2.4 Endogenous explanatory variables  (Page 3/10)

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The thick red line shows the regression that would result from using OLS to estimate either of the two structural equations. As illustrated, an OLS estimate of the slope estimate will be biased. We need to use some other estimation technique than OLS.

Estimation

As noted earlier, the basic problem created by the endogeneity problem is that the endogenous explanatory variable is correlated with the error term. The most logical approach would be to replace this variable with one that is not correlated with the error term but highly correlated with the endogenous variable. Consider the value of the price predicted by the reduced form equation (5):

${\stackrel{⌢}{p}}_{t}^{w}={\stackrel{⌢}{\gamma }}_{0}+{\stackrel{⌢}{\gamma }}_{1}{I}_{t}+{\stackrel{⌢}{\gamma }}_{2}{p}_{t}^{c}+{\stackrel{⌢}{\gamma }}_{3}{W}_{t}$

where ${\stackrel{⌢}{\gamma }}_{i}$ is the OLS estimate of ${\gamma }_{0}=\frac{{\beta }_{0}+{\beta }_{1}{\alpha }_{0}}{1-{\alpha }_{1}{\beta }_{1}},$ ${\gamma }_{1}=\frac{{\alpha }_{2}{\beta }_{1}}{1-{\alpha }_{1}{\beta }_{1}},$ ${\gamma }_{2}=\frac{{\alpha }_{3}{\beta }_{1}}{1-{\alpha }_{1}{\beta }_{1}},$ and ${\gamma }_{3}=\frac{{\beta }_{2}}{1-{\alpha }_{1}{\beta }_{1}}.$

Clearly, ${\stackrel{⌢}{p}}_{t}^{w}$ is correlated with ${p}_{t}^{w}.$ It also is true that the covariance between ${\stackrel{⌢}{p}}_{t}^{w}$ and ${\epsilon }_{t}$ goes to zero as the sample size increasing. Thus, we can use (8) to construct a variable that will produce a consistent estimator of ${\alpha }_{1}.$ It is this conclusion that underlies the strategy of both two-stage least squares (TSLQ) and instrumental variable (IV) estimators.

Two-stages least squares

The easiest way to understand two-stage least squares is to think of the estimation process as being in the following two steps (although the computer programs calculate the estimators in one step):

Stage 1: obtain a OLS predictions for any endogenous variable on the right-hand side of the equation to be estimated using as the explanatory variables all of the exogenous variables in the system.

Stage 2: estimate the parameters of the equation using OLS and replacing the endogenous variable on the right-hand side of the equation by the its predictions as obtained in step 1.

For obvious reasons he TSLS method works best when the full model is specified or when you know and can measure all of the exogenous variables in the system.

Instrumental variables (iv)

While the use of instrumental variable (IV) estimators is appropriate in a large number of situations, the two situations where they are most commonly used are (1) in the presence of endogenous explanatory variables and (2) in cases when errors arise in the measurement of an explanatory variable (or the errors-in-variables problem). Since I have already described the endogeneity problem, I now turn to a brief discussion of errors-in-variables.

Consider the following simple model:

${y}_{i}={\beta }_{1}{x}_{i}^{\ast }+{\epsilon }_{i}\text{and}{x}_{i}={x}_{i}^{\ast }+{\mu }_{i}.$

In this model the researcher observes ${x}_{i}$ but not the desired ${x}_{i}^{\ast }$ because of some random measurement error. Using OLS to estimate (9) using the observable ${x}_{i}$ instead of the correct ${x}_{i}^{\ast }$ is equivalent to estimating:

${y}_{i}={\beta }_{1}{x}_{i}+\left({\epsilon }_{i}-{\beta }_{1}{\mu }_{i}\right).$

The important thing to note in estimating (10) using OLS is that the explanatory variable, ${x}_{i}$ , is correlated with the error term, $\left({\epsilon }_{i}-{\beta }_{1}{\mu }_{i}\right).$ As was the case with the endogeneity problem, the OLS estimate of ${\beta }_{1}$ is biased. Murray (2006) summarizes the situation as follows:

In both examples, ordinary least squares estimation is biased because an explanatory variable in the regression is correlated with the error term in the regression. Such a correlation can result from an endogenous explanator, a mismeasured explanator, an omitted explanator, or a lagged dependent variable among the explanators. I call all such explanators “troublesome.” Instrumental variable estimation can consistently estimate coefficients when ordinary least squares cannot—that is, the instrumental variable estimate of the coefficient will almost certainly be very close to the coefficient’s true value if the sample is sufficiently large—despite troublesome explanators. [Murray (2006a): 112]

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
Do somebody tell me a best nano engineering book for beginners?
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
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
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
how did you get the value of 2000N.What calculations are needed to arrive at it
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Berger describes sociologists as concerned with
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