An introduction to model implied instrumental variables using two stage least squares (MIIV-2SLS) in structural equation models (SEMs).

2021 ◽  
Author(s):  
Kenneth A. Bollen ◽  
Zachary F. Fisher ◽  
Michael L. Giordano ◽  
Adam G. Lilly ◽  
Lan Luo ◽  
...  
Keyword(s):  
Least Squares ◽  
Instrumental Variables ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Two Stage ◽  
Two Stage Least Squares

scholarly journals ASYMPTOTIC DISTRIBUTION OF JIVE IN A HETEROSKEDASTIC IV REGRESSION WITH MANY INSTRUMENTS

2011 ◽  
Vol 28 (1) ◽  
pp. 42-86 ◽  
Author(s):  
John C. Chao ◽  
Norman R. Swanson ◽  
Jerry A. Hausman ◽  
Whitney K. Newey ◽  
Tiemen Woutersen
Keyword(s):  
Least Squares ◽  
Instrumental Variables ◽  
Standard Errors ◽  
Asymptotic Covariance Matrix ◽  
Limited Information ◽  
Two Stage ◽  
Asymptotically Normal ◽  
Many Instruments ◽  
Two Stage Least Squares ◽  
The Many

This paper derives the limiting distributions of alternative jackknife instrumental variables (JIV) estimators and gives formulas for accompanying consistent standard errors in the presence of heteroskedasticity and many instruments. The asymptotic framework includes the many instrument sequence of Bekker (1994, Econometrica 62, 657–681) and the many weak instrument sequence of Chao and Swanson (2005, Econometrica 73, 1673–1691). We show that JIV estimators are asymptotically normal and that standard errors are consistent provided that $\root \of {K_n } /r_n \to 0$ as n→∞, where Kn and rn denote, respectively, the number of instruments and the concentration parameter. This is in contrast to the asymptotic behavior of such classical instrumental variables estimators as limited information maximum likelihood, bias-corrected two-stage least squares, and two-stage least squares, all of which are inconsistent in the presence of heteroskedasticity, unless Kn/rn→0. We also show that the rate of convergence and the form of the asymptotic covariance matrix of the JIV estimators will in general depend on the strength of the instruments as measured by the relative orders of magnitude of rn and Kn.

scholarly journals ECONOMETRIC MODELING OF THE ECONOMY OF LATVIA

2013 ◽  
Vol 1 (5) ◽  
pp. 167
Author(s):  
Iveta Mietule ◽  
Gajane Gukasjan
Keyword(s):  
Gross Domestic Product ◽  
Least Squares ◽  
Structural Equation ◽  
Time Series Data ◽  
Domestic Product ◽  
Series Data ◽  
Two Stage ◽  
Endogenous Variables ◽  
Two Stage Least Squares ◽  
The Government

The article is devoted to the estimation of econometric models of the Latvian economy. The Klein's simplified macroeconomic model of the Latvian economy is discussed. The endogenous variables are consumption, net investment, gross domestic product (excluding net exports and additions to reserves). An exogenous variable is the government spending. The model is just-identified, and Two-stage least squares (2SLS) method provides consistent estimates of the parameters of a structural equation. The modified Keynеsian model was also considered, where the lagged variable - gross domestic product of the previos period is presented. It is proved that the model is over-identified, and the Two-stage least squares (2SLS) method provides estimates of the parameters of a structural equation. We have estimated the models with annual time-series data of the Latvia economy for the years 1995 through 2011 (at basic prices in 2000).

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