Cite equation using tables notes

In the following MWE, I have done the following changes in comparison to the original code:

• commented out duplicate package. Please only load packages once especially, avoid conflicting package options. I have also correctly placed hyperref at the end of the preamble.

• removed the & in the equation and the occurences of \ outside of the table

• added the missing definitions of tc according to the comments and of Controls according to my guess

• added math-mode where needed and removed redundant $s

• removed multirow commands in the lower part of the table in order to fix the horizontal alignment

• corrected the table-format option of sisetup according to the numbers that are present in the table

• removed redundant multicolumn{1}{c}{}

• replaced the wrong $label{eq:1}$ in the notes part with cref{eq:1}.

Additionally to the above mentioned changes, I would also suggest to use a simple tabular for your table. Forcing the table wo be as wide as the textwidth introduces a lot of white space and makes the table harder to read. I also replaced the threeparttalbe's tablenotes environment with a simple minipage in order to make sure the notes part below the table stays as wide as the textwidth:

documentclass{article}
usepackage[margin=2.5cm,a4paper]{geometry} % set page parameters suitably
%usepackage{booktabs} %<-- removed. don't load packages more than once!
usepackage{siunitx}
%usepackage[skip=1ex]{caption} %<-- removed. don't load packages more than once!
usepackage{natbib}
usepackage{amsmath}
usepackage{amsthm} 
usepackage[protrusion=true,expansion=true]{microtype} 
%usepackage{multirow} %<-- removed. don't load packages more than once!
usepackage{graphicx}
usepackage{amssymb}
usepackage{mathtools}
usepackage{enumerate}
usepackage{placeins}
%usepackage{varioref} % <--- moved to the end of the preamble. Mind the correct load order
usepackage{float}
usepackage{cuted}
usepackage[english]{babel}
usepackage[latin1]{inputenc}       
usepackage[figurename=Fig.]{caption}
usepackage{booktabs, makecell, multirow, threeparttable}
%usepackage{caption} %<-- removed. don't load packages more than once!
usepackage{xparse}    
%usepackage{hyperref} % <--- moved to the end of the preamble. Mind the correct load order
%usepackage[nameinlink,noabbrev]{cleveref} % <--- moved to the end of the preamble. Mind the correct load order
usepackage{xstring}
usepackage{xfrac}
usepackage{nicefrac}
usepackage{dcolumn}
%usepackage{booktabs}%<-- removed. don't load packages more than once!
usepackage{relsize}
%usepackage{booktabs, makecell} %<-- removed. don't load packages more than once!
usepackage[referable]{threeparttablex}
%usepackage{siunitx} %<-- removed. don't load packages more than once!
%usepackage[skip=1ex]{caption} %<-- removed. don't load packages more than once!
%usepackage{booktabs, makecell} %<-- removed. don't load packages more than once!
%usepackage[referable]{threeparttablex} %<-- removed. don't load packages more than once!
%usepackage{booktabs,dcolumn} %<-- removed. don't load packages more than once!
%usepackage{multirow, booktabs, makecell, caption} %<-- removed. don't load packages more than once!
%usepackage{threeparttable} %<-- removed. don't load packages more than once!
%usepackage{siunitx} %<-- removed. don't load packages more than once!


usepackage{varioref}
usepackage{hyperref} 
usepackage[nameinlink,noabbrev]{cleveref}

    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
renewcommand{theadfont}{smallbfseries}
captionsetup{font=bf}


newcommand{Risk}{mathop{textnormal{slshape Risk}}nolimits}
newcommand{CEOPC}{mathop{textnormal{slshape CEO_PC}}nolimits}
newcommand{Boardind}{mathop{textnormal{slshape Board_ind}}nolimits}
newcommand{OP}{mathop{textnormal{slshape OP}}nolimits}
newcommand{OF}{mathop{textnormal{slshape OF}}nolimits}
newcommand{Zscore}{mathop{textnormal{slshape Z_Score}}nolimits}
newcommand{NPLs}{mathop{textnormal{slshape NPLs}}nolimits}
newcommand{NPL}{mathop{textnormal{slshape NPL}}nolimits}
newcommand{LnZ}{mathop{textnormal{slshape Ln_Z}}nolimits}
newcommand{LnZscore}{mathop{textnormal{slshape LnZ_score}}nolimits}
newcommand{LTS}{mathop{textnormal{slshape LTS}}nolimits}
newcommand{EA}{mathop{textnormal{slshape EA}}nolimits}
newcommand{LT}{mathop{textnormal{slshape LT}}nolimits}
newcommand{PF}{mathop{textnormal{slshape PF}}nolimits}
newcommand{EF}{mathop{textnormal{slshape EF}}nolimits}
newcommand{LV}{mathop{textnormal{slshape LV}}nolimits}
newcommand{LGI}{mathop{textnormal{slshape LGI}}nolimits}
newcommand{AGI}{mathop{textnormal{slshape AGI}}nolimits}
newcommand{DD}{mathop{textnormal{slshape DD}}nolimits}

newcommand{Controls}{mathop{textnormal{slshape Controls}}nolimits}
usepackage{xcolor}
newcommandtc[1]{textcolor{blue}{#1}}

begin{document}

we use the following model

begin{equation}
   Risk_{i,t} = c + alpha Risk_{i,t-1} + beta_{1}CEOPC_{i,t} + beta_{2}Boardind_{i,t} + 
 beta_{k}Controls_{i,t}+epsilon_{i,t}label{eq:1}
end{equation}

