0:02

Okay, so lets have a look at a fixed co estimation of a model of diffusion.

Â So what I'm going to do is now work with diffusion and actually bring it to some

Â data and see what we can learn from that, and I'm just going to do an application.

Â One I've been involved in, to sort of show you

Â how this might work, and how we can build models.

Â So something that I've been thinking about quite

Â a bit and, and so take you through that.

Â So this is the paper with

Â Abhijit Banerjee, Arun Chandrasekhar and Esther Duflo.

Â And what we're going to do is, we are going to map a social network through

Â surveys, so we have a series of surveys,

Â we've mapped out the villages you've seen before.

Â We observe then behavior over time and we are going to model diffusion and fit

Â a model based on that to try and understand exactly what was going on.

Â And in particular you know, kinds of

Â questions we could think about is you know,

Â what determines behavior generally.

Â So when we think about a diffusion process where

Â individuals are making some choice, do I adopt a technology?

Â Do I buy some new product?

Â In this case, do I end up taking out a

Â loan from a new possibility in terms of micro finance?

Â Is it, is, is, the, when people don't do it, is it because they don't have

Â information, just basic information, they don't even know

Â the opportunities out there, or are there complementarities

Â between individuals, so that I'm more likely to do when a friend ends up doing

Â it for, for various reasons, because either I

Â learned from that or I feel peer pressure

Â or may be there is just benefits from both of us taking out loans and

Â then we could end up learning from each

Â other and, and having useful interactions from that.

Â So that's one kind of question.

Â And another question that we, we'll actually

Â look at here is the role of non-participants

Â in diffusion processes.

Â So, so sometimes you see this in the epidemiology literature as well.

Â It could be, so when we think about something like the flu, generally

Â to pass the flu on you might, you have to have the flu.

Â But there could be people that are asymptomatic who don't actually come

Â down with the disease who could still catch something and transmit it.

Â And in this case, we could ask, is it possible

Â that somebody finds out about the availability of micro-finance loans?

Â They hear about it from friends.

Â They end up not taking out a loan, but nonetheless they still

Â pass information along and are useful

Â process useful in the process of diffusion.

Â So what we're going to do is, is model, take our

Â network model seriously, and then fit that to the data.

Â 2:27

Okay?

Â So, and here we, we know the set in, in

Â this particular instance, we know the set of initially formed nodes.

Â I'll tell you a little more about that.

Â And then we see how

Â things are going to work and where we

Â are going to model this as initially formed nodes.

Â They are going to pass information to their friends at random

Â and then their friends can pass information on and so forth.

Â So we'll just do a, a very simple diffusion model where we can

Â estimate that directly and then once you're

Â informed people will decide whether to participate.

Â Okay?

Â So the background here. There were 75 villages in Karnataka.

Â Relatively isolated

Â from having availability of loans before.

Â A bank went in, into 43 of these villages and those are the ones we'll look at here.

Â And offered microfinance.

Â Okay, so they started offering loans, and these are relatively poor villages.

Â 3:16

On the order of $1 or so a day, per capita, income.

Â So, fairly poor villages, and the way in which the

Â information was got out by was by word of mouth.

Â So the

Â bank would come in, identify a few people in the village, and then

Â tell them about micro finance and say bring, inform your friends about those.

Â And we know who the first people they talked to are.

Â We've surveyed the network, the villages and got network information,

Â and then we can track the micro finance over time.

Â Okay, so now how are we going to go about

Â modeling this and, and bringing diffusion explicitly into the picture?

Â Okay, so here's Karnataka,

Â here's the kind of networks we collected. We've seen a little bit of these.

Â You know.

Â If you had to borrow 50 rupees from a day,

Â for a day, who would you go and to borrow from?

Â So the borrowing network here, we

Â have these households are groups of individuals.

Â 4:32

And then we will, we can link up the households

Â based on whether they borrow money, kerosene and so forth.

Â So we have these different who do you go to temple with?

Â Who do you ask for advice? Who comes to you to buy kerosene?

Â Who do you go to for medial help?

Â So what we going to do is, is just build a, a, a, a full network

Â to say that two households can communicate if

Â they have any of these relationships in common.

Â And then we also have micro finance participation demographics, age, gender,

Â sub-cast, religion, wealth variables. Does the house have a latrine?

Â What, how many rooms does they have? What kind of roof does it have?

Â 5:17

And so, before we get into the diffusion model, let's just do a benchmark of

Â the standard way that we would, we might

Â think of doing a peer-effects kind of analysis.

Â So we, we can do is say what's the probability that

Â a given individual participates in the, in the, takes out a loan.

