Social Interaction and Cost-Benefit: Initial observations

Social Interaction and cost-benefit analyses in economics: Initial observations

by Hans O. Melberg

Introduction: The question
Imagine that you are asked to do a cost-benefit analysis of drug-treatment programs. You diligently go about trying to measure the reduction in drug consumption and crime and other variables based on interviews of several hundred drug users who have been treated (ignore the fact that you should also have people who have no been treated). You then present your conclusions: One dollar spent on drug treatment produces on average x% reduction in drug use, y% reduction in crime, z% increase in job participation and so on. Having presented your conclusion on a conference for policy makes, a person stands up and says that you have seriously underestimated the benefits of treatment because you have missed one important aspect of drug use. What?

The answer – theory
Assume, for instance, that the person complaining is a well known police officer with long experience in drug affairs. The use of drug, he claims, is contagious. In the words of a former Police Chief in Norway: “every new drug abuser lures or persuades about 3-4 of his acquaintances to try the drug. Each of these make 3-4 others join and so on, thus creating an increase like a geometric pattern: 3-9-27-72 and so on” (quoted in Hauge 2000, p. 241. Imperfect translation by Melberg …). Hence, the person concludes, your estimates of the benefits of treatment is only a fraction of the true benefits since you only consider the changes relating to the person itself and not the fact that when we successfully treat one drug user he will no longer recruit new users. In short, you have not considered the interactive nature of drug use.

Devastated by the critique you go back to your office determined to correct your mistakes. The initial question is then: How to account for the contagious nature of drug use in a cost-benefit analysis?

Immediate reactions
First of all you note that the importance of the variable is potentially enormous. How large it is depends, among other things, on how fast the drug use spreads. However, even if we use the most conservative assumptions the quotation suggests that all the benefits should be multiplied by a factor of three. The conservative assumptions being that the time unit is “life” (each drug user recruits 3-4 new users over a life period, not every month or year) and we ignore the fact that the recruits also recruit new users. Hence, the argument is potentially very important.

Second, after a few seconds you might realize that the first though about the importance of interaction is wrong. Why? The quotation assumes that the interaction is always negative in the sense that a drug user recruits other drug users. This could be wrong since drug users may also have a deterring effect on potential users. For instance, Manski (2000) suggests that the crack epidemic of the 1980s in the USA subsided when potential users observed the devastating effects of the drug on old users. Hence, interaction need not, as the initial quotation suggest, only increase the number of users. In fact, taking interaction into account may reduce the benefits of treatment. Imagine, for instance, that potential users are scared away from drugs by observing the problems older addicts have. You then remove (treat) the old addicts and since they no longer walk around on the streets the potential addicts no longer observe the harmful side-effects of drugs. Unable to observe this, the young potential users start using drugs. If this deterring interaction dominates the positive interaction, the net effect would be to reduce the benefits of treatment. Overall the effect of treatment is theoretically indeterminate.

Although the possibility of deterring interaction reduces the size of the overall effect of contagion, it sounds wrong to argue that it reduces the importance of looking at the phenomena of interaction. A phenomena can be very important in an explanation even if the net effect on the dependent variable is miniscule. In short, two large effects may almost cancel each other out but this does not imply that we are justified in ignoring the effects when we try to explain the phenomena.

Third, the use of the term “contagion” seems to be the wrong. Clearly, drug use is not contagious in the same way that – say – the flue! Admittedly, as Fekjær (1987) notes, we sometimes use the term contagious about behaviour and not only bacteria and viruses that go from person to person. For instance, laughter and yawning is sometimes said to be contagious. However, these phenomena have a more involuntary character than taking drugs for the first time. Yawning is largely an involuntary muscle reflex while taking drugs for the first time is more or less a conscious choice. This makes the analogy between contagious drug use and contagious diseases less than perfect.

