From its very beginning, network theory has emphasised that different link formation rules result in fundamentally different network structures (Bala and Goyal 2000). This in turn may have dramatic implications for the way resources are allocated across the network. Yet we know very little about the data generation process behind the links we observe in the data.
In our new paper, we propose a testing methodology to shed light on the interpretation of self-reported link data in relation to the two key issues (Comola and Fafchamps 2014).
- Are survey respondents listing actual links?
- If so, are these links formed in a bilateral or unilateral manner?
The nature of reported links
The difference between alternative link formation processes and the importance of distinguishing between them is best described with an example. Imagine asking students in a university classroom: “Who do you ask when you have a question about mathematics?” – and it turns out that students who mention talking to the lecturer get higher marks. Is it right to conclude that talking to the lecturer improves their mathematics performance?
In most universities, lecturers are required to have office hours, and students have equal access to lecturers. This case corresponds to what the researchers call ‘unilateral link formation’: one party can unilaterally initiate contact without the consent of the other. In this context poor exam performance cannot, by design, be ‘caused’ by lack of lecturer contact since it is endogenous. Correlation between student marks and lecturer contact may nevertheless suggest that talking to the lecturer helps those students who take advantage of it.
The situation is different if the lecturer has discretion about which students to help. This scenario corresponds to ‘bilateral link formation’: the consent of both parties is needed for a link to be formed – which is a natural assumption for voluntary favour exchange. Here, contact with the lecturer may have a causal effect on student performance: had the lecturer refused to see a student, he or she would have performed worse.
Given the specific framing of this question (“Who do you ask when you have a question about mathematics?”) it is also conceivable that answers do not actually measure existing social links, but simply the ‘desire to link’. Imagine no student has seen the lecturer but better students list the lecturer, knowing they would ask the lecturer if they had a question. That would mean there is a correlation between listing the lecturer and exam performance despite no direct social contact.
As the example illustrates, whether respondents report existing links or the desire to link – and whether link formation is unilateral or bilateral – determines whether social contact has a causal effect on the outcomes of interest or not. The contribution of our paper is primarily methodological, as we propose a non-nested log-likelihood test to compare these alternative data generation processes on link formation and find which one is more adapted to the data at hand (Vuong 1989). Doing so, our study provides new insights into whether we can interpret pre-existing links in a causal manner, and whether we can draw policy recommendations based on that.
We illustrate our methodology with two separate observational datasets:
- One from risk-sharing in a Tanzanian village;
- Another of communication among Indian farmers.
The first illustration focuses on informal risk-sharing in a Tanzanian village, where respondents were asked to enumerate all their risk-sharing partners:
“Can you give a list of people who you can personally rely on for help and/or that can rely on you for help in cash, kind or labour?”
This question is open to multiple interpretations. One possibility is that respondents gave the names of people from whom they wish to seek assistance. If this is the case, answers are best understood as representing simple ‘desire to link’ rather than actual links. Another interpretation is that respondents provided information on actual links. In the latter case, it is a priori uncertain whether these observed links are generated by a bilateral or unilateral link formation process. Previous literature has indeed debated as to whether risk-sharing links should be seen as implicit contracts grounded in mutual self-interest – which would be compatible with the bilateral link hypothesis – or whether social norms impose an element of moral or social pressure that makes it difficult for households to refuse to help or be helped by others – which would result into an unilateral link formation process (Coate and Ravallion 1993, Platteau 2000, Ligon et al. 2001).
We find that in our data that the ‘desire to link’ model provides the best fit: respondents seem to list households with whom it is in their objective interest to link, whether or not such a link exists. This result is compatible with the existence of egalitarian social norms that make it impossible to refuse providing assistance to others (Platteau 2000).
The second illustration uses survey data collected among farmers in the Indian state of Maharashtra. Each respondent was asked about his interpersonal communication with every other farmer in his village:
“How often do you discuss agricultural issues with this person or members of his household?”
Our results indicate that in this context, survey responses are best interpreted as existing links rather than desire to link, and that the unilateral link formation model fits the data better than the bilateral model.
This suggests that less experienced farmers can secure information about farming practices from more knowledgeable neighbours even though the latter have little to gain objectively from agricultural information exchange. This reassuringly suggests that information about agricultural technology is likely to flow from more knowledgeable to less knowledgeable farmers, and it opens up interesting opportunities from a policy intervention perspective – for example, targeting extension services to more knowledgeable farmers who are better able to absorb and subsequently disseminate information about new technology.
Bala, V and S Goyal (2000), “A Non-Cooperative Model of Network Formation”, Econometrica, 68(5): 1181-1229.
Comola, M, and M Fafchamps (2014) “Testing Unilateral and Bilateral Link Formation”, Economic Journal 124(579): 954-76.
Coate, S and M Ravallion (1993), “Reciprocity Without Commitment: Characterization and Performance of Informal Insurance Arrangements”, Journal of Development Economics, 40: 1-24
Ligon, E, J P Thomas, and T Worrall (2001), “Informal Insurance Arrangements in Village Economies”, Review of Economic Studies, 69(1): 209-44
Platteau, J-P (2000), Institutions, Social Norms, and Economic Development, Harwood Academic Publishers, Amsterdam
Vuong, Q H (1989), “Likelihood ratio tests for model selection and non-nested hypotheses”, Econometrica, vol. 57(2), pp. 307–33.