提交: 8700cfef6c536d9547f22acdb240dfa902c7bc9f - myprojects-hg-reborn (hg)

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• 修訂: 8700cfef6c536d9547f22acdb240dfa902c7bc9f (tree)
• 時間: 2020-02-06 22:37:10
• 作者: Lorenzo Isella <lorenzo.isella@gmai...>
• Commiter: Lorenzo Isella

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A tex file showing how to use the bibtex file for bibliography and how to put the bibliography at the end and ensure that any picture is placed in its section.

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• add: latex-documents/report_composite_indicator.tex

差異

diff -r c5059bd950f5 -r 8700cfef6c53 latex-documents/report_composite_indicator.tex
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+++ b/latex-documents/report_composite_indicator.tex	Thu Feb 06 14:37:10 2020 +0100
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+ \documentclass[12pt,a4paper]{article}
+% \documentclass[14pt, a4paper]{extarticle}
+\usepackage[utf8x]{inputenc}
+\usepackage[english]{babel}
+\usepackage{graphicx}
+\usepackage{amsmath}  
+\usepackage{xcolor}
+\usepackage{caption}  
+\usepackage{url}
+\usepackage{esvect}
+% for placeholder text
+\usepackage{lipsum}
+ % \usepackage[margin=0.5in]{geometry}
+\usepackage{mathtools}% Loads amsmath
+   \usepackage[section]{placeins}
+ \usepackage{tabularx}
+\usepackage{colortbl, xcolor}
+\usepackage{booktabs}
+\usepackage{doi}
+
+% \usepackage[backend=bibtex,style=verbose-trad2]{biblatex}
+% \bibliography{mybibfile} 
+
+
+\title{Annex I: Methodology for Composite Indicator on Non-Tariff Measures}
+%  \author{Lorenzo Isella}
+\date{}
+
+\begin{document}
+\maketitle
+  
+\abstract{
+We detail the methodology and the calculations behind the construction
+of a composite indicator for the non-tariff measures based on the
+UNCTAD data available at
+\url{https://trains.unctad.org/Forms/Analysis.aspx}. We follow the
+methodology in \cite{nicoletti} and \cite{oecd-composite}.
+}
+\section{Data Overview}
+The discussion of the economic meaning of the various non-tariff
+measures (NTMs) is beyond the scope of this document, as is the data
+processing of the UNCTAD database.
+The starting point is given by the already cleaned, aggregated and restructured NTM
+dataset (a raw dowload of the database will not directly provide the
+same input data as the one used for this manuscript).
+For all the $85$ reporters listed in the database we calculated the
+total number of NTMs they impose on third-country imports broken  down
+by ntm 1-digit code.
+
+The UNCTAD database contains information about the following
+NTM 1-digit codes
+\begin{itemize}
+\item A SANITARY AND PHYTOSANITARY MEASURES
+\item B TECHNICAL BARRIERS TO TRADE
+\item C PRE-SHIPMENT INSPECTION AND OTHER
+FORMALITIES
+\item D CONTINGENT TRADE-PROTECTIVE MEASURES
+\item E NON-AUTOMATIC LICENSING, QUOTAS,
+PROHIBITIONS AND QUANTITY-CONTROL
+MEASURES OTHER THAN FOR SPS OR TBT
+REASONS
+\item F PRICE-CONTROL MEASURES, INCLUDING
+ADDITIONAL TAXES AND CHARGES
+\item G FINANCE MEASURES
+\item H MEASURES AFFECTING COMPETITION
+\item I TRADE-RELATED INVESTMENT MEASURES
+\item J DISTRIBUTION RESTRICTIONS
+\item K RESTRICTIONS ON POST-SALES SERVICES
+ \item {L SUBSIDIES (EXCLUDING EXPORT SUBSIDIES UNDER P7)}
+\item M GOVERNMENT PROCUREMENT RESTRICTIONS
+\item N INTELLECTUAL PROPERTY
+\item O RULES OF ORIGIN
+\item {P EXPORT-RELATED MEASURES}
+\end{itemize}
+
+We leave out of the analysis P and L, since they are measures taken by
+the exporting rather than the importing  country (in other words, they
+affect the imports, but they are not the consequence of some policy of
+the importing country).
