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Pittsburgh Tribune-Review: “Calculating real wages”

In my February 19th, 2006, column for the Pittsburgh Tribune-Review I did my best to explain some pitfalls of adjusting changes in nominal into changes in real prices.

(For some reason, all but two of my Trib columns from late December 2005 through early April 2006 are unavailable on-line. They appeared only in print. I thank the editors of the Trib for sending to me the texts of these columns.)

Calculating real wages

Like many pundits today, New York Times columnist Paul Krugman often asserts that middle-class Americans have suffered stagnant income growth since the mid-1970s. In one of his columns last June, Krugman summarized his gloomy assessment of economic performance in America over the past three decades: “The middle-class society I grew up in no longer exists.”

He’s right. The society that he (and I) grew up in indeed is history. But this fact deserves applause because ordinary Americans standard of living today is so much higher than it was 30 years ago.

I admit that standard-issue data mask the truth of my claim. Most notably, after adjusting for inflation, wages of the average worker haven’t risen since the mid-70s — while during the previous 30 years these wages escalated impressively.

But data can be tricky. For a variety of reasons, the data relied upon by Krugman and others to paint a picture of an economy that’s failing the middle-class are incomplete or misleading.

One of the trickiest maneuvers for statisticians is to adjust wages for inflation. This adjustment is typically done by (as economists say) deflating actual wage numbers by the Consumer Price Index (CPI). In theory, as the average of all consumer-goods prices rise, so does the CPI. And the higher the CPI, the higher the reported rate of inflation and, hence, the greater the amount by which actual wages must be discounted to translate them into “inflation-adjusted” (or “real”) wages.

Average hourly wages of private-sector workers in 1975 were $4.73; today this figure is $16.34. But when deflated by the CPI, we find that today’s average wage is worth only $4.62 in 1975 dollars. Looks bad for the average wage earner.

But can we trust the CPI? I think not. For a variety of reasons, it significantly overstates the amount of inflation we’ve suffered — and, thus, it misleads us in estimating changes in real wages over time.

Let’s explore in some depth.

To calculate inflation, statisticians cannot literally look at all goods and services that consumers buy. Instead, statisticians who compile the CPI choose a “basket” of goods and services that represents what the typical American family purchases. Changes in the prices of these goods and services are then used to measure inflation.

How, though, to select which goods and services to put into this basket? The obvious answer is to choose those items that ordinary consumers routinely buy. Putting in a loaf of bread makes sense; putting in a Tahitian vacation does not.

The problem arises because the set of things consumers routinely buy is itself affected by prices. The lower the price of something, the more likely is the typical American family to buy that something. In contrast, something whose price is quite high won’t be routinely purchased and, hence, isn’t a good candidate for inclusion in the CPI basket.

Prices, though, change over time. Because consumers can and do switch their consumption patterns to adjust for these price changes — buying lesser quantities of items whose prices rise and buying greater quantities of items whose prices fall — the CPI basket chosen today gives too little weight to items whose prices fall tomorrow and too much weight to items whose prices rise tomorrow.

The result — the CPI overstates inflation.

Here’s an example to make the point clearer. Back in 1972, basic pocket calculators cost $100. They were so expensive that ordinary Americans didn’t buy them. So statisticians at the Bureau of Labor Statistics understandably excluded calculators from the basket of items used to determine the CPI.

As time passed, of course, the price of calculators plummeted. A calculator similar to one priced at $100 in 1972 sells today for about $7.95. (In real terms, this is a price decline of about 98 percent.) So, ordinary Americans now routinely buy calculators. But because calculators weren’t suitable to be added to the basket of items used for calculating the CPI until their prices dropped and they became affordable, much of the price decline of calculators was ignored by the CPI.

Relatedly, as consumers substitute away from goods whose prices rise and into goods whose prices fall, the relative importance to consumers of these higher-priced goods declines as the importance of the lower-priced goods rises — but the weights that the CPI gives to these goods aren’t immediately adjusted.

The result is that, in the CPI, items whose prices rise are weighted too heavily while items whose prices fall are weighted too lightly — or (as in with the calculator) not at all.