Applied Econometrics: Panel Lecture

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Applied Econometrics Panel Lecture

• Chapter 16, Gujarati
• In Panel Data, the Same Cross-sectional Unit Is
  Surveyed Over Time.

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Introduction

• Today we will examine panel econometrics.
• One of the biggest areas of modern econometrics.
• See Gujarati for introduction.
• More advanced panel textbooks outside the scope
  of our discussion.
• Today we will introduce these topics and look at
  some empirical examples.

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Topics of Discussion

• Types of data cross sectional/time
  series/panel.
• Reexaming economic models.
• Types of panel.
• Example of panel.
• Estimating panel models.
• Fixed effects versus random effects.

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Main Point of Lecture

• Panel econometrics is a huge field and to cover
  everything would not be possible. This lecture
  aims to introduce you to panel econometrics using
  research examples. Particularly, I want to
  discuss when and why you would use fixed versus
  random effects models.

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Terminology

• Time series cross section data/ micropanel
  data/longitudanal data/cohort analysis/ event
  history analysis.
• Many authors use the above terms
  interchangeably. Will talk about some potential
  distinctions.

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Why Panel Data?

• Allows one to analyse issues such as persistency
  (e.g. Unemployment).
• Allows one to examine complex behavioural models
  (e.g. Life cycle models of saving/consumption).
• Allows one to explicitly take in to account
  individual heterogeneity.

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Limitations of Panel Data

• (i) Measurement Error that can arise in survey
  data
• (ii) Self-Selection in to the panel
• (iii) Non-Response
• (iv) Attrition
• (v) Typically, micro-panels cover a short time
  dimension e.g. the Living in Ireland covers only
  from 1994 to 2001.

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Some Examples of Panel

• Labour economics, welfare economics and several
  other fields rely heavily on household panel
  studies.
• Panel study of income dynamics (Michigan).
• Industrial economics utilises very large panel
  datasets (e.g. Amadeus).
• In Ireland, the ESRI ran the living in Ireland
  survey panel from 1994 to 2001 (will examine some
  of this later in the class).

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Famous Panel Studies

• Canadian Survey of Labour Income Dynamics
• Japanese Panel on Consumers
• Korea Labor and Income Panel Surveys
• Household Income and Labor Dynamics in Australia
• Indonesia Family Life Surveys

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Economic Modelling

• Very similar principles of economic modelling
  apply to panel as applied to the other techniques
  we have examined.
• Specification issues e.g. Omitted variables or
  irrelevant included variables.
• Distributional issues e.g. Non-normality.

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An Example of a Panel Model (1)

• Grunfelds (1958) investment data.
• A little dated but will help us to work through
  the stuff in gujarati.
• Q how does investment depend on the real value
  of the firm and the real capital stock?
• Data 4 companies for 20 years (from 1935
  1954).

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5 Ways of Estimating a Panel Model

• Assume that intercepts and slopes are the same
  over time and individuals.
• Assume that slopes are constant but that
  intercepts vary over individuals.
• Assume that slopes are constant but that
  intercepts vary over time and individuals.
• Assume that all coefficients vary over
  individuals.
• Assume that all coefficients vary over
  individuals and time.

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Fixed Effect Panel Model

• The intercept in the regression is allowed to
  differ among individuals in recognition of the
  fact that each individual (unit) may have
  characteristics of their own.
• Also known as the least squares dummy variable
  model.

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Why use Fixed Effects

• Fixed Effects are generally used when there is a
  correlation between the individual intercept and
  the independent variables.
• Generally used when n is relatively small and t
  is relatively large.

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Random Effects Model

• Random Effects models assume that the intercept
  of an individual unit is a random drawing from a
  much larger population with a constant mean
  value.
• Also (less frequently) know as the Error
  Components model.

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Fixed Effects or Random Effects

• IF N is large and T is small, and if the
  assumptions underlying RE hold, the RE are more
  efficient estimators.
• Use Fixed Effects if the errors and the
  observations are correlated (e.g. countries).
• The Hausman test is distributed Chi-Squared
  Asymptotic around the null hypothesis that Random
  Effects is appropriate.

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Hausman Test

• Hausman (1978).
• The null hypothesis is that the FE and RE do not
  differ substantially.
• Test is distributed asymptotically chi-squared.
• FE is consistent under both the null and the
  alternative.
• RE is consistent under the null and inconsistent
  under the alternative.
• We can test the appropriateness of RE using
  critical values.

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An Example of a Panel Model (2)

• Did people get better off over the course of the
  Celtic tiger?
• We certainly became richer but how about happier
  or more satisfied with our income?
• To address this question I have been analysing a
  panel of people tracked from 1994 to 2001.

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An Example of a Panel Model (3)

• What are the determinants of international
  disputes.
• Beck et. al. (1998) in their paper on
  international conflict, and consist of
  time-varying data on 827 politically-relevant
  dyads in the international system. Each dyad has
  one observation for each year from 19501985,
  inclusive. Omitting observations with ongoing
  conflicts, this yields a total N 20448.
• This data is taken from Chris Zorns Easter
  Workshop on Panel Econometrics at Oxford.

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• Dyadid The dyad identification number.
• Year The year identifier.
• Dispute 1 if a militarized interstate dispute
  occurred between the members of that dyad in that
  year, 0 otherwise.
• Start The starting counter variable.
• Duration The duration variable.
• Democ Rescaled POLITY democracy variable (
  -1,1).
• Growth Lagged measure of growth, as a proportion
  of GDP.
• Allies 1 if the dyad members are allied, 0
  otherwise.
• contig 1if the members of the dyad are
  geographically contiguous, 0 otherwise.
• Capratio The natural log of the ratio of the two
  states military capacities, as measured by the
• Correlates of War (COW) data.
• Trade The ratio of bilateral trade to GDP, in
  constant US dollars.

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Outside the Scope (1)

• Generalised Panels can utilise many different
  distributional forms with many different types of
  data.
• Quasi-Maximum Likelihood Techniques that make
  less assumptions about the full distribution have
  become increasingly utilised.
• STATA package of choice for most researchers but
  other packages such as LIMDEP and R have become
  increasingly used.

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Outside the Scope (2)

• A great deal of work has been conducted on what
  to do with the problem of unbalanced panel data.
• Sample selection models to deal with panel
  attrition have also become increasingly important
  in the literature.