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I am studying the effect of social capital on households' income. I am doing multiple regression to estimate this effect. For this, I have households' income as dependent variable and social capital as explanatory variable. I have also included human capital and some other household characteristics as control variables for multiple regression. Social capital and household income have two-way causality as it is argued that social capital is endogenous variable. This is proven theoretically and empirically in various research studies. To avoid this problem and to get unbiased and consistent estimates. I intend to use two stage linear regression (2SLS) or instrumental variable technique. Can someone suggest which method is preferable in my case and how to perform my analysis exactly in both cases if:

  1. I have valid instrument, or
  2. I don't have valid instrument for the endogenous variable?
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2 Answers

If you don't have a valid instrument, then the bias can actually be worse using TSLS/IV as compared to the standard linear model. If you have a valid instrument, then your bias will be 0 on average, but your standard errors will be larger. For some information on these cases, see

Bound, John, David A. Jaeger, and Regina M. Baker. 1995 "Problems with Instrumental Variables Estimation When the Correlation Between the Instruments and the Endogeneous Explanatory Variable is Weak." Journal of the American Statistical Association. 90(430): 443--450. [jstor]

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For 2SLS, you need to have more instruments that endogenous variables. That does not sound like the case here, so you're stuck with basic IV if you have only one.

If you don't have a valid instrument (relevant for the endogenous $x$, exogenous with respect to $y$), you need to pursue an alternative causal estimation strategy, but it's hard to give specific advice.

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Thanks for immediate reply. I need more clarification. If I have one endogenous explanatory variable and one valid instrument, can I still use 2SLS? or do I need more than one valid instruments to ensure the legitimate use of 2SLS in my case? –  user14152 Sep 18 '12 at 16:02
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