Another argument against using the term “contagion” literally is, as Evang (1972) has pointed out, that it tends to produce wrong ideas about how to deal with drug use. Usually when something is contagious we (1) Eliminate or reduce whatever it is that is contagious; (2) Isolate the agent carrying the contagious disease until he is treated and no longer contagious; (3) Immunize people who are not affected (vaccine etc). Evang argues that these steps are not appropriate when it comes to drug use since we do not know how to treat it or how to make people immume, as well as the fact that the cause is not a single bacteria, but complex interrelationship of social and other variables. Based on these arguments from Fekjær and Evang, it seems more correct to say that we have a case of interaction – people affecting the behaviour of other people – than literal contagion. (Of course, if one is aware of the problems with the direct analogy one may use whatever label one wants, including a less literal use of the term “contagious.”)

I have so far only established that the phenomena is potentially very important, that its importance depends on assumptions about the number of people recruited (3-4), the time unit used (year, life?) and the nature of the interaction (positive or negative). Finally I have rejected the term “contagious” in favour of the more general “interaction.” The question the remains: How should we account for interaction when doing our cost-benefit anlysis.

Two general answers
a) No microfoundations
To quantify the effects you have to do some kind of calculations based on a model. In general the model can be of two types: Either with or without micro-foundations. Consider, for instance, Lederman’s total consumption model. The hypothesis is that there is a relationship between the average consumption of alcohol and the number of heavy drinkers (constant over time and across countries?). This is a statistical relationship that can be estimated using historical data. Based on our answer we could say things like “If average consumption increases by 0.5 litre, the number of heavy-users will increase by 2104 people.” The point to note is that we can do these calculations without saying exactly why the prevalence of heavy drinkers depends on average consumption. We just assume that there is a link and measure the effect. In short, we do not say anything about the nature of the interaction or the microfoundations on which the quantification is based. Lederman himself might not agree that his theory is without microfoundations since he also included some speculations about what he called “boule de neige.” However, as Skog (1980) notes this did not amount to an explanation of why the average and the prevalence for heavy drinkers affect each other.

b) With microfoundations
The other approach to estimating the effect of interaction, would be to build a model in which we tried to include the type of interaction we believe was important. It is important to note that this is not about just including moderating variables in our regression. For instance, assume you want to see how much more (or less) a person drinks when accompanied by a heavy drinker. This was the question asked by Caudill and Marlett in their classic paper from 1975. Since then several similar experiments have been conducted and Quigley and Collins (1999) provide an overview of the conclusions from these studies. They also measure the effects of several moderating variables (such as the gender of the participants, the social status of the heavy drinker, the warmth of the interaction and so on). Although interesting this is not the same as providing microfoundations. As Quigley and Collins admit they only present information on correlations between variables without saying anything about exactly why and how the variables are causally relevant.

To get an idea of “real” microfoundations, we could use information from the already mentioned article by Skog. Here he discusses two suggested microfoundations that could provide the link between average consumption and the number of heavy drinkers. The first goes something like this: Person X drink more often à offer alcohol to Y (who previsouly drank just below the limit for heavy drinking) more frequently à Y feels must reciprocate and offer X alcohol more often (on visits) à Y drink more (both becayse he is offered more and because he offers more) and Y may cross the threshold to heavy consumption. This is essentially the microfoundation suggested by K. Bruun and Skog labels it “contagion between persons.” I am unsure whether this idea is rigorous enough to be called a mechanism or a microfoundation.

A second possible mechanism behind the Lederman model, could be that increases in consumption happen when “new situations are added to the old repertoire of drinking situations” (Skog 1980). If, for instance, the habit of non-alcoholic beverages to regular meals in Norway is changed – so that we become more like the Italians who drink wine to meals – then average consumption will increase as will the number of heavy drinkers. According to Skog this mechanism was suggested by Sulkanen and he labels it “contagion between situations.” Once again I am slightly unsure about whether it is fleshed out in enough detail to call it a “mechanism” but the two examples above should at least illustrate what is meant by microfoundations: Some kind of story making the linking between the average and the prevalence theoretically plausible.

My initial question was not about alcohol, but about drugs and interaction in cost benefit analysis of treatment. The reason for the digression into the Lederman model was that it provided a well known example that could be used to illustrate two general ways of estimating the size of interactions: with or without microfoundations. I should now be more specific and suggest how the approaches could in the context of cost-benefit analysis. The purpose here is not to provide a model, but to present ideas of how to do things. Later on I will try develop some of the ideas in a more formal model and estimate this using real data.

