Skip to main content

Impact of social network structure on content propagation: A study using YouTube data


We study how the size and structure of the local network around a node affects the aggregate diffusion of products seeded by it. We examine this in the context of YouTube, the popular video-sharing site. We address the endogeneity problems common to this setting by using a rich dataset and a careful estimation methodology. We empirically demonstrate that the size and structure of an author’s local network is a significant driver of the popularity of videos seeded by her, even after controlling for observed and unobserved video characteristics, unobserved author characteristics, and endogenous network formation. Our findings are distinct from those in the peer effects literature, which examines neighborhood effects on individual behavior, since we document the causal relationship between a node’s local network position and the global diffusion of products seeded by it. Our results provide guidelines for identifying seeds that provide the best return on investment, thereby aiding managers conducting buzz marketing campaigns on social media forums. Further, our study sheds light on the other substantive factors that affect video consumption on YouTube.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10


  1. See

  2. In fact, unobserved product quality is problematic in other respects too. A high quality product is more likely to have a higher price, higher consumer ratings, and higher advertising expenditure, i.e., unobserved and observed product attributes are likely to be correlated. Hence, if the former is not controlled for, then our results on the role of observed product attributes are also likely to be biased.

  3. While exists a large stream of literature on Bass models (Bass 1969; Mahajan et al. 2000), these models cannot be used to establish causality between network structure and product diffusion because they assume random mixing or interactions over a fully connected network.

  4. The fact that we are only able to analyze videos whose authors have publicized their friendships may cause some selection bias. There is no direct test to confirm or refute this. However we can test for selection bias indirectly by comparing the viewership distributions of the two samples of authors (i.e., the ones who publicized their friendship links and the ones who didn’t). Since an author’s social network affects her video’s viewership, if we find the viewership distributions of both samples to be similar, then we can infer that both samples are drawn from the same social network distribution. Therefore we compared the viewership distributions of the two samples using Kolmogorov-Smirnov tests at t = 10, 20, and 30. In all three cases, the two distributions were statistically indistinguishable. Hence, we can safely say that any selection bias, if it exists, is not substantial.

  5. Closeness is defined as the average geodesic distance of a node to the rest of the network. In a two-hop network, Closeness is \( c{s_i} = {{{({d_i} + 2s{d_i})}} \left/ {{({d_i} + s{d_i}}} \right.}) \). This can be rewritten as \( c{s_i} = 2 - \left( {{{1} \left/ {{(1 + af{f_i})}} \right.}} \right) \).

  6. Note that there can be more than one geodesic between two nodes. For example, in Fig. 6(b), there are two shortest paths between nodes F3 and F4: F3-S2-F4 and F3-O-F4.

  7. While 2-Beteweenness can be interpreted as a measure of local centrality, many have argued that it is in fact superior to global Betweenness. In 2-Betweenness, only geodesics of length two or less are considered, while global Betweenness considers geodesics of all lengths. However, lengthy paths are seldom used for communication. So taking them into account can result in a distorted picture of centrality. Therefore, some researchers advocate the use of 2-Betweenness even when complete network data is available. See Gould and Fernandez (1989), Friedkin (1991), and Borgatti and Everett (2006) for a comprehensive discussion of these issues. Moreover, both Everett and Borgatti (2005) and Borgatti et al. (2006) have shown that local Betweenness is highly correlated with global Betweenness.

  8. Notice that the degree distribution of first-degree friends looks very different from that of the author’s degree distribution (see Table 3), i.e., Mean (Friend of friends) >Mean (Friends). As noted by Feld (1991), this property is common in social networks because well-connected people (with large Degree) tend to show up disproportionately more often in everyone’s friends lists. Hence, in any social network, random sampling of authors (or nodes) will give rise to a sample of first-degree friends, which will contain some high-degree nodes. In Section 6.4, we perform robustness checks to confirm that our results are not driven by such high-degree nodes.

  9. Stephen and Toubia (2010) also study the impact of local Clustering, but in the context of a sellers’ network. In their setting, a node’s (seller’s) goal is to generate high incoming traffic, whereas in our context a node’s goal is to maximize the outgoing information on video. So their findings are not applicable to our context.

