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Informally, in attempting to estimate the causal effect of some variable X ("covariate" or "explanatory variable") on another Y ("dependent variable"), an instrument is a third variable Z which affects Y only through its effect on X. For example, suppose a researcher wishes to estimate the causal effect of smoking (X) on general health (Y). [5]
The estimator requires data on a dependent variable, , and independent variables, , for a set of individual units =, …, and time periods =, …,. The estimator is obtained by running a pooled ordinary least squares (OLS) estimation for a regression of Δ y i t {\displaystyle \Delta y_{it}} on Δ x i t {\displaystyle \Delta x_{it}} .
The first term in the RHS describes short-run impact of change in on , the second term explains long-run gravitation towards the equilibrium relationship between the variables, and the third term reflects random shocks that the system receives (e.g. shocks of consumer confidence that affect consumption). To see how the model works, consider two ...
It is often convenient to express the theory using the algebra of random variables: thus if X is used to denote a random variable corresponding to the observed data, the estimator (itself treated as a random variable) is symbolised as a function of that random variable, ^ ().
In the examples listed above, a nuisance variable is a variable that is not the primary focus of the study but can affect the outcomes of the experiment. [3] They are considered potential sources of variability that, if not controlled or accounted for, may confound the interpretation between the independent and dependent variables .
In estimating the mean of uncorrelated, identically distributed variables we can take advantage of the fact that the variance of the sum is the sum of the variances.In this case efficiency can be defined as the square of the coefficient of variation, i.e., [13]
Simultaneous equations models are a type of statistical model in which the dependent variables are functions of other dependent variables, rather than just independent variables. [1] This means some of the explanatory variables are jointly determined with the dependent variable, which in economics usually is the consequence of some underlying ...
In econometrics, the Arellano–Bond estimator is a generalized method of moments estimator used to estimate dynamic models of panel data. It was proposed in 1991 by Manuel Arellano and Stephen Bond , [ 1 ] based on the earlier work by Alok Bhargava and John Denis Sargan in 1983, for addressing certain endogeneity problems. [ 2 ]