Fun With Stats: Big Cities Are Actually Cheaper Than Elsewhere!

From VoxEU:
Rethinking PPP: Are big cities expensive? 

It’s a common perception that big cities are expensive. This column argues that most of the variation in prices across cities can be attributed to flaws in the conventional indexes. One problem with the standard methodology is that it compares prices of similar but not identical goods. A second issue is that most price indexes do not adjust for the availability of goods across locations. Correcting for these two problems, the authors find that grocery prices are actually lower in large cities. 

It’s a common perception that big cities are expensive places to live. Big cities like New York are typically reported to have a cost of living more than double that of small cities like Des Moines, Iowa with nominal wages that are only 40% higher on average. Why then isn’t there a massive exodus from large cities into small ones?

New evidence

A common explanation is that larger cities offer better amenities (Glaeser and Kerr 2008). In our forthcoming paper (Handbury and Weinstein 2014), we suggest a much simpler explanation for this discrepancy – the standard price indexes are wrong. We study the prices of barcoded grocery items sold across cities in the US and find that almost all of the variation in prices across cities can be attributed to flaws in the data used to make spatial price comparisons.

• Our results suggest that, when measured correctly, there is in fact very little variation in prices across cities!

We choose to focus our analysis on barcoded grocery items because one needs to worry much less about unobserved quality variation when comparing the price of, say, a 12-ounce can of Coca-Cola across cities than when comparing the price of a two-bedroom apartment. Even in this set of products, conventional price indexes that are widely used in economic studies and wage setting guidelines suggest massive variation in prices across cities. For instance, it is not uncommon for these indexes to register that consumers in some cities pay over 75% more for their groceries than consumers in other cities.

Biases in current methodology

One of the problems with these conventional indexes is that they compare the prices of similar, but not identical, goods. The first problem with this methodology stems from the fact that there is a wide variation in the prices of items like eggs, cheese, and milk depending on the variety chosen. For example, the price of a half-gallon of whole milk can easily vary by over 100% within the same store depending on the brand. As a result, simply comparing the price of, say, milk across locations can be very misleading if different types are chosen in different locations. These price comparisons misleadingly indicate prices are higher in large cities if richer consumers tend to prefer more expensive varieties of the same category of good, since richer people tend to congregate in large cities.

• We call this first problem ‘product heterogeneity bias’ because it arises when consumers think of similar products very differently and as a result are willing to pay very different prices for different varieties.
• A second important source of bias comes from not carefully controlling for where goods are bought.

For example, it is not a surprise that richer people shop in nicer stores that provide a better shopping experience. Since consumers know that they typically pay more when they shop in a nicer store, a price comparison should not compare prices in a low-end grocery store with prices in a high-end one. Instead, one should control for store heterogeneity and compare the prices of identical goods purchased in the same type of store.

We can see the effect of correcting for these biases in Figure 1, where we plot the food price indexes for 49 US cities. As we can see from the plot, while there is a clear upward association between average city prices and a price index constructed using the conventional methodology with Nielsen scanner data, the positive association almost vanishes entirely when we correct for the product and store heterogeneity biases. Moreover, one can also see that virtually all of the variance in prices across cities disappears once we control for heterogeneity biases. On average, the prices of groceries are almost identical in all cities in the US.

Figure 1. Adjusted and conventional food price indexes

Note: Using Nielsen HomeScan data we see that there is a positive relationship between city size and food prices when we construct the index using conventional methodologies. The relationship disappears when we adjust for product and store heterogeneity biases

A second major problem with price indexes used to compare price levels across space is that they make no adjustment for the availability of goods in different locations. Existing price indexes compare the prices of a commonly available set of goods, but large cities typically have many more varieties than small ones. For example, we estimate that there are four times more varieties of grocery items in New York than in small cities like Des Moines. This result helps explain an intuitive feeling big city residents often feel in small cities – it’s hard to find many of the goods that they want to buy. Indeed, the tremendous diversity of products available in large cities like New York is one of their great attractions....MORE