In practice, almost every survey suffers from the problem of non-response. The problem of non-response arises mainly due to the refusal of the persons to respond, and sometimes when there is unavailability of some persons, households, firms because of invalid addresses or wrong telephone numbers, inability of the interviewer to reach the household in remote areas or failure to collect the required information from a sample member in the mail surveys (Armstrong and Overton, 1977; Hox and deLeeuw, 1994). In the context of panel surveys, non-response occurs when the sample members don’t participate in a particular wave of the study. This kind of non-response is called wave non-response. On the other hand, when a sample member participates in the initial wave of the survey but refuses to participate in the later waves of the survey, this kind of non-response is called panel attrition. Panel attrition is a common problem in panel surveys, which reduces sample size and can lead to biased inferences when the propensity to drop out is systematically related to the substantive outcome of interest. In this thesis, we are mainly concerned with the problem of non-response in panel surveys. Like any non-mandatory survey, a panel survey suffers from substantial non-response at its start. 30 to 70% of the initial sample persons refuse to cooperate. The motivation and causation for this behaviour don’t distinguish from standard cross-sectional surveys. However, in panel surveys, the respondents are repeatedly interviewed in later waves. With this repeated measurement it is possible to analyze gross-change, i.e., individual change, for example, changes between poverty and non-poverty. These individual changes have a substantial impact on the distribution of the variable interest in later waves of the panel. As a consequence, an initial bias resulting from selective non-response at the start of the panel may “fade-away” in later panel waves. The fade-away phenomenon can be empirically observed for those rare cases where a panel is selected from the register and where it is possible to make statistical inferences also for the non-responders based on the register information. Motivated by examples from the Finnish sub-samples of the European Community Household Panel (ECHP), the European Statistics on Income and Living Conditions (EU-SILC) and the German Panel Labor Market and Social Security (PASS) Alho et al. (2017) have developed a statistical framework in the context of Markov chains which explains the fade-away effect of initial non-response bias. Non-response in surveys may create a bias in the estimates. However, one advantage of panel surveys over cross-sectional surveys is that under some regularity conditions an initial non-response bias may fade-away over later panel waves. Sisto (2003) and Rendtel (2013) studied the effect of initial non-response on the income quintiles estimates from the European Community Household Panel (ECHP) and poverty rates from the European Union Statistics of Income and Living Conditions (EU-SILC). They reported that the effect of initial non-response bias declines very fast for income quintiles and poverty states in the subsequent panel waves. Such a hypothesis of the fade-away effect doesn’t only base on the information provided by the respondent sample but also depends on the information obtained from the non-respondent sample, where information about the non-respondents is available via registers. Rendtel (2013) used the concept of the Markov chain to explain the fade-away phenomenon. The purpose of using this approach is the possibility to use the steady-state distribution of the Markov chain. If the transition law of the Markov chain is stable over time, then under some regularity conditions the distribution on the state space of the Markov chain converges to a stable distribution, called the steady-state distribution. Alho (2015) extends the approach to regression analysis. He uses a two wave panel to explain the fade-away phenomenon of initial non-response bias in the framework of regression analysis with a single covariate. In the proposed regression model the covariate and the error term are decomposed into permanent and nonpermanent variance components. Alho concludes that the initial non-response bias fades-away in the case of low non-permanent components of the covariate and/or the error term. The thesis is divided into three parts: Part I contains the theoretical foundations for the fade-away effect of initial non-response bias in panel surveys. In part II of this thesis, a simulation study is conducted to investigate the fade-away effect of the initial non-response bias in a multi-wave panel survey. The purpose of the simulation study is to investigate the accuracy of the bias approximation in a simulation setting and check the size of the fade-away effect in later panel waves with no analytical bias approximation. Alho (2015) has investigated the bias of cross-sectional OLS estimates under not missing at random (NMAR) non-response at the start of the panel. He derived analytical bias approximation for the OLS estimate of the slope coefficient of the variable of interest. His underlying model used a variance component model with two components: a fixed individual component and an auto-regressive shock component (Alho’s model will be discussed in Subsection 2.3.2 of Chapter 2). However, in multi-wave panel surveys, the analytical expression for Alho’s bias approximation formula becomes very intractable for later waves. Therefore, we extend the results to a longer panel wave via a simulation study. In Chapter 3 of this thesis, we have conducted a simulation study to verify the approximate results of Alho (2015), and investigated the accuracy of the bias approximation in a simulation setting. We checked the size of the fade-away in later panel waves with no analytical bias approximation. The speed of the fade-away effect of the initial non-response bias is then investigated for different stability scenarios of covariates and error terms, with and without any attrition patterns in later panel waves. As the speed of the fade-away depends on the stability of the covariates and error terms it is important to investigate this effect not only for simulated data but also for real longitudinal data. Therefore, in the application part (Part III) of this thesis, we switch to real data from the German Socio Economic Panel (SOEP): specifically to income data and life satisfaction scores data of the SOEP.