Borrowed Money

Some interesting time series charts from the Federal Reserve in St. Louis I've been looking at recently.  They involve consumer revolving credit.  In the aftermath of the Great Recession, Americans are re-balancing their accounts and, for the first time in forever, reducing their revolving debt levels.  Check this:

-- Per-capita revolving debt in 2005 constant dollars (shaded regions represent recessions)

We can see the big increase beginning in the 1990s, with the development of considerably more sophisticated credit models.  These models allowed credit card companies to separate the unsecured credit market into correct risk categories.  Because of this, we should probably interpret this big increase as both an increase in credit demand as well as in increase in credit supply: the equilibrium where we are able to separate credit riskiness probably has lots more loans being offered than the equilibrium where we have to pool the risky households with the safe ones.

But since the recession, we see decreases in these borrowing amounts.  It is important to note that these are separate from the loans that have been written off or otherwise defaulted; similarly significant changes also live in time series that look at cohorts of stable accounts that have not defaulted.

There are several interesting possible explanations for this shift in consumer behavior.  The two that I find most interesting are the changes in government spending and the lack of change in personal disposable income.  A couple more charts should make the point.


Here is the Federal spending as a percent of GDP.  Note that, during the Clinton years, this percent was decreasing ("The era of big government is over.") and consumer borrowing was increasing rapidly.  Meanwhile, as government spending has increased significantly, consumers perhaps grasp that all that spending has to be repaid by somebody and so you'd better start saving for the time when taxes increase to pay that debt off.

So, this has some plausible affect on the level of consumer borrowing.  The other -- and to my mind more interesting -- time series is the constant dollar household disposable income, per capita.  Check this nightmare out:

Here is the per-capita disposable (that is, after tax) income series since 1991.  This measure has stalled entirely since 2006.

This gives some support to the feeling that consumers perceive that their lifetime income profile might not be as good as they used to think.  We can match this picture up with all sorts of poll data that suggests people think the next generation won't be as well off, or that the country is on the wrong track, or that consumers are gravely concerned about the economy.  This chart provides a pretty good explanation.

In an environment where real disposable incomes are increasing, real wealth is increasing rapidly (we don't need a picture of housing prices!) and credit supply is expanding (because the companies can tell good risks from bad ones), it shouldn't surprise us that consumers want to pull lots of future consumption into right now.  Our borrowing should have increased in that situation (maybe not as much as it actually did, but still..).

I suspect that people interpret the decrease in wealth associated with the housing bust, the significant increase in government debt, and the six years of no income increases as strong signals that the future income will be small enough that they don't want to pull as much of it into today.  

This is a praticular risk for firms and individuals who buy consumer debt.  And there are forward-looking indicators that should be of keen interest to them.

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.