  10. Note that authors from close-knit groups are more likely to post niche videos (videos of interest to only those close to them), which could dampen the global diffusion of their videos. We allow for this possibility within the model through Assumption 10.6, i.e., we allow for correlations between the unobserved content of the videoand its author’s network properties. In the estimation, when specifying moment conditions, we ensure that this correlation is not violated. Hence, we can safely state that the negative effect of Clustering doesn’t stem from the correlation between a video’s content (niche or broad) and the clustering in its author’s network.

  11. On a related note, Granovetter (1973) suggests that new information often comes from weak ties or acquaintances and not from close friends. Since members of close-knit groups tend to be close friends and those of loosely knit groups tend to be acquaintances, this result can also be interpreted as acquaintances being more valuable than close friends from a seed’s perspective.

  12. We expect videos of central authors to receive high attention, thus leading to larger viewership. However, one might suspect otherwise if central authors are also more likely to post many videos in quick succession, thereby diluting the attention per video. To test if this is true, we counted the number of other videos (apart from the one in our dataset) posted by the most central authors. Specifically, of the 1806 authors in our dataset, 116 have a Betweenness value of 1 and these 116 authors posted an average of 0.53 other videos during the interval of our observation. Given our 38-day observation interval, this amounts to a mere 0.0138 videos per day. Thus, the attention fragmentation hypothesis is unlikely to be true.

  13. Both lagged Daily Num. Ratings and lagged Daily Comments are likely to be correlated with lagged Daily Views, which can be problematic. However, we found that normalizing these variables by lagged Daily Views also doesn’t make them significant.

  14. For a sufficiently long T, the number of instruments available for Equations 10 and 11 expands rapidly. While theoretically using all instruments increases consistency, Tauchen (1986) and Ziliak (1997) have shown that there is a consistency-efficiency trade-off in finite samples. In our case, we find that one set of lagged differences and four to six sets of lagged levels are sufficient to get consistent results without any significant loss in efficiency.

  15. Note that we choose 10 periods as the point of demarcation even though ‘early’ in the YouTube context might mean just 4–5 days. We do this primarily because we need sufficient time periods for the analysis. In Model 11, we use 6 lags of Daily views on the right hand side; this leaves us only 4 data points or less per video. If we shortened the span of the early stage, then we would have even fewer data points per video, making analysis difficult.

  16. In the estimation, ln (d i  + 1) is significant in Model 11, but not in Model 12, while ln (sd i  + 1) is significant in Model 12, but not in Model 11 (see Table 8). Given this pattern, the use of a composite variable like ln (aff i ) that contains both sd i and d i is problematic because it makes it difficult to ascertain whether d i is significant in its own right (see Woolridge 2008). So we instead use ln (d i  + 1)and ln (sd i  + 1)directly.


  • Acemoglu, D., & Robinson, J. (2001). A theory of political transition. The American Economic Review, 91(4), 938–963.

    Article  Google Scholar 

  • Anderson, T. W., & Hsaio, C. (1981). Estimation of dynamic models with error components. Journal of the American Statistical Association, 76(375), 598–606.

    Article  Google Scholar 

  • Arellano, M., & Bond, S. (1991). Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations. The Review of Economic Studies, 58, 277–97.

    Article  Google Scholar 

  • Bandeira, O., & Rasul, I. (2006). Social networks and technology adoption in Northern Mozambique. The Economic Journal, 116, 869–902.

    Article  Google Scholar 

  • Bandiera, O., Barankay, I., & Rasul, I. (2009). Social connections and incentives in the workplace: evidence from personnel data. Econometrica., 77, 1047–94.

    Article  Google Scholar 

  • Barabasi, A. L., Albert, R., & Jeong, H. (2000). Scale-free characteristics of random networks: the topology of the world wide web. Physica A, 281, 69–77.

    Article  Google Scholar 

  • Barry, K. (2009). Ford bets the fiesta on social networking. Wired.

