National Economics University
Advanced Program in Finance
Introductory Econometrics
FINAL EXAMNATION EXAMNATION
INSTRUTIONS!
- This is the open-book exam, all materials can be used in the room except laptop - Time allowed: 90 minutes. - Mark for each question is gien next to the question!s number.
"n order to explain the #$ defense budget, %ou are using the data from &9'( to &9)& with the following ariables *all measured in billions #$+ and estimate the corresponding model *Model &:*#se 0.0/ for references t: 1(t: 15t: 16t: +&t:
+efense budget outla% for %ear t 234 for %ear t #$ militar% sales in %ear t 7erospace industr% sales in %ear t +umm% ariable presenting the militar% conflict inoling more than &00,000 troops8 +&t& if more than &00,000 troops are inoled and equal to 0 if fewer than &00,000 troops are inoled.
Dependent Depende nt Variable: Y Method: Least Squares Variable "oe##icient " 21$(!2)1 D1 &(8$2198* ,2 !$!1+8*9 ,+ !$!*+1(6 ,( 1$+89*)+ ,(-D1 1$)(!*92 ,2-D1 !$!22(!6 .&squared !$996+66 /d0usted .&squared .&squared !$99(688 S$%$ o# reression 2$1119*2 Sum squared resid )*$98))( Lo lielihood &+9$!2++8 Durbin&atson stat 2$2++**1
Sample: 1962 1981 Included obserations: 2! Std$ %rror t&Statistic 'rob$ 1$(969(* 1($29*(( !$!!!! 6$8*1)(( &*$!1*+28 !$!!!! !$!!+2!* ($+28!62 !$!!!8 !$2!+8!) !$+)89!2 !$*2)( !$1+!19* 1!$6*(2+ !$!!!! !$+2)!!) ($*(!818 !$!!!( !$!!)*81 +$8*6!+8 !$!!19 Mean dependent ar 8+$86!!! S$D$ dependent ar ar 28$9***1 /aie in#o criterion ($6!2++8 Sch3ar4 criterion ($9)!8() 5&statistic )9+$981) 'rob75&statistic !$!!!!!!
&. &0;xplai &0;xplain n the meaning meaning of of each estimated estimated coeff coefficien icientt and < ( in the aboe model. (. &0Test &0Test for for significanc significancee of each independent ariable ariable and test for oerall oerall signifi significance cance of the model. 5. &/=onduct &/=onduct the test test of autocorre autocorrelatio lation n in the model using using the informati information on aboe. $tate $tate clearl% clearl% the conditions to appl% this test> "f those conditions are not met, name other tests %ou can use instead. 6. &0?hen &0?hen 234 increas increases es b% & bil #$+ *other ariabl ariables es unchanged, unchanged, what is the confidenc confidencee interal interal of the difference in the changing leels of defense budget between the cases of there are more than &00,000 or fewer than &00,000 &00 ,000 troops inoled in the militar% conflict>
/. (0@or the case when there are fewer than &00,000 troops inoling in the conflict *this condition indicates that we are concerning on the coefficients of 1( and 16 onl%, if we simultaneousl% increase 1( and 16 b% & billions #$+, test the proposition that the defense budget will increase &.6 billions #$+. ?hat is the confidence interal for the increase in the leel of defense budget in this case> *The coariance between two estimated coefficients of ( ariables 1( and 16 is -0.0005 '. '. &/+o %ou think that the militar% budget does not depend on the number of troops inoling in the conflict gien that if %ou regress on 1(, 15 and 16 *with intercept, %ou get < (0.9A& and <$$6'&.()> A. (02ien the information below, test for all possible problems in the model & aboe. "n each test specif% clearl% t%pe of test, t%pe of problem, the statistic used, null and alternatie h%pothesis and conclusion about the problem. @or result *(, how man% degree of freedom for chi-square statistic> @or result *6, write the auxiliar% regression model *we use fitted alue, the square and the cubic terms of fitted alues *Bhat, BhatC( and hatBhatC5 in this model. Result "#$ * Series: .esiduals Sample 1962 1981 bserations 2!
6 ) ( + 2 1 ! &(
&+
&2
&1
!
1
2
Mean Median Maimum Minimum Std$ De$ Se3ness ;urtosis
&1$1+%&1( !$1(!81+ 2$8))6+* &+$21)228 1$*(696! &!$218699 2$211*9+
!$6**1)) !$*12*8+
+
Result "%$ hite ?eterosedasticit> @est: 7Ao cross term 5&statistic 2$+*9+99 'robabilit> !$11(212 bs-.&squared 1)$+1*99 'robabilit> !$168+9*
Result "&$ =reusch&Bod#re> Serial "orrelation LM @est: /.72 5&statistic 1$9)!)+* 'robabilit> !$188+(9 bs-.&squared )$2+)96+ 'robabilit> !$!*29)!
Result "'$ .amse> .%S%@ @est: 5&statistic 2$11!1)( 'robabilit> Lo lielihood ratio *$(+2899 'robabilit>
!$1191!2 !$!)9+!8
(OO) LU*+
