UG Curse Outline EC2203: Quantitative Methds II 2017/18 Autumn: Instructr: Pierre0-Olivier Frtin Office: Hrtn H214 Phne: +44 (0) 1784 276474 E-mail: pierre-livier.frtin@rhul.ac.uk Office hurs: Tuesdays and Wednesdays frm 10 t 11 Spring: Instructr: Michael Mandler Office: Hrtn Phne: +44 1784 443985 E-mail: M.Mandler@rhul.ac.uk Office hurs: TBA AUTUMN TERM Aims Much f the ecnmics yu have seen s far and which yu will cntinue t study this year cnsists f theretical mdels. Ecnmics, hwever, is mre than that. Many ecnmists analyse data t learn hw the wrld wrks and t test which ecnmic mdels best describe the facts. The first half f the curse is intended t prvide yu with a slid understanding and practical experience f the essentials f empirical research techniques (ie ecnmetrics) used by applied ecnmists. Learning Outcmes By the end f this term, students shuld: - use, understand and distinguish between standard ecnmetric techniques - be able t carry ut frmal statistical tests f ecnmic hyptheses - manipulate and analyse data sets and cnduct yur wn ecnmetric investigatins, bth written and using cmputer sftware. Curse Delivery There will be a tw-hur lecture and a ne-hur class each week. The lectures will cmbine discussin f ecnmetric thery alng with demnstrative use f the ecnmetrics package Stata t enable students t understand the practical art f ecnmetrics as well as the underlying theries and assumptins. There will be a set f lecture slides fr each lecture, which will be made available n Mdle a day in advance. Students are expected t make ntes n these slides during lectures and after (by cnsulting the relevant pages in the curse texts). The curse is very much an 'applied hands-n' ecnmetrics full f real wrld data and practical examples. Students wh d nt attend lectures r classes and wh d nt attempt prblem sets will find this curse very difficult. Prblem Sets One prblem set will be given ut and discussed each week which will invlve bth written questins and cmputer-based exercises. T have any hpe f ding well in the end f year examinatin and the dissertatin all these prblem sets shuld be attempted. Students shuld bring written answers t the class t be discussed by the class teacher. Students will be allwed t Page 1 f 6
retain their wrk s that they can add cmments and rectify errrs during the discussin. There will nt be time t discuss all the answers t every questin in the prblems sets. Students will be expected t wrk thrugh the answers t thse questins nt cvered in classes in their wn time. T facilitate this, answers t the prblems sets alng with lecture hand-uts and data sets - will be psted (with a lag) n the curse Mdle page http://mdle.rhul.ac.uk/ and n the curse website http://persnal.rhul.ac.uk/uhte/006/ec2203/index2.html Cmputer Exercises T really understand ecnmetrics and empirical wrk, yu need t have experience f ding it yurself. Mst f the prblem sets assigned during term will include questins requiring use f real wrld data sets and use f the Stata regressin package. Detailed instructins fr using the package will be included in a separate handut and in the prblem sets. The seminars will take place in the cmputer labs. S yu will have plenty f pprtunity fr practice. Reading The curse text, which yu shuld prbably buy (thugh there are several cpies in the library) is C. Dugherty, Intrductin t Ecnmetrics 4th Editin", Oxfrd University Press, (Library Cde: 330.01 DOU) The lecture will nt fllw the text page by page, but the bk is a useful cmpanin t the lecture ntes yu will be prvided with. Other useful texts are D. Gujarati, Basic Ecnmetrics", McGraw-Hill Press, (Library Cde: 330.01 GUJ) J. Wldridge, Intrductry Ecnmetrics: EMEA Editin (Library cde: 330.01 WOO) J. Stck and M. Watsn, Intrductin t Ecnmetrics, 3rd Editin, Pearsn Internatinal. (Library cde: 330.01 STO) (the last tw are prbably pitched just abve the verall level f this curse, but are mre cmprehensive and cntain lts f useful intuitin and wrked examples). The lectures and assciated classes will nt cver basic statistical issues like expected values, cvariance, the nrmal distributin, hypthesis testing r cnfidence intervals. It is assumed that yu have a gd knwledge f these tpics frm last year. If yu need t revise them, T. Wnnactt & R. Wnnactt, "Intrductry Statistics fr Business and Ecnmics", Wiley Press (Library Cde: 330.0182 WON) is a gd surce. Time permitting, the curse will g ver the fllwing areas. Weeks 1-2. Simple Regressin Analysis Simple regressin mdel; derivatin f linear regressin equatin; gdness f fit. Page 2 f 6