More specific answers
How could we estimate the importance of interaction in our cost-benefit analysis. Without microfoundations I believe it we could do something like the following:

a) The crude alternative (no microfoundations)
Assume we have (or can estimate) the number of drug users at different points in time. Say we have 1000 users in year 1, 1200 in year 2, and so on. A crude assumption would then be to blame all the increase on the previous users; If we ignore the option of quitting, then each user “recruits” 0.2 new users every year. In addition to the benefits to the person himself – and assuming there is some symmetry here (no longer contagious when cured) – then “curing” an addict reduces the number of other addicts. How much? This depends on the number of years an addict lives and the number of years his recruits live. We could, of course, use age as a proxy here. The older an addict is the fewer users he will have time to recruit. And, the older the recruits are the fewer people they in turn will recruit. Of course, all the way we have to assume that users are similar in the sense that they are all equally “contagious.” And we might add the assumption that they have the same life expectancy to make things easier for us.

These are highly questionable assumptions. For instance, it might be the case that old addicts deter more than they recruit so they are not as negative contagious as the new users. In any case, just to see the structure of the calculation: Assume people start using drugs when they are 20 and stop (or die) when they are 40 and that they recruit 0.2 new users every year (who are 20 when they are recruited). These, in turn, recruit more users and so on. Using these assumptions we find that curing a user who just have begun (before he has recruited anyone) also saves society from 37 new users during the next 20 years. The formula is just the same as when you calculate how much money you have in the bank after t years i.e. S_t = S₀ (1+r)^t Hence the benefits of treatment as measured by change in one individual must be multiplied by 38 if we are to include the “interactive” benefits. Clearly this would make a huge difference in the estimate of the benefits of treatment. Even the relatively modest (?) assumption that every addict recruits one new addict about every five year results in a 37 fold increase in the estimated benefits from treatment!

As I have mentioned, the conclusion above cannot be taken as anything except illustrative. The problem is, of course, that there are too many unrealistic assumptions to take the answer literally. What if, for instance, old addicts deter instead of recruit new users? I guess one could still defend the calculations above based on an argument that the overall average (net) effect over the lifespan is more positive than negative and hence an average contagion (whole life cycle) of 20% is not wrong. It is more difficult to defend the assumption that all increases in drug use is due to contagion (which is needed to find the estimate of how many new users old users recruit). It seems more reasonable to at least assume that some of the new users are added not because they are persuaded or pressured by existing users or pushers, but because they simply want to use drugs. On the other hand even this might be influenced by others behaviour. For instance, a large number of existing users might serve to reduce the stigma attached to an activity and hence make more people willing to join in.

The observations above contain two lessons. First of all we need to be more precise about what we mean by interaction. Second, macroestimates in this area without microfoundations are not very useful or reliable since they miss important policy-relevant details and are prone to spurious correlation. That is not to say that adding microfoundations will produce “Paradise,” only that in this case macro is not enough. It might still not be enough if we add micromechanisms, although doing so may give us a beter grasp of the nature of the problem and sompe important policy lessons (such as a policy that focus on the old users may have unintended side effects – reduce deterrence – that increase the number of new users)

I have so far sketched how one might try to find an answer to the question of how to adjust for interaction in our cost-benefit analysis without providing microfoundations. I now turn to the second general method: Including interaction by models that have microfoundations.

b) Microfoundations, interaction, cost-benefit and drug use
In what sense can the use of drugs be contagious, or more generally, in what sense does it depend on interaction?

First of all there might be social learning. People learn about the benefits and costs of drugs from other users directly and indirectly. Directly friends tell and persuade each other to try (or not to try) new activities. Indirectly you observe, for instance, that people who use drugs are happy/unhappy, how it affects them over time and whether the claims about the damaging effects of drugs are true or not. I have not seen a model trying to formalize this effect explicitly in terms of drug use, but observational learning has been modelled in general – for instance by Bikhchandani, Hershleifer and Welch (1998).