Cref{tab2} presents the regression results :

begin{table}[ht]  
sisetup{table-format=-2.5,  % corrected values with respect to the numbers in your table
         table-number-alignment=center, 
         table-space-text-pre =(, 
         table-space-text-post=$^{***}$, 
         table-align-text-pre=false, 
         table-align-text-post=false}
centering          
caption{Risk}
label{tab2}
begin{tabular}{l*{2}{S}}
toprule
thead{Variable} & {thead{$NPLs$}} & {thead{$LnZscore$}} \
midrule
multirow{2}[1]{*}{Constant}       & -0.1064tc{***} & 5.0727tc{***} \
                                   & {(}-3.42{)}     & {(}5.35{)} \    
addlinespace
multirow{2}[0]{*}{$NPL_{i,t-1}$} & 0.021tc{***}   & \
                                   & {(}5.73{)}      & \
addlinespace
multirow{2}[1]{*}{$LnZ_{it-1}$}  &                 &  0.1452tc{***} \
                                   &                 & {(}5.83{)} \
addlinespace
multirow{2}[1]{*}{$CEOPC_{it}$}  & 6.4521tc{***}  & 0.0124 \
                                   & {(}11.14{)}     & {(}1.12{)} \  
addlinespace 
multirow{2}[1]{*}{$Boardind$}    & -0.1452tc{**}  & -0.1245tc{***}  \
                                   & {(}-2.11{)}     & {(}-8.25{)} \              
addlinespace
multirow{2}[1]{*}{$OF$}          & -0.0103tc{***} & 0.0345tc{**} \
                                   & {(}-2.45{)}     & {(}2.33{)} \              
addlinespace
multirow{2}[1]{*}{$OP$}          & -0.1445tc{*}   & 0.1478tc{*} \
                                   & {(}-1.91{)}     & {(}1.90{)} \            
addlinespace
multirow{2}[1]{*}{$LTS$}         & 0.1019tc{**}   &-0.2645tc{***} \
                                   & {(}2.45{)}      & {(}-3.47{)} \       
addlinespace
multirow{2}[1]{*}{$EA$}          & 0.2114          & 0.4789 \
                                   & {(}1.03{)}      & {(}0.10{)} \                
addlinespace
multirow{2}[1]{*}{$LT$}          & -0.1478tc{*}   & -0.2010\
                                   & {(}-0.45{)}     & {(}-0.14{)} \
addlinespace
multirow{2}[1]{*}{$PF$}          & -0.5240tc{*}   & -0.0520 \
                                   & {(}-3.06{)}     & {(}-1.24{)} \                   
addlinespace
multirow{2}[1]{*}{$EF$}          & 0.0120          & -1.2322tc{***} \
                                   & {(}4.20{)}      & {(}-2.20{)} \
addlinespace
multirow{2}[1]{*}{$LV$}          & -0.1478tc{***} &  \
                                   & {(}-11.02{)}    &  \ 
addlinespace
multirow{2}[1]{*}{$LGI$}         & 0.1247          &  \
                                   & {(}0.2010{)}    &  \    
addlinespace
multirow{2}[1]{*}{$AGI$}         &                 & 0.0012tc{***} \
                                   &                 & {(}0.1478{)} \  
addlinespace
multirow{2}[1]{*}{$DD$}          &                 & 0.14789 \
                                   &                 & {(}0.01236{)} \    
midrule
Year dummy                         & multicolumn{2}{c}{Yes} \
R$^2$                              &   -1.156        &  -2.452 \
Adjusted R$^2$                     &   0.652         & 1.562 \
Sargan test                        & 12.02tc{***}   & 41.02tc{***} \
bottomrule
end{tabular}
smallskip

begin{minipage}{textwidth}
small
textit{Note:} This table reports SGMM estimation results of cref{eq:1} where non-performing loans to total loans ($NPL$), and Z-score ($LnZ$) are the endogenous variables for bank $i$ and year $t$. The $NPL_{i,t-1}$ and $LnZ_{it-1}$ are lagged dependent variables. $OP$ and $OF$ is the independent PRIVATE (DUMMY), FOREIGN (DUMMY), passive shareholding ($PF$), minority active shareholding ($EF$) and active shareholding ($LTS$) are the main explanatory ownership variables. Bank size ($LTS$), corporate governance ($EA$), financial leverage ($LT$) are bank level control variables; and growth of product ($LGI$), rate of inflation ($AGI$) are two macro-economic control variables. T-statistics are between parentheses; enspace *** $p < 0.01$; enspace ** $p < 0.05$;enspace * $p < 0.10$. The Sargan test justifies the validity of the over identifying restrictions.
 end{minipage}
end{table}
end{document}