### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# Special Topics PSCI 7108

GPA 3.66

### View Full Document

## 20

## 0

## Popular in Course

## Popular in Political Science

This 8 page Class Notes was uploaded by Modesto Renner on Thursday October 29, 2015. The Class Notes belongs to PSCI 7108 at University of Colorado at Boulder taught by Ying Lu in Fall. Since its upload, it has received 20 views. For similar materials see /class/231921/psci-7108-university-of-colorado-at-boulder in Political Science at University of Colorado at Boulder.

## Reviews for Special Topics

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 10/29/15

Pooled Time Series Cross Sectional Models Dealing With Time Dependence The Nature of the Problem I Assume a ample tscs model y Xi u I For OLS to be optimal we require that the Variance covariance matrix of the residuals looks like this a 0 2 Q 0 r 0 erm V 0 0 0 1 This Implies That I The errors Within units 7 have the same variance as each other Within7unit homoscedasticity 7 are unrelated to the other errors in that unit Within7unit temporal independence I That the errors across units 7 have the same variance between7unit homoscedasticity re unr lated to contemporaneous or lagged errors in other units spatial independence I When not if we violate these assumptions we get biased estimates of our parameters standard errors The 9 Matrix I The key to modehng tscs data 1s 9 Ifwe know 9 or have a good estimate of1twe can use GLS to estimate our parameters and se s I We do not of course ever know 9 and the best we can do 1s come up wrth an esttmate of1t and use FGLS I Key concerns 1n modehng tscs data 1s the structure of Q The Parks Method I A standardtradlttonal approach to dealing wrth tscs data was proposed by Parks 1967 He assumed that 7 the errors follow a temporal AR1 process If Rum V we can assume that the rhos are common across umts or that they are d1fferentsmce we assume that the Bs are constant ac umts why no a me that the rhos are as well 7 Th approach to serlal correlatxon 1s relatwely standard use conslstent estxmates ofB here based on OLS to generate reslduals whxch promde us a way to estxmate rho X can then use the PrastXmsten transformation on each umt I Wrth regard to contemporaneous Spattal correlatton thlngs become more drf cult because we wo contemporaneous correlatton of errors Use 2 to denote the VCV Vanancercovanance matrlx of errors and recall that 200 020 9 NTXYN 0 OHS I We can look more closely at the elements of Z 2 71 012 am 2 2 012 72 am 2 am UZN UN I The problem 1s that there are NN 12 dlstlnct off d1agonal contemporaneous correlatlons that we need to estimate wth NT observatlons Thls means that we are umng 2tN observatlons to estlmate each Vanance IfT 1s close to N then we are uslng on average only 2 observatlons to estimate each Vanance Thls means 7 the Parks method cannot be used lfTgtN 7 m practlce the Parks method glVeS ternble results unless T15 SIGNIFICANTLY larger than N I Beck and Katz 1995 show V1a Monte Carlo s1mulat1ons that the Parks method has ser1ous problems Therr MCs show that the Parks method y1elds standard error that are far ll too small 7 up to 600 off thls leads to Very ll bad 1nferences I They recommend usmg Parks only 1fT 1s Very large relattve to I In stata the Parks method 1s 1mplemented ma 7 xtgls PaneleCorrected Standard Errors I Beck and Katz propose an alternattve 7 panel corrected standard errors Note at 1n order to use pcses we must rst nd the data of ser1al correlatLon uslng Prals Wlnsten d1fferenc1ng etc I Under these cond1t1ons OLS glves conmstent esthates of but the standard errors must be aduste e mputat1ons are ab1t complex see Beck and Katz 1995 for detalls I Note PCSEs are for use when there 1s no temporal autocorrelat1on A New Data Set Exchmgreen Barry and Damd Leblang 2003 Capxtal Account beemhzahon and rwth Wm M Mahathu mghsvquot Intematmzalfmmalaf F m m Emmamm 8 20544 Duchess vambles hm a constant enmevuymg mpm condmonzl on the mtemntmnzl currency gm gold mum1g button weeds post button woods Dependent Vanable ls growth mte over 5 yearpenod currency and interaction between cases and controls