Adjusting Compensation for Geographical Differences

Adjusting Compensation for

Geographical Differences

Dan A. Black

Harris School

Three parts of the talk

• First, I will give you some background about prices across geography and how markets handle this problem

• Second, I will tell you: “You cannot • Second, I will tell you: “You cannot

correctly do what you are charged to do” • Third, I will offer you some

recommendations on what I think you should attempt to do

Price indices

• Typically, a price index is used to measure prices changes across time

• Price indices answer the question: How much does it cost to purchase a bundle of goods and services today relative to the base period?

• This is largely a well posed problem that the BLS • This is largely a well posed problem that the BLS

attempts to provide in their PPI or CPI indices

• You need a geographic cost-of-living index: By what factor must I adjust base location expenditures to leave the consumer equally well off?

• BLS does not produce such geographic cost-of-living indices. It produces metro area price indices

BLS city specific indices

• According to the BLS:

– Comparing the CPI for an area to the U.S. CPI or to the CPI for another area gives an indication of differences among the areas’ rates of price change. In other words, such a comparison

indicates whether —over time—prices of items that consumers in one area tend to buy have risen more or less rapidly than the prices of items that consumers in another area tend to buy. It prices of items that consumers in another area tend to buy. It does not indicate _{whether the average level of prices in an}

area is higher or lower than the average level in another area.

• BLS norms these indices to have the same value in their base year

• Why? Because the BLS does not want to construct regional cost-of-living indices

What is a price index?

• Many flavors, but let me suggest we think about the Laspeyres price index

• A Laspeyres price index ask the question: “How much do I need to today to purchase “How much do I need to today to purchase the bundle of goods and services that I

bought in the base period?”

1 0 1 0 0 i i i i

p x

P

p x

=

∑

∑

What is a price index?

• This is simple: Now we only need two things: prices and quantities

• We have surveys that measure what people consume and we have surveys to see what consume and we have surveys to see what prices are so we have data

• Why not simply construct an index for Buffalo using San Francisco as a base location such

as: ₀ 0 Buf i i Buf SF i i

p

x

P

p x

=

∑

∑

What is a price index?

• This would be a very bad idea because, of course, Buffalo is different than San

Francisco

• Most people strictly prefer San Francisco • Most people strictly prefer San Francisco

to Buffalo so we want people to have to pay for the privilege of living in San

Francisco

• Let us look closer at both the prices and quantities in our index formula

Markets

• An area in which buyers and sellers interact to exchange resources

• “When world proletarian revolution takes place, the Soviet will have to keep one capitalist country so we know how to price our products.”

Old Soviet Joke Old Soviet Joke

• Markets do a good job of determining the economic cost • How big is a market?

– Value of the item

– Density of sellers and buyers – Transportation costs

• Problem: No real competitive market for medical services

Labor markets

• Firms and workers interact to exchange labor

• The more valuable the commodity, the larger is the potential market

larger is the potential market

• Again, transportation or commuting costs will play a critical role

• Workers and firms may change location, about which I will have much more to say

Labor markets

• Employers and employees interact to determine market prices

• Employers seek to pay the low wages for a given worker • Employees seek high wages

• In the absence of externalities, you cannot provide • In the absence of externalities, you cannot provide

another allocation that makes all the participants better off

• You might hope that the labor market has solved your indexing problem

• Let us look at some of these prices to see the labor market has solved your problem

Market for truck drivers

• Look at white, non-Hispanic male truck drivers who are 25 to 60 years old

• Exclude people with advanced degrees • Consider self-employed as well as wage • Consider self-employed as well as wage

and salary from the ACS

• Reasonably low education, 70 percent have not completed one year of college • Look at median earnings from 13 cities

Median earning of truck drivers City Median Earnings City Median Earnings Atlanta $40,000 Minneapolis $46,600

Boston $48,000 New York $50,000

Chicago $50,000 Philadelphia $48,000 Dallas $45,000 Phoenix $43,000 Dallas $45,000 Phoenix $43,000 Detroit $38,400 Pittsburgh $40,000 Houston $45,000 Washington $40,000 Los Angeles $45,000 Minimum $38,400 Maximum $50,000 Range $11,600 Percentage variation 30.21%

Observations

• Chicago and New York have the highest earnings

• Detroit has the lowest earnings

• Why does not everyone move to New York and Chicago?

Chicago?

• Prices and amenities differ

• At the margin, workers must be indifferent

between New York and Detroit. Why are prices higher in New York?

Median earning of accountants

Boston $87,500 New York $100,000

Chicago $75,000 Philadelphia $82,500 Dallas $85,000 Phoenix $70,000 Dallas $85,000 Phoenix $70,000 Detroit $70,000 Pittsburgh $58,000 Houston $99,500 Washington $95,000 Los Angeles $79,500 Minimum $58,000 Maximum $100,000 Range $42,000 Percentage variation 72.41%

More observations

• The highest is again New York and the lowest is Pittsburgh

• These do not look like one another:

Chicago earnings are only 75 percent of Chicago earnings are only 75 percent of New York earnings

• Los Angeles is the median despite the high cost of living

• Compare the relative price of truck drivers and accounts

Ratio of accountants to truck drivers earnings City Ratio of Earnings City Ratio of Earnings Atlanta 1.75 Minneapolis 1.55

Boston 1.82 New York 2.00

Chicago 1.50 Philadelphia 1.72 Dallas 1.89 Phoenix 1.63 Dallas 1.89 Phoenix 1.63 Detroit 1.82 Pittsburgh 1.45 Houston 2.21 Washington 2.38 Los Angeles 1.77 Minimum 1.45 Maximum 2.38 Range 0.93 Percentage variation 63.79%

What is going on here?

There are at least three problems here:

1. There are differences in the goods and services consumed among workers

2. There are differences among workers in how 2. There are differences among workers in how

amenities are valued

3. There are unobserved quality differences in workers across location

Consumption differences

• When can I use a price index as a cost-of-living index? When the bundle of goods and services approximates the workers consumption choices

• When will accountants and truck drivers

have the same cost-of-living index? When they consume the same share of their

income on each consumption item • Problem: Income shares differ

Differences in the valuation of amenities

• Chicago has a marvelous symphony and lousy winters

– Who values the symphony more? – Who detests the winter more?

• When will the amenities of Chicago versus New York be valued the same by

accountants and truck drivers? Under the strong assumptions that imply amenities do not affect consumption

Differences in unobserved worker quality

• Social science data are not very good at explaining wages

• Most of the variation is not the result of location or other factors commonly

observed in survey data observed in survey data

• Observably, workers in larger, more

expensive cities are much better educated than workers in cheaper, smaller cities

• We expect some of the differences to productivity that is unobserved

What to do?

• First, do no harm

– Recognize that high real estate prices in an area is a signal about the quality of the

location location

– Recognize that the adjustment needed by a nurse may be different than the adjustment needed by a physician

What to do?

• Second, try to mimic the market

– Firms perform this calculation all the time. They are not, however, worried about these problems, but are simply trying to attract the problems, but are simply trying to attract the appropriate work force

– Examine the flows of young workers (physicians)

The Problem of Hospitals

• At first glance, compensating hospitals, nursing homes, and other institutions

seems a simple problem. Amenities do not matter for them

• Problem: What is the optimal scope of operations for hospitals, particularly

hospitals in smaller urban areas • In market economies, the market