Welcome to TeX.SX! There are a few issues with your example code.
Basic Document Format
Since you do not appear to be defining a documentclass here, you should start with a simple preamble that defines which documentclass you are using. If you are unsure, article is a common choice. For example:
\documentclass{article}
\begin{document}
...
\end{document}
Be sure to include the beginning and ending of your document (in fact, you should \end{...} anything that you \begin{...}). Including packages with \usepackage{...} should go before \begin{document} but after \documentclass{...}.
Applying these principles, so far your code should look like this:
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation}
\begin{split}
\textrm{Y}_{it} = \beta_{0}+\beta_{1}\textrm{Education Construction}_{it}+ \beta_2\textrm{economic slack}_{it} + \beta_3\textrm{economic slack}*\textrm{Education Construction}_{it}+ & \\ \beta_4 X_{it} + \sum fe_{i} + \sum fe_{t} + \mu_{it}
\end{split}
\end{equation}
\end{document}
How To Handle Long Equations
There are already questions that address this problem (for example here and here), but I suggest you use a simple align approach. You designate the location within the equation you would like to align your following lines to (left-align) with the & character. I tend to pick the =, so it's as simple as &=. You do not need split or equation in this case, you simply use the align environment. A simple replacement of your above method with the align method will yield:
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align*}
\textrm{Y}_{it} &= \beta_{0}+\beta_{1}\textrm{Education Construction}_{it}+ \beta_2\textrm{economic slack}_{it} + \beta_3\textrm{economic slack}*\textrm{Education Construction}_{it} \\
&+ \beta_4 X_{it} + \sum fe_{i} + \sum fe_{t} + \mu_{it}
\end{align*}
\end{document}
And to shorten or lengthen lines, simply change where you want to break them up at. For example, your equation would fit on the page if constructed as follows:
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align*}
\textrm{Y}_{it} &= \beta_{0}+\beta_{1}\textrm{Education Construction}_{it}+ \beta_2\textrm{economic slack}_{it} \\
&+ \beta_3\textrm{economic slack}*\textrm{Education Construction}_{it} \\
&+ \beta_4 X_{it} + \sum fe_{i} + \sum fe_{t} + \mu_{it}
\end{align*}
\end{document}
Final Comments
@JouleV makes a good argument in the comments that your equation does contain a lot of text. I suggest removing or reducing the text, which would also help it to fit into more compact space.
Hope this helps!
&) in the first line. That's necessary. Also (off topic) it's more usual to put a+at the beginning of a continuation line rather than at the end of the first, broken, line. – barbara beeton May 20 '19 at 14:47\documentclass. (And\usepackagebelongs in the preamble.) – barbara beeton May 20 '19 at 14:49&in both lines, to set the position where the second line should start. The&at the end of the first line isn't really doing anything. What I'd do is move that to just before the=, and start the second line with&\qquad +so that it doesn't line up exactly with the=. Take a look at theamsmathuser guide for examples. – barbara beeton May 20 '19 at 15:19documentclassenvironment??, please test the code you have posted and check that anyone can run it to see the issue that you are asking about. – David Carlisle May 20 '19 at 16:30