Note:  I’m pretty sure there is an error in the example that I am about to provide, and if so I know my commenters will find it.

Let’s suppose you have $10,000,000 for retirement.  Sounds pretty good, doesn’t it?  How much would that enable one to spend on consumption each year?  Well it depends on your investment choice, but surely one can’t go too far wrong by following the investment advice of a Nobel-winning finance professor:

The Magic Number: 4%

What It Means: This is another spending guideline. It suggests that a retiree spend an inflation-adjusted 4% of his or her total retirement assets each year, keeping the balance invested with a mix of stocks and bonds.

What’s Wrong With It: No less an authority than Nobel laureate William Sharpe, professor of finance, emeritus, at the Stanford Graduate School of Business has written extensively about this “rule” and why it can ultimately be harmful.

The rigidity of the spending plan is among its problems. If a portfolio underperforms, staying the course is a clear path to running out of money. When returns are better than expected, there is an unspent surplus.

Sharpe offers an alternative to the 4% rule. Instead, invest in TIPS (Treasury Inflation-Protected Securities). If those returns prove insufficient, an investor can always dial up portfolio risk and seek better returns.

I can see the advantage of this strategy.  You preserve your nest egg (in real terms), and you live off the interest on the $10,000,000 investment.  So let’s see how it works out.  I will take a fairly simple example, where the money is invested in 10 year TIPS, and the inflation rate is 2%.  10-year TIPS are currently yielding 1.26%, which would provide an annual income of $126,000, indexed to inflation.

But wait, the income is taxable.  So maybe you only have around $90,000 to spend after taxes.  Still that provides a comfortable lifestyle for the average couple.

But wait, I seem to recall reading that the tax on TIPS applies to both the real interest payments and the inflation adjustment.  So let’s assume that there is 2% inflation, which is roughly the recent trend rate of inflation.   Now your “taxable income” will be $326,000, which puts you into a pretty high tax bracket.  Let’s assume your average income tax rate on $326,000 is about 35% (it’d be lower today, but Obama has big plans.).  In that case you’d have a tax liability of $114,900.  Still, it seems like you’d have a lot of money, even after taxes.

But wait, the $200,000 inflation adjustment isn’t really “income,” it is merely a nominal adjustment in the principle invested in your TIPS, which keeps its real value stable.  It’s not like the Treasury sends you a check each year for $326,000; your actual “income” is still just $126,000.  After you pay your $114,900 tax liability, your net after-tax income on the $10,000,000 investment is $11,900/year.  I hope you like dogfood!

Seriously, I know there are all sorts of strategies that can result in higher retirement incomes.  You can take advantage of our finite lifespans by buying an annuity, for instance.  Obviously someone with $10,000,000 would do fine, more than fine.   But I do have a couple serious points to make:

1.  From my perspective, the state employees who have pensions with COLAs have a pretty sweet deal.  If I was 62 I’d rather have $65,000 a year for life, adjusted for inflation, than $1,000,000 in a 401k.  Peace of mind.  BTW, the average 55-64 year old has $69,127 in their 401k.  Time to start saving folks!  (Full disclosure, I have a 403b, which is similar to a 401k.)

2.  Both wealth inequality and income inequality data are extremely misleading, for all sorts of reasons.  This is just one of those reasons.  I doubt there are too many people who invest in the way I suggested.  Many of the TIPS are probably held in tax deferred accounts, for instance.  But there are definitely some wealthy people who report large interest incomes on their tax forms.  And if they invest conservatively their actual real after-tax income might be only a tenth, or even one one-hundredth of the reported income that shows up in Gini coefficient calculations.  I’m not saying this particular problem is enough to seriously distort those statistics.  It probably isn’t.  But there are also many other flaws that make the indices virtually worthless (flaws which I will explore in future posts.)  In fact, statistics showing consumption inequality are the only valid way to measure economic inequality.  Both income and wealth data are flawed in so many ways as to be nearly worthless.

3.  When you read left-wingers complain that workers pay X% tax rates and billionaires only pay Y%, keep in mind that the statistics they are quoting are completely meaningless.  They are assuming that a 35% tax rate actually means 35%, whereas in the example I just gave the effective tax rate was over 90%.  Again, I am not saying this sort of example is common, but even if our tax system were 100% indexed to inflation, the tax rate comparison between labor taxes and capital income taxes would be meaningless, as capital income is double taxation of labor income, and thus the only efficient and fair tax rate on capital income is zero.

Here’s my optimal tax system:

1.  A progressive consumption tax or a progressive payroll tax.

2.  A set of Pigou taxes (carbon, not cigarettes)

That’s all.

Krugman has suggested that Ryan Avent and I look at the literature on labor supply elasticities.  Or perhaps, as Ambrosini suggests, just the half of that literature with which he agrees:

Today he says that Sumner and Avant should read the literature on macro vs micro labor supply elasticities. Well, ok, he says they should only read half of that literature. Over the last decade, Prescott has been doing a lot of work showing that differences in taxes explain differences in employment and hours worked between Europe and the US. I think his Nobel speech was about this.

The micro people threw fits though because their estimates of the response of labor supply to tax changes is much less extreme than Prescott’s finding suggest. They basically find labor supply curves are vertical. This would mean that taxes simply can’t have an effect on labor supply.