Controlvanables endogenous growth Vanables mmal levels of gap pnmaxy and secondary ecmcahon STATA Example Temporal Dynamics I Both Parks and PCSEs deal wth ehmlnateP senal correlatton by usmg the Prals Wsten or other transformatton Thls 1gnores the d armc nature of the data and treats 1t sn39nplyO as a nulsance relegated to the error term I Ofcourse we need to thmk about the dynarnlc behamor of the Vanable Ln questton Dealing with Dynamics Treat the model as stat1c and the temporal correlatton as a nmsance This as we have done means that we deal wth senal correlatton 1n the res1duals and do not directly confront dynarmcs Ln the model 1tself N Speclfy a dynamic model whereby autocorrelauon 1s a funcuon of a laged dependent Vanable LDV y Wm Xm 04 11quot I This model has a laged endogenous variable and unit level effects 7 ignore for now whether those unit effects random or Xed I What happens ifwe estimate this via OLSgt lfwe leave out the unit effects we get a model that has both unit level and spherical components in the error y WM X a 14 a Hi I lfwe lag this one period we have problems yH mm 96243 12 MM I Why is this a problemgt th yH and u quot contain in which means that in estimating r u 2 u S o E u o N o 8 E39 a o 1 u o m lt o E rmquot 3 r N 1 9 i s d d inconsistent estimates ofB and lt13 With regard to lt1 the bias will be negative provided that ogt0gt increasing in magnitude in lt1 the degree of autoregression a lagged endogenous variable model Simply estimating xed effects for the as does not solve the problem because there is still a correlation between y H and the transformed u t Solution First Difference Estimator I Anderson and Hmao 1981 sugested differencing the model to eliminate unit effects yn rym Wm r yH X r XML3 04 419 n rum I we can rewrite this using the rst difference operator Ax Myra Mm M I while this does eliminate the unit effects it does not get rid of the correlation between the covariates and the errors because y r1 is still correlated With um1 I Solutlon to thls correlatlon between errors and Vanables 1s throu the use of mmWIem l amiabler7 a set of Vanables Z that are hrghly correlated wrth X but uncorrelated wrth the errors I If for example there 1s no serial correlatlon whlch we are assumlng for now then 1t turns out that both A57 and ymz are correlated wrth A57 through y Both of these are uncorrelated wrth Au I Anderson and lls1ao sugest 7 use AM as 2 as an mstrument forum and 7 use ym2 ltself as Z I In theory thls y1elds cons1stent estimates for 3 and D But I In practlce these estlmators have problems 7 The estlmator lS problemath when lt1 15 close to 1 7 The estlmator ylelds blased results when n 15 smal 7 The estlmator ylelds blased results when t 15 short 7 The estlmator lS lnef clent of course thls lS relatlve to an altern athe estlm ator Arellano and Bond s Dynamic Estimator I AB show that 1f we have errors that are mean zero and senally uncorrelated then the drfferenced res1duals Au t are uncorrelated wrth all y t and X from t 2and before 7 thls means that we can use all those Values as Instruments for 7 we can get good estlmates of the parameters under a Wlde range of Clrcumstances 7 as t mcreases then we have anmereasmg1y1arge number of Instruments Whlch Wlll glVe us better estlmates I Dlsadvantages the model 15 llke a xedeeffects estimator covanates that do not Va over time are dropped the rst dxtference model cannot use the rst two observatlons be f differencing and laggmg ngher order models lose addltlonal observatlons whlch IS a problem 1ft sma 1 And recall that the AB estimator requlres that the errors are senally uncorrelated There 1s of course a test for thls They note that 1f the us are uncorrelated then the d1fferenced us w l have negative rst order Serial Correlation no second and higher order serial correlation because the us are now MAO Stata Examples

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

#### "I used the money I made selling my notes & study guides to pay for spring break in Olympia, Washington...which was Sweet!"

#### "Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

#### "It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.