Panel Data Course Lecture 1

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Panel Data CourseLecture 1

• Trinity Term 2006
• Dr David Rueda

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Today Introduction to Panel Data

• Some practical issues about the class.
• Todays Lecture
• Introduction and terminology.
• Panel data variation.
• Single-Equation Linear Model.
• To pool or not to pool.
• Unit heterogeneity fixed effects.
• Advantages and disadvantages of fixed effects.
• Stata Session
• Introductory TSCS command.
• Introductory TSCS analysis.

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Some Practical Issues about the Class (1)

• Topics and Schedule for the Term
• Week 1
• Introduction and Terminology. Panel Data
  Variation. Single-Equation Linear Model. Unit
  heterogeneity fixed effects.
• Week 2
• Random Effects. Fixed versus Random Effects.
• Week 3
• More on TSCS/Panel Models. The Parks Method.
  Panel-Corrected Standard Errors. Temporal
  Dynamics in TSCS/Panel Data.
• Week 4
• More on Temporal Dynamics in TSCS/Panel Data.
  First Difference Estimators. Arellano and Bond.
  Random Coefficient Models.

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Some Practical Issues about the Class (2)

• Taking the Course for Credit?
• This course will be examined in the form of an
  assignment to be set by the lecturer. Those
  students taking the course for credit should talk
  to the lecturer during the first session. The
  assignment will involve data analysis and writing
  a report covering all topics examined during the
  course. The assignment will be due during the
  last week of Trinity term (or by arrangement with
  the instructor). Details to be agreed with the
  instructor.

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Some Practical Issues about the Class (3)

• Class is divided into two halves.
• In the first half, we do the lecture. In the
  second we do the related Stata session.
• All material for this course are on my website
• The rubric is there (it will change, keep
  checking).
• Class and Stata session presentations will be
  there.
• Go to my website (http//users.ox.ac.uk/polf0050/
  ) and then teaching, Oxford, etc.
• Go to the class website directly
  http//users.ox.ac.uk/polf0050/page8.html
• You can/should take the time series class with
  Mark Pickup.
• We emphasize intuitions in this class and do not
  provide a lot of mathematical proofs.
  References.
• However, we will be using matrix notation.
• About the lectures
• If I say something that is not clear, stop me.
• If I am going too fast, stop me.

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Introduction and Terminology 1

• The data we are going to be looking at
• It varies both through time and across
  cross-sections.
• Examples of cross-sections?
• Countries, regions, individuals in panel survey,
  households in a panel survey, executives,
  parliamentary committees, etc, etc.
• We will refer to time units as t 1, 2, 3, , T.
• We will refer to cross-sectional units as i 1,
  2, 3, , N.
• Total number of observations NT.
• More terminology
• Panel data usually refers to data that are mostly
  cross-sectional, meaning NgtT (often much
  greater).
• Time-series cross-sectional (TSCS) data usually
  refers to data that are mostly time series,
  meaning TgtN, or data in which TN, or even data
  in which NgtT but T is relatively high.
• In this course, however, we are going to use the
  two terms indistinctively.

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Introduction and Terminology 2

• Example of panel data and how we usually organize
  it
• Cross-sectional units countries.
• Time units years.
• Country Year Y X1 X2
• ASL 1955 1 2 3
• ASL 1956 2 3 4
• ASL 1957 3 4 5
• . . . . .
• AUS 1955 1 2 3
• AUS 1956 2 3 4
• AUS 1957 3 4 5
• . . . . .
• Within the context of panel data, we can have two
  kinds of variation
• Between cross-sectional units.
• Within cross-sectional units.
• (Or obviously both or none).

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Panel Data Variation

• Within the context of panel data, we can have two
  kinds of variation
• Between cross-sectional units.
• Within cross-sectional units.
• (Or obviously both or none).
• Consider the cross-sectional mean
• Within cross-sectional unit variation

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Single-Equation Linear Model (1)

• The single-equation linear model is the workhorse
  of empirical political science
• 
  or
• What are we assuming in this model?
• The usual OLS assumptions (look at your notes
  from previous terms).
• That the constant term is constant across
  different observations, different cross-sectional
  units and through time.
• That the effect of X over Y is constant across
  different observations, different cross-sectional
  units and through time.
• The two last assumptions are likely to be
  violated in the panel and tscs context (there are
  often reasons why the constant term or the effect
  of X on Y may be different across cross-sectional
  units and through time).

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Single-Equation Linear Model (2)

• We also assume the error term is homoscedastic
  and uncorrelated both across cross-sectional
  units and through time (if not, the estimates
  will not be biased but our inferences will be
  inaccurate).
• We also assume that the explanatory variables Xi
  are exogenous.
• In this context, we will define endogeneity the
  following way an explanatory variable Xj is
  endogenous if it is correlated with uit.
• With the data that we use in social science, this
  kind of endogeneity can arise because of three
  reasons (see Wooldridge, chapter 4 for details).
• Omitted variables we fail to include a relevant
  variable into the model. The observed
  explanatory variable may be correlated to the
  unobserved explanatory variable.
• Measurement error we observe an imperfect
  measure of X, the difference between the observed
  and unobserved X goes into the error. The
  observed explanatory variable may be correlated
  to the unobserved explanatory variable.
• Simultaneity if X is determined partly as a
  result of Y, then X an uit are generally
  correlated.

