计算方法统计代写 R语言代写

Homework 11

计算方法统计代写 Question 1 (6 points) PART (A) (1 POINT) Read sections 1 to 3.1, and 4 to 4.1 of “Environmental Kuznets Curve Hypothesis: A Survey

Question 1 (6 points) 计算方法统计代写

Part (a) (1 point)

Read sections 1 to 3.1, and 4 to 4.1 of “Environmental Kuznets Curve Hypothesis: A Survey” (of course, you may read more, but these sections contain the most relevant information for this week’s homework). Briefly summarize the idea of the Environmental Kuznets Curve (EKC). Specifically, what kind of relationship does it posit between economic development and environmental impact, for example CO₂ emission?

Part (b) (1 points) 计算方法统计代写

library(tidyverse)
library(ggplot2)
load("world_bank.rda") # loads world_bank table 

head(world_bank)

## # A tibble: 6 x 4
## Country GDP Population CO2
## <chr> <dbl> <dbl> <dbl>
## 1 Afghanistan 20484885120. 32758020 9809.
## 2 Albania 13228247844. 2889104 5717.
## 3 Algeria 213810022462. 39113313 145400.
## 4 American Samoa 643000000 55437 NA
## 5 Andorra 3350736367. 79223 462.
## 6 Angola 145712200313. 26920466 34763.

These data contain three different variables measured on countries and other entities in 2014. Describe how you can use these data to investigate the EKC. (Note: countries have vastly different populations. How will you account for that?)

Part (c) (2 points) 计算方法统计代写

Section 4.1 of the EKC paper includes a specification for a model that relates country income to CO2 per capita. For our purposes, we will fix a single observation per country (t = 1 for all observations) and not include any other predictors (labeled z in the model).

Fit an OLS model using the specification given in equation (1) on page 440. Interpret your results using the listing of possible outcomes given on pages 440 and 441 by applying hypothesis tests that the parameters equal zero (you may use summary(model) to get the p-values of the tests). Do you think there is evidence to support the EKC theory? Can we rule out the EKC theory?

Part (d) (2 points)

As an alternative specification, we could use kernel smoothing to estimate the conditional mean of CO2 emissions given GDP. Using leave one out cross validation, select a bandwidth to use with a Gaussian/Normal kernel. Plot your result and interpret the curve with respect to evidence for or against the EKC.

Question 2 (4 points) 计算方法统计代写

While we can motivate ordinary least squares (OLS) as finding the maximum likelihood estimates for Y ∼ N(β′x, σ² ), OLS has wider applicability and still nice properties.

When we model E(Y | x) = β′x and assume a constant variance, ordinary least squares OLS is the best linear unbiased estimator of the β parameters (i.e., among all methods that are linear functions of Y and would have unbiased estimates of the parameters, OLS has the smallest variance.)

read.delim("https://dept.stat.lsa.umich.edu/~bbh/s485/data/israel_severe_covid_2021_08_15.tsv")

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