Aims: knw the frmulae fr the regressin cefficients and understand the principle underlying hw they are derived; knw the definitin f R 2 and hw it is related t the residual sum f squares. Weeks 3-4: Prperties f Regressin cefficients Gauss-Markv cnditins and unbiasedness f the regressin cefficients; precisin f the regressin cefficients; Gauss-Markv therem; t test f a hypthesis relating t a regressin cefficient; Type I errr and Type II errr; cnfidence intervals; F test f gdness f fit. Aims: Hw t interpret a regressin cefficient; hw t investigate whether r nt estimatrs are biased. Week 5. Multiple Regressin Analysis Regressin with 2 explanatry variables; prperties f multiple regressin; Hypthesis testing. Aims: T be able t perfrm F tests, Chw tests, and give ecnmic interpretatin f estimated cefficients. Week 6. Specificatin f Regressin Equatins Functinal frm; F tests in multiple regressin mdel; transfrmatin f variables elasticities; dummy variables; mitted variable bias. Aims: T be able t chse apprpriate functinal frm fr given datasets and interpret cefficients f the chsen mdel accrdingly. Week 7. Endgeneity Definitin and cnsequences f endgeneity; simultaneus equatin systems; measurement errr; tests fr endgeneity; instrumental variable estimatin as a slutin t prblem. Aims: Demnstrate cnsistency f IV estimatin and perfrm relevant tests. Week 8. Autcrrelatin Definitin and cnsequences; tests fr AR(1) autcrrelatin; autcrrelatin with lagged dependent variable. Aims: T be able t perfrm tests and be aware f pssible slutins t autcrrelatin. Week 9. Mdels using Time Series Data and Nn-Statinary Prcesses Dynamic mdels; shrt and lng-run cefficients; statinary and nn-statinary prcesses; cintegratin. Aims: T be able t analyse shrt and lng-run implicatins f dynamic mdels; determine whether a time series is statinary; understand the principles behind the unit rt test. Week 10 Heterskedasticity Meaning and cnsequences f heterskedasticity. Tests fr heterscedasticity. Aims: T knw hw t undertake tests fr heterskedasticty. Page 3 f 6
Week 10. Panel Data The idea f panel data. Fixed Effects and Randm effects. Aims: T have a simple appreciatin f panel mdels. SPRING TERM Aims The secnd term f QMII is devted primarily t the mathematical thery f ptimisatin. Understanding ptimisatin thery will als require the study f linear algebra and calculus. In the secnd term, yu will develp yur ecnmetric and statistical skills, and yu will use thse skills t analyse data sets. This utline primarily cncerns the first term. Learning Outcmes Upn cmpletin f the curse yu shuld: Have a thrugh understanding f the main mathematical tls used in ecnmics and f ptimisatin thery in particular, (Maths) Be able t use this knwledge t manipulate and slve prblems and mdels, (Maths) Be familiar with the lgic f prfs f mathematical therems and be able t cnstruct simple prfs yurself, (Maths) Understand the thery and practice f statistical inference and regressin analysis in ecnmics, (Ecnmetrics) Be able t analyse data sets and t cnduct frmal tests f statistical hyptheses. (Ecnmetrics) Curse Delivery The curse will be delivered thrugh tw hurly lectures every week, plus a ne-hur seminar. Seminars will be based upn prblems assigned in the previus week s lecture, sme f which will cme frm the recmmended text. Prblem sets will be given weekly. Althugh these will nt be part f the frmal methd f evaluatin, yu are advised that slving the prblems will be f enrmus help in examinatins and tests. Seminar attendance is cmpulsry and failure t attend can lead t students being issued with a frmal warning. Yu shuld prepare answers t the prblems befre the weekly seminars and expect t present them t the rest f the grup. Skeletn prblem slutins will be psted n the web, after the relevant seminars. Reading There is n set textbk fr this half f the curse, the mst apprpriate textbk is: Alpha Kevin Wainwright, Fundamental Methds f Mathematical Ecnmics, McGraw-Hill. (Nte that the previus editin authred slely by Chiang is als suitable, thugh chapter numbers are different). The lecture ntes will be self-cntained fr thse students wh attend the lecture and numerus examples will be prvided during the lecture. Page 4 f 6
