I think that I use the term "money illusion" somewhat differently from how many writers use it, though I think my use is slightly more appropriate to the ordinary use of those words separately and is a more useful and coherent phenomenon. In either case, the essential point is that a dollar five years from now is different from a dollar now, and that mistakes can be made by decision-makers who assume otherwise. One of the ways in which this manifests itself is in a maxim against "dipping into capital", which holds that retirees, endowed non-profits, and those people from Jane Austen novels who "had" an income of so-many-pounds per year unconnected from any employment, should only spend the "income" derived from retirement savings / endowment / whereever that money came from, and never sell down the asset. There are surely circumstances in which that's a good rule of thumb for boundedly rational agents to avoid worse mistakes, but it seems in part to suppose that one thereby has "the same amount" of capital later as one has initially. In solving a Ramsey problem with a perfectly liquid instrument of savings, however, there is no distinction between "principal" and "interest", and if a risk-free asset pays an interest rate that varies with time, the optimal solution will typically involve selling some of the asset to increase consumption at certain times and buying more of it at other times to save for later; the exact result will depend on other details, but even if the dollar amount of savings tends to return to some constant dollar amount over long period of time, it is rarely optimal to keep it exactly constant all the time.
A related phenomenon is "reaching for yield": when investors, especially bond investors and often in denial, view the interest rates available on safe investments as insufficient, they may become more inclined to buy the bonds of riskier companies, which tend naturally to pay higher rates of interest, until, of course, they don't.[1] While this is often done by investors who just seemingly can't really believe that interest rates are as low as they are, and feel entitled to the interest rates that prevailed in the Carter administration, sometimes the people who do this are people drawing a line between "capital" and "income", and looking to turn a higher portion of the expected return into a form that their rules of thumb will allow them to spend. They would often, perhaps generally, be better off buying a bond with a 3% yield and selling off 1% of their holdings each quarter[2] than buying a bond with a 7% yield so that they don't have to sell it.
This post is loosely triggered by a badly flawed column at wsj.com yesterday; a somewhat more coherent version of its argument, though, is that an environment of low interest rates encourages income investors to buy stocks with higher dividend yields[3] and thereby reduces investment as companies use cash to raise their dividends instead of spending it on research and development.[4] One of my favored models of a liquidity shock, especially when thinking about things intuitively, is as a suddenly high private discount rate on cash; I suddenly need dollars very urgently, such that putting them off until next month or even perhaps next week is very costly to me in some sense, so that I'll take $1000 now instead of $1100 next week or $1300 next month; in particular, if I have an asset that I think is, in some longer-run sense, worth more than $1100, I might find liquidating it in a hurry at $1000 to be better than whatever consequences would befall me if I spend time trying to find a better price. More generally, I've treated the ability to sell an asset as giving it some "just in case" value; it's more attractive than an otherwise similar illiquid asset because I don't know whether there will be a liquidity shock. The ability to sell all at once if necessary, though, and the ability to sell a bit at a time according to a previously anticipated schedule, are likely at least to be closely related, if not, in presence of systemic events, to be exactly the same.
Let's incorporate the "don't dip into capital" mentality by supposing that, even if assets could be sold easily for cash, that the owner won't sell them; they are, if you will, practically illiquid because of the owner's behavioral biases, even though the market exists. With the realistic incomplete markets, the marginal discount rate of a serviceable amount of cash for most people most of the time is likely to track general interest rates reasonably well; somewhere between what you get from relatively safe savings and the rate at which you could borrow if you needed to.[5] If it weren't in that range, you'd presumably borrow or save more or less than you do. If you're intent on putting most of your money into assets that you refuse to sell, though, the private discount rate and the general market rates have considerable room to diverge, and the conditional optimization problem requires that you discount future cash flows at your own, private discount rate — which, if the cash flows tend to be very long term, is likely to be somewhat high.[6] If dividend yields are low, presumably because the markets think the values of stocks lie more in their payouts in the distant future than their payouts in the next year or two, then if most of your income is from stocks that you refuse to sell, your private valuation of a stock that you're considering buying (and, we suppose, holding forever) should be driven by expected dividends discounted at that private rate — thus valuing higher dividend yields at a higher fraction of their market value than low dividend yields. The same would apply to bonds; this, then, may be a serviceable "reaching for yield" kind of model to use where we think we have agents of that sort we want to incorporate into our financial/economic model.
[1] Until 30 years ago, the extra interest rates that risky companies paid on their bonds actually did more than make up for the risk of default by a sizeable margin, and a diversified portfolio of such bonds that could absorb losses on a few bonds would more than make up for it in the extra income payments. That gap generally tightened in the 1980s, and, while it has still been generally positive in the last 25 years, it's more of a strategy that generally gets a reasonable premium for a risk, not a reliable way to secure a high return. That said, of course some high-yield bonds will in fact make all of their scheduled payments without default, but it shouldn't be forgotten that there's a reason they're trading with a higher yield to maturity than the safer portions of the bond market.
[2] I mean, this is false, and in an important way; corporate bonds are much more expensive to buy and sell than large-cap stocks, for example, and I'll note later in passing how illiquidity might justify the behavior to some degree. The right approach is probably to buy the 3% bond, but not with all of your money; keep some of your money in shorter-term instruments that mature as you'll need the cash.
[3] Note that here the caveat in the previous footnote has much less force; you can sell down stock holdings somewhat gradually with relatively little in the way of transaction costs.
[4] A bit off topic, but a quick list of problems with the column: 1) it notes that companies are buying back their shares, which runs exactly counter to the idea that they're turning long-run share value into income; holders have to sell their shares to receive the payouts; 2) the corporate sector as a whole is holding a lot of cash on balance sheets right now, even after giving some of it to shareholders; a failure to engage in R&D is not plausibly due to a shortage of cash caused by shareholder payouts; 3) those low interest rates also enable most companies to borrow money cheaply, financing either payouts to shareholders or R&D or both that way, and it isn't reasonable to imagine that higher payouts to confused shareholders are anywhere near the scale needed to cancel out that effect.
[5] This range may be big compared to some things, especially in the short term, but on the scale of years will be at least reasonably well defined.
[6] E.g. if you "have an income" that is safe and expected to grow for decades, you might be motivated to smooth your consumption in time, spending more now and less later, rather than living on beans now and in luxury later, even if you had to pay a somewhat high interest rate in order to borrow to move that consumption sooner.
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