Estimating the Dynamic Impact of Media Coverage on Public Opinion
 Using Exposure History Matrices and Flexible Distributed Lag Models

Scholars studying public opinion dynamics are often interested in assessing the effects of lagged covariates. Specifically, the goal may be to determine the time delay or the duration of effects. For this purpose, content analysis data of the media coverage can be linked to public opinion surveys through the creation of exposure history matrices. To evaluate the dynamic impact based on such exposure history matrices, different methods have been used. At one extreme, unconstrained lag models have been applied, potentially leading to an excessive number of parameters to be estimated. At another extreme, a functional form of the decay function has been imposed on the data which may, however, result in considerably biased estimates when the true underlying function differs from the imposed function. Against this background, this paper proposes the use of flexible distributed lag models to evaluate the influence of exposure histories taking a middle ground between these two extremes. The flexible distributed lag model allows to estimate a smooth curve of lag coefficients from the data with a parsimonious number of parameters. The paper discusses the advantages and limitations of different approaches and assesses the properties of flexible distributed lag models using a simulation study. As a practical example of how the flexible distributed lag model can be utilized to study real-world political dynamics, the duration of agenda-setting effects during an election campaign is analysed linking media content analysis and rolling cross-section data. The results show that the flexible distributed lag model allows to efficiently assess the duration of effects when theoretical priors about the functional form and the length of lagged effects are weak. The paper concludes that exposure history matrices in conjunction with the flexible distributed lag model provide a useful tool for the study of public opinion dynamics.