PS111

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University of California, Davis *

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ECONOMETRI

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Economics

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Feb 20, 2024

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pdf

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2 Question 1: Development is multidimensional. As we argued in class, income per capita is a good yardstick of development if it is strongly correlated with important indicators that directly measure well-being, such as education, health, and gender disparity. In this problem, you will empirically explore the strength of the relationships between income per capita, health, and gender disparity using data from the World Bank. Go to the World Bank database of development indicators and download the three variables listed below for all countries for the year 2021 . See section slides if you don ’ t remember how to navigate the World Bank database website. • GDP per capita (constant 2015 US$) : This measures a country ’ s average income per person. • Mortality rate, under 5 (per 1,000 live births): This measures the probability per 1,000 that a newborn baby will die before reaching age five. • Proportion of seats held by women in national parliaments (%): This is the number of seats held by women members in single or lower chambers of national parliaments, expressed as a percentage of all occupied seats. (HINT: Make sure you do not download data points for regions like “ Small states ” , “ World ” , “ East and Pacific ” , etc.) A. Generate two scatter plots with trendlines: 1. Under 5 Mortality Rate against GDP per capita using the POWER trendline. Title this plot “ Figure A1: Under 5 Mortality rate vs GDP per capita for 2021. ” 2. Seats held by women in national parliaments (%) against GDP per capita using the LOGORITHMIC trendline. Title this plot “ Figure A2: Women in national parliament vs GDP per capita for 2021 . ” Hint: Set max for horinzonzontal axis at 50,000 & label Axes appropriately. Figure A1

3 Figure A2 B. For each trendline, comment on whether it is upward or downward-sloping. What does it mean for the trendline to be upward or downward-sloping? How does the slope of each trendline change with GDP per capita? For figure A1, the trend line initially slopes downwards very steeply, then eventually flattens out as GDP increases. This trend demonstrates that small changes to GDP per capita UNDER 10000 greatly affect if infant mortality rate increases or decreases, but once GDP per capita rises above 10000 increases to GDP have minimal impact on infant mortality levels. Ultimately, this graph illustrates a negative correlation between infant mortality and GDP per capita. In Figure A2, the trend line is ever so slightly sloping upwards, demonstrating a positive correlation between Women in National Parliament and GDP per capita. However, this correlation (according to the graph) does not appear to be incredibly strong. There are many outliers both above and below the trendline, indicating that there are countries with few women in parliament but a high GDP per capita, and vice versa.

4 Question 2: Human Development Index (HDI) in Papua New Guinea The HDI was modeled after Sen ’ s notion of development. According to the UNDP 1 , “ the HDI was created to emphasize that people and their capabilities should be the ultimate criteria for assessing the development of a country, not economic growth alone. The HDI is a summary measure of average achievement in key dimensions of human development: a long and healthy life, knowledge, and decent living standards. The HDI is the geometric mean of normalized indices for each of the three dimensions. ” In this problem, we will practice computing the HDI, plotting HD over time, and interpreting our results for the country of Papua New Guinea (PNG). Go to Canvas Files/Problem Sets/Problem Set 1. The Excel file PS1_HDI_PNG_template contains time series data on the four HDI components listed below for PNG from 1990-2021. The four components are: 1. LE: Life Expectancy at birth. This variable is defined as the average number of years a newborn is expected to live if mortality patterns at birth remain constant. 2. EYS: Expected years of Schooling. This variable is forward looking and provides an indication about the years of schooling that the current school-age population will complete. It is defined as the number of years of schooling a child of school entrance age (6 years old) can expect to complete if prevailing patterns of age-specific enrolment rates persist throughout the child ’ s schooling life. 3. MYS: Mean years of Schooling (MYS ). This variable is defined as the average years of schooling completed by adults in the population who are ages 25 and over. This indicator reflects the average level of education of the current working age (and elderly) population. 4. GNI PC: GNI per capita . This variable is defined as Gross National Income. It is similar to Gross National Product as discussed in class. A. Let ’ s take a closer look at EYS and MYS, the two education variables, over the past thirty years in PNG. Fill in the cells in Table 2A below with the values of EYS and MYS for the specific years listed in the table. Table 2A. The Evolution of Education in PNG: 1990 - 2020 Education Variable 1990 2000 2010 2020 EYS MYS 1 UNDP is the United Nations Development Program. 3.78 5.83 8.20 10.36 2.32 3.26 3.95 4.74