  • Bass, F. M. (1969). A new product growth model for consumer durables. Management Science, 15, 215–227.

    Article  Google Scholar 

  • Bertrand, M., Luttmer, E. F. P., & Mullainathan, S. (2000). Network effects and welfare cultures. Quarterly Journal of Economics, 115, 1019–1056.

    Article  Google Scholar 

  • Blundell, R., & Bond, S. (1998). Initial conditions and moment restrictionsin dynamic panel data models. Journal of Econometrics., 87, 115–43.

    Article  Google Scholar 

  • Borgatti, S. P. G., Jones, C., & Everett, M. G. (1998). Network measures of social capital. Connections, 21, 27–36.

    Google Scholar 

  • Borgatti, S. P., Carley, K. M., & Krackhardt, D. (2006). On the robustness of centrality measures under conditions of imperfect data. Social Networks, 28, 124–136.

    Article  Google Scholar 

  • Borgatti, S. P., & Everett, M. G. (2006). A graph-theoretic perspective on centrality. Social Networks, 28, 466–84.

    Article  Google Scholar 

  • Bramoullé, Y., Djebbari, H., & Fortin, B. (2009). Identification of peer effects through social networks. Journal of Econometrics., 150, 41–55.

    Article  Google Scholar 

  • Brock, W. A., & Durlauf, S. N. (2007). Identification of binary choice models with social interactions. Journal of Econometrics, 140(1), 52–75.

    Article  Google Scholar 

  • Burt, R. (1995). Structural holes: The social structure of competition. Harvard University Press.

  • Clark, C. C., Doraszelski, U., & Draganska, M. (2009). The effect of advertising on brand awareness and perceived quality: an empirical investigation using panel data. Quantitative Marketing and Economics, 7, 207–236.

    Article  Google Scholar 

  • Coleman, J. S., Katz, E., & Menzel, H. (1966). Medical innovation: A diffusion study. Indianapolis: Bobb-Merrill.

    Google Scholar 

  • Durlauf, S., Johnson, P., & Temple, J. (2005). Growth econometrics. In P. Aghion & S. Durlauf (Eds.), Handbook of econometric growth (Vol. 1A, pp. 555–677). Amsterdam: North-Holland.

    Google Scholar 

  • Everett, M. G., & Borgatti, S. P. (2005). Ego-network betweenness. Social Networks, 27(1), 31–38.

    Article  Google Scholar 

  • Feed Company. (2008). Viral video marketing survey: The agency perspective.

  • Feld, S. L. (1991). Why your friends have more friends than you do. The American Journal of Sociology, 96(6), 1464–77.

    Article  Google Scholar 

  • Freeman, L. C. (1979). Centrality in social networks: a conceptual clarification. Social Networks. pp. 1–21.

  • Friedkin, N. E. (1991). Theoretical foundations for centrality measures. The American Journal of Sociology, 96, 1478–1504.

    Article  Google Scholar 

  • Greenberg, K. (2010). Ford fiesta movement shifts into high gear. Marketing Daily.

  • Girvan, M., & Newman, M. E. J. (2002). Community structure in social and biological networks. Proceedings of the National Academy of Science of the United States of America, 99(12), 7821–26.

    Article  Google Scholar 

  • Goldenberg, J., Sangman, H., Lehmann, D. R., & Hong, J. W. (2009). The role of hubs in the adoption process. Journal of Marketing, 73, 1–13.

    Article  Google Scholar 

  • Gould, R. V., & Fernandez, R. M. (1989). Structures of mediation: A formal approach to brokerage in transaction networks. In C. C. Clogg & A. Arbor (Eds.), Sociological methodology (pp. 89–126). MI: Blackwell.

    Google Scholar 

  • Granovetter, M. (1973). The strength of weak ties. The American Journal of Sociology, 78(6), 1360–80.

    Article  Google Scholar 

  • Hansen, B. E. (2008). Econometrics. available at:

  • Hartmann, W. R., Manchanda, P., Nair, H., Bothner, M., Dodds, P., Godes, D., et al. (2008). Modeling social interactions: identification, empirical methods and policy implications. Marketing Letters, 19(3).

