My dissertation consists of three chapters that evaluate the social welfare effect of either antitrust policy or industrial transition, all using discrete choice model estimation as the front end for counterfactual analysis. In the first chapter, I investigate the economic impact of the merger that created the world's largest hotel chain, Marriott's acquisition of Starwood, thereby shedding light on the antitrust authorities' performance in protecting competitive markets for the benefit of consumers. Different from traditional merger analysis that focuses on the tradeoff between the upward pricing pressure and the cost synergy among the merging parties while fixing the market structure, I endogenize firms’ entry decisions into an oligopoly price competition model. To tackle the associated multiple equilibria issue, I use moment inequality estimation and propose a novel lower probability bound that reduces the computational burden from being exponential to being linear in the number of players. It also adds to the scant empirical evidence on post-merger cost synergy by showing that every one more affiliated hotel in the local market reduces a hotel's marginal cost by up to 2.3%. Then a comparison between the simulated with-merger and without-merger equilibria indicates that this merger enhances social welfare. In particular, for those markets that are previously not profitable for any firm to enter, because of the post-merger cost saving, Marriott or Starwood would enter 6% - 24% of them, which provides a new perspective for merger reviews. The second chapter, joint with Mingli Chen, Marc Rysman and Krzysztof Wozniak, studies the determinants of the US payment system's shift from paper payment instruments, namely cash and check, to digital instruments, such as debit cards and credit cards. With a 5-year transaction-level panel data, for the first time in the literature, we can distinguish the short-term effects of transaction size from the long-term changes in households’ preferences. To do so, we incorporate a household-product-quarter fixed effect into a multinomial logit model. We develop a new method based on the Minorization-Maximization (MM) algorithm to address the prohibitive computational challenge of estimating over one million fixed effects in such a nonlinear model. Results show that over a short horizon (within a quarter), the probability of using card increases with transaction sizes in general but exhibits substantial household heterogeneity. While over long horizon (five-year period of the data), with the estimated household-product-quarter fixed effects, we decompose the increase in card usage into different channels and find that only a third of it is due to the changes in household preferences. Another significant driver is the households' entry and exit into the sample. In the third chapter, my coauthors Jacob LaRiviere, Aadharsh Kannan, and I explore the "death of distance” hypothesis with a novel anonymized customer-level dataset on demand for cloud computing, accounting for both spatial and price competition among public cloud providers. We introduce a mixed logit demand model of spatial competition estimable with detailed data of a single firm but only aggregate sales data of a second. We leverage the Expectation-Maximization (EM) algorithm to tackle the customer-level missing data problem of the second firm. Estimation results and counterfactuals show that standard spatial competition economics hold even when distance for cloud latency is trivial.

Le contrôle explicite de la convergence des sommes convenablement normalisées de variables aléatoires, ainsi que l'étude du principe de déviations modérées associé à ces sommes constituent les thèmes centraux de cette thèse. Nous étudions principalement deux types de processus. Premièrement, nous nous intéressons aux processus indexés par un arbre binaire, aléatoire ou non. Ces processus ont été introduits dans la littérature afin d'étudier le mécanisme de la division cellulaire. Au chapitre 2, nous étudions les chaînes de Markov bifurcantes. Ces chaînes peuvent être vues comme une adaptation des chaînes de Markov "usuelles'' dans le cas où l'ensemble des indices à une structure binaire. Sous des hypothèses d'ergodicité géométrique uniforme et non-uniforme d'une chaîne de Markov induite, nous fournissons des inégalités de déviations et un principe de déviations modérées pour les chaînes de Markov bifurcantes. Au chapitre 3, nous nous intéressons aux processus bifurcants autorégressifs d'ordre p (). Ces processus sont une adaptation des processus autorégressifs linéaires d'ordre p dans le cas où l'ensemble des indices à une structure binaire. Nous donnons des inégalités de déviations, ainsi qu'un principe de déviations modérées pour les estimateurs des moindres carrés des paramètres "d'autorégression'' de ce modèle. Au chapitre 4, nous traitons des inégalités de déviations pour des chaînes