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5 B. Plot a times series graph that includes both EYS and MYS over the period 1990 – 2021. Title your graph “ Figure 2A: EYS and MYS of Papua New Guinea, 1990-2021 ” Figure 2A. PNG ’ s EYS & MYS Now let’s use Table 2A and Figure 2A to interpret the evolution of education in PNG over the past 30 years . C. What has happened to EYS & MYS over this period? D. What is the relationship between EYS and MYS at any point in time? Why do you think this is the case? We have seen steady growth in both EYS and MYS over this time period, with comparatively more growth in EYS than MYS. The EYS is directly correlated with the MYS. The MYS is a real value based on actual data, the mean years of schooling adults 25 and over have. Because the EYS is a prediction meant to apply to children entering schooling at age 6, this projection is based upon "prevailing patterns of age-specific enrollment rates," a factor that increases the EYS and MYS concurrently, showing a strong correlation between the two.

6 E. What has happened to the difference between EYS and MYS over this period? Why do you think this is the case? F. Now let’s turn to the sub -indices and the overall HDI. In your Excel spreadsheet, calculate the value of each of the sub- indices and the HDI in each year. Generate a time-series graph that includes four curves, one for each of the three component indices: I(LE), I(E), I(GNI) and one for the overall HDI over the period 1990 – 2021. Title this plot “Figure 2B: PNG’s HDI over time.”. Shade I(HDI) red and increase I(HDI)’s width to 3pt so that it stands out from the components. Figure 2B: PNG ’ s HDI over time EYS has increased at a higher rate than MYS. One theory for why this may be is that, even if the EYS is accurately predicting expected years of schooling for children entering academia, the MYS takes into account ALL persons mean years of schooling over the age of 25, a much larger sample size than children age 6. Therefore, even as students have (according to the EYS) been attending school for more years, their statistical impact on the real value of the MYS is "watered down" in the sense that the increases present less impact in the final mean calculation due to the larger pool of adults over 25.

7 G. Interpretation. Comment on the trend of HDI in Papua New Guinea over the 1990 – 2021 period. Which component indices seem to be the most critical drivers of change over this period? Question 3: Purchasing Power Parity To make meaningful comparisons of GDP per capita between two countries, we need to make sure GDP in both countries is converted into a common currency, usually USD . One option to make this conversion is to use the official exchange rate (OXR). 2 For example, using the OXR , the GDP per capita of Namibia and Switzerland were $5,129 and $84,122 in 2019, respectively 3 . Can we say that the Swiss were 16.4 times richer than Namibians in 2019? Not so fast! In this problem, we will see the importance of accounting for price differences between two countries to account for each country ’ s real purchasing power of income. The PPP exchange rate accounts for differences in relative prices and thus provides a better measure to compare living standards across countries. Table 3.1 contains the local currency prices of rice, a restaurant meal (for one person), and an iPhone as well as expenditure shares on these three goods for three countries . To keep things simple, we assume that the expenditure shares are the same in all countries. Table 3.1. Expenditure Shares and Local Prices Item Expenditure Share Prices in local currencies Colombia Uganda USA Rice (1 kg) 0.70 4,000 COP 5,000 UGX 2.2 USD Restaurant meal 0.20 39,000 COP 18,000 UGX 23 USD iPhone 0.10 4,342,140 COP 3,200,000 UGX 750 USD COP: Colombian Peso; UGX Ugandan shillings; USD: US Dollar A. According to the World Bank, in 2021, the official exchange rates were as follows: 1 USD = 4,257 2 The official exchange rate is the number of units of the local current that is needed to buy one US dollar. 3 See data from section 1 if curious. In the graph, we see 4 lines, in decreasing order they are HDI, GNI, EI, and LEI. The similarity between the slope of the HDI and the other factors tells us which factors are the most critical drivers of change. For instance, we see that the slope of the GNI and HDI are quite similar over the 30 year period, indicating that GNI is a critical driver of change over this period. Alternatively, w see that the slope for the LEI is very small and does not greatly mirror that of the HDI, showing us that LEI is not a critical driver of change over this period. The EI is somewhere between these two, having a slope more like the HDI compared to LEI but less compared to GNI, showing that it is somewhat a driver of change, just not as consequentially as GNI.