  • Hitwise Experian. (2010). Top 20 sites and engines. available at:

  • Katona, Z., Zubcsek, P. P., & Sarvary, M. (2009). Network effects and personal influences: Diffusion of an online social network. Working paper.

  • Katz, E., & Lazarsfeld, P. F. (1955). Personal influence: The part played by people in the flow of mass communications. Glencoe: Free.

    Google Scholar 

  • Mahajan, V., Muller, E., & Wind, Y. (2000). New product diffusion models: From theory to practice. In V. Majan, E. Muller, & Y. Wind (Eds.), New product diffusion models. Boston: Kluwer.

    Google Scholar 

  • Manski, C. F. (1993). Identification of endogenous social effects: the reflection problem. The Review of Economic Studies, 60(3), 531–42.

    Article  Google Scholar 

  • McCracken, G. (2010). How Ford got social marketing right. The Conversation, Harvard Business Review.

  • McPherson, M., Smith-Lovin, L., & Cook, J. M. (2001). Birds of a feather: Homophily in social networks.

  • Mislove, A., Marcon, M., Gummadi, K., Druschel, P., & Bhattacharjee, B. (2007). Measurement and Analysis of Online Social Networks. In Proceedings of the 5th ACM/USENIX Internet Measurement Conference, San Diego, CA.

  • Moynihan, R. (2008). Key opinion leaders: independent experts or drug representatives in disguise. British Medical Journal, 336, 1402–03.

    Article  Google Scholar 

  • Nair, H., Manchanda, P., & Bhatia, T. (2009). Asymmetric social interactions in physician prescription behavior: The role of opinion leaders. Working paper.

  • Nickell, S. (1981). Biases in dynamic models with fixed effects. Econometrica, 39, 359–87.

    Google Scholar 

  • Nielson Online. (2010). Nielsen net ratings April 2010.

  • Rogers, E. M. (2003). Diffusion of innovations (5th ed.). New York: Free.

    Google Scholar 

  • Sacerdote, B. (2001). Peer effects with random assignment: results for Dartmouth roommates. Quarterly Journal of Economics, 116, 681–704.

    Article  Google Scholar 

  • Stephen A. T., & Toubia, O. (2010). Deriving value from social commerce networks. forthcoming Journal of Marketing Research.

  • Tajfel, H., & Turner, J. C. (1986). The social identity theory of inter-group behavior. In S. Worchel & W. G. Austin (Eds.), Psychology of intergroup relations (2nd ed., pp. 7–24). Chicago: Nelson-Hall.

    Google Scholar 

  • Tauchen, G. (1986). Statistical properties of generalized method of moments estimators of structural parameters obtained from financial market data. Journal of Business and Economic Statistics, 4(4), 397–416.

    Article  Google Scholar 

  • Trogdon, J., Nonnemaker, J., & Pais, J. (2008). Peer effects in adolescent overweight. Journal of Health Economics, 27(5), 1388–1399.

    Article  Google Scholar 

  • Tucker, C. (2008). Identifying formal and informal influence in technology adoption with network externalities. Management Science, 55(12), 2024–2039.

    Article  Google Scholar 

  • Valente, T. W., & Pumpuang, P. (2007). Identifying opinion leaders to promote behavior changes. Health Education & Behavior, 34, 881–96.

    Article  Google Scholar 

  • Watts, D. J., & Dodds, P. S. (2007). Influentials, networks, and public opinion formation. Journal of Consumer Research, 34, 441–58.

    Article  Google Scholar 

  • Watts, D. J., & Strogatz, S. H. (1998). Collective dynamics of ‘Small-World’ networks. Nature, 393(4), 440–42.

    Article  Google Scholar 

  • Windmeijer, F. (2005). A finite sample correction for the variance of linear efficient two-step GMM estimators. Journal of Econometrics, 126(1), 25–51.

    Article  Google Scholar 

  • Woolridge, J. (2008). Introductory econometrics: A modern approach. 4th ed., South-Western College Pub.

