Different bibliographies for each chapter with shared references

References will not be generated as required because of the incorrect usage of \chapterbib with natbib. The correct usage is:

\usepackage[sectionbib]{natbib}
\usepackage{chapterbib}  

When natbib is not being used as the citation manager, the usage of \chapterbib for references at the end of each chapter is:

\usepackage[sectionbib]{chapterbib}

This is the complete file to generate the list of references at the end of each chapter based on the code that was uploaded. A few commands from the original file are suppressed for convenience. To avoid getting orphan chapter headings I moved the \chapter commands inside the included files. I also deleted the paths to the included and bib files for simplicity.

Remember to run the compiler (PDFLaTeX) on the main file which will generate auxiliary (aux) files for each included file. Then open each auxiliary file and run bibtex on each of those files. This will generate bbl files for each chapter. Then go back to the main file and rerun the compiler twice.

\documentclass[12pt, twoside]{book}
\usepackage[utf8]{inputenc}
\usepackage[english]{babel}
\usepackage{graphicx}
\usepackage[pagestyles]{titlesec}
\titleformat{\chapter}[display]{\normalfont\bfseries}{}{0pt}{\Huge}
%\newpagestyle{mystyle}
%{\sethead[\thepage][][\chaptertitle]{}{}{\thepage}}
%\pagestyle{mystyle}\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Don't use this                                               %
%\usepackage[semicolon,round,sort&compress,sectionbib]{natbib} %
%\usepackage[sectionbib]{chapterbib}                           %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Replacement                                                  %
\usepackage[semicolon,round,sort&compress,sectionbib]{natbib}  %
\usepackage{chapterbib}                                        %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{hyperref}
\usepackage{epstopdf}
\usepackage{rotating}
\usepackage{amsmath}
\usepackage{multirow}
\usepackage{booktabs}
\usepackage{pdflscape}
\usepackage{calc}
\usepackage{float}
\usepackage{indentfirst}
\usepackage{chronology}
\usepackage[toc,page]{appendix}
\usepackage{graphics}
\usepackage{color,soul}
\usepackage{tablefootnote}
\usepackage{epsfig}         
\usepackage{subfigure}
\usepackage{grffile}        
\usepackage{soul}
\usepackage{longtable}
\usepackage{lscape}
\usepackage{url}
\usepackage{epsfig} 
\graphicspath{ {images/} }
\usepackage{caption}
\usepackage[a4paper,width=150mm,top=25mm,bottom=25mm,bindingoffset=6mm]{geometry} % this was incomplete
\usepackage{filecontents}
% Create bib file for Introduction chapter
\begin{filecontents*}{bib0.bib}
@article{acemoglu2000,
    title={The colonial origins of comparative development: An empirical investigation},
    author={Acemoglu, Daron and Johnson, Simon and Robinson, James A},
    year={2000},
    institution={National bureau of economic research}
}
@book{acemoglu2012,
    title={Why nations fail: the origins of power, prosperity and poverty},
    author={Acemoglu, Daron and Robinson, James A and Woren, Dan},
    volume={4},
    year={2012},
    publisher={SciELO Chile}
}
\end{filecontents*}
%
% Create bib file for chapter 1. Note that it is not a requirement to have different bib files for each chapter.
\begin{filecontents*}{bib1.bib}
@article{acemoglu2000,
    title={The colonial origins of comparative development: An empirical investigation},
    author={Acemoglu, Daron and Johnson, Simon and Robinson, James A},
    year={2000},
    institution={National bureau of economic research}
}
@article{ackerberg2006,
    title={Structural identification of production functions},
    author={Ackerberg, Daniel and Caves, Kevin and Frazer, Garth},
    year={2006}
}
%
%Create Introduction
\end{filecontents*}
\begin{filecontents*}{chap0.tex}
    \chapter{Introduction}
    This is Chapter ``Introduction'' from included file chap0.tex. \\
    This is a citation for \cite{acemoglu2000} from bib0. \\
    \citep{acemoglu2012} is a citation for the second reference. \\
    The Reference list for introductory chapter appears next. \\
    \bibliographystyle{apalike}
    \bibliography{bib0}
\end{filecontents*}
%
% Create Chapter 1
\begin{filecontents*}{chap1.tex}
    \chapter{chap1}
    This is Chapter 1 from included file chap1.tex. \\
    This is a citation for \cite{acemoglu2000} from bib1. \\
    \citep{ackerberg2006} is a citation for the second reference. \\
    The Reference list for the chapter appears next. \\
    \bibliographystyle{apalike}
    \bibliography{bib1}
\end{filecontents*}
\begin{document}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Suppress content not required for this solution %  
%\include{chapters/titlepage}                    %
%                                                %
%\mainmatter                                     %
%\tableofcontents                                %
%\listoffigures                                  %
%\listoftables                                   %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\include{chap0}
\include{chap1}
\end{document}