We will als use the bk as a surce fr prblems. It is nt the respnsibility f the library t stck large cpies f standard texts, s I strngly recmmend that yu buy a cpy f this bk shuld yu struggle t keep up with lectures. Dwling, Edward T., Thery and Prblems fr Mathematics fr Ecnmists, Schaum is a cheap supplement that cntains many wrked examples. If yu wrk with a study partner yu may wish t buy ne cpy f each text between yu. Curse materials will be available n Mdle. I will hand ut the ntes in lecture, these will be blanked t encurage yu t wrk n the prblems during the lecture, but yu shuld g t the website fr additinal cpies and fr prblem slutins; which will be upladed with abut a tw week lag. Weekly Timetable Week Title Learning Outcmes Reading 1 Intrductin t ptimisatin thery. By the end f this tpic yu shuld be familiar with the rle f ptimisatin in ecnmics and be reminded f the rules f differentiatin and the first rder cnditins fr uncnstrained maximizatin. Wainwright, Chapter 7 parts 1-4 and Chapter 9 parts 1 and 2. Chapter 12 parts 1 and 2. 2-3 Nnlinear prgramming By the end f this tpic, yu shuld understand hw Lagrange multipliers can be used t slve nnlinear cnstrained maximisatin prblems and able t apply the methd t varius ecnmic prblems. 4 Vectrs By the end f this tpic yu shuld understand the cncept f a vectr in n-dimensinal space, be able t perfrm basic peratins n vectrs, and understand the cncepts f linear cmbinatins f vectrs, linear independence, and the inner prduct f vectrs. 5-7 Matrices and slving systems f linear equatins. By the end f this tpic, yu shuld understand the cncept f matrix, knw the rules f matrix algebra, knw what an inverse f a matrix is and hw t calculate it, knw what a determinant is, be able t define the rank f a matrix, knw hw t perfrm elementary rw peratins n a matrix, use matrix algebra t slve systems f linear equatins, Wainwright, chapter 13, sectins 1-3. Wainwright, chapter 4, sectins 1, 3 Wainwright, chapter 4, sectins 1-2, 3-5, chapter 5, sectins 1-4. Page 5 f 6
8 Further applicatins f prgramming and matrix algebra: Input- Output Analysis. 9-10 Secnd rder cnditins and Cmparative Statics Final Week Revisin understand cmparative statics analysis in linear mdels. By the end f this tpic, yu shuld hw matrix algebra can be used fr input-utput analysis, understand hw t calculate input requirements given an utput requirement and understand hw t check fr prductiveness f in input utput system. By the end f this tpic, yu shuld knw what cncave and cnvex functins are, understand hw t check secnd-rder cnditins fr a maximum using matrix methds and be familiar with sme basic methds f cnducing cmparative static analysis. Chiang, chapter 5, sectin 7. Wainwright, chapter 11, chapter 12 sectin 3. Assessment 60% f the curse grade will cme frm an examinatin taken during the summer term. The exam will test yur knwledge f and understanding f the material cvered in bth parts f the curse and yur ability t manipulate and slve related prblems Assessment cmprises an Ecnmetrics prject (based n material cvered in the Autumn term) t be handed in early in the Spring term. Students will have t devise their wn ecnmetric prject, find data and present estimatin results - t be cmpleted by the beginning f the Spring term. Mre details abut the prject will als be given in a separate handut in the Autumn term. The prject carries a weight f 20%. There will be a written 1 hur mid-term test in each term wrth 5% each. There will als be 2 assessed nline tests in each term. Each nline test carries a weight f 2.5%. Yu will receive standardised feedback n yur prject and tests. Test and prject hand-in dates can be fund in the student handbk and reminders will be prvided in Mdle Page 6 f 6