+\section{Correlation Analysis}
+We calculate the total number of NTMs, broken by
+1-digit codes, that each reporter (a set of 85 countries or country aggregates
+including the EU28) adopts (sum of its NTMs on all the imports 
+from any third country).
+
+We then look at the structure of the correlations which are illustrated
+in Figure \ref{cor-mat}. A screening of the correlation matrix reveals
+several interesting properties
+\begin{enumerate}
+\item All the statistically significant correlations are positive.
+\item Subindicators H and I are not significantly correlated to any other
+  subindicator. We therefore choose to leave them out of the analysis.
+ % \textcolor{red}{Is this a sound decision (statistically
+ %    speaking)? Economically speaking it may make sense since I
+ %    includes also measures affecting the producer and  not only the
+ %    importer and the same applies to H.}
+\item There is an extremely high correlation between subindicators N and
+  O. This is a spurious correlation due to both O and N consisting
+  primarily of zero values. As a consequence, they are also left out.
+\end{enumerate}  
+
+% \textcolor{red}{Discarding subindicators H, I, N and O is also the direct result of
+% eliminating all the subindicators for which the non-zero values are less
+% than $10\%$ than the total number of data.} If we believe in the
+% integrity of the database (which does not explicitly mention missing
+% data), the absence of information about a e.g. rules of origins
+% (subindicator O)
+% measures imposed by country A from country B should mean that the
+% number of measures related to the rules of origins is zero and not
+% missing. Several conversation with UNCTAD however leave ample space to doubt.
+
+   
+% % \end{itemize}
+
+% We also notice the extremely high correlation between N and O.
+% We do not have an explanation for that, since rules of origin and
+% intellectual property are definitely two distinct categories of
+% measures, but the level of correlation is such that we choose to
+% discard indicator N.
+% \begin{itemize}
+% \item \textcolor{red}{Once again, any comments on this?}
+% \end{itemize}  
+
+\begin{figure}
+\includegraphics[width=\columnwidth]{correlation_subindicators.pdf}
+\caption{Correlation matrix. Crossed values are not statistically
+  significant at the $p=0.05$ level.}
+\label{cor-mat}
+\end{figure}
+
+\subsection{Outliers}
+
+The remaining indicators are all affected by outliers, as one can see
+in Figure \ref{outliers}. We are very reluctant to treat them, despite
+the impact they may have on the PCA, because they are not supposed to
+be measurement errors, but they stand for countries imposing an
+unusually high number of NTMs on their imports.
+
+% \textcolor{red}{Any thoughts on this?}
+
+
+
+
+
+\begin{figure}
+\includegraphics[width=\columnwidth]{indicators_box_plot2.pdf}
+\caption{Boxplots of the NTM 1-digit distributions.}
+\label{outliers}
+\end{figure}
+   
+
+\section{Principal Component Analysis}
+In this section we resort to principal component analysis (PCA) to
+statistically determine the weights of the components of the NTM composite
+indicator we intend to construct. In the following, unless otherwise stated, we will use the
+terms component and factor interchangeably.
+The methodology is taken from \cite{nicoletti} and \cite{oecd-composite}.
+
+First, we carry out a PCA on the centred and scaled subindicators and we
+determine the number of factors we want to include in the analysis.
+According to Table \ref{table-pca} the first three components satisfy
+the following conditions (laid out in Ref. \cite{nicoletti}).
+\begin{itemize}
+\item The associated eigenvalue is larger than $1$.
+\item Each component accounts for at least $10\%$ of the total
+  variance.
+\item   Together, they account for more than $60\%$ of the total variance.