de Markov bifurcantes sur un arbre de Galton-Watson. Ces chaînes sont une généralisation de la notion de chaînes de Markov bifurcantes au cas où l'ensemble des indices est un arbre de Galton-Watson binaire. Elles permettent dans le cas de la division cellulaire de prendre en compte la mort des cellules. Les hypothèses principales que nous faisons dans ce chapitre sont : l'ergodicité géométrique uniforme d'une chaîne de Markov induite et la non-extinction du processus de Galton-Watson associé. Au chapitre 5, nous nous intéressons aux modèles autorégressifs linéaires d'ordre 1 ayant des résidus corrélés. Plus particulièrement, nous nous concentrons sur la statistique de Durbin-Watson. La statistique de Durbin-Watson est à la base des tests de Durbin-Watson, qui permettent de détecter l'autocorrélation résiduelle dans des modèles autorégressifs d'ordre 1. Nous fournissons un principe de déviations modérées pour cette statistique. Les preuves du principe de déviations modérées des chapitres 2, 3 et 4 reposent essentiellement sur le principe de déviations modérées des martingales. Les inégalités de déviations sont établies principalement grâce à l'inégalité d'Azuma-Bennet-Hoeffding et l'utilisation de la structure binaire des processus. Le chapitre 5 est né de l'importance qu'a l'ergodicité explicite des chaînes de Markov au chapitre 3. L'ergodicité géométrique explicite des processus de Markov à temps discret et continu ayant été très bien étudiée dans la littérature, nous nous sommes penchés sur l'ergodicité sous-exponentielle des processus de Markov à temps continu. Nous fournissons alors des taux explicites pour la convergence sous exponentielle d'un processus de Markov à temps continu vers sa mesure de probabilité d'équilibre. Les hypothèses principales que nous utilisons sont : l'existence d'une fonction de Lyapunov et d'une condition de minoration. Les preuves reposent en grande partie sur la construction du couplage et le contrôle explicite de la queue du temps de couplage. / The explicit control of the convergence of properly normalized sums of random variables, as well as the study of moderate deviation principle associated with these sums constitute the main subjects of this thesis. We mostly study two sort of processes. First, we are interested in processes labelled by binary tree, random or not. These processes have been introduced in the literature in order to study mechanism of the cell division. In Chapter 2, we study bifurcating Markov chains. These chains may be seen as an adaptation of "usual'' Markov chains in case the index set has a binary structure. Under uniform and non-uniform geometric ergodicity assumptions of an embedded Markov chain, we provide deviation inequalities and a moderate deviation principle for the bifurcating Markov chains. In chapter 3, we are interested in p-order bifurcating autoregressive processes (). These processes are an adaptation of $p$-order linear autoregressive processes in case the index set has a binary structure. We provide deviation inequalities, as well as an moderate deviation principle for the least squares estimators of autoregressive parameters of this model. In Chapter 4, we dealt with deviation deviation inequalities for bifurcating Markov chains on Galton-Watson tree. These chains are a generalization of the notion of bifurcating Markov chains in case the index set is a binary Galton-Watson tree. They allow, in case of cell division, to take into account cell's death. The main hypothesis that we do in this chapter are : uniform geometric ergodicity of an embedded Markov chain and the non-extinction of the associated Galton-Watson process. In Chapter 5, we are interested in first-order linear autoregressive models with correlated errors. More specifically, we focus on the Durbin-Watson statistic. The Durbin-Watson statistic is at the base of Durbin-Watson tests, which allow to detect serial correlation in the first-order autoregressive models. We provide a moderate deviation principle for this statistic. The proofs of moderate deviation principle of Chapter 2, 3 and 4 are essentially based on moderate deviation for martingales. To establish deviation inequalities, we use most the Azuma-Bennet-Hoeffding inequality and the binary structure of processes. Chapter 6 was born from the importance that explicit ergodicity of Markov chains has in Chapter 2. Since explicit geometric ergodicity of discrete and continuous time Markov processes has been well studied in the literature, we focused on the sub-exponential ergodicity of continuous time Markov Processes. We thus provide explicit rates for the sub-exponential convergence of a continuous time Markov process to its stationary distribution. The main hypothesis that we use are : existence of a Lyapunov fonction and of a minorization condition. The proofs are largely based on the coupling construction and the explicit control of the tail of the coupling time.