Many important social and economic variables are naturally defined for pairs of agents (or dyads). Examples include trade between pairs of countries (e.g., Tinbergen, 1962), input purchases and sales between pairs of firms (e.g., Atalay et al., 2011), research and development (R&D) partnerships across firms (e.g., Konig et al., 2019) and friendships between individuals (e.g., Christakis et al., 2020). Dyadic data arises frequently in the analysis of social and economic issues. See Graham (2020) for many other examples and references. While the statistical analysis of network data began almost a century ago, rigorously justified methods of inference for dyadic or network statistics are only now emerging (cf., Goldenberg et al., 2010).

This dissertation studies statistical inference problems of dyadic data. Throughout I focus on target parameters of fundamental theoretical and applied interest. These include density functions, regression functions, density-weighted average derivatives, and coefficients in linear regressions. Dyadic data exhibits a distinct kind of local dependence property: i.e., any random variables of dyads that share one or two indices/agents may be dependent. The four chapters of this dissertation develop a broad set of theoretical results for estimation and inference of nonparametric, parametric, and semiparametric models for dyadic data and present generic and in some cases surprising implications of the local dependence.

In Chapter 1 I study nonparametric estimation of density functions for undirected dyadic random variables (i.e., random variables defined for all n=N(N-1)/2 unordered pairs of agents/nodes in a weighted network of order N). In this setting, I show that density functions may be estimated by an application of the kernel estimation method of Rosenblatt et al. (1956) and Parzen (1962). I suggest an estimate of their asymptotic variances inspired by a combination of (i) Newey's (1994) method of variance estimation for kernel estimators in the “monadic” setting and (ii) a variance estimator for the (estimated) density of a simple network first suggested by Holland and Leinhardt (1976). More unusual are the rates of convergence and asymptotic (normal) distributions of these dyadic density estimates. Specifically, I show that they converge at the same rate as the (unconditional) dyadic sample mean: the square root of the number, N, of nodes. This differs from the results for nonparametric estimation of densities and regression functions for monadic data, which generally have a slower rate of convergence than their corresponding sample mean. Then I study the robustness of the normality-based and the bootstrap-based inference procedures. Since the distribution of this kernel density estimator depends on both the unknown presence/absence of dyadic dependence and the bandwidth choice, successfully approximating its distribution under a wide range of scenarios is both nonstandard and especially desirable. Toward this goal, I first establish the robustness of the normality-based inference by showing that the consistency of variance estimator and asymptotic normal approximation are valid under both dependence regimes with both commonly used and small-bandwidth asymptotics (Cattaneo et al., 2014). Then, I establish asymptotic inconsistency of a wide class of generalized bootstrap (tailored toward U-statistics) in this setting. Finally, I propose a simple modification of the bootstrap procedure and show its consistency holds robustly. The chapter ends with a semiparametric efficiency bound calculation for density estimation and shows that the kernel density estimator achieves optimal asymptotic variance. Section 1.1, 1.2, 1.3 of this chapter are joint work with Bryan Graham and James Powell.

In Chapter 2 I study nonparametric estimation of regression functions for directed dyadic data. Let i=1,...,N index a simple random sample of units drawn from some large population. For each unit, researchers observe the vector of regressors X_i and, for each of the N(N-1) ordered pairs of units, an outcome Y_{ij}. The outcomes Y_{ij} and Y_{kl} are independent if their indices are disjoint, but dependent otherwise (i.e., “dyadically dependent”). Let W_{ij}=(X_i',X_j')'; using the sampled data I seek to construct a nonparametric estimate of the mean regression function g(W_{ij})=E[Y_{ij}|X_i,X_j]. I present two sets of results. First, I calculate lower bounds on the minimax risk for estimating the regression function at (i) a point and (ii) under the infinity norm. Second, I calculate (i) pointwise and (ii) uniform convergence rates for the dyadic analog of the familiar Nadaraya-Watson (NW) kernel regression estimator. I show that the NW kernel regression estimator achieves the optimal rates suggested by the risk bounds when an appropriate bandwidth sequence is chosen. This optimal rate differs from the one available under iid data: the effective sample size is smaller and d_W=dim(W_{ij}) influences the rate differently. This chapter is joint work with Bryan Graham and James Powell.