Â And so what we might do in that situation.

Â Without modelling diffusion is just say okay, we'll just

Â do this in a standard logistic form, so the

Â logs that, the probability that take up a loan

Â compared to not is going to depend on their characteristics.

Â So it might be higher depending on which profession they are in or which religion

Â they have or. Whether or not they are in a certain

Â caste group, or of a certain age.

Â And so we have a whole series of characteristics

Â we can put in there, that's going to affect their choice.

Â And then the standard peer effect, we'll say, does it also depend

Â on how many of their friends participate, or the fraction of their friends?

Â So am I more likely to participate, all else equal,

Â if 80% of my friends participate compared to 20%, okay?

Â 6:19

And we do have to worry about homopholy here,

Â that's going to be an issue behind the scenes,

Â because it could be that part of the reason that I participate compared

Â to my friends is that there's things that we have in common that

Â we're not seeing, and it's not that my friends influenced me, but it's

Â just that I am friends with people who are very similar to me.

Â Okay, so homopholy could be behind the scenes.

Â It's actually not going to be so much of an

Â issue for us because we are going to find it

Â eventually when we properly do a diffusion model, we are

Â not going to find these peer-effects, but it is something that

Â we have to keep in mind. So let's run that standard regression.

Â If you run that with a whole series of characteristics you

Â could find all the details of these regressions in the paper.

Â But effectively what you're going to end up with

Â is, a parameter here of 2.5, highly significant.

Â Which would seem to indicate that the more my friends par, the, the higher

Â the fraction my friends participate, the more likely I am to participate.

Â We can't say causal, but, but it seems to be there's a high correlation there.

Â And in particular, how do we make sense of

Â 2.5 given that we're looking at log of odds ratios.

Â So what does that mean?

Â So if you do some calculations, if, if you took my fraction of my friends

Â from zero to one, holding all the other

Â characteristics at their average, you would increase the

Â odds ratio by a factor of 12.

Â To make it relative likelihood of me

Â participating compared to not, 12 times higher, okay?

Â So, so that, that's a huge impact, and if you

Â took it from just 0.1 to 0.3, which is closer in

Â within one standard deviation of, of what the actual numbers

Â are, you'd still go up by a factor of about 1.65.

Â So you get, you still get a, a substantial impact of just moving

Â one standard deviation in the fraction of friends participating comes to,

Â to a 50% increase in the relative likelihood of participation, okay?

Â So, so we see a very strong effect if we just do the regression, and now

Â the only network information we're using is just

Â in terms of who are my friends, right?

Â So.

Â So basically we, now we're going to try and use bring a diffusion model into this.

Â And get a little more understanding of what that 2.5

Â really represents or what's going on behind the scenes there.

Â So we're going to use network information, not just with my friends.

Â But we'll keep track of people who

Â hear about microfinance or repeatedly pass information to

Â friends and then once I hear, will make a decision of whether or not to participate.

Â Okay, so we're going to bring diffusion officially into the picture now.

Â So let's stick first of all with the participation decision.

Â So once I'm informed, I'm going to make a decision of whether or not to participate.

Â And, we'll allow the, the choice to basically vary the same way it did before.

Â Okay, so exactly the same, logistic kind of regression we, we had before.

Â The log odds of ratio that I'll participate

Â once I'm informed, will look like something which depends

Â on my characteristics, and depends on the fraction

Â of, of friends I have who are also informed,

Â who are participating.

Â Okay, so now we'll keep track of who's informed and keep track of whether or

Â not I participate as a function of

Â my characteristics and the fraction of friends participating.

Â But what we're doing differently is we're actually going to

Â map out the information flow, and so whether or

Â not I participate whether or not, I choose to

Â participate will be conditional on whether or not I'm informed.

Â Okay. So how are we going to do that?

Â We're, we're going to have just a very simple model of passing information.

Â 9:51

And so, if I become informed, then I will pass information randomly to my friends.

Â And in particular what we're going to do

Â is, we'll allow for two different pro, probabilities.

Â If I chose not to participate, so if I'm a

Â person who thinks that I don't want to take up microfinance.

Â I'm going to pass information along with some probability q superscript N.

Â And if I chose to participate, so N for not participate.

Â If I choose to participate, I'm going to be

Â allowed to pass it with a different probability.

Â Okay?

Â So we're going to try and estimate

Â what these probabilities are from the diffusion process.

Â 10:26

So if I, if I didn't participate I pass with one probability.

Â If I participate, I pass with a different probability.

Â So let's look at what a typical thing would look like.

