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## 编译环境 操作系统 * [x ] Windows 7/8/10 * [ ] macOS * [ ] Linux `若需勾选，请把[ ]改成[x]` Tex发行版 * [2018 ] TexLive `年份` * [ ] MikTeX `版本号` * [ ] CTeX `若需勾选，请把[ ]改成[x]` ## 我的问题 \documentclass[12pt]{article} \usepackage{mathrsfs} \usepackage[centertags]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsthm}%ams四件套 %\usepackage{cases} %\usepackage{indentfirst} %\usepackage{epsfig} \usepackage{graphicx}%图片 \usepackage{color} \usepackage{extarrows}%长箭头 \usepackage{listings}%引用代码 \usepackage{xcolor} \usepackage{subfigure} \usepackage{caption} \usepackage{float} \usepackage{subfloat} \usepackage{array} \linespread{1} \parskip 1ex \pagestyle{plain} \oddsidemargin 0in \topmargin 0.0in \headheight 0in \textwidth 6.5in \textheight 9.0in \lstset{numbers=left, %设置行号位置 numberstyle=\tiny, %设置行号大小 keywordstyle=\color{blue}, %设置关键字颜色 commentstyle=\color[cmyk]{1,0,1,0}, %设置注释颜色 frame=single, %设置边框格式 escapeinside=``, %逃逸字符(1左面的键)，用于显示中文 breaklines=true, %自动折行 extendedchars=false, %解决代码跨页时，章节标题，页眉等汉字不显示的问题 xleftmargin=2em,xrightmargin=2em, aboveskip=1em, %设置边距 tabsize=4, %设置tab空格数 showspaces=false %不显示空格 } \newtheorem{theorem}{Theorem}[section] \newtheorem{corollary}{Corollary}[section] \newtheorem{lemma}{Lemma}[section] \newtheorem{condition}{Condition}[section] \newtheorem{proposition}{Proposition}[section] \newtheorem{remark}{Remark}[section] \newtheorem{definition}{Definition}[section] %\numberwithin{equation}{section} \renewcommand{\theequation}{\thesection.\arabic{equation}} \def\P{\operatorname*{P}} \def\E{\operatorname*{E}} \def\Var{\operatorname*{Var}} \def\Cov{\operatorname*{Cov}} \def\sign{\operatorname*{sign}} \def\N{\operatorname*{\mathbb{N}}} \def\Z{\operatorname*{\mathbb{Z}}} \def\Q{\operatorname*{\mathbb{Q}}} \def\R{\operatorname*{\mathbb{R}}} \def\F{\operatorname*{\mathbb{F}}} \allowdisplaybreaks[4] \begin{document} \title{\bf How the economic environment influences the strikes in France?} \author{Fanshu Sun, Wantao Huang, Junbei Zhang} \date{\today} \section{Motivation} As we all know, France has always taken a significant role in European society. In recent years, France has drawn global attention because of its “yellow vest protesters” and strikes in large scale. Even though we believe that the reason for these strikes origins from different aspects, what we are interested in here is how the economic environment influences the strikes in France. We hope that our analysis on this topic can offer a concise picture of relationships between French economy situation and its strikes. Also, we want to provide some suggestions on smoothing the strikes from economic perspective. \section{Literature Review} The previous studies on reasons why strikes are so common in France mostly focused on the class struggle and the social security system. The mixed social security system adopted by France has in fact become an economic and political tool for different social groups to achieve and maintain their own interests, which leads to the frequent occurrence of strikes in France.(Jianding Ding, Lin Guo,2011 ) Such frequent strikes and the violence they have caused had an adverse effect on the investment climate in France.(Gaochao Li,2015) . But how the economic environment influences the strikes in France? During the capitalist world economic crisis began in 1929, the strikes was low in recession and showed no significant increase in depression. Only when it came to resurgence, the strikes surged. A severe economic crisis and the presence of a large number of the unemployed are disincentives to strikes.(Mingxian Shi,1986) We aim to break down the economic reasons to find out the impact of various factors on the number of strikes in France, providing data support and supplement to previous studies. \section{Empirical methodology} \subsection{Regression method selection} \indent Firstly, we run a collinearity diagnostic to check whether multicollinearity exists, and we got illustration at Table 1. We denote $X_{i}$, i=1, 2, …,7, as French GDP growth rate, Consumer Confidence Index (CCI), inflation rate, unemployment rate, GNI per capita, government’s total tax income, and real GDP respectively. Y is the number of days not worked due to strikes and lockouts by economic activity. (Date resources: FRED, CEIC, ILOSTAT and Macro Trends) \begin{table}[!hbp] \begin{center} \caption{Collinearity Diagnostics} \begin{tabular}{c c c c c c c c c c c} \hline Dimension& Eigenvalue& Condition Index& \multicolumn{8}{c}{Variance Proportions}\\ \multicolumn{3}{c}{}& (Constant)& x1& x2& x3& x4& x5& x6& x7\\ \hline 1& 7.268& 1.000& .00& .00& .00& .00& .00& .00& .00& .00\\ 2& .493& 