In Chapter 3 I study estimation of the density-weighted average derivative for directed dyadic data. This parameter is of substantial practical interest as it is proportional to the coefficients in single index models (Powell et al., 1989), which encompasses various models of limited dependent variables. Besides carefully setting up the directed dyadic single index regression model with both monadic and dyadic explainable variables, the main contributions of this chapter are extending the kernel-based estimator of the density-weighted average derivatives from the “monadic” iid (e.g. Stoker, 1986; Powell et al., 1989; Newey and Stoker, 1993) to directed dyadic data and proving its robust asymptotic normality (asymptotic normality holds under both nondegeneracy and degeneracy and across a wide range of bandwidth sequences) using asymptotic quadratic approximation. This robust asymptotic normality result presents an interesting contrast between this kernel-based semiparametric estimator and the sample mean of dyadic data, which exhibits asymptotic non-normality when dyadic dependence is absent and whose uniform nonconservative inference procedure does not exist (Menzel, 2021). This chapter marks the start of my analysis of estimation of semiparametric models for dyadic data, which is continued in the next chapter.

In Chapter 4 I study error components models of dyadic data, of which a major motivation is separating the monadic and dyadic components of variation. The development parallels that of error components with panel data: I progressively enrich the random effect model by going from being without covariates to being with covariates and from homoskedasticity to multiplicative heteroskedasticity. Throughout enriching the models, I focus on estimating the coefficients in a linear regression, which includes both monadic and dyadic explanatory variables. To understand the nature of the estimation problem under different error components models, I study the performance of intuitive OLS estimators, propose more efficient estimators, calculate the asymptotic efficiency bounds (Cramer-Rao lower bound, CRLB), and compare the efficiency bounds to variances of the estimators. Under homoskedasticity, I prove the sample mean, which converges at rate O(N^{-1/2}), and least square estimator with double-differencing operation, which converges at rate O(binom{N}{2}^{-1/2}), achieve the CRLB and are asymptotically efficient for estimating the marginal expectation and the coefficients of dyadic variables in a linear regression respectively. Under unknown multiplicative heteroskedasticity, I show that the intuitive two-step semiparametric generalized score estimator for estimating the linear regression coefficients, which is a natural extension of the classical feasible generalized least square estimator (FGLS) for linear regression with heteroskedasticity for the “monadic” iid data, is not adaptive to the unknown heteroskedasticity. Its convergence rate is faster than that of the OLS estimator, O(N^{-1/2}), but slower than the rate suggested by CRLB, O(binom{N}{2}^{-1/2}). This result makes a distinction from a familiar result in the monadic iid setting, i.e. a two-step semiparametric generalized score estimator often indeed achieves adaptivity and CRLB in iid setting. The gap between the performance of the best available estimator and the CRLB suggests that for this estimation problem with dyadic data either there exists a better estimator that is adaptive and achieves the CRLB, or there is a tighter efficiency bound. I point this gap out for further research.

This dissertation contains three essays that study relationships among firms. Firms connect to each other via direct and indirect relationships. A network describes these relationships as linkages among firms. This dissertation empirically studies the roles of firms in networks, in particular the incentives firms face when forming linkages with each other.

Chapter 1 studies the structure of supplier-buyer networks of U.S. tech firms from 2003 to 2014. For each year, a supplier-buyer network describes which firms supply to which firms, and equivalently, which firms buy from which firms. I identify four firms - Apple, Dell, IBM, and Microsoft - as the most significant firms in the supplier-buyer networks. Using a community detection method, I find that these four firms each belongs to a different community of firms, indicating that they are closely linked to distinct groups of firms. On the other hand, the four communities, each associated with one of the four firms, are composed of firms in similar industry sectors. These suggest that there exists a certain degree of exclusivity in supplier-buyer relationships of the four firms. Moreover, I rank their significance in the network using measures of centrality and modular centrality, where the latter accounts for the community structure. I find that IBM was by far the most significant firm, both as a supplier and a buyer, until 2010. However, the centrality of Microsoft grew and surpassed IBM in 2014. Furthermore, the growth of Apple's centrality over the years is remarkable.

Chapter 2 describes the relationships among U.S. credit card issuers, hotel chains, and airlines. These firms operate loyalty programs, in which customers may earn points by making purchases. Moreover, they form partnerships with other firms so that the points can be transferred to the loyalty programs of partner firms. Via such transfer partnerships, customers may redeem the points for not only the goods and services offered by the firm but also those offered by the partner firms. Thus, the set of partners possessed by a firm is an important marketing tool, and it has an incentive to form partnerships with a select set of firms, as a means of competition. Chapter 2 also describes the data collection procedure, which contains annual observations on transfer partnerships among 3 credit card issuers, 7 hotel chains, and 43 airlines and quarterly observations on their firm-level characteristics from 2014 to 2018.

