Development and Growth Facts

Transcription

1 Development and Growth Facts Ths chapter documents some of the key development and growth facts that need to be explaned. In dong so, t frst descrbes the methods that have been used to compare nternatonal ncomes, and the data sets that have been constructed usng these methods. It then documents the long-run propertes of these data- the so called Development and Growth Facts. I. The Data on Internatonal Outputs A sngle naton s Gross Domestc Product (GDP) or Gross Natonal Product (GNP) s reported n ts own natonal accounts n unts of ts own currency. Obvously, t makes no sense to compare the GDP of dfferent economes measured n ther own currences. For nstance, you cannot tell whether Japan s more productve than the Unted States f you are only told that Japan s 2003 GDP s 590 trllon yen and the U.S. s 2003 GDP s 4.5 trllon dollars. Obvously, comparsons can only be made f the two measures are expressed n the same unts. Hstorcally, there are two methods that have been used to convert ndvdual country s GDP measures nto a common currency: the exchange rate method and the purchasng power party (PPP) method. The mportant pont that we wll establsh s that the PPP method s superor to the exchange rate method because the former ensures that the same prces are used to wegh the quanttes of goods produced n each country whereas the 1

2 latter does not. Usng the same prces s the key to generatng accurate measures of ncome dfferences across countres. 1.1.a The Exchange Rate Method We begn wth the Exchange Rate Method, whch has a longer hstory relatve to the PPP method. To begn, let us wrte the GDP of a country n year t n ts own currency as (GDP OC) GDP t J j1 p x, where J s the number of fnal goods and servces produced n the economy, p s the prce of good j n country, and x s the quantty of good j produced n country. Remember that GDP only consders fnal goods and servces, so that t s the meanng of x. The exchange rate method s straghtforward. It take each country s output n domestc prces gven by equaton (GDP OC) and multples t by the exchange rate of ts currency wth the US dollar so as to convert the measure nto US dollars. More specfcally, let et denote the exchange rate of a country s currency wth the US dollar n year t,.e., $ s per unt of domestc currency. Then the dollar equvalent output of country s e t = (GDP Ex) e GDP t t J j1 e p t x The exchange rate method s smple to mplement, but does t generate accurate estmates of output dfferences across countres? In order to make accurate comparsons of output across countres, a method must ensure that the same prce s used to value the quantty of each partcular good n each country. Wth respect to the exchange rate method, the 2

3 procedure wll produce relable comparsons only f the dollar equvalent prce of the good s the same for all countres, namely f, e p p for each good j=1, 2,3,,,,J. t US Ths relaton s known as the Law of One Prce. It s based on the dea that n a frctonless world wth no trade costs and perfectly compettve markets, arbtrage opportuntes would equate the dollar prce and the dollar equvalent prce of the good n the foregn country. In a frctonless world, the arbtrager could make nfnte profts by buyng the good n the low-prce locaton and sellng t n the hgh prce locaton. Of course, the world s not frctonless. There are real costs to movng goods. Some goods and servces are too costly to move, and hence are traded nfrequently. Harcuts are an extreme example of ths. Moreover, most markets are not characterzed by perfect competton and free entry. Entry n many markets s artfcally restrcted and n others t requres huge costs assocated wth settng up dstrbuton centers and retal outlets. Not surprsngly, the data does not support the law of one prce. Ths falure s dramatcally dsplayed n the Bg Mac Index that has been compled by the Economst snce In 2012, for example, the dollar prce of a Bg Mac n Swtzerland was $6.81, n the U.S. $4.20 and n Thaland $2.46. As a result, the exchange rate method mples that dfferent prces are used to value the same good n dfferent countres. Consequently, comparsons of nternatonal ncome levels that are based on the exchange rate method are not very relable. Addtonally, 3

4 there s a bas assocated wth the exchange rate method that actually makes poor countres appear even poorer than they actually are. The reason for ths bas s that the law of one prces tends to be volated n a systematc way n the case of non-tradeable goods and servces wth, e p p. Consequently, non-tradeables n poor countres t Poor Nt US Nt are gven a smaller weght compared to non-tradeables n rch countres. The problem s exacerbated by the fact that most of a poor country s output conssts of non-tradeables. Ths makes poor countres look poorer than they actually are. 1.1.b Purchasng Power Party In contrast to the exchange rate method, the Purchasng Power Party (PPP) method guarantees that the same prce s used to value the quanttes of a good n dfferent countres. Ths explans the current domnance of ths approach among data collectng nsttutons. For example, The Organsaton of Economc Co-operaton and Development (OECD), the Internatonal Monetary Fund n ther World Economc Outlook database and the World Bank n ther World Development Indcators all provde PPP adjusted estmates of GDP. If we go back to the Bg Mac example from above, the purchasng power party essentally gves us the exchange rate between two countres that guarantees that the dollar equvalent prce of a Bg Mac s the same n both countres, or that guarantees you can buy the same quantty of the same good or servce n each country. Thus, f a Bg Mac sold for 1 n Germany and $5 n the Untes States, the purchasng power party rate s 1 Euro to $5. The Bg Mac Index table reports purchasng power party rates. As you 4