3.841& .00& .32& .00& .02& .00& .00& .00& .00\\ 3& .181& 6.330& .00& .03& .00& .30& .00& .00& .00& .00\\ 4& .037& 13.984& .00& .46& .01& .18& .02& .01& .00& .00\\ 5& .017& 20.637& .00& .17& .05& .04& .03& .09& .00& .00\\ 6& .003& 47.656& .00& .00& .13& .04& .08& .54& .03& .00\\ 7& .001& 88.900& .03& .01& .72& .37& .02& .16& .02& .01\\ 8& .000& 558.350& .97& .01& .09& .05& .85& .20& .95& .99\\ \hline \end{tabular} \end{center} \end{table} We conclude that there is multicollinearity among the exogenous variables. The reasons are as follow: a. The Eigenvalues of Dimension 6,7, and 8 are about 0; b. The condition indexes of Dimension 4-8 are above 10; c. There are values approximately equal to 1 in the correlation coefficient matrix (Dimension 8: constant, $X_{4}$, $X_{6}$, and $X_{7}$). Therefore, we cannot use OLS to do the regression. We sacrifice some bias to get a significant drop on the variance by applying ridge regression. $$\hat{\beta}^{R}=\arg \min _{\beta}\left[\left(y-\beta_{0}-\sum_{i=1}^{p} \beta x_{i}\right)^{2}+\lambda \sum_{i=1}^{p} \beta_{i}^{2}\right]$$ where $\lambda$ is a tuning parameter that controls the strength of the penalty term $\sum_{i=1}^{p}\beta_{i}^{2}$. Then, we construct a multiple linear regression model, $$ y=\beta_{0}+\beta_{1}X_{1}+\beta_{2}X_{2}+\cdots+\beta_{p}X_{p}+\varepsilon $$ \subsection{Regression Results} \indent After doing Ridge Regression, we have results shown in Table 2 and Figure 1: \begin{table}[!hbp] \begin{center} \caption{R-square and beta coefficients for estimated values of k -- Part} \begin{tabular}{c c c c c c c c c} \hline k& RSQ& $X_{1}$& $X_{2}$& $X_{3}$& $X_{4}$& $X_{5}$& $X_{6}$& $X_{7}$\\ \hline .00300& .21261& -.135271& -.203864& -.492407& .231234& -.744295& -.497406& 1.066763\\ .00400& .21110& -.132980& -.205007& -.486605& .202900& -.723852& -.384226& .921711\\ .00500& .20986& -.131099& -.205005& -.481984& .181842& -.707090& -.301800& .814888\\ .00600& .20881& -.129486& -.204285& -.478132& .165508& -.692764& -.239282& .732849\\ .00700& .20792& -.128060& -.203094& -.474812& .152418& -.680149& -.190381& .667794\\ \hline \end{tabular} (Here we only show value related k larger or equal to 0.003 and smaller or equal to 0.007, whole table is shown in the Appendix) \end{center} \end{table} \begin{figure} \includegraphics[width = 8cm]{2.png} \caption{Figure 1} \centering \end{figure} By choosing k = 0.05 using the Ridge Trace method, we get the standardized Ridge Regression equation of y to $X_{i}$, where i=1, 2, …, 7, as follows: $$ y=-.131099X_{1}-.205005X_{2}-.481984X_{3}+.181842X_{4}-.707090X_{5}-.301800X_{6}+.814888X_{7} $$ \section{Conclusion} \subsection{Intuitive Interpretation} GDP growth rate, Consumer Confidence Index, inflation rate, GNI per capita, and tax have negative effect on French strikes, while unemployment rate and real GDP have positive effect on it. As the economy grows faster, the consumers are more confident. Also, with their increasing income, French people are less unsatisfied. So they conduct less strikes. Higher inflation rate increases prices and decreases purchasing power, which will impair the feasibility of strikes. Higher unemployment rate stimulates strikes by giving more people cost-free time and increasing people’s dissatisfaction. Growing GDP stimulates the strikes in a degree. In fact, slumping economy is unfit for strikes because workers are faced with relatively high risk of being fired, which increases the difficulty of conducting strikes. \subsection{Suggestions} Normally, it’s believed that fewer strikes mean a more stable social environment even in countries which have a strike culture like France. To reduce the strikes, the government is supposed to put more effort in stimulating GDP growth rate, increasing GNI per capita, launching some political and economic policies to improve consumer’s confidence. On the other hand, working hard in controlling the unemployment rate will have a significant contribution to the reduction of the number of strikes. \newpage \bibliographystyle{plain} \bibliography{spectral} \begin{thebibliography}{1} \bibitem{01} Jianding Ding \& Lin Guo. \newblock{The formation and influence of the characteristics of mixed social security system in France after the war} \newblock{\em French Studies}, 2011(04):72-80. \bibitem{02} Gaochao Li. \newblock{Strikes hurts French Economy?} \newblock{\em International Business}, 2015-10-19(A04). \bibitem{03} Mingxian Shi. \newblock{On the strike movement in 1929 during the capitalist world economic crisis} \newblock{\em Journal of Inner Mongolia Normal University (philosphy and social science)}, 1986(01):7-14+6. \end{thebibliography} \end{document} 好像文件的标题和作者都显示不出来