You have data about seven countries. For every country, you observe variables y (GDP) and x1 (Size of the financial sector) for 10 years between 1990 and 1999. You run four regressions. The table below shows the output. The first regression is a simple univariate regression of y and x. The second includes dummies per country. The third uses country-fixed effects via within-transformation. The fourth is a two-way fixed effects regression. Standard errors are in parentheses.

x1 country==2 country==3 country==4 country==5 country==6 country==7 Year=1991 Year 1992 Year 1993 Year 1994 Year 1995 Year 1996 Year 1997 Year 1998 Year 1999 Observations R2 0.495 2.476 2.476 1.389 (0.779) (1.107) (1.107) (1.320) -1.938 (1.265) -2.603 (1.596) 2.282 (1.261) -1.483 70 0.0059 (1.268) 1.130 (1.289) -1.865 (1.497) 0.296 (1.503) 0.145 (1.547) 2.874 (1.504) 2.848 (1.661) 0.974 (1.567) 1.673 (1.632) 2.992 (1.627) 0.367 (1.588) 1.259 (1.512) 70 70 70 0.2276 0.0747 0.2323 4.1. Interpret the coefficients for x1 in columns (1)-(3). Further, give an interpretation for the coefficient for country=-2 in column (2). 4.2. Explain both ways in which country-fixed effects are implemented in column (2) and (3). Discuss how fixed effects may help here and give an example. Sketch two graphs to highlight the difference. 4.3. Explain the difference of regressions in column (3) and (4) and the consequences for the x1 coeffi- cient. Give an example of a time fixed effect in this setup.