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| {{for|endogeneity in a non-econometric sense|Endogeny}}
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| {{refimprove|date=December 2012}}
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| In a [[statistics|statistical]] [[Statistical model|model]], a [[parameter]] or [[variable]] is said to be '''endogenous''' when there is a [[correlation]] between the parameter or variable and the [[error term]].<ref>{{cite book |last=Wooldridge |first=Jeffrey M. |title=Introductory Econometrics: A Modern Approach |location=Australia |publisher=South-Western |year=2013 |edition=Fifth international |pages=82–83 |isbn=978-1-111-53439-4 }}</ref> Endogeneity can arise as a result of [[measurement error]], [[autoregression]] with [[autocorrelation|autocorrelated]] errors, simultaneity and [[Omitted-variable bias|omitted variable]]s. Broadly, a loop of [[causality]] between the [[independent variable|independent]] and [[dependent variable]]s of a model leads to endogeneity.
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| For example, in a simple [[supply and demand]] model, when predicting the quantity demanded in equilibrium, the price is endogenous because producers change their price in response to demand and consumers change their demand in response to price. In this case, the price variable is said to have '''total endogeneity''' once the demand and supply curves are known. In contrast, a change in [[consumer]] tastes or [[preference]]s would be an [[exogenous]] change on the [[demand curve]].
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| == Exogeneity vs. endogeneity == | |
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| In a [[stochastic model]], the notion of the usual exogeneity, sequential exogeneity, strong/strict exogeneity can be defined. Exogeneity is articulated in such a way that a variable or variables is exogenous for parameter <math>\alpha</math>. Even if a variable is exogenous for parameter <math>\alpha</math>, it might be endogenous for parameter <math>\beta</math>.
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| When the explanatory variables are not stochastic, then they are strong exogenous for all the parameters.
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| <!-- The following paragraph is not good --> | |
| The problem of '''endogeneity''' occurs when the [[independent variable]] is [[correlation|correlated]] with the [[error term]] in a [[Regression analysis|regression]] model. This implies that the regression coefficient in an [[Ordinary least squares|Ordinary Least Squares (OLS)]] regression is [[Bias of an estimator|biased]], however if the correlation is not contemporaneous, then it may still be [[Consistent estimator|consistent]]. There are many methods of overcoming this, including [[instrumental variable]] regression and [[Heckman correction|Heckman selection correction]].
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| === Static models ===
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| The following are some common sources of endogeneity.
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| ==== Omitted variable ====
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| {{further|Omitted-variable bias}}
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| In this case, the endogeneity comes from an uncontrolled [[confounding variable]]. A variable is both correlated with an independent variable in the model and with the error term. (Equivalently, the omitted variable both affects the independent variable and separately affects the dependent variable.) Assume that the "true" model to be estimated is,
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| : <math> y_i = \alpha + \beta x_i + \gamma z_i + u_i</math>
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| but we omit <math>z_i</math> (perhaps because we don't have a measure for it) when we run our regression. <math>z_i</math> will get absorbed by the error term and we will actually estimate,
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| : <math> y_i = \alpha + \beta x_i + \varepsilon_i</math> (where <math>\varepsilon_i=\gamma z_i + u_i</math>)
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| If the correlation of <math>x</math> and <math>z</math> is not 0 and <math>z</math> separately affects <math>y</math> (meaning <math>\gamma \neq 0</math>), then <math>x</math> is correlated with the error term <math>\varepsilon</math>.
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| Here, x and 1 are not exogenous for alpha and beta since, given x and 1, the distribution of y depends not only on alpha and beta, but also on z and gamma.
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| ==== Measurement error ====
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| Suppose that we do not get a perfect measure of one of our independent variables. Imagine that instead of observing <math>x_i</math> we observe <math>x_i=x^{*}_{i}- \nu_i</math> where <math>\nu_i</math> is the measurement "noise". When we try to estimate the following univariate regression,
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| : <math> y_i = \alpha+\beta x_i + \varepsilon_i </math>
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| we actually end up estimating,
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| : <math> y_i = \alpha+\beta(x^{*}_{i}-\nu_i) + \varepsilon_i </math>
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| : <math> y_i = \alpha+\beta x^{*}_{i} +(\varepsilon_i - \beta\nu_i) </math>
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| : <math> y_i = \alpha+\beta x^{*}_{i} +u_i </math> (where <math>u_i=\varepsilon_i - \beta\nu_i</math>)
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| Since both <math>x^{*}_{i}</math> and <math>u_i</math> depend on <math>\nu_i</math>, they are correlated. Measurement error in the dependent variable, however, does not cause endogeneity (though it does increase the variance of the error term).
