes those decisions.

14. CoRev

Ivars, I have different sensibilities to econ-political aggressions. It would appear we could already have reached the tipping point in the Middle East. I believe it is more likely to emanate from there than in the Far East. Nukes just make the danger level higher than the catalyst, religious fervor.

15. tj

2slugs,
I would prefer the elimination of personal and corporate write-offs coupled with a simplified tax code. Increasing tax rates on corp’s and the ‘rich’ within a grossly inefficient tax collection system is not the way to go, imho. Let’s make sure that corp’s and those in the upper income brackets are paying a fair effective rate. Posted tax rates are meaningless thanks to special interests.
Your callous attitude toward the elderly is appalling and offensive. Unfortunately, most of your progressive brethren share the same attitude. I have a living will, so you don’t need to worry about the government having to force anybody to pull my plug.

16. Ricardo

Ivars wrote:
Interesting citation from Keynes:
“John Maynard Keynes, perhaps the single most influential economist of the 20th century, said that, ‘by a continuing process of inflation, governments can confiscate, secretly and unobserved, an important part of the wealth of their citizens.'”
But did Keynes think this was good or bad? Hmmmmm!

17. Ivars

CoRev: “Ivars, I have different sensibilities to econ-political aggressions. It would appear we could already have reached the tipping point in the Middle East. I believe it is more likely to emanate from there than in the Far East. Nukes just make the danger level higher than the catalyst, religious fervor.”
You are right, I call them skirmishes compared to WWIII. The sensitivity of current Western population to a full scale war is one of the reasons it won’t commence early.
Though sometimes early bloodletting may help to avoid the big clash with much more disastrous consequences. I am being cynically rational here, but human nature won’t accept voluntary small pain today in exchange of unavoidable huge war later. That prefer the last , hoping ( in vain) it will never come.
Small conflicts have to be lived through and in fact HAPPEN in order to diffuse build up for big ones. But our sensitivities and life styles adopted over last 70 years would not allow anyone to make that decision.
What do you think of the USA making Anschluss of Canada in about 10-20 years to add resources? And occupy Mexico to add even more after that?. Mexico has oil and silver, Canada oil and gold etc. When will sensitivities accept such solution which will by that time become a matter of survival for the USA? I think its about 20 years away from today, around 2030.
I did not mean anything bad here. Just rational extrapolation of what is going on. But later than you think. Major powers will not get directly involved in opposing each other in next 10 years, that is for sure, what ever happens in the middle East.

18. CoRev

Ivars, I do not think we will strengthen political alliances with Canada, and definitely DO NOT see an occupation of Mexico within the next few decades. We have enough of Mexico’s problems and populace here already.
As for your assertion: “Major powers will not get directly involved in opposing each other in next 10 years, that is for sure, what ever happens in the middle East.” In ten years the ME will be a major power with nukes. I think we are seeing the ME Caliphate being formed today. The religious wars will be between Sunni and Shi’a to determine which religion leads it. The winner will then turn against Israel and the West.
We’ve taken this thread too far off topic.

19. Ivars

CoRev:”I think we are seeing the ME Caliphate being formed today.”
True. But still, more than 10 years. And its still FAR from a major power even if it had nukes. Today everyone has /will have nukes, or nuclear power stations which has worse effects when bombed than nukes potentially have when aimed. Nukes contain small amounts of radioactive elements compared to power stations.
Europe will deal with it initially, as it has been dealing with NA caliphates and Ottoman empire for centuries and millenia.
Let us hope there will be a thread that includes such comments as this is all pure economics, just not based on linear regression or efficient markets. Behavioral political economics.

20. Nemesis

http://imperialeconomics.blogspot.com/2011/04/pictures-of-peak-oil-and-greatest.html
While economists and political hacks argue over the number of angels that can fit on the head of a needle, the real story of the onset of the post-Oil Age Greatest Depression is presented, in part, in pictures at the link above.
Specifically, there has been no growth in civilian employment and private payrolls per capita since the mid- to late ’80s, the period the secondary peak for US domestic oil production occurred and the US economy was deindustrialized, financialized, and feminized.
Despite the post-crash surge, real retail sales per capita are only back to the levels of the recessions of ’08-’09 and ’00-’02.
The real 10-year avg. growth of private GDP per capita turned negative in ’10.
Now we have the pace of gov’t spending to GDP at a post-WW II high, and consumer credit outstanding, total gov’t spending, and US gov’t debt at unsustainable levels per capita.
Since US peak domestic oil production and the onset of US deindustrialization, we have grown the US economy using public and private debt and cheap oil imports (no more) at a rate 3-4 times the underlying sustainable rate of growth of US productive capital stock per capita; but this ended when peak global oil production occurred in ’05-’08.
Now it’s only a matter of time before a large enough plurality of the public “gets it” that real private economic activity per capita is no longer possible, and the post-Oil Age effects begin a mass-social conditioning toward a shift to a post-growth (decline and collapse) zeitgeist.
It is hereafter impossible to sustain the post-1920s oil- and auto-based, suburban/exurban/penturban, Disneyland US (world) economic model.
We are on the fiscal, economic, political, and social road to perdition. Adapting as quickly as possible to a much lower socially acceptable material standard of consumption is an imperative to resilience and ultimately survival for the vast majority of us.

21. 2slugbaits

CoRev Any cut will result in cost shifting.
You believe this because you have no formal training in economics. There is such a thing as deadweight costs that do not accrue as a benefit to anyone. Those can and should be minimized. There is also an important difference in cuts that eat into normal economic returns and cuts that eat into economic rents. A lot of the increase in healthcare costs is due to rent seeking behaviour. You can cut that without adversely affecting the quality or quantity of medical services delivered by the health sector. Yes, it will make the rentiers unhappy (they tend to vote Republican), but those are important cuts that should be made. Another point to keep in mind is that medical research tends to follow the money.
it appears that you do not have experience in this area. If you had, the fallacy of this statement would be obvious. It is seldom the elder individual that makes those decisions.
Well, I do have experience in this area. While it’s true that those in the last few weeks of life don’t usually have a lot to say about those decisions, they do have a a lot to say and demand from the government before they get to the end. They vote with an eye towards that end and demand that Medicare keep them alive at all costs. Remember the teabagger demanding that the government keep its hands off his Medicare?
tj My experience with living wills has been that people tend to change them just when they sense that the end is near. It’s easy to write a living will when you’re 30 advising people not to invoke heroic actions. But when the doctor tells the patient the bad news is imminent, those living wills are usually quickly amended. In my personal experience I can only think of one case in which that didn’t happen.
Your callous attitude toward the elderly is appalling and offensive.
Is it? What would you call Ryan’s plan? My approach is to reduce Medicare as a percent of the budget by reducig healtcare costs as a percent of GDP. Ryan just wants to reduce Medicare as a percent of the budget. That’s what’s wrong with Ryan’s plan. He just gives seniors a worthless voucher. He might as well give someone with documented suicidal tendencies a voucher to purchase life insurance. It’s ridiculous on the face of it.