pooled OLS VS multiple linear regression somebody help me to understand the difference between pooled OLS vs multiple linear regression. 
i learned panel data analysis consists of three: 1. pooled OLS 2.fixed 3. random 
my understanding about pooled OLS is that it disregards the space and time dimensions of the pooled data and just estimate OLS regression. 
and my question is there any difference between pooled OLS and multiple linear regression? 
 A: Richard Hardy answered the question in the comments, but I'm reposting his comment as an answer for completeness:

Multiple linear regression is a very general thing that can be applied in many different settings. Meanwhile, pooled OLS comes from a panel data context and thus it is not as general. However, by specifying pooled OLS you are specifying a multiple linear regression. That is, pooled OLS could be treated as a special case of multiple linear regression. 

So yes. Pooled OLS is multiple linear regression applied to panel data.
A: Here is my understanding of Pooled OLS after reading Hayashi's exposition on this topic. He puts this estimator in the chapter on multiple equation GMM. So this is how I would describe the estimator as well. First of all, realize that when you run pooled OLS, for each individual you are treating each time observation as one equation. Now For this estimator to make sense, you have to have common coefficients. That is you are estimating a model of this form $y_{it} = z_{it}'\delta + \epsilon_{it}$. Notice that there is no subscript on $\delta$. Essentially, pooled OLS is just multiple GMM exploiting the orthogonality condition $E[\sum\limits_{t=1}^T z_{it}\epsilon_{it}] = 0$. Notice that this does not involve any cross orthogonality, i.e. $E[z_{im}\epsilon_{ih}] = 0$, so it's robust to cross equation correlations, which in this case means cross-time correlation (I might be wrong on this point). The key takeaway is that, pooled OLS is a consistent estimator of the model parameter $\delta$, but the trick is that standard error reported by statistical software running OLS is not the correct one. The one they should report is the GMM standard error with weighting matrix $I \otimes (1/n\sum\limits_{i=1}^n z_iz_i')^{-1}$.
