By Cheng Hsiao
This ebook offers a complete, coherent, and intuitive evaluation of panel facts methodologies which are necessary for empirical research. considerably revised from the second one variation, it comprises new chapters on modeling cross-sectionally based facts and dynamic platforms of equations. the various extra complex innovations were additional streamlined. different new fabric comprises correlated random coefficient versions, pseudo-panels, period and count number facts types, quantile research, and substitute methods for controlling the impression of unobserved heterogeneity in nonlinear panel facts types.
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Additional info for Analysis of Panel Data
He treated output, y, as a function of labor, x1 ; real estate, x2 ; machinery, x3 ; and feed, fertilizer, and related expenses, x4 . However, because of the difficulties of measuring real estate and machinery variables, he also tried an alternative specification that treated y as a function of x1 , x4 , a current-expenditures item, x5 , and fixed capital, x6 . Regression results for both specifications rejected the overall homogeneity hypothesis at the 5 percent significance level. 1. 88 when αi and λt are introduced.
2) where yi T ×1 ⎡ ⎤ yi1 ⎢ ⎥ = ⎢ yi2 ⎥ ⎢ .. ⎥ , ⎣ . ⎦ ⎡ Xi T ×K x1i1 ⎢ x1i2 =⎢ ⎢ .. ⎣ . x2i1 x2i2 .. x1iT x2iT ui 1×T = yiT e = 1×T Eui = 0, (1, 1, . . , 1), Eui ui = σu2 IT , ··· ··· ⎡ ⎤ ⎤ X1 xKi1 ⎢ X2 ⎥ xKi2 ⎥ ⎢ ⎥ ⎥ .. ⎥ , X = ⎢ .. ⎥ ⎣ . ⎦ ⎦ . xKiT (ui1 , . . , uiT ), Eui uj = 0 if i = j, XN 36 Simple Regression with Variable Intercepts IT denotes the T × T identity matrix. Let X˜ = (d1 , d2 , . . , dN , X), where di is an N T × 1 vector dummy variable with the first (i − 1) × T elements equal to 0, (i − 1)T + 1 to iT elements equal to 1, and 0 from iT + 1, .
879 a All output and input variables are in service units, measured in dollars. Source: Hoch (1962). with scale. 1, when the production hyperplane of larger firms lies above the average production plane and the production plane of smaller firm below the average plane, the pooled estimates, neglecting firm differences, will have greater slope than the average plane. Some confirmation of this argument was provided by Hoch (1962). 2 lists the characteristics of firms grouped on the basis of firm-specific effects αi .