Â So let's call the leader is the first people who

Â are informed in the village.

Â So the bank comes in and tries to find the, the village leaders.

Â It looks for people they think are important.

Â They tell a few of them.

Â And they start with those people and then they say tell your friends about it.

Â Okay, so let's suppose that we had, this is just a snap

Â shot of part of a network and here we see two different people.

Â So one of the leaders chose not to

Â participate, one decides to participate in the loan program.

Â So we've got these two people.

Â Now what are they going to do?

Â Well, they can randomly tell some of their friends.

Â Right?

Â So these are relatively, word of mouth is the way that information's flowing

Â in these villages, so now they can randomly talk to some of their friends.

Â So we, allowing for different probabilities of passing, we might say,

Â okay, maybe if, if somebody's not excited about it, they didn't take

Â out the loan, they're, they're going to talk about it less than somebody

Â who just took out a loan and is more excited about it.

Â So, if those probablilities differ,

Â this person might tell three friends.

Â This person ends up telling only one friend.

Â So, now we've got some friends who are informed.

Â Now, they can look around and this person's going to make a decision.

Â This person's going to make a decision.

Â This person.

Â So, we got four people that are now making decisions.

Â They're going to make those decisions based on their characteristics,

Â but these people all have a friend whose taken up.

Â This person has a friend

Â who hasn't taken up, right?

Â So now we'll get some variation and we can begin

Â to see once they're informed, do they still take up with?

Â 12:13

And so these nodes decide, some of them decide

Â to participate, some decide not to, and the information keeps

Â spreading and so forth, okay?

Â So it goes on and, and new people become informed.

Â And the idea here these new people becoming informed.

Â This person has half of their friends who've

Â had a chance to take up micro finance participating.

Â This person has 100% of the friends who haven't had a chance to participate.

Â And so we can begin to see after

Â we account for the fact that information is flowing.

Â Through this network. And

Â I'm more likely to become informed because I'm next to somebody

Â who knows about it, who then has another chance to participate.

Â Whether we still get a pure effect after that, that

Â I'm more likely to participate if more of my friends do.

Â Okay? So that's the idea.

Â And we just keep iterating on this model. So what's the estimation technique?

Â So the estimation technique is we going to, first of

Â all, estimate some of the parameters through this logistic just

Â from the initially informed and that saves

Â on just computer's space and the, the three

Â things we are really interested in on

Â are what's the probability that non-participants pass information?

Â What's the probability that participants pass information?

Â And, what does this, peer effect kind of, or endorsement effect,

Â parameter look like once we've corrected for the passing?

Â So, we're going to, allow for the number of times that people can pass information

Â to be proportional to the nubmer of

Â trimesters, that the bank was in each village.

Â Depending on the village that goes from three to eight trimesters, so

Â were either passed three times or passed eight times, you can actually estimate.

Â We also did this by estimating that

Â endogenously, which allows you to another parameter.

Â It doesn't really

Â help that much, often it comes up between four and seven or so.

Â So this seems to be a fairly good estimate in any case.

Â And then how are we going to do this?

Â We're going to try and, so we search on a grid of these, so we'll, we'll, we'll

Â look at various parameters, so, you know, start

Â at probability of 0.0, 0.05, 0.1, and so forth.

Â So we'll march across a grid of different possible parameters.

Â And if for each one we can simulate the model, see what

Â comes out, and then try and match that to the observed moments.

Â So this is a form of general, generalized

Â method moments, in fact simulated method moments here.

Â So for instance what we could do is let's suppose that we set qN to be 0.15.

Â qP to be 0.3 and b-peer to be 0.5.

Â So if we did that and we ran, we just simulate

Â the model now, so we start with the actual data of the, the

Â network, we know who the initially formed ones are, we know which ones.

Â So then we randomly some choose to participate, they pass information

Â depending on whether they participate or not based on these probabilities.

Â 15:37

you know, less spreading from people who didn't participate and

Â more spreading in the neighborhood of people who did participate.

Â So this person participates, it spreads more, and

Â then people are more likely to react to that.

Â So we get, we're going to get a different

Â pattern of data as we vary those parameters.

Â And so what we'll do, is then as we vary the parameters, look for the parameters

Â that produce the most accurate participation data.

Â So if we match with the variance in participation,

Â what's the mean participation, and so on and so forth.

Â So we can have a series of moments, and

Â then try and match those to the actual data.

Â So we're just going to search across the grid, run simulations for

Â each one, figure out which one best matches what, what actually happens.

Â So if you go ahead and do that, then what do you end up with?