  • Ziliak, J. P. (1997). Efficient estimation with panel data when instruments are predetermined: an empirical comparison of moment-condition estimators. Journal of Business and Economic Statistics, 15(4), 419–31.

    Article  Google Scholar 

Download references


Discussions with Dina Mayzlin, Harikesh Nair, Sridhar Naryanan, and Jiwoong Shin have greatly improved this paper. Comments from the Editor, Greg Allenby, and two anonymous reviewers have also helped the paper considerably. Finally, thanks are also due to the participants of the PhD Student Research Workshop at the Yale School of Management 2009, NASMEI 2009, UT Dallas Forms Conference 2009, Marketing Science Conference 2010, Marketing Dynamics Conference 2010, Stanford Marketing Seminar 2010, Haas Marketing Seminar 2010, and University of Washington Marketing Seminar 2011, for their feedback.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Hema Yoganarasimhan.



A.1. Technical details on data collection

We collected the YouTube data using a set of custom scripts written in Perl. We bootstrapped the data collection process using a Perl script to find the list of newly uploaded videos to YouTube. We then used a separate script to periodically access the statistics page corresponding to the videos, collected the relevant video characteristics, and stored them in a MySql database for later analysis. The Perl script parsed the HTML content of the statistics pages by looking for key markers in the HTML tags associated with the various video related data. We used Perl’s “HTML Parser” library to perform the data extraction.

Concurrently, we used a separate set of Perl scripts deployed on a cluster of workstations to collect data on the social network of the authors that have seeded the videos. The video page provided the link to the author’s page, which in turn contained data on the author and the author's social network. For instance, the author’s page contains the identities of his or her directly connected friends. We used a cluster of workstations in order to collect a snapshot of the social network structure within 4 days. The entire process was managed by a centralized controller that was responsible for handing out the network crawling tasks to the individual computers, monitoring their progress, and occasionally reissuing tasks if they are not completed within a specified time interval. The social network data was also stored in a MySql database and then analyzed using custom programs written in C. The analysis yielded the various social network metrics that we use in the paper, e.g., degree, number of second-degree friends, clustering, and Betweenness centrality.

We make all of the above scripts available for researchers interested in collecting YouTube data, at We do note that YouTube changes its webpage layout and data format regularly, so it is likely that our scripts would have to be modified to account for recent changes.

A.2. Initial conditions assumption

This assumption ensures that the impact of the unobserved fixed effect η i on growth (y i,t ) remains constant over time. Let \( {A_K} = \sum\limits_{k = 1}^K {{\alpha_k}} \) and \( {\eta_0} = \frac{{(1 + {\kappa_X}\gamma + {\kappa_Z}\beta )}}{{1 - {A_K}}} \). Recall that X i,t and Z i are linearly correlated with η i . Hence, they can be expressed as \( {X_{i,t}} = {\lambda_X}{X'_{i,t}} + {\kappa_X}{\eta_i} + {\delta_{i,t}} \) and \( {Z_i} = {\lambda_Z}{Z'_i} + {\kappa_Z}{\eta_i} + {\xi_i} \), where \( {X'_{i,t}} \) and \( {Z'_i} \) is not correlated to η i and δ i,t and ξ i are random shocks such that E(δ i,t ) = 0, E(ξ i ) = 0 and E(δ i,t .η i ) = 0, E(ξ i .η i ) = 0. Using these expansions recursively in tandem with Assumption 10.7, we now show that the impact of η i has a constant y i,t in all periods.

Lemma 1: The effect of the unobserved fixed effect η i on y i,t is constant for all periods and is equal to η 0.

