Among the many sources of risk explaining corporate bond spreads, the role of liquidity is the least well understood. This paper investigates the impact of liquidity risk of unknown functional form on the yield spread over time. Heterogeneity is introduced via a latent group structure explaining differences in nonlinear liquidity effects across groups. A key feature of the model is that it can be estimated from highly unbalanced longitudinal data, allowing us to work with data at minimum levels of temporal aggregation. In an extensive empirical study we apply the suggested method to a large panel of trade data for US corporate bonds. Our procedure identifies nonlinear liquidity effects for a large fraction of the securities. Nonlinearities become more pronounced as bond-idiosyncratic illiquidity increases. The classification clearly distinguishes groups differing e.g. in bond characteristics such as spread levels and trading activity. While groups share similar dynamics of liquidity effects, their magnitudes as well as the interplay between idiosyncratic and market illiquidity are different across groups.

A new partial functional linear regression model for panel data with time varying parameters is introduced. The parameter vector of the multivariate model component is allowed to be completely time varying while the function-valued parameter of the functional model component is assumed to change over K unknown parameter regimes. Consistency is derived for the suggested estimators and for the classification procedure used to detect the K unknown parameter regimes. Additionally, the convergence rates of the estimators are derived under a double asymptotic differentiating between asymptotic scenarios depending on the relative order of the panel dimensions n and T . The statistical model is motivated by a real data application considering the so-called "idiosyncratic volatility puzzle" using high frequency data from the S&P500.

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