Marginal Utility

by Tom Bozzo

Yves Smith finds Wolfgang Münchau of Eurointelligence wondering if U.S. official statistics massively understate inflation. Münchau buries his lede:

There is a website called Shadow Government Statistics, for whose accuracy I cannot vouch, which claims that the pre-Clinton era inflation index shows current inflation at close to 8%, while opposed official CPI inflation is only half that level. [link in original]

Let's forget for the moment about the accuracy of SGS. (Münchau is suspicious that the alternative inflation series is just an upward shift of the official series.) What of their methodology?

SGS's primer on CPI focuses on the supposed evils of accounting for substitution of goods in CPI, versus the supposedly "simple and straightforward concept" of measuring price changes using a fixed basket of goods, and to a lesser extent quality adjustments of price changes, or "hedonics." This is not promising. Why takes some explanation, so bear with me (I'd have installed a jump, but that's bloggered for the moment).

To set some bounds here, I'm not going to discuss the tendencies of policymakers to (sometimes) over-focus on "core" CPI (stripping out major expenditure categories) versus headline CPI. I sometimes sympathize with the inflation-ex-inflation crowd and sometimes don't. Nor will I get much into actual or incipient injustices in how CPI statistics are applied in the real world; count me as opposed, for instance, to indexing Social Security initial benefit levels to prices instead of wages.

With that out of the way, it has to be recognized that there is a fair amount of sausage-making in the compilation of statistics like CPI, but a great deal of it occurs because the "simple and straightforward" is not so easy in practice.

Take the idea of measuring price changes with the same basket of goods over long periods of time. This would be fine up to a point if all people consumed were commodities that are marketed in essentially the same form over long periods of time, but that just ain't so. If I were to make a comparison of prices between now and, say, 1980, how do I account for things in my field of vision (MacBook Pro, iPhone, organic blue corn tortilla chips, no-iron dress shirts, Gillette Fusion Power razor) that weren't marketed back then? How do you deal with existence of products called the "Chevrolet Monte Carlo" (our family car in 1980) existing in both periods but not being the same thing? The unavailabilty now of gasoline with added tetraethyl lead? Not so simple now, eh?

Yves picks up the substitution theme and puts the objection more succinctly than SGS:

What did the Boskin Commission think was out of line? According to Wikipedia:

The report highlighted four sources of possible bias:

Substitution bias occurs because a fixed market basket fails to reflect the fact that consumers substitute relatively less for more expensive goods when relative prices change.

Outlet substitution bias occurs when shifts to lower price outlets are not properly handled.

Quality change bias occurs when improvements in the quality of products, such as greater energy efficiency or less need for repair, are measured inaccurately or not at all.

New product bias occurs when new products are not introduced in the market basket, or included only with a long lag.

So the Boskin report would have us believe that if I switch from steak to hamburger because beef prices are up, we should only capture the change in how I consume (ie, inflation is new hamburger/old steak price, not new steak/old steak). That is patently bogus. Similarly, the outlet substitution seems rife for abuse ("Ooh, the number is going to be really bad this month! Can we find anywhere selling X cheaper so we can put that in the model instead?").

To give Yves some credit, we could have a deep philosophical discussion of what constitutes inflation. Some simple macroeconomic models avoid the question by positing a composite consumption good whose price change is trivially inflation. In reality, there is an enormous menu of goods whose prices change in different directions and magnitudes, and not all of those changes represent macro inflation (or deflation) phenomena. Otherwise, she's on shaky ground at best.

I'm an economist, so my inclination is to consider inflation in terms of the price of maintaining a level of welfare. This is not the same as maintaining consumption of any given set of goods. One thing people should get from such economics training as they may have (but often don't) is that no pattern of consumption is uniquely privileged. Usually, failures to recognize that (e.g., "Americans will never get out of their hulking SUVs") confuse preferences ("more of everything!") with the realities of choices under expenditure constraints, or the inability to remember that demand curves for consumer goods generally do slope downwards.

Yves and SGS both commit a foul by blaming the substitution bias concept on Boskin (and, at SGS, Greenspan) and implying that taking into account substitutions necessarily ratifies a lower standard of living. In fact, the substitution falls out of elementary economics of consumer choice and there's no reason why CPI changes incorporating substituion need imply a reduction in living standards.

