The puzzle of newspaper pricing

In the simple economic model of supply and demand, when demand decreases the price decreases (except in some special cases such as when supply is perfectly elastic). Typically, the same holds true for other market structures such as monopoly - when demand decreases, the monopolist's profit-maximising price usually decreases.

That makes the recent experience of newspaper subscriptions increasing in price, in the wake of decreasing demand, somewhat of a puzzle. Fortunately, a 2016 paper by Adithya Pattabhiramaiah (Georgia Tech), S. Sriram (University of Michigan), and Shrihari Sridhar (Texas A&M) unpacks the puzzle for us, and ultimately it rests on the fact that this is a platform market (or a two-sided market) - a market where a firm brings together two sides (e.g. in this case the readers and the advertisers), both of whom benefit by the existence of the platform (the newspaper), and both of whom may (or may not) be charged (in this case, the readers are charged a subscription, and the advertisers are charged for advertising). As Nobel Prize winner Jean Tirole has noted, in platform markets it is common for one of the two sides to subsidise the other. To be more precise, the side of the market with relatively more inelastic demand (or greater willingness-to-pay for access to the platform) will subsidise the side of the market with relatively more elastic demand (or lower willingness-to-pay for access to the platform).

So, one potential explanation for the puzzle of increasing subscription prices for readers in the face of decreasing demand is that the decreasing number of readers reduces the value of advertising in the newspaper, which reduces advertisers' willingness-to-pay for advertising, which in turn reduces the optimal subsidy the newspaper will apply to subscriptions. And it is this explanation that Pattabhiramaiah et al. set out to test.

They use data for 2006-2011 from a top-50 regional newspaper in the U.S., supplemented by microdata from 5565 subscribers, to construct models of: (1) the subscribers' decisions about whether to subscribe (and which of three subscription choices to select); (2) the advertisers' decisions about whether to advertise (and whether to do so in classifieds, display, or inserts); and (3) the newspaper's decision about subscription prices. A bit of background first though:

During the period of our analysis (i.e., 2006-2011), 14% of households in the newspaper’s market subscribed to the focal newspaper...

Conditional on subscribing to the focal newspaper, 72.4% (71.6%) of readers within (outside) the core market opt for the Daily option. The corresponding numbers for the Weekend and Sunday only options are 5.4% (4.4%) and 22.2% (23.9%), respectively...

The Daily option witnessed the steepest price increase of nearly 77%, both within and outside the core market, while prices of the Weekend and Sunday only options also increased by 52% and 38%, respectively...

On average, across the three options, the newspaper’s circulation witnessed steep year-on-year declines within (outside) the core market of between 7-10% (2-6%)...

While display and inserts lost 57.7% and 43.4%, respectively during our analysis period, Classifieds ad revenues experienced the steepest decline of 88.3%...

Between 2006 and 2011, classifieds ad rates at the focal newspaper declined by 66%, possibly as a result of the growing popularity of Craigslist. The rates for display ads and inserts experienced smaller declines of 16.7% and 10.8%, respectively.

So, subscription prices for readers increased (and readership decreased), and advertising rates (the price advertisers pay) decreased and so did advertising revenue. However, that decrease in readership was likely to be both the result of decreased price (and so was the result of a movement along the demand curve), and the result of changing reader preferences to (a decrease in demand, or a shift of the demand curve to the left). This creates an identification problem (which I've written on before, here) - which of the movement along the demand curve or the shift in the demand curve has contributed the most to the change in price? [*]

Pattabhiramaiah et al. then used their model to:

...compare how optimal markups evolved between 2006 and 2011 in each of the three cases: actual markups (computed based on our model parameters), the case where we switch off the decline in readers’ preferences, and the case where we switch off the decline in the incentive to subsidize readers at the expense of advertisers.

They find that:

...within the core market, the decline in readers’ preferences accounted for between 8-21% of the increase in subscription prices. On the other hand, nearly 79-92% of the increase in subscription prices between 2006 and 2011 can be traced back to the decreasing incentive on the part of the newspaper to subsidize readers at the expense of advertisers.

So, their results support the argument that the puzzle is explained by decreasing subsidies from the advertiser side of the platform market to the reader side.

There are two final (statistical) points I want to make about this paper, which may leave us with some concern about the results. The first is illustrated by this quote from the paper:

We find that the correlation between the subscription of the local newspaper and the local subscription of national newspapers is 0.8, suggesting that it is not a weak instrument... Overall, these results suggest that the instruments, along with other exogenous variables, explain 83% of the variation in readership. Compared to the first stage regression with only the exogenous variables, but excluding the instruments, the proposed instrumental variables improve the R-squared by 12-14% for ad rates and 11-15% for readership. Therefore, we contend that we do not have a weak instruments problem.

What the hell? There are actual statistical tests that you can run for testing whether you have weak instruments (Stock and Yogo have a whole chapter on it here), but rather than report the results of those tests they obfuscate instead? On the basis of what they have written, we are left with little idea about whether their instruments do a good job or not (for more on instrumental variables, see my post here). The second issue is somewhat hidden in a footnote:

Our in-sample MAPD ranges between 17.4%-17.8%. The out of sample MAPD range between 12.1%-16.8%.

The MAPD (Mean Absolute Percentage Deviation) is a measure of the error in their model, and it is extremely unusual for a model to show a lower error on data that was held over for validating the model (out-of-sample data) than on data that was used to construct the model (in-sample data). After all, most models are constructed to minimise the in-sample error. So this should leave us a little concerned about their model (or their calculation of MAPD). Or perhaps it's just luck that their data does a better job of predicting the 2010-2011 period than the 2006-2010 period?

[HT: Marginal Revolution]

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[*] Pattabhiramaiah et al. use their data to first eliminate the alternative possibilities of increasing quality of the newspaper leading to an increase in price, or increasing marginal costs leading to an increase in price (in fact, they find that marginal costs actually declined over the period).