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To Pool or not to Pool? (1)

• The advantages of pooling
• Pooling adds data! If the assumptions we are
  making to pool work, this means more accurate
  estimates.
• Generalizability We want our conclusion to
  apply to many cases, many time periods.
• The theoretical claims require it Often
  questions in political science involve both
  comparative and time series issues.
• Pooling provides the variation needed to answer
  questions we couldnt answer with TS or CS data
  alone.
• Pooling can help us with the measurement error
  and omitted variables problems we could have if
  using TS or CS data alone.

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To Pool or not to Pool? (2)

• Complications?
• Pooled data analysis relies on the assumption
  that the relationship between X and Y does not
  vary cross-sectionally or through time.
• This means the relationship between X and Y is
  exactly the same for all i and for all t, and the
  process affecting the uit is also the same for
  all i and for all t. OK, but

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To Pool or not to Pool? (3)

• This assumption can be more complicated than it
  seems. Example from Bartels (1996)
• Imagine data that in reality contains two
  different kinds of relationships between X and Y
  for two groups of data (could be different
  countries, or years, etc).
• The pooled estimate of the coefficients will be a
  weighted combination of the two separate ßs, the
  weights being inversely proportional to the
  variancecovariance matrix of that particular
  parameter vector. (See the math in Bartels 1996)
• This means that in the pooled estimate, the more
  precise of the two coefficients will dominate
• Ceteris paribus, the kind of data that will
  dominate the pooled estimate will be the one
  with the larger N, the larger values of the
  coefficients, and/or the smaller standard errors.

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To Pool or not to Pool? (4)

• Deciding whether or not to pool should be the
  first stet in our analysis!!
• The question Are the units comparable and are
  the processes the same?

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Unit Heterogeneity Fixed Effects (1)

• We mentioned above that a key assumption in panel
  data analysis is that observations have the same
  coefficients. But we can relax this.
• There are two general ways fixed effects and
  random effects.
• Today fixed effects (within estimator), aka
  least squares dummy variable estimation (see
  Hsiao, chapter 3).
• A simple way to think about this is in terms of a
  unit-specific intercept (allowing some units to
  have different average levels of Y).
• We may be interested in change over time within a
  panel data context.
• We want to control for unit specific omitted
  variables.
• Differences across units can thus be captured in
  differences in the constant.
• We introduce dummies to model these unique
  sources of variation, to model the heterogeneity.
• Our equation is transformed
• 
  or

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Unit Heterogeneity Fixed Effects (2)

• Because the fixed effects are constant over time
  or across units, their effects can be absorbed
  into the intercept
• The estimates will be unbiased and efficient.
• They will also be consistent as long as N or T or
  both tend to infinity.
• Why is least squares dummy variable estimation
  the equivalent of having a constant per unit?
• How about the general constant?
• Least squares dummy variable estimation is the
  equivalent of ANOVA.

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Advantages and Disadvantages of Fixed Effects

• Reasons to Include Fixed Effects
• To avoid the dangers of specification bias (which
  is a big problem)!
• Easy to interpret Unit effects have an easy
  explanation.
• Popularity They are used very widely (in
  economics and political science particularly).
  Readers will understand.
• Reasons NOT to Include Fixed Effects
• It is a problem when you are interested in
  unit-specific variables. Why?
• Fixed effects models cant include covariates
  that are constant within units (because they are
  perfectly collinear with the fixed effects).
• For variables that vary little within the unit,
  the effects will be hard to estimate precisely
  (they will be highly collinear with the fixed
  effects).
• Inefficiency can be a problem. Fixed effects may
  use a lot of degrees of freedom.

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References

• Bartels, Larry M. 1996. Pooling Disparate
  Observations. American Journal of Political
  Science 40 905-42.
• Hsaio, Cheng. 2002. The Analysis of Panel Data,
  2nd Ed. New York Cambridge University Press.
• Wooldridge, Jeffrey. 2002. Econometric Analysis
  of Cross Section and Panel Data. Cambridge, Mass
  MIT Press.

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Stata Session Introducing the Dataset.

• Comparative Political Data taken from Klaus
  Armingeon, Philipp Leimgruber, Michelle Beyeler,
  Sarah Menegale. Comparative Political Data Set
  1960-2002, Institute of Political Science,
  University of Berne 2004.
• cps.dta.
• Countries Australia Austria Belgium Canada
  Denmark Finland France Germany Ireland
  Italy Japan Luxembourg Netherlands New
  Zealand Norway Sweden Switzerland United
  Kingdom USA.
• Years 1960-2002.
• Variables
• year, country, countryn (countrynumber).
• gov_right, gov_cent, gov_left right, center, and
  left parties in percentage of total cabinet
  posts, weighted by days.
• effpar effective number of parties in parliament
  according to Laakso/Taagepera.
• fed federalism coded 0 no, 1 weak, 2
  strong.
• gdpgr growth of GDP, change from previous year.

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Stata Session Introductory TSCS Commands

• You can always sort your data using when
  analyzing panel and/or TSCS data in Stata for
  example, sort country year
• The series of commands in Stata for analyzing
  panel and tscs data all begin with the letters
  xt
• We need to tell Stata that our data are in panel
  format to be able to use xt commands.
• We do this by specifying the i and t variables
• . iis name
• . tis year
• Or we can do both
• . tset ccode year
• We can examine the between versus the within
  variation in writing separately, using Statas
  xtsum

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Stata Session Introductory TSCS Analysis

• See computer class notes.
• See Stata file in Student_Shared folder.
• It is annotated with explanations of commands and
  procedures.