+\end{itemize}  
+
+
+% latex table generated in R 3.6.1 by xtable 1.8-4 package
+% Tue Nov 26 09:51:34 2019
+\begin{table}[ht]
+\centering
+\caption{Summary statistics of PCA (without rotation).} 
+\begin{tabular}{rrr}
+  \toprule
+Eigenvalue & Share of total variance & Cumulative share of variance \\ 
+  \midrule
+\bf{2.53} & \bf{0.32} & \bf{0.32} \\ 
+   \rowcolor[gray]{0.9}\bf{1.49} & \bf{0.19} & \bf{0.50} \\ 
+  \bf{1.11} & \bf{0.14} & \bf{0.64} \\ 
+   \rowcolor[gray]{0.9}0.91 & 0.11 & 0.75 \\ 
+  0.80 & 0.10 & 0.85 \\ 
+   \rowcolor[gray]{0.9}0.66 & 0.08 & 0.94 \\ 
+  0.32 & 0.04 & 0.98 \\ 
+   \rowcolor[gray]{0.9}0.18 & 0.02 & 1.00 \\ 
+   \bottomrule
+\end{tabular}
+\label{table-pca}
+\end{table}
+
+
+The second step consists in performing a PCA followed by a varimax
+rotation by limiting the number of factors to three.
+The loadings of the rotated components are provided in Table \ref{table-varimax}.
+
+% latex table generated in R 3.6.1 by xtable 1.8-4 package
+% Tue Nov 26 10:29:58 2019
+\begin{table}[ht]
+\centering
+\caption{Loadings of the rotated components (varimax rotation).} 
+\begin{tabular}{lrrr}
+  \toprule
+Subindicator & Component 1 & Component 2 & Component 3 \\ 
+  \midrule
+A & 0.82 & 0.39 & 0.09 \\ 
+   \rowcolor[gray]{0.9}B & 0.70 & 0.37 & -0.03 \\ 
+  C & 0.38 & 0.38 & -0.10 \\ 
+   \rowcolor[gray]{0.9}D & -0.05 & 0.88 & -0.04 \\ 
+  E & 0.03 & 0.71 & 0.54 \\ 
+   \rowcolor[gray]{0.9}F & 0.62 & -0.23 & 0.13 \\ 
+  G & 0.08 & -0.02 & 0.95 \\ 
+   \rowcolor[gray]{0.9}H & 0.63 & -0.13 & 0.03 \\ 
+   \bottomrule
+\end{tabular}
+\label{table-varimax}
+\end{table}
+
+At this point, we follow the procedure by \cite{nicoletti}. First, we
+calculate the normalised squared factor loadings, which are reported
+in Table \ref{squared-loadings}.
+We then do the following
+\begin{enumerate}
+\item we select the subindicators with the highest factors loadings in
+intermediate composite indicators. They are highlighted in Table
+\ref{squared-loadings};
+\item we then weight each composite using the proportion of the
+  variance explained in the data set. In order to do so we calculate
+  the sum of the unnormalised squared factor loadings (explained
+  variance) and we divide it by the total variance accounted for by
+  the rotated factors (sum of the highlighted eigenvalues in Table \ref{table-pca}).
+\end{enumerate}
+  
+Combining the results in Tables
+\ref{squared-loadings}-\ref{squared-loadings2}, we get the
+weights for the subindicators illustrated in Table
+\ref{final-weights}.
+Finally, although this has no impact on the ranking of the countries,
+we normalise to one the sum of the weights of the indicators, as shown
+in Table \ref{final-weights-norm}.