A second possibility for linking average use of drugs to one person’s decision to use drugs (interaction) could be the reduction of stigma associated with something that many people engage in. A good example is divorce. As long as almost nobody got divorced the negative social stigma attached to divorce made it very costly and hence few people opted for that option. In a situation where many people get divorced the social stigma is reduced and this, in turn, increases the number of divorces (positive feedback effect). As it happens this kind of effect has been modelled formally not only in general, but also specifically in the area of drug use (see Moene 1999). It has, however, not been incorporated into a frame where the task is to model costs and benefits of treatment.

The first “interactive” link I mentioned was about how other people affect your expectations. The second was about how the cost of an activity is changed as a result of more people joining in. A third possible link, is that people’s desires interact. For instance, I may want to do the same as my idols (imitation). Similarly, I may want to be accepted in a groups by doing whatever they do (peer pressure?).

There are a host of other mechanisms and links that may be labelled “social interaction”: When more people use drugs availability increases and this in turn may increase use; Drug use may have a shared meaning (anti-establishment) that motivates use; Advertisement and pushing may affect drug use; Price of drugs is affects by how other people behave; Indeed, one might even argue that unemployment and other social problems that cause drugs are “interactive.” Clearly you are affected by another person (interaction?) when - say - you become a drug user because your parents (due to their own drug use) neglected you to the extent that using drugs became your “best” option/escape.

The examples above point to at least two lessons. First of all, it is necessary to be more precise about exactly what we mean by social interaction. If “everything” is social interaction then the concept looses much of its meaning and it becomes impossible to use it in an analysis of costs and benefits. Second, there is a need to make the mechanisms more rigorous both in order to “discover” problems and interesting features that appear when we look at the mechanism in and because we need to be more formal before the model can be used to say anything about costs and benefits of treatment when we include interaction.

Conclusion
I am persuaded that cost-benefit analyses of treatment for addiction should try to consider the “interactive” nature of drug use if it aims to capture all important “benefits” from treatment. I am much less sure that it is possible to do so in a reliable fashion. Estimation without theory (no microfoundations) is always questionable. Estimation with microfoundations raises the question of how to model the interaction and there are many different mechanisms that could be used. We do not know (and it is difficult to discover) the “true” interaction that takes place and for this reason it may be difficult to give answers as to the size of the “external” benefit of drug treatment. I will however, continue to pursue the topic. First of all I need to look more closely at the concept of “social interaction” itself. I will so in another paper by comparing two different approaches viz. T. Schelling vs. C. Manski. Second, I need to be more rigorous and precise about the mechanisms involved and I will do so by a review of Moene’s model.

Literature

Manski, Charles F. (2000) Economic Analysis of Social Interactions. Journal of Economic Perspectives 14(3): 115-136.

Hauge, Ragnar (2000) Har narkotikapolitikken spilt fallitt. Nordisk Tidsskrift for Kriminalvitenskap 87(3):241-245.

Bikhchandani, Sushil, David Hershleifer and Ivo Welch (1998) Learning from the behavior of others: Conformity, Fads, and Informational Cascades. Journal of Economic Perspectives 12(3): 151-170.

Moene, Karl Ove (1999) “Addiction and Social Interaction” In Jon Elster and Ole J. Skog Getting Hooked. Cambridge University Press. pp. 30-46.

Skog, Ole-Jørgen (1980) Social interaction and the distribution of alcohol consumption. Journal of Drug Issues 10: 71-92.

Quigley, Brian M. and R. Lorraine Collins (1999) The Modeling of Alcohol Consumption: A Meta-Analytic Review. Journal of Studies on Alcohol 1: 90-98.

Schelling, Thomas (1998) ” Social mechanisms and social dynamics” in Peter Hedström and Richard Swedberg (eds.) Social Mechanisms. Cambridge. Cambridge University Press.

Evang, Karl (1973) Narkotika, generasjonene og samfunnet. Oslo. Tiden Norsk Forlag. (2. utgave) (pp. 175-184: ”Er narkomani en smittsom sykdom?)

Fekjær, Hans Olav (1987) Alkohol og narkotika : myter og virkelighet. Oslo. Gyldendal