The midterm examination for the Econometric Analysis of Panel Data course consists of four parts, with weights of 15, 15, 30, and 40, respectively. It is an open-book exam, allowing students to use any available information but prohibiting communication devices. This section covers the two basic approaches to modeling unobserved effects in panel data: fixed effects and random effects. The fixed effects model assumes that the intercept varies across entities but is constant within time, while the random effects model assumes that the intercept is constant across entities. The benefits and costs of each approach are discussed, along with the extension to models where all parameters are heterogeneous. For the random parameters case, the estimators under both assumptions are described. This part involves a dataset on 10 firms over 25 years, with variables including log value added, capital, labor, and energy. The model proposed is $y_{it} = \alpha_i + \mathbf{x}_{it}' \beta + \delta d_{it} + \varepsilon_{it}$, where $d_{it}$ indicates whether the firm is in the service or manufacturing sector. The strategy involves estimating the equation separately for each firm using a specific weighting matrix and then averaging the estimates. If there is correlation across firms, a different weighting matrix is used, and the estimator is a weighted average of the individual estimates. This section examines a dynamic, linear, cross-country regression model with random effects. The model includes national income per capita, domestic investment, and labor input. The questions explore the consistency of different estimators under various assumptions, including constant and varying coefficients across countries. The Anderson and Hsiao approach, Hausman and Taylor approach, and GMM estimators are discussed, along with their implementation and efficiency. This part analyzes a panel dataset on Swiss railway companies, focusing on the cost function. The essential model includes log total costs, log output, and log prices of various inputs. The analysis involves testing hypotheses about linear homogeneity in input prices, constant returns to scale, and the endogeneity of output variables. The Mundlak approach is also discussed as a compromise between fixed and random effects models. The two-step procedure for computing fixed effects and random effects estimators is analyzed, and its validity is evaluated.The midterm examination for the Econometric Analysis of Panel Data course consists of four parts, with weights of 15, 15, 30, and 40, respectively. It is an open-book exam, allowing students to use any available information but prohibiting communication devices. This section covers the two basic approaches to modeling unobserved effects in panel data: fixed effects and random effects. The fixed effects model assumes that the intercept varies across entities but is constant within time, while the random effects model assumes that the intercept is constant across entities. The benefits and costs of each approach are discussed, along with the extension to models where all parameters are heterogeneous. For the random parameters case, the estimators under both assumptions are described. This part involves a dataset on 10 firms over 25 years, with variables including log value added, capital, labor, and energy. The model proposed is $y_{it} = \alpha_i + \mathbf{x}_{it}' \beta + \delta d_{it} + \varepsilon_{it}$, where $d_{it}$ indicates whether the firm is in the service or manufacturing sector. The strategy involves estimating the equation separately for each firm using a specific weighting matrix and then averaging the estimates. If there is correlation across firms, a different weighting matrix is used, and the estimator is a weighted average of the individual estimates. This section examines a dynamic, linear, cross-country regression model with random effects. The model includes national income per capita, domestic investment, and labor input. The questions explore the consistency of different estimators under various assumptions, including constant and varying coefficients across countries. The Anderson and Hsiao approach, Hausman and Taylor approach, and GMM estimators are discussed, along with their implementation and efficiency. This part analyzes a panel dataset on Swiss railway companies, focusing on the cost function. The essential model includes log total costs, log output, and log prices of various inputs. The analysis involves testing hypotheses about linear homogeneity in input prices, constant returns to scale, and the endogeneity of output variables. The Mundlak approach is also discussed as a compromise between fixed and random effects models. The two-step procedure for computing fixed effects and random effects estimators is analyzed, and its validity is evaluated.