Â The diffusion parameters 0.05 and 0.55 in terms of these probabilities.

Â So you're about

Â ten times more likely to pass information along

Â if you're a participant than not, according to this.

Â 17:05

So the, the point parameter estimate is negative and it's insignificant.

Â So looks like there is really not that much

Â influence going on and if anything it's slightly negative.

Â You, you can tell a story that maybe.

Â there's, I'm less likely to take up a loan if my

Â friend does, because now I can borrow from them, but this is

Â statistically insignificant, so it's hard to

Â tell whether it's even different from zero.

Â Okay, so, what do we see?

Â We see that, that adding this diffusion model gives

Â us a very different picture of what's going on.

Â It's saying that the reason that we are seeing a lot of correlated take up between

Â people and their friends is not because they're

Â paying attention to what their friends are doing

Â and, and being influenced by that once they're informed.

Â It's that I'm much more likely to hear

Â about information if I have friends who participate.

Â So if my friends participate, I'm getting passed information at a

Â much higher rate, and that's what seems to account for this correlation.

Â So, when you fit this diffusion model, we get a different picture that comes out.

Â Okay?

Â Now, again, this isn't a causal we can't make causal inferences here.

Â We have to be careful. All we know is we fit

Â a model and these, we've got parameters which seem to come out, and

Â to the extent that this mo-, this model captures important features of reality.

Â Then, we're, we're picking something up.

Â 19:02

So what we can do now, and this sort of makes the point of why

Â is it important to have models we can work with, we can do counter factuals.

Â So we can say okay, suppose now we reran the model,

Â but we muzzle all the nonparticipants.

Â So we don't allow the nonparticipants to talk any more.

Â So we keep everything else the same, but we just

Â say, okay, if you're a nonparticipant, don't tell your friends.

Â And, let's see what happens.

Â And then that allows us to figure out how much did they actually

Â contribute, because we kept everything else equal and we only zeroed them out.

Â So then we can say, what was the marginal effect

Â if the change in the participation rate is going to be entirely

Â due to their passing at 0.05 compared to passing at zero.

Â Okay, so we can do that, next.

Â Okay, so the model as fit, we had 86% of the

Â people who were informed, and the participation rate ended up around 21%.

Â If you rerun it, everything else held constant and just

Â set the non-participants to not passing information any longer, the informedness

Â drops to about 59%. Participation drops to about 14%.

Â So roughly a third drop in each one of

Â these things by just changing that 0.5 to a zero.

Â And what's going on here?

Â Well, even though they are passing at a fairly small

Â rate, there's a lot of people who are non participants.

Â And so, the fact that most people choose not to

Â participate, about 80% of the people end up not particpating.

Â That gives you an idea that they can still be very important

Â in passing information even if they are passing at a lower rate.

Â Okay, okay, so we've fit this model we get significant

Â information passing, insignificant peer effects now once we've corrected for the

Â diffusion process, the information passing depends on whether you are not

Â you're, you're a participant and

Â non-participants still play an important role.

Â Okay, so,

Â conclusions well, what, why do we go through this, what we begin to see is by

Â actually including that model of diffusion and explicitly

Â taking into account the network pattern of diffusion.

Â We got a much better handle on what was going on in the peer effects.

Â And if we just run that regression at the start and got

Â that 2.5 we'd have no idea of why it was that I'm

Â being influenced by friends.

Â And here it begins to tell us it looks

Â more like it's just information passing than actual influence.

Â And that can be very important for policies.

Â So if you want to enhance micro-finance diffusion in these villages, it says that

Â it's basically information spreading that's the more

Â important part and it's not pure influences right.

Â So, so it's not that you need the help over come peer influences,

Â it's more that you need to enhance information spreading.

Â 21:48

You could also begin to, you know, bring, relate this back to network structure.

Â Would changing homophily structure help information spread better?

Â You could do counterfactuals on this.

Â So once you fit one of these models, then you could actually do a whole

Â series of things by changing things and, and begin to see how things would operate.

Â So, you know, so basically that's just a, a look

Â at one diffusion model that allows us to say something and

Â get a handle on, on different peer effects.

Â And one thing to emphasize here, the conclusion

Â should not be that it's always information passing.

Â That was true in this one instance.

Â Instead we really want to take away from this the methodology.

Â Of, of explicitly, carefully taking into account information

Â passing, separating it out from decision processes, so

Â our diffusion model is a little richer than

Â we were looking at before where it's just simple-like

Â food like [INAUDIBLE] now we allow for these different things.

Â We can map that out.

Â Work with data. Try and see what's going on.

Â