Panel Workshop Feb 08

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PANEL DATA WORKSHOP

BRUNEL UNIVERSITY

FEBRUARY 29, 2008.

Practical exercises with STATA 9.2

Objectives:

I. Consider basic data management and preliminary data analysis issues.

II.

Consider some useful and more general econometric issues.

III.

Consider the estimation and testing of static random and fixed effects models

IV. Consider the estimation of dynamic panel data models.

I. Data management and preliminary analysis.

Task 1: Open the firm-level panel data set panel_workshop.dta, which is in STATA

9.2 format. The panel units are identified by the variable firm and time is defined by

the variable year. Declare the dataset to be a panel data and study its content. The

panel data is organised in the so-called long form: there is an explicit time variable

(year), so the time-varying variables (e.g. capital) are not indexed by time. However,

it may sometimes be more convenient to work with the wide form of a panel data.

This attaches a time index to all time-varying variables. Organise the data into a wide

form and describe and browse the content of the data. Finally revert back to the long

format and study the structure of the panel.

Task 2: Generate some descriptive statistics to better understand the data. Comment

on the evolution of the number of exporting firms across the years. Also find out the

probability of moving from being a non-exporter to an exporter, and vice versa.


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Decompose the total variance of the variables into variability between firms and

variability across time. Comment on the results.

Task 3: In panel data analysis, it is often of interest to obtain summary statistics by

panel units or time units. Now generate variables that enable you to get the following

information:

a. The maximum value of labour by year.

b.

The minimum value of capital by firm.

c.

The standard deviation of output by firm.

d. The number of firms with a median value of capital greater than 9.

Task 4: Generate the partial correlation coefficients between the output, and labour

and capital. Analyse the pattern of these correlations across the years.

II. Various econometric issues within the pooled model:

Task 5: The aim is to estimate a production function, which relates output with inputs

(labour and capital ). The Cobb-Douglas production function is the most popular

model in studies of productivity analysis. For firm i at time t, this is specified as

it it it it K L y ε β β β +++= 210 (1)

where y is log of output, L is log of labour, K is log of capital and ε is a random error

term.

a. Estimate Model 1 by OLS, correcting standard errors for heteroscedasticity

and within-firm serial correlation.

b.

Interpret the regression coefficients.

c.

Test for constant returns to scale.


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d. Test whether, on average, firms in underdeveloped regions are less

productive than firms in more developed regions.

e.

Estimate the model with time effects (dummies) and test for the joint

significance of the time effects. Comment on your results.

f. Test whether the elasticity of output with respect to capital has changed

after 1999. Comment on your results.

Task 6: Using Model 1 with time effects, test the following propositions:

a.

The elasticity of output with respect to labour is greater for exporters

compared to non-exporters.

b. The elasticity of output with respect to capital is smaller for firms with

above average value of labour.

c.

The elasticity of output with respect to labour has remained the same in

most years.

Task 7: The Translog production function generalises the Cobb-Douglas production

function, and affords more flexibility in productivity analysis. It adds three terms to

the Cobb-Douglas function and is specified as

it it it it LK KK LL K L y ε β β β β β β ++++++= 543210 (2)

.where the three additional terms are defined as LL = 0.5*L2 , KK = 0.5*K 2 and

LK = L*K.

a.

Generate the three additional terms and estimate a Translog production

function.

b. Test for the joint significance of the additional terms ( i.e. test whether

the Cobb-Douglas or the Translog functional form is to be preferred).


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c. Generate a variable that gives the elasticity of output with respect to

labour.

d.

Test whether the elasticity of output with respect to labour is greater

for exporters compared to non-exporters.

e. Study the development of the correlation between the two factor

elasticities across the years.

III. Fixed (correlated) and random effects static panel models

Task 8: The random/fixed effects models can be written as

it iit it it f K L y ε β β β ++++=

210 (3)

where denotes f firm-specific effects.

a. Estimate a random effects Cobb-Douglas production, interpret the regression

coefficients and test for constant returns to scale.

b.

Perform the Breusch and Pagan Lagrangian Multiplier test for random effects.

What is your conclusion?

c. Estimate a fixed (correlated) effects version of the model. How do the

estimated coefficients compare with the estimates from the random effects

model?

d. Perform a Hausman test for regressors-effects correlation. What is your

preferred model?

e. Using your preferred model, test, if possible, whether firms in underdeveloped

regions are less productive than firms in more developed regions?

Task 9:


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a. Estimate a Translog production function using both the random and fixed effects

models, decide which model suits the data best. Based on the preferred specification:

b. Test the proposition that the elasticity of output with respect to capital is the same

for exporters and non-exporters.

c. Draw a histogram of the elasticity of output with respect to capital for the year

2000.

d. What is the proportion of firms with negative elasticity of output with respect to

labour?

IV. Dynamic Panel data modelling:

Task 10: Consider the following dynamic (with two lags) Cobb-Douglas production

function with firm-specific effect (f) and time dummies (D).

it it it it it it it f D K L y y y ε β β α α β +++++++=

−− 2122110 (4)

a.

Using a first-differenced GMM estimator your choice, estimate Model (4).

b.

Perform a test for the validity of the over-identifying restrictions. What is

your conclusion?

c. Test for the absence of second order serial correlation in the first-differenced

model. What is your conclusion?

d. What are the short and long run elasticities of output with respect to labour?

e.

Calculate the 95% confidence interval of the long run elasticity of output with

respect to labour?

f. Would your conclusions change significantly had you estimated a dynamic

panel data model by treating labour as an endogenous variable?


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Task 11: Consider an extended version of Model (4) which includes the dummy

variable for underdeveloped regions.

a.

Using a system-GMM estimator of your choice, estimate the parameters of the

model and test for the appropriateness of your estimator.

b. Repeat the above exercise based on firms that have never exported only.

Professor Sourafel Girma

University of Nottingham

[email protected]

Documents

Panel Workshop Feb 08