Suppose there are only two goods in the economy, let's say chicken and beef, and a representative utility-maximizing consumer chooses to buy two pounds of each given today's prices and budget B0, giving the consumer utility of U0. Then the price of beef increases, while the price of chicken and the budget stay the same. The consumer can no longer afford to buy two pounds of each; instead, consumption of beef will fall, consmption of chicken will rise relative to beef (maybe, or maybe not, in absolute terms), and the consumer will get a lower level of utility U1.

Now let's say that we want to calculate an inflation index for this situation. One approach — my preference, from above — is to figure out by how much the consumer's budget would need to be expanded (to B1) to get back to utility U0. This amount, by definition, could not be said to make the consumer worse off. The candidate inflation measure here is (B1/B0)-1. What we can say about this amount of money is that (1) with it, the consumer still will buy more chicken relative to beef, and (2) the consumer will not be able to afford the original two pounds of each. In accord with my welfare-centric concept from above, this preserves the original welfare level here, not the consumption levels. As far as calculating a hypothetical CPI consistent with this concept, to get an equivalent of (B1/B0)-1 from the price changes, we have to change the weights on chicken and beef.

(Added in response to Ken's comment.) This is shown graphically below — this is cut-and-pasted from Deaton and Muellbauer's Economics and Consumer Behavior (Cambridge, 1980).

The original equilibrium is at point A (on indifference curve U0), then moves to B when the price of beef (q1) increases. The new equilibrium with compensation to return to U0 is at point C; note that A is outside the associated budget constraint leading to C (dashed line). The graphical representation of pushing the new-price budget constraint back through A is left as an exercise for the reader.

It follows that we'd need to add even more money (to B2>B1) to the previous scenario for the consumer to again be able to afford the original two pounds of both chicken and beef. Obviously, (B2/B0)-1 will give a higher "inflation" measure. What would happen if the consumer had B2 to spend? Put simply, the consumer wouldn't choose the original mix of two pounds each of chicken and beef. At the higher price of beef, the last bites don't provide marginal utility (!) in excess of the price, and the consumer still will consume relatively more chicken. The consumer will also get more utility, U2, than U0 from the re-optimized choice.

I'm not opposed in principle to making people better off, but if the goal of an inflation measure is to tell us what people need to be made whole given some set of price changes, then this measure overshoots its goal. In any case, far from being "patently bogus," reweighting of the price changes is necessary to properly capture the welfare consequences of price changes for h. economicus. I grant that H. sapiens may think that change is bad per se and thus be made (at least temporarily) unhappy, but whether (let alone how much) to compensate people for that is no simple matter.

Outlet substitution is more straightforward. Partly there's a technical issue regarding how changes in points of purchase are incorporated in CPI, the upshot of which is that to the extent consumers do switch to lower-price outlets, CPI doesn't reflect the savings (see here). Unreality can't be claimed here, since real consumers actually search for low-price outlets for the goods they purchase, at least to some extent. But "hey, let's look for a low-priced outlet to deliver sufficiently low CPI" isn't how the measurement is done.

SGS takes on the quality bias issue, misrepresenting how the "hedonic" quality adjustments work:

Hedonics adjusts the prices of goods for the increased pleasure the consumer derives from them. That new washing machine you bought did not cost you 20% more than it would have cost you last year, because you got an offsetting 20% increase in the pleasure you derive from pushing its new electronic control buttons instead of turning that old noisy dial, according to the BLS.

The notion that the quality improvements directly offset — or, in the case of goods like computers with rapidly improving quantitative specs, even proportionally offset — price increases is simply wrong. If anything, some of the adjustments could be said to be conservative.

For instance, as I'd noted back in '05, my then-new computer's specs were in the ballpark of 20x or more better than those of one of its predecessors, while the corresponding deflation factor over roughly a decade was only 10x. A remaining objection is that someone who bought a $3,000 computer 10 years ago isn't buying a $300 computer now. But, conversely, the $3000 computer of 10 years ago probably isn't marketable for $300 now, even in mint condition.

A better objection, to which there may even be some substance, is that quality adjustments are unevenly applied, and in particular are less likely to be applied to areas of quality deterioration (say, air travel). I don't happen to think that an outbreak of quality deterioration fairly characterizes personal consumption as a whole, though.

In summary, then, there's no reason to think that bringing CPI methods back to the dark ages would conceptually improve CPI as an inflation measure. Nostalgia for those methods is misplaced.

Labels: Economics, Inflation