Regressing dependent variable on instruments I am reading a paper (News drought, News Floods, and U.S. Disaster Relief by Eisensee and Stromberg (2007)) in which they study the effect of news coverage on disaster reliefs sent by US. They instrument "news coverage" with other newsworthy events that may crowd out disasters from tv, i.e. "Olympics" and "World Series". 
My question is about a reported result, i.e. the results from a regression of the dependent variable "relief" on the two instruments. What's the point in doing that? I mean I thought that the only thing to do was to regress the endogenous variable "news pressure" on the instruments as a first stage of a TSLS approach.
Moreover, my professor called it reduced form equation but looking around the net I found that this should not be the case. How should I call it instead?
 A: When you have an outcome $Y$, an endogenous explanatory variable $D$, a valid instrument $Z$, and controls $X$, then your two-stage least squares (2SLS) equation system would be
$$
\begin{align}
Y &= \alpha + \beta D + \gamma X + \epsilon \\[0.5em]
D &= a + \pi Z + \delta X + \eta
\end{align}
$$
where the second equation is the so-called "first stage" regression. Now rather than estimating these two equations step-by-step (as the name 2SLS suggests), the reduced form "reduces" the problem to a one equation estimation by substituting the first-stage into the second-stage:
$$
\begin{align}
Y &= \alpha + \beta (a + \pi Z + \delta X + \eta) + \gamma X + \epsilon \\[0.5em]
 &= (\alpha + \beta a) + \beta \pi Z + (\gamma + \beta \delta)X + (\epsilon +  \beta\eta)
\end{align}
$$
Note that this isn't really the official definition of "reduced form" but in my opinion it helps to think about it in this way. So this is what your researchers are doing. They regress $Y$ on $Z$ and obtain the parameter $\beta\pi$.
Now why do they do this? The first stage regression and the reduced form give you your 2SLS estimate because
$$
\beta_{2SLS} = \frac{Cov(Y,Z)}{Cov(D,Z)} = \frac{\beta\pi}{\pi} = \beta
$$
(after partialling out $X$) where $\beta\pi$ is our reduced form coefficient on $Z$, and $\pi$ is the first stage coefficient from the regression of $D$ on $Z$. Knowing the first stage and reduced form coefficients, you can tell


*

*the size of the 2SLS coefficient, $\beta_{2SLS}$

*the sign of the 2SLS coefficient


Personally I usually skip this exercise because in the end everyone runs their 2SLS regressions in order to also have the standard errors and confidence intervals for $\beta_{2SLS}$ and there you get your final result anyway.
Edit:
Also see Dimitriy V. Masterov's explanation of what reduced form means here. Also note that the above discussion is valid for one endogenous variable and one instrument. When you have multiple instruments, i.e. your endogenous variable is over-identified, $\beta_{2SLS}$ will be an optimally weighted GMM average and there is no way to directly get from the reduced form and first stage coefficients to the target parameter $\beta_{2SLS}$ because you would need to know the weights for each instrument (see these slides by Steve Pischke).
