12. Assessing Importance of Time-Series Versus Cross-Sectional Changes in Panel Data: A Study of International Variations in Ex-Ante Equity Premia and Financial Architecture

In the study of economic and financial panel data, it is often important to differentiate between time series and cross-sectional effects. We present two estimation procedures that can do so and illustrate their application by examining international variations in expected equity premia and financial architecture where a number of variables vary across time but not cross-sectionally, while other variables vary cross-sectionally but not across time. Using two different estimation procedures, we find a preference for market financing to be negatively associated with the size of expected premia. However, we also find that US corporate bond spreads negatively determine financial architecture according to the first procedure but not according to the second estimation as US corporate bond spreads change value each year but have the same value across countries. Similarly some measures that change across countries but do not change across time, such as cultural dimensions as well as the index of measures against self-dealing, are significant determinants of financial architecture according second estimation but not according to the first estimation. Our results show that using these two estimation procedures together can assess time series versus cross-sectional variations in panel data. This research should be of considerable interest to empirical researchers.

We illustrate with simultaneous-equation modeling. Following a Hausman test to determine whether to report fixed or random-effects estimates, we first report random-effects estimates based on the estimation procedure of Baltagi (Baltagi 1981; Baltagi and Li 1995; Baltagi and Li 1994). We consider that the error component two-stage least squares (EC2SLS) estimator of Baltagi and Li (1995) is more efficient than the generalized two-stage least squares (G2SLS) estimator of Balestra and Varadharajan-Krishnakumar (1987). For our second estimation procedure, for comparative purposes we use the dynamic panel modeling estimates recommended by Blundell and Bond (1998). We employ the model of Blundell and Bond (1998), as these authors argue that their estimator is more appropriate than the Arellano and Bond (1991) model for smaller time periods relative to the size of the panels. We also use this two-step procedure and use as an independent variable the first lag of the dependent variable, reporting robust standard errors of Windmeijer (2005). Thus, our two different panel estimation techniques place differing emphases on cross-sectional and time series effects, with the Baltagi-Li estimator emphasizing cross-sectional effects and the Blundell-Bond estimator emphasizing time series effects.