For this project you will study macroeconomic outcomes as they pertain to growth and development. You will carry out your empirical analysis using R. Your submission must be a zipped folder consisting of all files that you use to generate your results, including the underlying data as well as the write-up. I’ve provided Excel files with the raw data that you will need, as well as links to those data sources.

1. For this question you will perform development accounting using data from version 10.0 of the Penn World Table to examine sources of cross-country income differences within a point in time. Specifically, to what degree do differences in productivity or differences in access to factors of production account for the observed differences in income per capita? Begin with an aggregate production function, written in per-capita form:

yn  = An (An )α

You may set α = 0．33.  The variable yn  is the real income per capita in country n, while An  is capital per capita.  For cross-country comparison we will need to use data measured at common purchasing power parity: You can read these variables from the Penn World Table as cgdpe/pop and cn/pop, respectively. You can then construct the TFP term, An  as a residual defined as An  = yn）(An )α .

Taking the natural logarithm of the production function, it becomes log-linear: ln(yn ) = ln(An ) + α ln(An )

Leverage the log-linearity and measure the cross-country dispersion in each term using

basic statistical properties of variance

var(ln(y)) = var(ln(A)) + var(α ln(A)) + 2cov(ln(A)( α ln(A))

Assess the contribution from each component:

var(ln(A))     var(α ln(A))     2cov(ln(A)( α ln(A))

var(ln(y))      var(ln(y))              var(ln(y))

↘                                          -            ↘                                                -            ↘                                                                                      -

Productivity                           Factor                                            Interaction

contribution                     contribution                                    contribution

(1)

(a) Focus on the year 1990. First, provide some summary statistics of the data. What

is the number of countries in your sample? What is the ratio of income per capita in the median country relative to the U.S., and what is the name of this country? What are the corresponding ratios for the countries in the 10th and 90th percentiles of the income distribution and who are these respective countries?  Second, for these particular countries, report the contributions from productivity, factors and their interaction based on equation (1).

(b) Now focus on 2019.  First, describe how the overall variance in log-income per

capita has changed. Has it increased? Has it decreased? By how much? Second, update all of the information that you calculated in part (a) as it pertains to 2019. Explain how the data have changed from 1990 to 2019.

2. For this exercise you will perform growth accounting using the Penn World Table data to assess the relative contribution from productivity and factors to overall growth in income per capita within a country, over time.  Beginning with the same production function as in question 1, we can state the log-changes in income per capita between

1990 and 2019 as follows

ln ╱ 、 = ln ╱ 、 + α ln ╱ 、

Therefore, we can express the relative contributions from productivity and factors as

ln /  、     α ln /  、

ln /  、       ln /  、

↘                                       -            ↘                                               -

Productivity                         Factor

contribution                   contribution

(2)