+
+
+
+
+
+% latex table generated in R 3.6.1 by xtable 1.8-4 package
+% Tue Nov 26 10:49:08 2019
+\begin{table}[ht]
+\centering
+\caption{Normalised squared loadings of the rotated components in
+  Table \ref{table-varimax}.} 
+\begin{tabular}{lrrr}
+  \toprule
+Subindicator & Component 1 & Component 2 & Component 3 \\ 
+  \midrule
+A & \bf{0.32} & 0.08 & 0.01 \\ 
+   \rowcolor[gray]{0.9}B & \bf{0.23} & 0.08 & 0.00 \\ 
+  C & 0.07 & \bf{0.08} & 0.01 \\ 
+   \rowcolor[gray]{0.9}D & 0.00 & \bf{0.43} & 0.00 \\ 
+  E & 0.00 & \bf{0.29} & 0.24 \\ 
+   \rowcolor[gray]{0.9}F & \bf{0.18} & 0.03 & 0.01 \\ 
+  G & 0.00 & 0.00 & \bf{0.73} \\ 
+   \rowcolor[gray]{0.9}H & \bf{0.19} & 0.01 & 0.00 \\ 
+   \bottomrule
+\end{tabular}
+\label{squared-loadings}
+\end{table}
+
+
+
+% latex table generated in R 3.6.1 by xtable 1.8-4 package
+% Tue Nov 26 12:47:14 2019
+\begin{table}[ht]
+\centering
+\caption{Squared loadings of the rotated components in
+  Table \ref{table-varimax}.} 
+\begin{tabular}{lrrr}
+  \toprule
+Subindicator & Component 1 & Component 2 & Component 3 \\ 
+  \midrule
+A & 0.68 & 0.15 & 0.01 \\ 
+   \rowcolor[gray]{0.9}B & 0.49 & 0.14 & 0.00 \\ 
+  C & 0.15 & 0.14 & 0.01 \\ 
+   \rowcolor[gray]{0.9}D & 0.00 & 0.77 & 0.00 \\ 
+  E & 0.00 & 0.51 & 0.30 \\ 
+   \rowcolor[gray]{0.9}F & 0.39 & 0.05 & 0.02 \\ 
+  G & 0.01 & 0.00 & 0.90 \\ 
+   \rowcolor[gray]{0.9}H & 0.40 & 0.02 & 0.00 \\ 
+  \midrule
+  Explained Variance & 2.11 & 1.78 & 1.23 \\ 
+  Explained/Total Variance & \bf{0.41} & \bf{0.35} & \bf{0.24} \\ 
+   \bottomrule
+\end{tabular}
+\label{squared-loadings2}
+\end{table}
+
+   
+% latex table generated in R 3.6.1 by xtable 1.8-4 package
+% Tue Nov 26 14:41:44 2019
+\begin{table}[ht]
+\centering
+\caption{Final weights for the subindicators.} 
+\begin{tabular}{lr}
+  \toprule
+Subindicator & Weight \\ 
+  \midrule
+A & 0.13 \\ 
+   \rowcolor[gray]{0.9}B & 0.10 \\ 
+  C & 0.03 \\ 
+   \rowcolor[gray]{0.9}D & 0.15 \\ 
+  E & 0.10 \\ 
+   \rowcolor[gray]{0.9}F & 0.08 \\ 
+  G & 0.17 \\ 
+   \rowcolor[gray]{0.9}H & 0.08 \\ 
+   \bottomrule
+\end{tabular}
+\label{final-weights}
+\end{table}
+
+
+
+% latex table generated in R 3.6.2 by xtable 1.8-4 package
+% Thu Feb  6 11:57:53 2020
+\begin{table}[ht]
+\centering
+\caption{Final weights for the subindicators after normalisation.} 
+\begin{tabular}{lr}
+  \toprule
+Subindicator & Weight \\ 
+  \midrule
+A & 0.16 \\ 
+   \rowcolor[gray]{0.9}B & 0.12 \\ 
+  C & 0.03 \\ 
+   \rowcolor[gray]{0.9}D & 0.18 \\ 
+  E & 0.12 \\ 
+   \rowcolor[gray]{0.9}F & 0.09 \\ 
+  G & 0.21 \\ 
+   \rowcolor[gray]{0.9}H & 0.09 \\ 
+   \bottomrule
+\end{tabular}
+\label{final-weights-norm}
+\end{table}
+
+
+
+
+% \section{Final Questions}
+% Any feedback on the methodology (misunderstandings on our side;
+% possible refinements, improved choice of the number of components, etc...) is more than welcome.
+% If needed, we can provide more information (including the input data
+% and the R code for the PCA calculations).
+
+% We have a question about Table 6.2 in \cite{oecd-composite}, page
+% 57: what is the normalisation of ``Expl./Tot'' (last line in the table)?
+% We thought it should be normalised to $1$, like the ``Weight of
+% factors in summary indicator'' in Tables 8,9 and 11 of
+% \cite{nicoletti}. 
+
+
+\clearpage
+
+\bibliography{mybibfile} 
+\bibliographystyle{apalike}
+
+
+\end{document}
\ No newline at end of file