# 2.2 Panel data models  (Page 2/10)

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## Estimation issues

Hsiao (2003: 27-30) discusses a convenient example of a panel data model that illustrates many of the important issues that arise with panel data. We make use of this example in what follows. Assume that we want to estimate a production function for farm production in order to determine if the farm industry exhibits increasing returns to scale. Assume the sample consists of observations for N farms over T years, giving a total sample size of $NT.$ For simplicity, we assume that the Cobb-Douglas production is an adequate description of the production process. The general form of the Cobb-Douglas production function is:

$q={\alpha }_{0}{I}_{1}^{{\beta }_{1}}\cdots {I}_{k}^{{\beta }_{k}},$

where q is output and ${I}_{j}$ is the quantity of the j-th input (for example, land, machinery, labor, feed, and fertilizer). The parameter, ${\beta }_{j},$ is the output elasticity of the j-th input; the farms exhibit constant returns to scale if the output elasticities sum to one and either increasing or decreasing returns to scale if they sum to a value greater than or less than one, respectively. is the quantity of the j -th input (for example, land, machinery, labor, feed, and fertilizer). The parameter, is the output elasticity of the j -th input; the farms exhibit constant returns to scale if the output elasticities sum to one and either increasing or decreasing returns to scale if they sum to a value greater than or less than one, respectively.

Taking the natural logarithm of (5) gives $\mathrm{ln}q=\mathrm{ln}{\alpha }_{0}+{\beta }_{1}\mathrm{ln}{I}_{1}+\cdots +{\beta }_{k}\mathrm{ln}{I}_{k}.$ We can re-write this equation (adding an error term, as well as farm and year subscripts) giving:

${y}_{it}={\beta }_{0}+{\beta }_{1}{x}_{1it}+\cdots +{\beta }_{k}{x}_{kit}+{\epsilon }_{it,}$

where ${y}_{it}=\mathrm{ln}{q}_{it},$ , ${\beta }_{0}=\mathrm{ln}{\alpha }_{0},$ ${x}_{jit}=\mathrm{ln}{I}_{jit},$ for $j=1,\dots ,k$ and ${\epsilon }_{it}$ is an error term. One way to account for year and time effects is to assume:

${\epsilon }_{it}=\lambda {F}_{i}+\eta {P}_{t}+{\upsilon }_{it},$

where F i is a measure of the unobserved farm specific effects on productivity and P t is a measure of the unobserved changes in productivity that are the same for all farms but vary annually. Substitution of (7) into (6) gives: ${y}_{it}=\left({\beta }_{0}+\lambda {F}_{i}+\eta {P}_{t}\right)+\sum _{j=1}^{k}{\beta }_{j}{x}_{jit}+{\upsilon }_{it}$ or

${y}_{it}={\alpha }_{it}+\sum _{j=1}^{k}{\beta }_{j}{x}_{jit}+{\upsilon }_{it},$

where ${\alpha }_{it}={\beta }_{0}+\lambda {F}_{i}+\eta {P}_{t}.$ Thus, (8) is equivalent to (2). Moreover, if we assume that $\eta =0,$ we get

${y}_{it}={\alpha }_{i}+\sum _{j=1}^{k}{\beta }_{j}{x}_{jit}+{\upsilon }_{it},$

where ${\alpha }_{i}={\beta }_{0}+\lambda {F}_{i}.$ Thus, (9) is equivalent to (1).

## Fixed-effects models

A natural way to make (9) operational is to introduce a dummy variable, D i , for each farm so that the intercept term becomes:

${\alpha }_{i}={\alpha }_{1}+{\alpha }_{2}{D}_{2}+\cdots +{\alpha }_{m}{D}_{m}={\alpha }_{1}+\sum _{j=2}^{m}{\alpha }_{j}{D}_{j},$

where ${D}_{j}=1$ if $j=i$ and 0 otherwise. This substitution is equivalent to replacing the intercept term with a dummy variable for each farm and letting the farm dummy variable “sweep out” the farm-specific effects. In this specification the slope terms are the same for every farm while the intercept term is given for farm j by ${\alpha }_{1}+{\alpha }_{j}.$ Clearly, the intercept term for the first farm is equal to just ${\alpha }_{1}.$ This specification is known as the fixed effect model and is estimated using ordinary least squared (OLS). We can extend the fixed-effects model to fit (8) by including a dummy variable for each time period except one.

In sum, fixed-effects models assume either (or both) that the omitted effects that are specific to cross-sectional units are constant over time or that the effects specific to time are constant over the cross-sectional units. This method is equivalent to including a dummy variable for all but one of the cross-sectional units and/or a dummy variable for all but one of the time periods.

what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
how did you get the value of 2000N.What calculations are needed to arrive at it
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