Panel Lecture - Gujarati

8/12/2019 Panel Lecture - Gujarati

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Applied Econometrics:Panel Lecture

Chapter 16, GujaratiIn Panel Data, the Same Cross-sectional Unit Is Surveyed Over

Time.


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Introduction

Today we will examine paneleconometrics.

One of the biggest areas of modern

econometrics. See Gujarati for introduction.

More advanced panel textbooksoutside the scope of our discussion.

Today we will introduce these topicsand look at some empiricalexamples.


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Topics of Discussion

Types of data cross sectional/timeseries/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 fieldand to cover everything would notbe possible. This lecture aims tointroduce you to panel econometricsusing research examples.Particularly, I want to discuss when

and why you would use fixed versusrandom effects models.


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Terminology

Time series cross section data/micropanel data/longitudanaldata/cohort analysis/ event historyanalysis.

Many authors use the above termsinterchangeably. Will talk about

some potential distinctions.


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Why Panel Data?

Allows one to analyse issues such aspersistency (e.g. Unemployment).

Allows one to examine complexbehavioural models (e.g. Life cycle modelsof 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 surveydata

(ii) Self-Selection in to the panel

(iii) Non-Response

(iv) Attrition

(v) Typically, micro-panels cover a short timedimension e.g. the Living in Ireland covers onlyfrom 1994 to 2001.


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Some Examples of Panel

Labour economics, welfare economics andseveral other fields rely heavily on householdpanel 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 (willexamine some of this later in the class).


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Famous Panel Studies

Canadian Survey of Labour IncomeDynamics

Japanese Panel on Consumers Korea Labor and Income Panel Surveys

Household Income and Labor Dynamicsin Australia

Indonesia Family Life Surveys


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Economic Modelling

Very similar principles of economicmodelling apply to panel as appliedto the other techniques we haveexamined.

Specification issues e.g. Omittedvariables 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 thereal 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 arethe 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 andindividuals.

Assume that all coefficients vary overindividuals.

Assume that all coefficients vary over

individuals and time.


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reg grossinv valuefirm capstock

Source | SS df MS Number of obs = 80

-------------+------------------------------ F( 2, 77) = 119.63

Model | 4849457.37 2 2424728.69 Prob > F = 0.0000

Residual | 1560689.67 77 20268.697 R-squared = 0.7565

-------------+------------------------------ Adj R-squared = 0.7502

Total | 6410147.04 79 81141.1018 Root MSE = 142.37

------------------------------------------------------------------------------

grossinv | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

valuefirm | .1100955 .0137297 8.02 0.000 .0827563 .1374348capstock | .3033932 .0492957 6.15 0.000 .2052328 .4015535

_cons | -63.30413 29.6142 -2.14 0.036 -122.2735 -4.334735

------------------------------------------------------------------------------


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. xtreg grossinv valuefirm capstock, fe

Fixed-effects (within) regression Number of obs = 80

Group variable (i): nofirm Number of groups = 4

R-sq: within = 0.8068 Obs per group: min = 20between = 0.7304 avg = 20.0

overall = 0.7554 max = 20

F(2,74) = 154.53

corr(u_i, Xb) = -0.1001 Prob > F = 0.0000

grossinv | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------valuefirm | .1079481 .0175089 6.17 0.000 .0730608 .1428354

capstock | .3461617 .0266645 12.98 0.000 .2930315 .3992918

_cons | -73.84946 37.52291 -1.97 0.053 -148.6155 .9165748

-------------+----------------------------------------------------------------

sigma_u | 139.05116

sigma_e | 75.288894rho | .77329633 (fraction of variance due to u_i)

------------------------------------------------------------------------------

F test that all u_i=0: F(3, 74) = 67.11 Prob > F = 0.0000


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. xtreg grossinv valuefirm capstock, reRandom-effects GLS regression Number of obs = 80

Group variable (i): nofirm Number of groups = 4

R-sq: within = 0.8068 Obs per group: min = 20

between = 0.7303 avg = 20.0

overall = 0.7554 max = 20

Random effects u_i ~ Gaussian Wald chi2(2) = 317.79corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000

------------------------------------------------------------------------------

grossinv | Coef. Std. Err. z P>|z| [95% Conf. Interval]

-------------+----------------------------------------------------------------

valuefirm | .1076555 .0168169 6.40 0.000 .0746949 .140616

capstock | .3457104 .0265451 13.02 0.000 .2936829 .3977378

_cons | -73.03529 83.94957 -0.87 0.384 -237.5734 91.50284-------------+----------------------------------------------------------------

sigma_u | 152.15823

sigma_e | 75.288894

rho | .80332024 (fraction of variance due to u_i)


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Fixed Effect Panel Model

The intercept in the regression isallowed to differ among individualsin recognition of the fact that eachindividual (unit) may havecharacteristics of their own.

Also known as the least squares

dummy variable model.


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Why use Fixed Effects

Fixed Effects are generally usedwhen there is a correlation betweenthe individual intercept and theindependent variables.

Generally used when n is relativelysmall and t is relatively large.


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Random Effects Model

Random Effects models assumethat the intercept of an individualunit is a random drawing from amuch larger population with aconstant 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 theassumptions 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 nullhypothesis that Random Effects is

appropriate.


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Hausman Test

Hausman (1978).

The null hypothesis is that the FE and REdo not differ substantially.

Test is distributed asymptotically chi-squared.

FE is consistent under both the null andthe alternative.

RE is consistent under the null andinconsistent under the alternative.

We can test the appropriateness of REusing critical values.


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. hausman fixed

---- Coefficients ----

| (b) (B) (b-B) sqrt(diag(V_b-V_B))

| fixed . Difference S.E.

-------------+----------------------------------------------------------------

valuefirm | .1079481 .1076555 .0002926 .0048738

capstock | .3461617 .3457104 .0004513 .0025204------------------------------------------------------------------------------

b = consistent under Ho and Ha; obtained from xtreg

B = inconsistent under Ha, efficient under Ho; obtained from xtreg

Test: Ho: difference in coefficients not systematic

chi2(2) = (b-B)'[(V_b-V_B)^(-1)](b-B)

= 0.07

Prob>chi2 = 0.9678


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Did people get better off over thecourse of the Celtic tiger?

We certainly became richer but howabout happier or more satisfied withour income?

To address this question I have been

analysing a panel of people trackedfrom 1994 to 2001.


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What are the determinants of international disputes.

Beck et. al. (1998) in their paper on international

conflict, and consist of time-varying data on 827politically-relevant dyads in the international

system. Each dyad has one observation for each yea

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 betweenthe 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 USdollars.


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Outside the Scope (1)

Generalised Panels can utilise many differentdistributional forms with many different types ofdata.

Quasi-Maximum Likelihood Techniques thatmake less assumptions about the full distributionhave become increasingly utilised.

STATA package of choice for most researchersbut other packages such as LIMDEP and R havebecome increasingly used.


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Outside the Scope (2)

A great deal of work has beenconducted on what to do with theproblem of unbalanced panel data.

Sample selection models to dealwith panel attrition have alsobecome increasingly important in

the literature.

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Panel Lecture - Gujarati