For a while, these guys had me convinced because, in general, micro/labor types do a much better job of identification and I trust their estimates more than I trust macro estimates. More recently, however,  macro people¹ have been making the case that the “labor supply elasticity” estimated by the micro people is different from the “labor supply elasticity” the macro people estimate. The difference isn’t due to statistical methodology, we were just calling two different things the same thing.

Of course, its the macro elasticity that matters for tax policy, though. Prescott’s work (and not the paper that PK links to) is the place to go for understanding differences between Europe and the US. He says that difference is due to differences in tax and transfer policies.

I haven’t studied the recent literature in this field, although of course I was aware of the Prescott study.  But if Ambrosini is right I feel much less ignorant than I feared.  Back in the 1970s at Chicago we were taught that you needed to use income compensated supply and demand curves when examining tax policy.  I just assumed that everyone knew that when government collected taxes, the money was injected back into the economy through various means.  I guess this insight only recently reached certain segments of the profession.  Now of course the progressives that favor high taxes can always argue that the government expenditures go to activities that are so worthless that society is impoverished.  In that case people keep working hard for the same reason Bangladeshis work hard.  But I’m going to assume they don’t want to make that argument. 
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Ryan Avent raises this interesting comparison:

Japan and France are both highly developed countries, with a high level of technological and institutional congruence. Their levels of per capita output are nearly identical. But France raises much, much more revenue as a share of output than does Japan. Why should revenue share have, apparently, very little effect on that output relationship but a comparatively enormous effect on the relationship between outputs in western Europe and America?
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This will be the last time I post an excerpt from my manuscript, although I will add some graphs next week.  But first a few comments on items in the blogosphere:

1.  Sweden’s Success:  Yglesias and Mulligan are both right (and Krugman’s wrong.)

I came across this interesting item in Matt Yglesias’ blog.

My rule of thumb for thinking about the global recession is that whenever you hear claims that some country has weathered it unusually well because of Favored Policy Initiative A, you ought to first ask yourself if it’s not really just an exchange rate issue. That seems to be the story of Israel’s relatively mild recession and I don’t think any effort to explain a country’s successs””especially a small country””that doesn’t take this into account isn’t very credible.

For example, Casey Mulligan seems to think that tax cuts and reductions in the size of the social safety net explain why Sweden’s unemployment rate hasn’t increased as much as Denmark’s. A different theory would note that though Denmark and Sweden are both small, open economies with generally high taxes and generous social expenditures, Sweden’s currency floats whereas the Danish Kroner is pegged to the euro. Consequently, the outbreak of the recession was associated with a substantial reduction in the price of the Swedish Kroner relative to the DKK/euro, the dollar, or the yen:

Despite being a non-economist, Yglesias has very good instincts regarding the importance of AD policies.  Then I checked the Mulligan post, and found this quotation, which is actually from Stefan Karlsson’s blog:

“In Sweden, the centre-right government elected in 2006 has implemented significant income tax reductions (and payroll tax reductions), particularly for low earners while at the same time, unemployment and sick leave benefits have been cut and it has become much more difficult to be able to receive such benefits.

In Denmark, by contrast, even though it too has a formally “centre-right government” it has largely refrained from reducing taxes or government hand-outs, and it has more specifically lacked the focus of their Swedish counterparts in strengthening incentives to work by reducing unemployment benefits and taxation of low income earners.”

This is the sort of policy mix that I keep advocating; efficient supply-side policies, lower payroll taxes to offset nominal wage stickiness, and expansionary monetary policy (the Swedish kroner depreciation that Yglesias mentioned.)  In contrast, Krugman has argued that lower unemployment benefits and reduced labor costs may reduce AD.  And those effects can’t be offset with monetary policy because we are stuck in a liquidity trap.  Somehow the Swedes found a way to adopt a more expansionary monetary policy than Denmark, despite near-zero rates.  So how did things work out for Sweden as compared to Denmark, which didn’t follow my policy mix?  Here’s Mulligan again:

Denmark’s employment has fallen 5% in the past year while Sweden’s is unchanged.

My favorite welfare state let me down last year.
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Ryan Avent criticized my recent defense of Mankiw:

That tax rates are driving the disparity in incomes is belied by the very data presented in Mr Mankiw’s initial post. His computation uses four economies with per capita incomes clustered closely together: France, Germany, Britain, and Japan. But while per capita outputs in those countries are very similar, the revenue shares of GDP are wildly different, ranging from 46.1% for France to 27.4% for Japan. And of the four, Japan’s per capita income is the lowest.

At no time did I argue that tax rates drove the disparity between the incomes of all countries.  Indeed I cited the Congo and Afghanistan as examples of how that could not possibly be true in all cases.  I also contrasted Italy and France.  Rather I suggested that the disparity between Western Europe and the US might be largely driven by different tax rates.  I’m not the only one who has made that suggestion, Prescott has done studies that reached similar conclusions.  I seem to recall that when French tax rates were at US levels (about 50 years ago I believe) the French worked just as much as Americans.  If so, then this would seem to conflict with the argument that greater European leisure time reflects cultural differences. 
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