Intr oduc tion to E c onome tr ic s Chapte r 3 E ze quie l Ur - PowerPoint PPT Presentation

Intr oduc tion to E c onome tr ic s Chapte r 3 E ze quie l Ur ie l Jimé ne z Unive r sity of Vale nc ia Vale nc ia, Se pte mbe r 2013

3 Multiple line ar r e gr e ssion: e stimation and pr ope r tie s 3.1 T he multiple line ar r e gr e ssion mode l 3.2 Obtaining the OL S e stimate s, inte r pr e tation of the c oe ffic ie nts, and othe r c har ac te r istic s 3.3 Assumptions and statistic al pr ope r tie s of the OL S e stimator s 3.4 Mor e on func tional for ms 3.5 Goodne ss-of-fit and se le c tion of r e gr e ssor s. E xe r c ise s Appe ndixe s

3.2 Obtaining the OL S e stimate s, inte r pr e tation of the c oe ffic ie nts, and othe r c har ac te r istic s E XAMPL E 3.1 Quantifying the influe nc e of age and wage on 3 Multiple linear regression: estimation and abse nte e ism in the fir m Bue nosair e s (file abse nt)          absent age tenure wage u 1 2 3 4  = - - - absent 14.413 0.096 age 0.078 tenure 0.036 wage i i i i (1.603) (0.048) (0.067) (0.007) = = 2 R 0.694 n 48 properties E XAMPL E 3.2 De mand for hote l se r vic e s (file hoste l) ( )  b + b + b + ln hostel ln( inc ) hhsize u 1 2 3   - + - ln( hostel ) 27.36 4.442ln( inc ) 0.523 hhsize i i i = = 2 R 0.738 n 40 E XAMPL E 3.3 A he donic r e gr e ssion for c ar s (file he dc ar sp)        ln( price ) volume fueleff u 1 2 3   + - ln( price ) 4.97 0.0956 volume 0.1608 fueleff i i i = = 2 R 0.765 n 214 [3]

3.2 Obtaining the OL S e stimate s, inte r pr e tation of the c oe ffic ie nts, and othe r c har ac te r istic s 3.4 Sale s and adve r E XAMPL E tising: the c ase of L ydia E . Pinkham 3 Multiple linear regression: estimation and (file pinkham)                2 3  V P P P u      t 1 1 t 1 1 t 2 1 t 3 t 1  = + + sales 138.7 0.3288 advexp 0.7593 sales - t t 1 = = 2 R 0.877 n 53 properties T he sum o f the c umulative effec ts o f advertising expenditures o n sale s :  ˆ 0.3288   1 1.3660    ˆ 1 0.7593 1 Perio ds o f time required to reac h half o f the to tal effec ts:  ln(1 0.5) ˆ(0.5)   h 2.5172 ln(0.7593) [4]

3.3 Assumptions and statistic al pr ope r tie s of the OL S e stimator s 3 Multiple linear regression: estimation and y y properties x j x j s s 2 2 ˆ ˆ a) big b) small s 2 ˆ E 3.1. Influence of on the estimator of the variance. . F IGUR [5]

3.3 Assumptions and statistic al pr ope r tie s of the OL S e stimator s 3 Multiple linear regression: estimation and y y properties x j x j 2 2 S S a) small b) big j j 2 S F E 3.2. Influe nc e of on the e stimator of the var ianc e .. IGUR j [6]

3.4 Mor e on func tional for ms xample 3.5 Salar y and te nur e (file c e osal2) E      2 ln( salary ) 6.246 0.0006 profits 0.0440 ceoten 0.0012 ceoten 3 Multiple linear regression: estimation and i i i i (0.086) (0.0001) (0.0156) (0.00052)   2 R 0.1976 n 177 Marginal effec t o f c e o te n o n salary, expressed in perc entage:     me % 4.40 2 0.12 ceoten / salary ceoten properties ginal e ffe c t in a c ost func tion (file c ostfunc ) E xample 3.6 T he mar      2 3 cost 29.16 2.316 output 0.0914 output 0.0013 output i i i i (1.602) (0.2167) (0.0081) (0.000086)   2 R 0.9984 n 11 Marginal c o st :       2 marcost 2.316 2 0.0914 output 3 0.0013 output i i i [7]

3.5 Goodne ss-of-fit and se le c tion of r e gr e ssor s E xample 3.7 Se le c tion of the be st mode l (file de mand) Alternative mo dels: 3 Multiple linear regression: estimation and      1) dairy inc u 1 2      2) dairy ln( inc ) u 1 2        3) dairy inc punder 5 u 1 2 3      4) dairy inc punder 5 u 2 3        5) dairy inc hhsize u properties 1 2 3      6) ln( dairy ) inc u 1 2        7) ln( dairy ) inc p under 5 u 1 2 3      8) ln( dairy ) inc punder 5 u 2 3 = = n 40 ln( dairy ) 2.3719 Co rrec ted AI C fo r mo de l 6) = + = + ´ AIC AIC 2ln( ) Y 0.2794 2 2.3719=5.0232 C [8]

3.5 Goodne ss-of-fit and se le c tion of r e gr e ssor s 3 Multiple linear regression: estimation and T E 3.1. Me asur e s of goodne ss of fit for e ight mode ls. ABL Model number 1 2 3 4 5 6 7 8 Regressand dairy dairy dairy dairy dairy ln( dairy ) ln( dairy ) ln( dairy ) intercept intercept intercept inc intercept intercept intercept inc Regressors inc ln( inc) inc punder5 Inc inc inc punder5 punder5 househsize punder5 R-squared 0.4584 0.4567 0.5599 0.5531 0.4598 0.4978 0.5986 -0.6813 properties Adjusted R-squared 0.4441 0.4424 0.5361 0.5413 0.4306 0.4846 0.5769 -0.7255 Akaike information 5.2374 5.2404 5.0798 5.0452 5.2847 0.2794 0.1052 1.4877 criterion Schwarz criterion 5.3219 5.3249 5.2065 5.1296 5.4113 0.3638 0.2319 1.5721 Corrected Akaike 5.0232 4.849 6.2314 information criterion Corrected Schwarz 5.1076 4.9756 6.3159 criterion [9]