In this master’s thesis, we examine a special linear structural causal model. The goal of the thesis is to derive and validate statements concerning the asymptotic variance of an estimator for a parameter within this model. The introduction provides a context for causal inference by first discussing the differences between correlation and causation. Following that, we briefly address potential issues that may arise in the field of causal inference. We also illustrate these challenges with relevant application examples. The second chapter of this thesis then provides the necessary theoretical background information for the structural causal model, which we explore in greater detail. We begin by introducing concepts from graph theory and structural equation models with a particular focus on linear structural causal models. Thereafter, we define cumulants and derive the multi-trek rule, which allows us to determine covariance matrices of structural causal models later on. Additionally, we formally introduce the specific model we aim to investigate and apply our previously established theory to this model. In the third chapter, we derive the main result of the thesis on the asymptotic variance of an estimator of a model parameter. We provide a comprehensive proof for this result using the central limit theorem and the delta method. Moreover, we utilize this result to construct confidence intervals for the real model parameter. We visualize these confidence intervals in the fourth chapter and analyze their evolution for growing sample sizes. To achieve this, we use the programming language R to simulate data along with the model. We thoroughly analyze the resulting confidence intervals based on a specific data distribution. The final chapter concludes our thesis by summarizing our results. It also provides an outlook on potential future research opportunities that could build on this master’s thesis to further generalize or develop our findings.      «

In this master’s thesis, we examine a special linear structural causal model. The goal of the thesis is to derive and validate statements concerning the asymptotic variance of an estimator for a parameter within this model. The introduction provides a context for causal inference by first discussing the differences between correlation and causation. Following that, we briefly address potential issues that may arise in the field of causal inference. We also illustrate these challenges with releva...     »