Chapter 3 utilizes the aforementioned data set to study the formation of transfer partnerships. After describing transfer partnerships among firms as a directed network, I exploit variations in transfer partnerships and characteristics of firms over time to study how major U.S. credit card issuers choose their airline partners. Partnerships between credit card issuers and hotel chains and partnerships among airlines are taken as given because these partnerships are typically determined by long-term contracts and hence little variation is observed in the data. Recognizing that characteristics of firms, the set of other partners possessed by a credit card issuer (i.e., complementarity of potential partnership to existing set of partners), the set of partners possessed by its partner hotel chains (i.e., indirect partnerships), and the set of partners possessed by other credit card issuers (i.e., partnerships of competitors) may affect the choice of a partner, this chapter uses a sequential network formation model to describe the partnership formation process. A key feature is that the state of the network affects partnership formation. A difficulty is that the order of events - the timeline through which partnerships were formed, rejected, or modified - is not fully observed. I use Markov Chain Monte Carlo to sample the order of events and to estimate model parameters. The result indicates that a credit card issuer tends to favor an airline partner that complements its other airline partners, is a partner of another credit card issuer, and is a partner of its hotel chain partner.

This dissertation studies how to leverage the unique characteristics of panel and network data, particularly repeated observations and symmetries, to recover the structural parameters of three econometric models of theoretical and applied interest.

In Chapter 1, I study parameter identifiablility and estimation of dynamic discrete choice models with strictly exogenous regressors, fixed effects and logistic errors. Specifications of this kind are popular in Labor Economics and Industrial Organization to disentangle the sources of serial persistence in agents’ decisions. The primary challenge lies in the nonlinearity of these models, making the treatment of fixed effects difficult in short panel settings. I introduce a new method that exploits the structure of logit-type probabilities and elementary properties of rational fractions to derive moment restrictions in a broad class of models. This includes binary response models of arbitrary lag order as well as first-order panel vector autoregressions and dynamic multinomial logit models. These moment restrictions are free from the fixed effects and provide a natural way to estimate the common parameters via the Generalized Method of Moments. I further establish the identification of a class of average marginal effects which are often of importance in empirical work. The approach is illustrated through an analysis of the dynamics of drug consumption amongst young people in a nationally representative sample.

In Chapter 2, coauthored with Stéphane Bonhomme and Bryan Graham, we study identification in a binary choice panel data model with a single predetermined binary covariate (i.e., a covariate sequentially exogenous conditional on lagged outcomes and covariates). The choice model is indexed by a scalar parameter θ, whereas the distribution of unit-specific heterogeneity, as well as the feedback process that maps lagged outcomes into future covariate realizations, are left unrestricted. This setup departs from Chapter 1 which imposed strict exogeneity of explanatory variables, effectively ruling out any influence of past outcomes oncovariates. In this framework, we provide a simple condition under which θ is never point-identified, no matter the number of time periods available. This condition is satisfied in most models, including the logit one. We also characterize the identified set of θ and show how to compute it using linear programming techniques. While θ is not generally point-identified, its identified set is informative in the examples we analyze numerically, suggesting that meaningful learning about θ may be possible even in short panels with feedback. As a complement, we report calculations of identified sets for an average partial effect, and find informative sets in this case as well.

In Chapter 3, I present an approach to address network endogeneity in a linear social interaction model. I consider a setting wherein individual-specific latent random effects influence both outcomes and link formation modelled as a conditionally independent dyad process. Using the exchangeability properties of the framework, I show that controlling or matching individuals by degree-centrality can be sufficient to eliminate the omitted variable bias induced by endogenous peer selection. I leverage this result and insights from Bramoullé et al. (2009) for the case of exogenous friendships to present two simple strategies for the identification and estimation of social effects. Asymptotic properties of the proposed estimators are derived for clustered samples and I illustrate their performance in Monte Carlo simulations.

