# 2.2 Panel data models  (Page 3/10)

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## Random-effects models

An alternative approach to treating the ${\alpha }_{i}$ in (1) as fixed constants over time is to treat it as a random variable. Returning to (1) where the intercepts vary due to individual level differences, we have ${y}_{it}={\alpha }_{i}+\sum _{j=1}^{k}{\beta }_{k}{x}_{kit}+{\epsilon }_{it}.$ Treating ${\alpha }_{i}$ as a random variable is equivalent to setting the model up as:

${y}_{it}=\alpha +\sum _{j=1}^{k}{\beta }_{j}{x}_{jit}+\left({\alpha }_{i}+{\lambda }_{t}+{\epsilon }_{it}\right).$

For simplicity we consider only the case when ${\lambda }_{t}=0.$ Thus, the error term for (11) is $\left({\alpha }_{i}+{\epsilon }_{it}\right).$ We assume that

We also assume that all of the elements of the error term are uncorrelated with the explanatory variables, ${x}_{j}.$

The key econometric issue is that the presence of ${\alpha }_{i}$ in the error term means that the correlation among the residual of the same cross-sectional unit is not zero; the error terms for one farm, for instance, are correlated with each other. Therefore, the error terms exhibit heteroskedasticity. The appropriate estimation technique is generalized-least-squares, a technique that attempts to adjust the parameter estimates (and their standard error estimates) for heteroskedasticity and autocorrelation. Alternatively one can assume that ${\alpha }_{i}$ and ${\epsilon }_{it}$ are normally distributed and use a ML estimator. Hsiao [2003: 35-41] and Cameron and Trivedi [2005: 699-716]offer greater detail on the estimation of the parameters of both the fixed-effects and the random-effects models. It is enough for our purposes to accept that the econometricians have found a number of ways to estimate these parameters.

## Random-effects or fixed effect model?

Economists generally prefer to use fixed-effects models. The decision to use fixed-effects or random-effects does not matter when T is large because the two methods will yield the same estimates of the parameters. When the number of individual categories ( N ) is large and the number of time periods ( T ) is small, the choice of which model to use becomes unclear. Hsiao summarized this somewhat arcane issue with the following observations:

If the effects of omitted variables can be appropriately summarized by a random variable and the individual (or time) effects represent the ignorance of the investigator, it does not see reasonable to treat one source of ignorance () as fixed and the other source of ignorance () as random. It appears that one way to unify the fixed-effects and random-effects models is to assume from
the outset that the effects are random. The fixed-effects model is viewed as one in which investigators make inferences conditional on the effects that are in the sample. The random-effects model is viewed as one in which investigators make unconditional or marginal inferences with respect to the population of all effects. There is really no distinction in the “nature (of the effect).” It is up to the investigator to decide whether to make inference with respect to population characteristics or only with respect to the effects that are in the sample. Hsiao [2003: 43]

Needless to say, Hsiao’s advice may well leave many researchers without any idea of whether to use a random-effects or a fixed-effects model. In your own research I suggest that you consult an econometrician for advice .

are nano particles real
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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
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