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| === Dynamic models ===
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| The endogeneity problem is particularly relevant in the context of [[time series]] analysis of [[causal]] processes. It is common for some factors within a causal system to be dependent for their value in period ''t'' on the values of other factors in the causal system in period ''t-1''. Suppose that the level of pest infestation is independent of all other factors within a given period, but is influenced by the level of rainfall and fertilizer in the preceding period. In this instance it would be correct to say that infestation is [[exogenous]] within the period, but [[endogenous]] over time.
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| Let the model be y=f(x,z)+u, then if the variable x is sequential exogenous for parameter <math>\alpha</math>, and y does not cause x in Granger sense, then the variable x is strong/strict exogenous for the parameter <math>\alpha</math>.
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| ==== Simultaneity ====
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| Generally speaking, simultaneity occurs in the dynamic model, but this example is static one.
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| Suppose that two variables are codetermined, with each affecting the other. Suppose that we have two "structural" equations,
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| :<math>y_i = \beta_1 x_i + \gamma_1 z_i + u_i </math>
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| :<math>z_i = \beta_2 x_i + \gamma_2 y_i + v_i</math>
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| We can show that estimating either equation results in endogeneity. In the case of the first structural equation, we will show that <math>E(z_i u_i) \neq 0</math>. First, solving for <math>z_i</math> we get (assuming that <math>1-\gamma_1 \gamma_2 \neq 0 </math>),
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| :<math>z_i = \frac{\beta_2 + \gamma_2 \beta_1}{1-\gamma_1 \gamma_2}x_i+\frac{1}{1-\gamma_1 \gamma_2}v_i+\frac{\gamma_2}{1-\gamma_1 \gamma_2}u_i</math>
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| Assuming that <math>x_i</math> and <math>v_i</math> are uncorrelated with <math>u_i</math>, we find that,
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| :<math>E(z_i u_i) = \frac{\gamma_2}{1-\gamma_1 \gamma_2}E(u_i u_i)</math>
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| :<math>E(z_i u_i) \neq 0</math>
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| Therefore, attempts at estimating either structural equation will be hampered by endogeneity.
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| == See also ==
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| * [[Virtuous circle and vicious circle]]
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| * [[Heterogeneity]]
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| == References ==
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| {{Reflist}}
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| == Further reading ==
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| *{{cite book |first=William H. |last=Greene |title=Econometric Analysis |location=Upper Saddle River |publisher=Pearson |edition=Sixth |year=2007 |isbn=978-0-13-513740-6 }}
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| *{{cite book |first=Peter |last=Kennedy |title=A Guide to Econometrics |edition=Sixth |location=Malden |publisher=Blackwell |year=2008 |page=139 |isbn=978-1-4051-8257-7 }}
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| == External links ==
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| * {{YouTube|dLuTjoYmfXs|Endogeneity: An inconvenient truth. Podcast with Prof. John Antonakis}}
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| [[Category:Causality]]
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| [[Category:Econometrics]]
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| [[Category:Statistical terminology]]
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| [[Category:Economics terminology]]
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| [[Category:Economics models]]
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Find the types of cleaning products they use for cleaning and see if these contain harsh chemicals. These companies also sometimes take care of tile cleaning along withcarpet-cleaning for providing complimentary services for their clients.
The qualities of an good cleaning company range from the skill to gauge the client's situation and suggest a plan that meets the requirements using capable staff and suitable equipment and materials for cleaning. As you already know, some companies would should deal with highly sensitive process or experiment and even the tiniest microscopic element make a difference the way these processes work.
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That is why you should find out which ones are the very best from on the list of host of cleaning services out there within the market. Please visit our website at to find helpful and useful tips on keeping your property clean and comfortable, wherever you live. Invariably, such machinery is going to be priced exorbitantly; therefore investing in one is hardly worth it.
If the buddies and family approach occurs with no leads, contact the Better Business Bureau. For example, a customer might ask your small business to fold laundry together with your regular cleaning service. Ceiling fans are simple to keep up with once they've got been thoroughly cleaned.
Will the completed task compensate your some time and effort. Now, before you decide to ask for your professional help of an cleaning service, make sure that you have a list from the areas in your house that you need to be cleaned up. Here are a handful of examples of issues your cleaning company and employees might come across:. By achieving this, you happen to be able to save money within the long run.
It's good to know what you might be paying for and know what is included within the price.