In the first chapter of this dissertation I present a new method to identify and estimate the strength of social spillovers in the classroom and the distribution of teacher and student effects. The identification depends on the assumptions of double randomization of teacher and students to classrooms and the linear in means equation of test scores. The linear independent factor representation of test scores allows the estimation of the parameters of interest by combining all the joint moments of different orders. I also present a theoretical model of social interactions in the classroom that yields the linear in means equation for test scores. In this model, the teacher and students play a game in which they choose how much effort to exert. The method I provide allows the estimation of moments of Rth order, recovering more features of the distribution of teacher and student effects than the mean and variance. Class size heteroskedastic teacher and student effects can be easily accomodated. For the estimation, I use a minimum distance procedure that combines the information coming from different moments. Using the Tennessee Project STAR dataset, I find sizeable spillovers in the classroom. Moreover, the distributions of teacher and student abilities seem to depart from the usual normality assumption, and the student distribution exhibits a high degree of heteroskedasticity in class size. Based on these estimates, I perform several counterfactual social planning experiments, comparing who are the losers and winners under different assignment rules. Assignment of good teachers to large classrooms increases the average test scores, with students in the left tail of the distribution benefiting more than the rest. Assignment of good students to small classrooms increases the test scores of students in the right tail of the distribution, while decreasing test scores of students in the left tail of the distribution, with an overall increase in mean test scores. Mixing good and bad students together results in a small effect on mean test scores, but reduces inequality.

In the second chapter I propose an estimator of the conditional distribution of an outcome variable in the presence of heterogeneous effects and a continuous endogenous treatment. The model is triangular, with both the first and the second stage equations being a linear-in-covariates quantile process. The endogeneity of the model is captured by the quantile copula of both equations, and it is identified by inverting the quantile processes conditional on a vector of covariates. Using quantile regression techniques, I estimate both conditional quantile processes, and the copula distribution can then be estimated either nonparametrically or parametrically. Integration of the copula for a given vector of the instruments, estimates the conditional distribution of the outcome variable. This allows to then estimate the distribution of the covariates on the unconditional distribution of the outcome variable, or any other function such as the unconditional quantile function or the Gini Index. Similarly, to estimate the effect of a policy on the unconditional distribution of the outcome variable, one simply needs to integrate the conditional distribution over the marginal of the covariates under the counterfactual policy. Uniform asymptotic distribution for these estimators is provided, allowing to make inference on them and constructing the usual confidence sets. I use data on twins to estimate the the unconditional quantile treatment effect of increasing education by one year to all individuals in the dataset. The results show an increase in the distribution of wages that ranges between 8% and 20%, with those at the upper quantiles of the distribution benefiting the most.

In the third chapter I propose an estimator of the unconditional distribution of an outcome variable, when this variable depends on a binary treatment that is endogenous to the unobservables, and the effect of the treatment and other exogenous variables on the outcome variable is heterogeneous. The estimator is based on a triangular model consisting on the probability of being treated and a quantile process that determines the outcome variable. Using a parametric assumption about the copula distribution and the exclusion restriction I identify the copula distribution. The estimation is a multi-step procedure that involves the estimation of the quantile process of the second stage equation, the probability of being treated by maximum likelihood, and the copula distribution. These estimators are then used to estimate the distribution of the outcome variable conditional on a set of instruments. Finally, I show the finite sample performance of the estimator with a Monte Carlo experiment.

This dissertation contains three essays on the relationship between the spatial distribution of economic activity and different types of public goods. In the first essay, I study how changes in transport infrastructure affect the location decisions of firms by examining how manufacturers responded to changes in road quality in Indonesia. Using new data, I document massive upgrades to Indonesia's highway networks during the 1990s, a period in which national transportation funding increased by 83 percent. I first show that these road improvements were accompanied by a significant dispersion of manufacturing activity, and that different industries responded in ways predicted by theory. To make better counterfactual predictions, I develop a structural model of location choice in which firms face a trade off: locating closer to demand sources requires firms to pay higher factor prices. The model predicts that some location characteristics relevant to firms are determined in equilibrium, necessitating the use of instrumental variables. I estimate a random coefficients logit model with endogenous choice characteristics and find significant differences in firms' willingness to pay for greater market access across different industrial sectors. Counterfactual policy simulations suggest that new toll roads connecting urban areas would cause a modest amount of industrial suburbanization. In contrast, upgrading rural roads would have little or no effect on equilibrium firm locations.