Proof: Period 1: Consider the growth equation for t = 1. By Assumption (10.7a), we have:

$$ {y_{i,1}} = c + {\eta_i}\left( {\frac{{1 + {\kappa_X}\gamma + {\kappa_Z}\beta {A_K}}}{{1 - {A_K}}}} \right) + \beta {Z_i} + {\varepsilon_{i,1}} $$

We know that Z i can be expressed as \( {Z_i} = {\lambda_Z}{Z'_i} + {\kappa_Z}{\eta_i} + {\xi_i} \), where Z i and ξ i are not correlated with η i . After substituting for Z i , (10.7a) can be expressed as follows:

$$ {y_{i,1}} = c + {\eta_0}{\eta_i} + {\lambda_Z}\beta {Z'_i} + \beta {\xi_i} + {\varepsilon_{i,1}}. $$

Since \( {Z'_i} \), ξ i , ɛ i,1 and c are independent of η i , the coefficient of η i is given by η 0.

Periods 2 to K: Next, consider the growth equations for the remaining (K-1) initial periods, i.e., 2 ⩽ tK. From Assumption (10.7b), we have:

$$ {y_{i,t}} = c + {\eta_i}\left( {\frac{{1 + ({\kappa_Z}\beta + {\kappa_X}\gamma ){A_K}}}{{1 - {A_K}}}} \right) + \gamma {X_{i,t - 1}} + \beta {Z_i} + {\varepsilon_{i,t}}{, }\forall { }2 \leqslant t \leqslant K $$

As before, we can substitute for Z i in (10.7b). In addition, we can also substitute for X i,t−1 as follows: \( {X_{i,t - 1}} = {\lambda_X}{X'_{i,t - 1}} + {\kappa_X}{\eta_i} + {\delta_{i,t - 1}} \)). Thus, (10.7b) can be rewritten as:

$$ {y_{i,t}} = c + {\eta_0}{\eta_i} + {\lambda_x}\gamma {X'_{i,t - 1}} + \gamma {\delta_{i,t - 1}} + {\lambda_Z}\beta {Z'_i} + \beta {\xi_i} + {\varepsilon_{i,t}}{, }\forall { }1 < t \leqslant K $$

Since \( {X'_{i,t - 1}} \), \( {Z'_i} \), δ i,t−1, ξ i , ɛ i,t and c are not correlated with η i , the coefficient of η i is given by η 0.

Period K + 1: Next, consider the growth in (K + 1)th period (from Equation 10)

$$ {y_{i,K + 1}} = c + \sum\limits_{k = 1}^K {{\alpha_k}{y_{i,t - k}}} + \gamma {X_{i,K}} + \beta {Z_i} + {\eta_i} + {\varepsilon_{i,K + 1}} $$

The η i term in \( \gamma {X_{i,K}} + \beta {Z_i} + {\eta_i} \) is given by \( (1 + {\kappa_X}\gamma + {\kappa_Z}\beta ){\eta_i} \). We know that each y i,tk term in \( \sum\limits_{k = 1}^K {{\alpha_k}{y_{i,t - k}}} \) contains η 0 and therefore, the total contribution \( \sum\limits_{k = 1}^K {{\alpha_k}{y_{i,t - k}}} \) to the η i term is A K η 0 η i . Thus, the complete coefficient of η i in Equation (10) is given by η 0.

Periods K + 2 to T: Now consider the growth in the (K + 2)th period:

$$ {y_{i,K + 2}} = c + \sum\limits_{k = 2}^{K + 1} {{\alpha_k}{y_{i,t - k}}} + \gamma {X_{i,K + 1}} + \beta {Z_i} + {\eta_i} + {\varepsilon_{i,K + 2}} $$

As before, the η i term from \( \gamma {X_{i,K + 1}} + \beta {Z_i} + {\eta_i} \) is \( (1 + {\kappa_X}\gamma + {\kappa_Z}\beta ){\eta_i} \) and since all y i,tk s in \( \sum\limits_{k = 2}^{K + 1} {{\alpha_k}{y_{i,t - k}}} \) contain η 0 η i , their contribution to the η i term is A K η 0 η i . Thus, the total η i term in y i,K+2 is η 0 η i , which is the same as the η i term in \( {y_{i,1}},...,{y_{i,K + 1}} \). Next, to show that the coefficient of \( {\eta_i} \) in y i,K+3 is η 0, we use two facts: 1) the functional form of y i,K+3 is the same as that of y i,K+2, and 2) the coefficient of η i in all the lagged terms \( {y_{i,K + 2}},...,{y_{i,3}} \), is η 0. So using the same technique as above, we can show that the coefficient of η i in y i,K+3 is also η 0. Similarly, by recursive induction, the coefficient of y i,K+j is also η 0 for all j > 3. Thus, all y i,t s can be expressed as follows:

