What is the rationale behind LARS-OLS hybrid, i.e. using OLS estimate on the variables chosen by LARS? I need some help to understand the relationship between the ranking of the variables from the LARS algorithm and the use of OLS to estimate the final model chosen by the LARS. 
I understand that the LARS algorithm is less greedy than forward stepwise regression because it does not require additional predictors to be orthogonal to the residual and the already included predictor. But after the LARS has ranked the variables and chosen the optimal number of predictors to include in the model, we use OLS to estimate the model. The OLS parameters are different from those assigned to the predictors in the LARS, right? So how can I intuitively explain why it is correct to first use LARS and then OLS on the model selected by LARS?
 A: The coefficient estimates from LARS will be shrunk (biased) towards zero, and the intensity of shrinkage might be suboptimal (too harsh) for forecasting. 
However, some shrinkage should be good, as there is a trade-off between bias and variance. For example, if lasso happens to have selected the relevant regressors and only them (which of course is never guaranteed in practice), you could show that a positive (thus nonzero) amount of ridge-type shrinkage is optimal* -- just as you can show it in a basic linear model with no variable selection (see e.g. the answer by Andrew M in the thread "Under exactly what conditions is ridge regression able to provide an improvement over ordinary least squares regression?"). (I do not know if you can show this for LARS-type shrinkage, but intuitively I would not expect zero shrinkage to always be optimal.)
This is what motivates (1) relaxed lasso (Meinshausen, 2007) where there are two shrinkage parameters: a harsher one for variable selection and a softer one of the coefficients of the retained variables); or (2) LARS-OLS where there is no shrinkage on the coefficients of the retained variables.
*Optimal in the sense that it minimizes the mean squared error of the estimator
 Meinshausen, Nicolai. "Relaxed lasso." Computational Statistics & Data Analysis 52.1 (2007): 374-393. 
