when there is simultaneous causation between dependent and independent variables often in papers we see a lagged variable being used in place of contemporaneous variable. For example, Clemens, Radelet, Bhavnani and Bazzi (2012) say - “We avoid poor-quality instrumental variables and instead address potential biases from reverse and simultaneous causation by the more transparent method of lagging". Hayo, Kutan, and Neuenkirch (2010) - “The vector of controls contains lagged returns...Contemporaneous U.S. returns are excluded to avoid simultaneity problems” However what is the rationale for lagging? This short article looks at estimators of lagged variables used in such cases. It deduces that either there is no serial correlation in the variable and the value of the lagged estimator is 0. Or that there is serial correlation and the value of the lagged estimator is quite a meaningless value of ((c+bf)/(1-be)), where b is the coefficient of x(t) on y(t), f is the serial correlation, e is the effect of y(t) on x(t) and c is the true effect of x(t-1) on y(t). Further the article finds that these estimators are consistent but converge to true value only for n>100 approximately, further leading to wrong significance interpretations. Given this, what is the rationale of using a lag to deal with simultaneity? If the lagged variable is not serially correlated its coefficient on y(t) is 0, it does not capture the effect of x(t) on y(t) and one only risks to make false significance inferences in small samples. If on the other hand the variable is serially correlated than it does capture the effect of x(t) on y(t), but only by the fraction of serial correlation and further that result is distorted in non linear way because the estimator also captures the effect of 1 - (y(t) on x(t) times x(t) on y(t)) in the denominator. So it is just a meaningless result. Henceforth, why do people use the lagged variables to address simultaneity endogeneity? It seems to make no sense.
The aforementioned article is this one: https://www.otago.ac.nz/economics/news/otago075947111111111.pdf
Your thoughts are much appreciated!