Recall that the model outlined in Section 3, provides predictions for the effect of search costs on the dispersion of prices, the maximum price in the market and the average price in the market. Calculation of the average and maximum prices is straightforward. We use the coefficient of variation as our measure of price dispersion. This is a commonly used measure of the relative dispersion of different distributions that does not vary with units of measurement. Table 3 presents summary statistics for each price distribution (PINFANT, PTODDLER, PPRESCH, PSCHOOL).
The raw data show that price dispersion increases with age. Moreover, these raw data show that markets with R&Rs tend to have greater price dispersion, higher maximum prices, and, higher average prices. These differences are surprising given most economic models, including our own. However, the differences may be explained by consumer demographics or input costs that are correlated with the presence of R&Rs. Table 1(a) shows that markets with R&Rs tend to have higher incomes, are more educated, have higher rents and are more urban than markets without R&Rs.
To control for other effects on the distribution of prices, we estimate the reduced form models described in the previous section. The explanatory variables are described in Section 4 and summarized in Table 1. The reduced form equations for the coefficient of variation are specified as:
where m indexes the market and p indexes the product (care for infants, toddlers, preschoolers, or school-age children). The dependent variable is the coefficient of variation; the regressors SUPPLY, DEMAND, and RANDR are as described above; and upm is the random error. Note that in these market-level regressions, explanatory variables are the average value for the market. For example, the center level data includes a binary variable NLCHAIN^ which is 1 if center us part of a national or local chain, 0 otherwise. If market m contains five centers of which two belong to a chain, then the NLCHAINm = 0.2.