Mortgage Defaults

Came across an interesting paper on mortgate defaults the other day while I was, actually, searching for some models of credit card default.

The authors, Campbell and Cocco, develop a microeconomic model of this important behavior and come up with some interesting results.

In particular, they make a clean connection between negative equity and borrowing constraints when it comes to default. Negative equity increases the default risk, of course, but the degree of negative equity that triggers a default depends on the degree to which the household is constrained in the credit markets. pofoundly constrained households can default at low levels of negative equity.

The other interesting result is the breakdown of the particular risks of the various types of home financing. For example, interest-only mortgages have the highest risk of default waves. Even so, there are ranges of risk events for which they have some clear advantages over other forms of financing. For one, these borrowers are less likely to face borrowing constraints than other types of borrowers. This benefit is generally overwhelmed by the equity risk they face -- interest-only homes are the most exposed to decreases in home value.

The paper is pretty deep and will take several readings to get a handle on the arguments. But the idea of approaching the question with a dynamic micro-model is significant.

New Product Launches -- Tobacco

In the last year or so, I’ve had the chance to monitor several product extension launches in the cigarette industry; all the big players have made some moves. For example, Marlboro has sequentially launched several Special Blend sub-brands, while Newport has successfully launched a non-menthol brand. Despite the different success levels we observe in terms of market share for these launches, all of them share a remarkable similarity in terms of their share diffusion in the market. I want (briefly) to look at some of the implications of this fact as it relates to the cigarette industry.

The basic Bass model suggests that the volume (share) of a new product is determined by the interaction of two effects. The first is the innovation/advertising effect, which is taken to drive people to experiment with the product quickly. The second effect is the imitation/word-of-mouth effect, which is assumed to spread the desire to try the product over time.

The sales as a function of time can be expressed:

Nt = Nt-1 + p(m-Nt-1) + q(Nt/m)(m- Nt-1)

Where N is the number of units sold (or, scaled appropriately, market share), m is the total market size for the product, p is the innovative/advertising effect, and q is the imitation/word-of-mouth effect. Typical values for p are said to be around 0.03 and for q around 0.4.

You might be able to see that the last term on the right hand side is the difference term that we see in simple models of population growth with carrying capacity, used to model the size of a colony of bacteria in a Petri dish, for example. So, the “q” term is the logistic or organic growth and the “p” term is the exponential or advertising-related growth. And overall volume is determined by the balance between these two effects.

So far, so good. But here is where it gets interesting. Below are a pair of simulated new product launches, the first from a product with typical coefficients and the second with coefficients that have been calibrated to yield weekly changes in volume that mimic those of the new products in the cigarette industry. Check out the graphs at the top of the page to see what I mean.

The overriding fact of all the new product introductions was a peak in the share change that happens in week #2, and the share changes generally fell to near zero by week #4 (though I haven’t modeled the drift that some products display subsequently). But the coefficients as calibrated are very far outside what is considered typical: the “p” value is 0.3 (up from 0.03) and the “q” value is 0.8 (as compared to a typical value of 0.4).

Now, these numbers are merely the result of a quick and dirty calibration, but they suggest the possibility that cigarettes are an unusual industry with respect to new product introduction.

New Product Inflection Points

New product diffusion is often modeled as an S-curve. The idea being that there is some period where the dare of the product is getting traction very slowly and that, when it hits, the share increases rapidly to some saturation point. The Bass-style diffusion models generally allow for this sort of process.

I'm thinking this is not a particularly good model for sophisticated CPG companies, especially if they are using some brand extension. This is so for two main reasons.

First, companies that rely one an extant sales organization are much better able to establish a wide number of outlets, reducing the search- and word-of-mouth effects.

Second, and more interesting (to me, anyhow), established organizations seem to benefit from a ready understanding by the market of the option value of new product trial.

The intuition is as follows. The market understands that a new product has both risks (overall product liking as well as switching costs, if any exist) as well as benefits (it could be much better). Brand extension serves both to reduce the variance on the prior belief about the liking as well as increase the prior estimate of the expected liking value. Higher expected value plus lower variance equals better deal.

In this case, we would expect the potential for a gain in utility to outweigh the risk for almost everyone who would consider trial of the new product.

It seems to me there are two implications from this thinking. First, such effects must be two-edged: reducing risk for consumers already purchasing something from the line but necessarily increasing risk for outsiders. If so, then trial should be weighted toward cannibalization at a greater than fair share proportion. That's interesting, I think.

Second, this might drastically shorten the length of time that new product promotions should be run: you wouldn't need long promotions if everybody already gets the idea that they should try the product sooner rather than later. In that case, what would matter would be things like watching for inflection points to know when most of the market has already seen the "option" purchasers act.

It would be interesting to look at these sorts of market penetration for line extensions to see when these points happen and how predictive they are of eventual share.

And We're Back

Long delay because of the relocation from Atlanta to Richmond, as well as the attendant school selections, spousal job searches, home search, and assorted adjustment costs.

Switching Costs and Learning

Came across a really interesting paper the other day by Matthew Osbourne of the U.S. D.O.J., Antitrust. I'll be working through it over the next couple days.

When it comes to introducing new products, there are lots of things going on that are easily confused. For starters, suppose that the new product is introduced with a low price, with the idea that the introductory price increases later. If we observe someone trying the product and then abandoning it, are we seeing a person who is very price sensitive, or are we seeing someone who learned that he didn't like the product? If you aren't careful, these two behaviors will look the same.

