Details of a household choice
As discussed in Sect. 3, the telephony service alternatives for households are (1) no phone, (2) just landline, (3) just cell phone, or (4) both. The data contain expenditures for a household from the quarter prior to the interview in many different categories defined by a universal classification code (UCC).Footnote 30 There is a unique UCC for cell phone expenditures and another unique UCC for landline expenditures. For a household with strictly-positive expenditure on the UCC of landline or cell service,Footnote 31 we record this expenditure as a choice between alternatives. That is, for an expenditure greater than zero, the household is recorded as choosing that category but recorded as not choosing that category otherwise. Choosing no phone is defined as zero expenditure in both categories while choosing both is defined as positive expenditure in both categories. The data are available dating to before the introduction of cell phone services, but all records of cell phone expenses are zero-valued in this dataset prior to 1994 even though cell phones were available about a decade earlier. For this reason, the usable data range from 1994 to 2012, a 19-year period during which the data contain more than 296,000 household choices between the defined alternatives.
Constructed price variables
In this section, we present two approaches to constructing prices from the expenditure data. The main goal of these approaches is to construct a measure of the price of a single phone. The first approach assumes all family sizes face the same prices. The second approach allows for different family sizes to face different prices with the idea being that families can get “family plans”, which offer discounts on multiple lines.
The first approach is to calculate the median expenditure by UCC for both cell and landline among CUs with family size equal to one who have nonzero expenditure in that category in a given year. This estimate assumes that CUs with family size of one only purchase one landline or one cell phone service given they choose that option. This is a reasonable assumption given that most individuals living alone do not have any reason to purchase more than one of each service and the median will certainly avoid any outliers.
The second approach allows for a different price for each option, family-size, region, year tuple. This approach is as follows:
Take the median expenditure on an option by single-person households with positive expenditure in a category. Define this as the base price for the category, region, year triple and do this for each of these triples.
For each family with family size greater than 1 and positive expenditure in a given category, divide the expenditure by one and calculate the absolute difference between this and the base price from step 1.
Repeat step 2 for each integer from 1 through the family size. That is, first divide the expenditure by one, then divide it by two, and so forth.
From these multiple prices (there are the same number of possible prices as there are individuals in the family), select the one with the smallest absolute difference between it and the base price for the option, region, year triple and call this the “temporary price”.
For each observed family size, define the price for the option as the median of this “temporary price” among households of that family size with positive expenditure in that category. Again, this step is done once for each option, region, year triple.
For some family sizes, there are no observations for an option. In this case, set the price equal to the price for the next family size down.
In either case, the time-series obtained through this process is less than ideal, likely due to changes in cell phone capabilities that require more extensive service plans indicating higher prices even though comparable service plans are generally decreasing in price through time. Nonetheless, our price proxies are highly correlated with the CPI categories for landline and cell phone prices, with correlation coefficients of 0.8681 and 0.7746, respectively.