In the second essay, co-authored with Bryan Graham, we provide estimates of the implicit prices that consumers and firms pay for access to infrastructure in Honduras. Without credible estimates of the welfare effects of infrastructure improvements, it is impossible for policymakers to know whether the benefits of these investments outweigh their substantial costs. A major challenge with trying to understanding the welfare consequences of improved transport infrastructure is an identification problem: transport improvements are never randomly assigned. We overcome this identification program by exploiting variation from a novel natural experiment: Honduras' infestation with Panama disease. The Honduran railroad network was constructed by fruit companies to ship bananas from plantations to port cities, but because of an unpredictable outbreak of Panama disease, major plantations and their associated railway infrastructure were abandoned. We argue that outbreaks of Panama disease were extremely difficult to predict, and because of this, conditional on the railway network that existed in the 1930s and a host of observable characteristics, the areas where railway lines were abandoned were randomly assigned. We use our identification strategy to uncover the implicit prices of access to infrastructure paid by consumers and the implicit production costs paid by firms.

In the third essay, co-authored with Rachel Glennerster and Edward Miguel, we study how spatial variation in ethnic diversity, which exists largely for historical reasons, affects the provision of local public goods in rural Sierra Leone. Scholars have pointed to ethnic divisions as a leading cause of underdevelopment, due in part to their adverse effects on public goods. We investigate this issue in post-war Sierra Leone, one of the world's poorest countries. To address concerns over endogenous local ethnic composition, we use an instrumental variables strategy relying on historical census data on ethnic composition. We find that local diversity is not associated with worse public goods provision across a variety of outcomes, specifications, and diversity measures, with precisely estimated zeros. We investigate the role that leading mechanisms proposed in the literature play in generating the findings.

This dissertation studies estimation and inference on models with dyadic dependence, that is models for double indexed observations where observations are correlated whenever they share an index. Data exhibiting this form of dependence are commonplace: from international trade (e.g. \cite{Rose2004}) to sales on online platforms (e.g. \cite{Bajari2023}) or social networks (\cite{FafchampsGubet2007}). Because of the particular dependence structure, very little is known about efficiency in these models. For instance, for parametric models, only a handful of examples have likelihood functions or maximum likelihood estimators that can be expressed in closed form or that are computationally feasible. The analyst is forced to sacrifice efficiency for computational ease and tractability. Unfortunately, unlike cross-sectional models, efficiency losses in dyadic models can manifest as drops in rates of convergence rather than just asymptotic variance, immensely impacting the precision of estimation.

The dissertation explores new estimation methods for different dyadic models, with a particular attention to efficiency and computational feasibility. Each of The three chapters in this dissertation studies a set of dyadic models and estimators for those models. The first and last chapters present efficiency results.

In the first chapter I propose a two step rate optimal estimator for an undirected dyadic linear regression model with interactive unit-specific effects. The estimator remains consistent when the individual effects are additive rather than interactive. We observe that the unit-specific effects alter the eigenvalue distribution of the data's matrix representation in significant and distinctive ways. We offer a correction for the \textit{ordinary least squares}' objective function to attenuate the statistical noise that arises due to the individual effects, and in some cases, completely eliminate it. The new objective function is similar to the \textit{least squares} estimator's objective function from the large $N$ large $T$ panel data literature (\cite{Bai2009}). In general, the objective function is ill behaved and admits multiple local minima. Following a novel proof strategy, we show that in the presence of interactive effects, an iterative process in line with \cite{Bai2009}'s converges to a global minimizer and is asymptotically normal when initiated properly. The new proof strategy suggests a computationally more advantageous and asymptotically equivalent estimator. While the iterative process does not converge when the individual effects are additive, we show that the alternative estimator remains consistent for all slope parameters.

Chapter 2 proposes a general procedure to construct estimators for exchangeable network models. For any network model, consider an auxiliary i.i.d. model where each observation has the same distribution as any observation in the original model. The procedure returns estimators for the original model whenever valid estimators are known in the auxiliary i.i.d. model. The chapter then studies the asymptotic behavior of the ``the average MLE", the estimators returned by the procedure for parametric binomial network models. I show that the average MLE behaves asymptotically like the composite maximum likelihood estimator. Interestingly, the average MLE does not require the entire network to be observed. For instance, I show that for a balanced bipartite graph, observing almost any sub-graph with more than $N^{\frac{3}{2}+\epsilon}$ edges for some $\epsilon>0$ (out of the total $N^2$ edges) is enough for the asymptotic result to hold. These results are readily extendable beyond the binomial model.

The final chapter studies the properties of the maximum likelihood estimator (MLE) for exponential families of distributions on network data. I show that, under some conditions, the MLE is asymptotically normally distributed with an asymptotic variance equal to the inverse of the information matrix. I also show that under those same conditions, the MLE is efficient compared to regular estimators with the same rate of convergence. This extends well known results on MLE for $i.i.d.$ models.