Another thing to consider is the counter-intuition behind a Bass-style diffusion process. (A Bass diffusion will tries to measure the different effects of early adopters with late adopters, with the result that the path to the full penetration of the new product can take several different paths). If it is true that learning has value (and it is true), then we would expect to see very rapid experimentation with new products, leading to a very rapid achievement of the steady state penetration.

That isn't what we see, typically. And one really good reason why is because of switching costs. If consumers havev switching costs, the value of learning has to be weighed against those costs, and the possibility that you will learn you don't like the new product and have to incurr the cost of switching back to the oringinal product.

So, it's risky and dynamic and forward-looking. Turns out, it's pretty important, too. According to Osbourne, ignoring learning will lead to models that underestimate own-price elasticity of new products by 30%, while ignoring switching costs will lead to underestimates of own-price elasticity of up to 60%.

So, it's a pretty big deal, since a firm could spend hundreds of millions introducing a new product and it is pretty important to get the pricing right. So, I'll be blogging some insights from the paper and looking for applications to various industries.

More CRM

So, we have information about customers -- our own and those not our own -- and we want to accomplish a few things:

1. We want to hold on to the customers with the greatest value
2. We want to encourage customers to increase their value
3. We want to change non-customers into customers

Not that complicated, really. And let's suppose that we could categorize everybody in the market with a nice vector containing their

1. Strength of preference for the firm
2. Contribution margin
3. Responsiveness to promotions

This assumes away a pretty big set of problems, but I want to focus on what a policy should look like from a strategic perspective. And there are interesting strategic problems with thte goals of CRM. A quick outline of them looks like this:

Customers have a high value either because their intrinsic preference for our firm makes them unlikely to switch or else because they have a high contribution margin. If they have a strong preference for our firm, there seem to be little reason to invest much trying to retain them. If they have a high contribution margin, they become prime targets for other firms who will invest resources trying to poach them. Obviously, having one firm investing in retention and another firm investing in poaching can result in high-value customers becoming lower-value customers, which wasn't what we wanted.

Making investments to increase their margins makes the customer into a high-value customer. Which increases their appeal as targets for other firms and could put us back into the bidding war outlined in the previous paragraph.

The customers that are the most attractive targets for switching to our firm are also those customers their current firm is most interested in keeping.

So, strategic interactions might matter quite a lot. To complicate matters, we sometimes start asking the wrong sorts of questions. For example, when it comes to loyalty programs, we might get into a debate over whether to target customers who occasionally make large purchases or customers who frequently make small purchases. Who can possibly say, without knowing why the customers purchase as they do?

So, are the frequent customers simply those who respond to promotions, or are they displaying a strong attachment to the brand? The right policy is determined by the answer to this question. Are the infrequent customers less prone to respond to promotions? If so, then competitors' attempts to poach them might be less effective -- suggesting a lower level of retention efforts would be required.

In short, we simply can't look at customers on a single dimension and expect to develop CRM policies that are right.

Strategic CRM

One of the interesting CRM challenges is in identifying whom to treat. One recent discussion for analytical marketing types on LinkedIn was over precisely this question. I think I can paraphrase it here:

For a customer loyalty program, is it right to choose customers on the basis of their total sales, total visits, etc., or is it better to choose customers based on their trends? In other words, who is more likely to be loyal: a customer who makes one or two big purchases infrequently or one who makes medium purchases frequently?

And the idea is that this form wants to set up some sort of loyalty program to keep the good purchase decisions going.


The reason why this question might cause the strategically inclined to wonder a little bit is because both sets of customers seem to be telling you that they are loyal to the firm's products. When you have a customer who chooses your firm with a high probability already, what do you hope to accomplish with a loyalty program?


One way to think about it is with a simple logistic probability structure.



Right. So, this is pretty simple -- a two-dimensional representation of probability. We might think of X being the loyalty of the customer, with higher loyalty making it more likely that customers will purchase from your company. (These numerical values are arbitrary).

Like everything in economics, the decision is made by comparing the marginal (incremental) affect of the proposed pollicy with the marginal cost. So, suppose we have some program that we figure will increase the loyalty score by a unit, from 25 to 26, 35 to 36, or whatever. Well, if we institute the program on people with loyalty scores of 35, the increase in probability is really small: you are already capturing nearly every purchase decision from those loyal customers to begin with.

Same thing is true on the lowest end of the loyalty scale: there just isn't much to be gained by bumping up these low-loyalty customers by a unit or two.

Clearly, the greatest response comes from increasing the loyalty of that bunch in the middle: the slope of the graph is highest for these cusomers. Which means that the investment in loyalty pays off best there.

So, in an important way, the discussion question misses the point. Who cares whether frequent purchases of small value imply greater loyalty than occasional purchases of large value? Both these groups are probably out on the right hand of the loyalty scale anyway and that means we probably are more interested in a way to exclude them from whatever loyalty program we'd want to inaugurate.

I think, following a really interesting article in Marketing Science by Musalem and Joshi, that we want to focus on three attributes of our customers: intrinsic preference for our company (intrinsic loyalty), margin (or lifetime value or something similar), and responsiveness to retention and acquisition efforts. Not only that, but an effective CRM program should consider the strategic interactions between competing firms through time.

And those subjects are going to be discussed next.