$$ {y_{i,t}} = {\eta_0}{\eta_i} + {f_t}\left( {{{X'}_{i,t - 1}},...,{{X'}_{i,1}},{\delta_{i,t - 1}},...,{\delta_{i,1}},{{Z'}_i},{\xi_i},{\varepsilon_{i,t}},...,{\varepsilon_{i,1}}} \right) $$

A.3. Moment conditions for first-differenced equation

The first-differenced equations are given by:

$$ \Delta {y_{i,t}} = \sum\limits_{k = 1}^K {{\alpha_k}\Delta {y_{i,t - k}}} + \gamma \Delta {X_{i,t - 1}} + \Delta {\varepsilon_{i,t}} $$

We specify two sets of moment conditions, 12(a) and 12(b), for Equation 11. In Proposition 1, we show that these moment conditions are true.

Proposition 1: For \( {\it{p}} = {\it{K,K + {\text1},}}...{\text{,t - 2}} \), \( E({y_{{\text{i}},{\text{p}}}}.\Delta {\varepsilon_{{\text{i}},{\text{t}}}}) = 0 \) and \( E({X_{{\text{i}},{\text{p}}}}.\Delta {\varepsilon_{i,t}}) = 0 \).

Proof: We start with moment conditions \( E({X_{{\text{i}},{\text{p}}}}.\Delta {\varepsilon_{i,t}}) = 0 \) where \( {\it{p}} = {\it{K,K + 1,}}...{\it{,t - {\text2}}} \). From Assumption (10.4), we have \( E({X_{i,t}}.{\varepsilon_{i,s}}) = 0{\text{ if s}} > t \) and \( E({X_{i,t}}.{\varepsilon_{i,s}}) \ne 0{\text{ if s}} \leqslant t \). This implies that X i,p is uncorrelated to Δε i,t for all pt − 2. Next, consider the moment conditions \( E({y_{{\text{i}},{\text{p}}}}.\Delta {\varepsilon_{{\text{i}},{\text{t}}}}) = 0 \), where \( {\it{p}} = {\it{K,K + 1,}}...{\it{,t - {\text 2}}} \). From Lemma 1, we know that all y i,t terms can be written as follows:

$$ {y_{i,p}} = {\eta_0}{\eta_i} + {f_p}\left( {{{X'}_{i,p - 1}},...,{{X'}_{i,1}},{\delta_{i,p - 1}},...,{\delta_{i,1}},{{Z'}_i},{\xi_i},{\varepsilon_{i,p}},...,{\varepsilon_{i,1}}} \right) $$

From Assumption (10.1), we know that \( E({\eta_{\text{i}}}.\Delta {\varepsilon_{{\text{i}},{\text{t}}}}) = 0 \). Also, from Assumptions 10.1, 10.4, 10.5, and 10.6, we know that \( {f_p}(.) \) is uncorrelated with Δε i,t for all pt − 2. So \( E({y_{{\text{i}},{\text{p}}}}.\Delta {\varepsilon_{{\text{i}},{\text{t}}}}) = 0. \)

A.4. Moment conditions for level equation

The level equations when t > K are given by:

$$ {y_{i,t}} = c + \sum\limits_{k = 1}^K {{\alpha_k}{y_{i,t - k}} + \gamma } {X_{i,t - 1}} + \beta {Z_i} + {\eta_i} + {\varepsilon_{i,t}} $$

We specify two sets of moment conditions for Equation (10) (see Equations 13a and 13b). In Proposition 2, we show that these moment conditions are true.

Proposition 2: For \( p = K,...,t - 1 \), \( E\left( {\Delta {y_{{\text{i}},p}}.({\eta_{\text{i}}} + {\varepsilon_{{\text{i}},{\text{t}}}})} \right) = 0 \) and \( E\left( {\Delta {X_{{\text{i}},p}}.({\eta_{\text{i}}} + {\varepsilon_{{\text{i}},{\text{t}}}})} \right) = 0 \).

