myprojects-hg-reborn

Fork

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\title{Definition of Key Statistics for the EU27 FDI}
% \author{Lorenzo Isella}
\date{}

\begin{document}
\maketitle
  
% \abstract{
% We give the definitions of growth rate and we introduce the main
% formulas for the calculations of the composite growth rate along a
% multi-period time span. After illustrating the shortcomings inherent to
% a straightforward calculation of the
% growth rate of trade flows, we suggest a methodology to bypass these
% issues which borrows from the theory of measurement of investment returns. 
% }
\section{Relation between EU28 and EU27 Statistics}
Hopefully this document will become soon obsolete due to EUROSTAT
adding the information we need.
We need to be able to calculate the investments involving the EU27
from/to the UK and the EU27 and the UK from/to the extra EU27.
We go step by step and we use the notation $X\to Y$ to mean
investments from country $X$ to country $Y$. I would like to avoid going through the
individual country, i.e. building up the EU27 as the sum of the
individual MS.

For clarity

\begin{equation}
EU27=EU28-UK
\end{equation}

and


\begin{equation}
extra\;\;EU27=extra\;\;EU28+UK
\end{equation}


By using the definitions in the case of investments of the EU27 to
country X I get

\begin{equation}\label{eu27-flow}
\boxed{EU27 {\to X}=EU28 {\to X}-UK {\to X}}
\end{equation}  

so, once I have the investments of the EU28 and the UK to a country X,
I get the EU27 investments to that country just by subtraction. 

We now define the investments of an entity X towards the extra
EU27. The extra EU27 consists of everything outside the EU28 plus the
UK, so as a consequence
\begin{equation}\label{extra-eu27}
\boxed{X {\to extra\;\;EU27}= X {\to extra\;\;EU28} + X {\to UK}}
\end{equation}

i.e. once I know the investment of a country X to the extra EU28 and
to the UK, I can obtain by a simple sum the investments of country X
to the extra EU27.
Let us apply this to the extra EU27 investments by the UK

\begin{align}
  \boxed{UK\to extra\;\; EU27=} & UK \to extra\;\; EU28+UK\to UK= \nonumber \\
  &\boxed{UK\to extra\;\; EU28}
\end{align}  

since the investments of the UK inside the UK are not included in
the FDI statistics ($UK\to UK=0$).
In the case of FDI, it looks like the extra EU27 investments from the
UK came for free.

Finally, here are  the investments of the
EU27 towards the extra EU27.

\begin{align}
  &\boxed{EU27 {\to extra\;\; EU27}=}  (EU28-UK)\to (extra\;\;EU28  +
    UK) \nonumber \\
  &=EU28\to extra\;\;EU28+EU28\to UK -UK\to extra\;\;EU28+ \nonumber \\
  & -UK\to UK \nonumber \\
  &=\boxed{EU28\to extra\;\;EU28+EU28\to UK -UK\to extra\;\;EU28}
\end{align}  


So the investments of the EU27 to the UK can be expressed purely in
terms of the investments of the EU28 and the UK towards the UK and the
extra EU28.




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%  & \boxed{EU27 {\to extra\;\;EU27}}  =  \\
% & EU28\to extra\;\;EU28+EU28\to UK -UK\to extra\;\;EU28  
% % \end{empheq}
% \end{align*}



\end{document}