Essays on Identification in Econometrics

This thesis is divided into four essays, which revolve around the theme of Identification of Models in Econometrics. Chapter 1 deals with the Identification of Direct and Indirect Treatment Effects, Chapters 2 and 3 analyze the Identification of Linear-in-Means Model of Peer Effects, and Chapter 4 studies Interval Subjective Probabilities in surveys.;Chapter 1, titled 'Identification of Direct and Indirect Treatment Effects', studies the channels through which treatment affects the outcome. This is done by identifying intermediate or 'mediating' variables that lie between the treatment and the outcome. Such analysis are called causal mediation analysis, and disentangle the treatment effect into two components. The first component seeks to identify the part of the treatment effect that is caused 'directly' by the change in treatment holding all other mediating variables constant, and is called the 'direct treatment effect'. The second component measures the part of the treatment effect that is caused 'indirectly' by the change in intermediate or mediating variables holding the treatment constant, and is called the 'indirect treatment effect'. For identifying the average direct and indirect treatment effects a partial identification approach is adopted. Monotonicity, Lipschitz continuity and Lexicographic order assumptions are made for identification. Additional variables and instrumental variables are used to further sharpen the identification. The identification of the distribution of the indirect treatment effect is also fnstudied under monotonicity using copula theory. Chapters 2 and 3 analyze the Linear-in-Means models of Peer Effects. Chapter 2, titled 'Weak Identification in Linear-in-Means Model', brings to the forefront the issue of weak identification in the instrumental variable based approach of the identification and estimation of the linear-in-means models. The main result of the chapter shows that the strength of identification is a function of the variance of the network sizes. A new ridge regression based instrumental variable estimator is proposed to estimate the model when weak identification makes the two-stage least squares estimator unreliable.;Chapter 3, titled `Disentangling Homophily from Peer Effects', studies an extension of the linear-in-means model discussed in Chapter 2. One of the major challenges in the identification of peer effects in the linear-in-means model of social interactions is the confounding of homophily and peer effects. This chapter presents a novel approach to deal with this challenge. The concept of strong and weak ties is introduced in the standard linear-in-means model, and the premise that strong ties are more homophilous in nature is used to identify homophily from peer effects. The new model is called the linear-in-means model with ties. It employs a more generalized version of the standard linear-in-means model where the strong ties and weak ties are allowed to have different social effects. An empirical illustration is presented using the data from project STAR where the ties are classified on the basis of gender. Results demonstrate that the social effects of the strong ties are higher than that of the weak ties. This implies that both homophily and peer effects are present in the social effects of strong ties, whereas the social effects of weak ties are only due to peer effects.;Chapter 4, titled 'Decoding Subjective Probabilities', uses the data from the Health and Retirement Survey to analyze subjective probabilities. The paper highlights the importance of eliciting subjective probabilities in terms of intervals. Interval subjective probabilities are probed to understand the reasons for and extent of rounding and approximation. Results demonstrate that both the probability of approximation, and the width of the interval are quadratic functions of the point subjective probabilities. For the respondents who approximate, an attempt has been made to understand the process by which they pick a point in the interval. Using the results, a procedure for constructing intervals from point probabilities is outlined and illustrated.