Proof: We start with \( E\left( {\Delta {X_{{\text{i}},p}}.({\eta_{\text{i}}} + {\varepsilon_{{\text{i}},{\text{t}}}})} \right) = 0 \). From Assumption (10.4), we have \( E({X_{i,t}}.{\varepsilon_{i,s}}) = 0{\text{ if s}} > t \) and \( E({X_{i,t}}.{\varepsilon_{i,s}}) \ne 0{\text{ if s}} \leqslant t \). This implies that X i,p is uncorrelated to ε i,t for all pt − 1 and by extension ΔX i,p is uncorrelated with ε i,t for pt − 1. From Assumption (10.5), we know that X i,p s are linearly correlated with η i , which implies that ΔX i,t−1 is uncorrelated with η i . Thus, ΔX i,p is uncorrelated to both η i and ε i,t . Next, consider the moments \( E\left( {\Delta {y_{{\text{i}},p}}.({\eta_{\text{i}}} + {\varepsilon_{{\text{i}},{\text{t}}}})} \right) = 0 \). Recall that, for pK + 1, y i,p can be written as \( {y_{i,p}} = {\eta_0}{\eta_i} + {f_p}(.) \), where \( {f_p}(.) \) is independent of η i . Hence, Δy i,p can be written as follows:

$$ \Delta {y_{i,p}} = {f_p}\left( {{{X'}_{i,p - 1}},...,{{X'}_{i,1}},{{Z'}_i},{\varepsilon_{i,p}},...,{\varepsilon_{i,1}}} \right) - {f_{p - 1}}\left( {{{X'}_{i,p - 2}},...,{{X'}_{i,1}},{{Z'}_i},{\varepsilon_{i,t - 1}},...,{\varepsilon_{i,1}}} \right) $$

Thus, the moment condition, \( E\left( {\Delta {y_{{\text{i}},p}}.({\eta_{\text{i}}} + {\varepsilon_{{\text{i}},{\text{t}}}})} \right) = 0 \), can be expressed as follows:

$$ E\left( {\left( {{f_p}\left( {{{X'}_{i,p - 1}},..,{{X'}_{i,1}},{\delta_{i,p - 1}},..,{\delta_{i,1}},{{Z'}_i},{\xi_i},{\varepsilon_{i,p}},..,{\varepsilon_{i,1}}} \right) - {f_{p - 1}}\left( {{{X'}_{i,p - 2}},..,{{X'}_{i,1}},{\delta_{i,p - 2}},..,{\delta_{i,1}},{{Z'}_i},{\xi_i},{\varepsilon_{i,t - 1}},..,{\varepsilon_{i,1}}} \right)} \right).({\eta_{\text{i}}} + {\varepsilon_{{\text{i}},{\text{t}}}})} \right) = 0 $$

We already know that \( {f_p}(.) - {f_{p - 1}}(.) \) is not correlated with η i for all p. Following Assumptions (10.1) and (10.4), it is easy to see that \( {f_p}(.) - {f_{p - 1}}(.) \) is also uncorrelated to ε i,t for all pt − 1. Therefore, \( E\left( {\Delta {y_{{\text{i}},p}}.({\eta_{\text{i}}} + {\varepsilon_{{\text{i}},{\text{t}}}})} \right) = 0 \). Finally, note that \( {f_p}(.) - {f_{p - 1}}(.) \) is correlated with X i,t−1, Z i and y i,tk s for pt − 1 ensuring that Δy i,p s are good instruments for all these terms.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Yoganarasimhan, H. Impact of social network structure on content propagation: A study using YouTube data. Quant Mark Econ 10, 111–150 (2012).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • Social network
  • YouTube
  • Diffusion
  • Social media
  • User-generated content
  • Network structure
  • Online video
  • Social influence
  • Contagion


  • C36
  • C33
  • M3
  • O33
  • L14