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8 COP and 1 USD = 3,661 UGX. Fill in the empty cells of Table 3.2 by converting the price of Rice, Restaurant Meal, and iPhones in Colombia and Uganda to USD using these official exchange rates. Report your answer to two decimal places. Table 3.2 Prices in USD Item Colombia Uganda USA Rice (1 kg) 2.2 USD Restaurant meal 23 USD iPhone 14 750 USD B. Discuss Table 3.2. Where are prices relatively higher? For which goods? Why do you think this is? (Remember the two potential explanations for differences in the price of a given good or service across countries). C. Fill in the empty cells in Table 3.3 using information from Table 3.1 and Question 3A. Column (C) uses column (B) to calculate GDP per capita as a percentage of GDP per capita in the US using the official exchange rate ( O XR). Column (F) uses column (E) to calculate GDP per capita as a percentage of GDP per capita in the US using the PPP XR. In columns (C) and (F), enter your answers as fractions between 0 and 1 with four decimals. The pdf form will automatically convert your answers to percentages. For example, if you enter 0.2673, your answer will appear as 26.73%. Finally, n ote that column D calculates the PPP XR in each country using the information provided earlier in question 3. You should NOT try to find a PPP exchange rate online or from the World Bank website. 3 0.94 1.37 9.16 4.92 1,020.00 874.08 Rice is relatively more expensive in the United States than in Colombia or Uganda. Because rice is a trade-able good, we assume that the difference in price could be due to costs associated with trade, such as transportation, taxes/tariffs, subsidies, etc. In the case of a restaurant meal, It is still the most expensive in the US, with Uganda being by far the least expensive. Because a restaurant meal is not a trade-able good, its price will be much higher in richer countries due to increased costs of inputs such as the ingredients, but most notably the cost of labor and real estate that get factored into the price of the meal (which are much lower in poorer countries). The iPhone is most expensive in Columbia, being 270 USD more expensive than in the US. Even though the iPhone is a tradeable good, the price could be higher due to unforeseen costs such as taxes and tariffs or transportation fees.

Table 3.3 Income Comparisons with Official versus PPP Exchange Rates Country (A) 2020 GDP per capita in local currency (LCU) (B) 2020 GDP per capita in USD using O XR (C) 2020 GDP per capita as a % of US using OXR (D) 2020 PPP XR (E) 2020 GDP per capita in USD using PPP XR (F) 2020 GDP per capita as a % of US using PPP XR US 63,543 USD 63,543.6 1 00% 1 63,543.6 1 00% Colombia 22,580,405 COP Uganda 3,722,000 UGX C. Compare columns C and F. Discuss the implications of converting income per capita to USD using the official exchange rate versus the PPP exchange rate. i.e., do Colombia and Uganda seem more or less poor (relative to the US) when you use the official exchange rate compared to the PPP exchange rate? Why? END 4 4 Again, as always, the TAs and the professor are here to help. So, if anything is not clear, please ask during the discussions or Office Hours. Good learning! 5,304.3 8.30% 2,370.8 9,524.4 14.90% 1,016.7 1.60% 2,174.1 1,712.0 2.70% When you use the OXR, Colombia and Uganda both seem realtively poorer compared to the US than when you use the PPP XR. When you use the PPP XR, both the GDP per capita in USD and the % share of US GDP are higher compared to using the OXR. This is because there are price differences in goods across different countries, meaning that 1 USD has more purchasing power in a lower income country than in the US. PPP XR accounts for this by taking into account the expenditure shares of these different goods as well as the price differences across countries, making comparisons of how well-off people are on average in these countries much more meaningful.

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