MAS6004/6062 S1 Project

Statistical analysis of economic growth

（因兼容性原因，故去除公式）

Background

Economic growth is commonly defined as an increase in the output that an economy produces over a period of time, usually a year. The most widespread measure of output is gross national product (GDP). Economic growth is one of the key drivers in public and private decision making: public policies such as wages, interest rates and spending are geared towards increasing GDP growth, while private investment strategies usually depend on the long term growth rate.

The econometrics literature suggests that,

Data and Statistical analysisis a simple but still suitable model for economic growth. Here y_t is the growth rate at time t, "_t is an idiosyncratic error term, assumed to be Gaussian with zero mean and precision ; is the effect of last period’s growth and is related to the long term growth rate. A common assumption in the econometrics literature is that this is a stationary process, i.e. that j j < 1 and if this is the case then the long term or steady state growth rate is D =.1 /.

The file (WB_PCGR.RData) contains the annual per-capita GDP growth rates of 264 countries and regions obtained from the world bank http://data.worldbank.org/indicator/NY.GDP.PCAP.KD.ZG/; it can be downloaded from the MOLE webpage along with the spreadsheet CountryCodes with the codes for the regions/countries. Your task is to select two different countries or regions and carry out the

following statistical analysis of their economic growth.

1. You should fit model (1) using two different priors:

a) We impose stationarity by using a re-scaled Beta distribution —to . 1; 1/— with parameters (1/2,1/2), as a prior for the AR(1) slope, ,

This is coded in the routine AR1_stationary.R.

b) If stationarity is not imposed, assume  . / =N   m ; 1=p  . This is coded in the routine

AR1_nonstat.R.

in both cases the priors for the other two parameters are

Describe the differences between your and my posterior distributions for f ;  ;  g.You should carry out informal checks for convergence by selecting different starting points and length of chains.

2. After talking to my economic consultant, my elicited prior parameters are

fm ; p ; a; bg D 0:02; 1=0:04²; 2; 0:6 and m ; p D f0; 1g

3. The model may be simplified if the data suggest that the slope is close to zero. One possible measure of model fit can then be the posterior odds,

4. You are asked to provide advice to the CEO of a large company which is considering investing in the countries you selected. She has two possible decisions:For each country you selected, calculate O from each prior specification and use it to decide if the data provides evidence in favour of a non-zero slope.

d_1i  : Invest in country i d_2i  : Do not invest in country i

After elicitation, her preferences, based on the long term growth rate, are described by

the best economic perspective, i.e. the one that will increase its growth more rapidly. As part ofwhere D  =.1 / is the long term growth rate. Otherwise, she will invest on the country with

your submission, prepare a short executive report advising the CEO on her optimal strategy.

Use MOLE to submit your work as a PDF file. Submission deadline is 6 February 2018 12pm. Your file name must be of the form 123456789_BayesProject.pdf where 123456789 is your student ID number. Marks will be deducted if the file is submitted otherwise.

There is no specific page limit, but you should give some thought to which material is in the main text and which is in appendices, if any. Also, if you include trace plots of very long runs, please thin the output to ensure that the size of your PDF file is not excessive.

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中文翻译：

MAS6004 / 6062 S1项目

统计分析经济增长

（因兼容性原因，故去除公式）

背景

经济增长通常被定义为经济在一段时间内（通常是一年）产出的增长。产出最为广泛的是国民生产总值（GDP）。经济增长是公共和私人决策的主要驱动因素之一：工资，利率和支出等公共政策的目标是增加GDP增长，而私人投资战略通常取决于长期增长率。

计量经济学文献表明，

数据和统计分析是一个简单但仍然适合经济增长的模型。这里t  是t时刻的增长率，“ t  是一个特殊的误差项，假设为高斯分布，具有零均值和精度;是上期增长的影响，与长期增长率有关。计量经济学的文献是这是一个平稳的过程，即  jj <1，如果是这种情况，则长期或稳态增长率是D = 1 /。

文件（WB_PCGR.RData）包含了来自世界银行的264个国家和地区的年人均国内生产总值增长率http://data.worldbank.org/indicator/NY.GDP.PCAP.KD.ZG/; 它可以从摩尔的网页与电子表格一起下载CountryCodes  与该地区/国家代码。你的任务是选择两个不同的国家或地区并执行

对其经济增长进行统计分析。

1.  你应该使用两个不同的先验模型（1 ）：

a）  我们通过使用重新分级的Beta分布来强加平稳性。1; 1 / – 作为AR（1）斜率的先验参数（1 / 2,1 / 2），

这在例行程序AR1_stationary.R中被编码。

b）  如果不强加平稳，则假设。/ = N m; 1 = p。这是在例程中编码

AR1_nonstat.R。

在这两种情况下，其他两个参数的先验是

描述你的和我的后验分布之间的差异。; g。你应该通过选择不同的出发点和链条的长度来进行收敛的非正式检查。

在和我的经济顾问交谈之后，我引用了以前的参数

fm; p; 一个; bg D 0:02; 1 = 0：04 2 ; 2; 0：6 和 m; p D f0; 1克

3.  如果数据表明斜率接近零，则模型可能会简化。模型拟合的一个可能的测量可以是后验概率，

4.  您被要求为正在考虑投资您选择的国家的大型公司的首席执行官提供建议。她有两个可能的决定：对于您选择的每个国家，计算每个事先规定的O，并用它来决定数据是否提供有利于非零斜率的证据。

d 1I   ：在国家投资我 ð 2I   ：不要投资于i国

启动后，她的偏好，根据长期增长率，描述

最好的经济视角，也就是  更快速增长的经济视角。作为其中 D = .1 /是长期增长率的一部分。否则，她会用这个国家来投资这个国家

你的意见，准备一份短期执行报告，就CEO的最佳战略提供建议。

使用MOLE将您的作品提交为PDF文件。提交截止日期是2018年2月6日12时 您的文件名必须是123456789_BayesProject.pdf  ，其中123456789  是您的学号。如果文件另外提交，标记将被扣除。

没有特定的页面限制，但是您应该考虑哪些材料在正文中，哪些在附录中（如果有的话）。另外，如果包含很长时间的痕迹，请减少输出以确保PDF文件的大小不会过大。