Semi-Daily Journal Archive

The Blogspot archive of the weblog of J. Bradford DeLong, Professor of Economics and Chair of the PEIS major at U.C. Berkeley, a Research Associate of the National Bureau of Economic Research, and former Deputy Assistant Secretary of the U.S. Treasury.

Saturday, December 23, 2006

I'm puzzled by McGrattan and Prescott, "Taxes, Regulation, and Asset Pricing"

A plea for help: Can somebody help me make sense of McGrattan and Prescott's argument?

McGrattan and Prescott, "Taxes, Regulation, and Asset Pricing": [Since World War II] the real before-tax return on the stock market should have been about 8 percent on average, as it was.

The real before-tax return on equity is the sum of three returns: the income return, the anticipated capital gain, and the unanticipated capital gain. The income return is the ratio of dividend to price. This ratio has been high, over 3 percent, for much of the postwar period because high tax rates have implied a low price of equity. Recently it has come way down and is now a little over 1 percent.

The anticipated capital gain is equal to the growth rate of productive assets, which was roughly 3.5 percent per year and is now down to around 3.3 percent.

The unanticipated capital gain is the growth in the price of equity due to unanticipated changes in tax rates. This growth rate has changed, falling from the range of 1 to 2 percent to 0 percent.

Adding these rates, we would expect an 8 percent (e.g., 3+3.5+1.5) real before-tax stock return in the early postwar period and, barring any further unexpected changes in tax rates, a return in the future that is a little over 4 percent (e.g., 1+3.3+0).

This raises the question, why was debt held if equity earned such a high return? In the early 1960s, over one-third of the 1.1 GDP of debt held directly or indirectly by households was held as pension and life insurance reserves. At that time, almost all of the assets held in these reserves were debt assets. The reason is that there were legal constraints imposed on fiduciaries to ensure sufficient liquidity for timely distributions and to ensure prudent investing.

A large amount of debt assets were also held directly by households for liquidity purposes. For some households in the early postwar period, debt assets were their main avenue for saving because transaction costs made holding a diversified stock portfolio infeasible.

An important corollary of our findings is that there is no equity premium puzzle in the postwar period. Mehra and Prescott (1985) found that the high return on equity relative to debt was puzzling because theory says that the premium for bearing non-diversifiable risk is small. Their finding lead many to conclude that growth theory cannot account for the historical facts concerning asset prices and returns, unless a fundamentally different preference ordering is assumed. We find that this is not the case once we take into account observed changes in taxes and regulations...

The way I see it, the return on equities re is equal to the sum of the dividend yield d and the capital gain g:

re = d + g

And the capital gain g can be divided into an expected component E(g) and an unexpected component g - E(g):

re = d + E(g) + (g - E(g))

McGrattan and Prescott say that this third component is 1.5% per year in the post-WWII U.S., due to unexpected reductions in taxes on capital income, and I understand that and why they say that and I agree that it is a reasonable estimate.

re = d + E(g) + 1.5%

McGrattan and Prescott then say further that E(g), the expected capital gains component, is equal to the rate of growth of real GDP, which is the sum of labor-force growth and the rate of growth of labor-augmenting productivity, which they say amounts to 3.5% per year. I agree that the sum of labor-force and labor-augmenting productivity growth is about 3.5% per year, and I agree that we can treat the U.S. economy as near enough to a steady-state with a constant capital-output ratio to say that the stock of productive assets is growing at that same 3.5% per year. But the growth rate of the stock of productive assets is not equal to expected capital gains. Capital gains plus net issues--call it ni--equals expected capital gains:

E(g) = ni + 3.5%

Which gives us:

re = d + ni + 5%

At this stage I am expecting McGrattan and Prescott to make an argument about why it has been the case that d=3% and ni=0% in the post-WWII economy. It doesn't come. Instead, they just assert that because d has been 3% "we would expect an 8 percent... real before-tax stock return" and "there is no equity premium puzzle in the postwar period."

This makes no sense to me. Suppose stocks had sold for half the value they actually have, so that dividend yields were 6% over the early post-WWII period. Would they then say that "we would expect an 11 percent real before-tax stock return" and "there is no equity premium puzzle"? That dividend yields have not been much lower than they were is not an explanation of but a feature of the equity premium puzzle.

If McGrattan and Prescott want to provide an equilibrium explanation for the 8% real return and claim that it is not puzzlingly high, then aren't they obligated to provide equilibrium explanations for all the pieces of it? We need to understand why the average dividend yield was 3% (rather than 6% with prices half their actual levels or 1% with prices three times there actual levels) if we are going to see this as an explanation rather than as an accounting identity: given that returns were so outrageously high and that capital gains were roughly 5%, dividend yields had to have been 3%. That's not an explanation of why returns were so puzzlingly high. That's a consequence

What am I missing here?

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