5 can see, these PPP rates n the Bg Mac Index table are expressed n terms of local currency to US dollars, so n the above example, the PPP rate would be.20 /$. Although the dea of purchasng power party rate s straghtforward, there are several deep ssues related to prce ndex theory that make applyng ths concept to output measures challengng. Returnng to our Bg Mac example, whereas t s straghtforward to fgure out the purchasng power partes for Bg Macs between any two countres, t s less so when we need to consder all the goods n the economy, as we need to do here. In truth, there s no unversally accepted PPP ndex out there; there are many PPP ndexes, each wth ts vrtues and defcences. In what follows, we descrbe the Purchasng Power Partes that are based on the Geary-Khams method as these are the ndexes that underle the constructon of the two man databases on nternatonal ncomes. The Gheary-Khams method calculates both a PPP ndex for each country as well as a set of world prces. The PPP of a country s essentally the rato of ts GDP evaluated at domestc prces to ts GDP valued at world prces, and the world prce of a good s the essentally a weghted average of the dollar equvalent prce of the good n each country, where the weghts are each country s share of total world producton of that partcular good. The prce and quantty data that are the key nputs n these calculatons are collected by the Internatonal Comparsons Project (ICP). The world prces of each good are fundamental to computng the PPP adjusted GDP measures for each country. For our purposes, t s not mportant that we know the method 5

6 for computng world prces. Once they have been computed, the procedure to construct PPP adjusted GDP nvolves three steps. For descrbng these steps, t s useful to ntroduce some addtonal notaton. Let E denote the nomnal expendtures on a good j (say apples) n country (say Japan) at date t. The steps that are used n the PPP approach s 1. Take total expendtures of good j n country, E, and dvde ths by the prce of good j n country, p to arrve at the quantty of good j, x. 2. Multply the quantty of good j n country by the world prce of good j, W p to obtan the value of the good n the world prce, p. W x 3. Repeat ths procedure for all goods and servces n country and sum these values to get P.P.P. adjusted output for country, namely, J j1 W p x. In ths way, the method guarantees that the same prce s used to value the quantty of a gven good n each country. Consequently, the ncome comparsons made wth the PPP method are far more accurate compared to the exchange rate method. 1.2 Databases Two data sources of PPP adjusted nternatonal ncomes domnate the emprcal growth and development lterature. The frst was started by Robert Summers and Alan Heston at 6

7 the Unversty of Pennsylvana and s referred to the Penn World Tables (PWT). 1 The second was started by Angus Maddson of the Gronngen Growth and Development Centre and s referred to as the Maddson Project (MP). The man dfference between the two data sets s that the PWT data cover the post 1950 perod for almost every country n the world whereas the MP provdes estmates for GDP gong back far earler n tme (bascally 1820) for a large number of countres. Through the years, the MP dataset has been modfed to nclude estmates for more and more countres gong further back n tme. As such, t has come to be more frequently used. Lke the PWT, the MP covers most every country over the post World War II perod. For most countres, there s lttle dfference between the GDP estmates n the PWT and MP. The one excepton s Chna. In 1952, the MP estmate for Chna s per capta GDP s 5.3 percent of the US level whereas the PWT estmate puts Chna to be at 2.7 percent of the US level. As you can magne, the PPP method s an extremely labor ntensve procedure, as t must be appled to each good n each country at each pont n tme. Obvously, there s a lmt to the amount of dsaggregaton of goods, so all goods must be lumped nto some broadly-defned category. Stll, the number of categores s large. For nstance, n the PWT there are 1,600 categores of goods, wth 1,200 of these beng consumpton goods and another 400 beng nvestment goods Per Worker vs. Per Capta measure 1 In the latest verson of the Penn World Tables, PWT 6.2, Bettna Aten has been added as a contrbutor. 7

8 Most comparsons of output between countres (and across tme wthn a gven country) are made on a per capta bass or a per worker bass. The per capta measure, whch s obtaned by dvdng a country s GDP by ts populaton, s a proxy for the average lvng standard and the overall well-beng of the country. The per worker measure, n contrast, whch s calculated by dvdng a country s GDP by ts workforce, s a measure of labor s productvty. Addtonally, for rch countres, comparsons are often made on a per work hour bass. Ths s calculated by takng a country s GDP and dvdng t by the total hours ndvduals. Ths s an even more nformatve measure of labor s productvty. Rankngs of countres can dffer between measures. For nstance, a country can have a low per capta GDP but a very hgh per worker GDP f unemployment s hgh or f the populaton conssts of a large fracton of chldren. Smlarly, t can have a hgh output per worker but a low output per work hour f labor works long hours. The Unted States, n fact, has the hghest GDP per worker n the world, but not the hghest output per work hour. Norway, France, and Belgum each have hgher labor productvtes measured by output per work hour. Workers n these countres do not produce as much n a day, however, because they work fewer hours than ther US counterparts. Why ndvduals n Europe work fewer hours than Amercans s an nterestng queston that we wll address later n ths book. 8

9 II. Some Key Development and Growth Facts Now that we understand the data, we can proceed to document the pattern of development over the last two thousand years. A lst of the key development and growth facts s: Pror to 1700, lvng standards were constant over tme and dd not vary much across countres. The factor dfference n per capta ncome across countres was more on the order of 2. Around 1700, England began to experence sustaned ncreases n per capta output. Intally, these ncreases were rregular and modest n sze, but after 1900 these ncreases became regular wth a doublng of per capta ncome every 35 years. Other countres started to experence ncreases n per capta ncome shortly after England. These countres nclude many Western European natons and the ethnc offshoots of England. Countres have dffered dramatcally n the date they have started to experence sustaned ncreases n ther lvng standards. Some countres, partcularly located n sub-sahara Afrca have only now begun to experence ncreases n ther lvng standards, although these ncreases are rather modest n sze and farly rregular. On account of these dfferent startng dates, the dsparty n nternatonal ncomes ncreased dramatcally snce 1700, especally untl Snce 1950, the dsparty n nternatonal ncomes has not ncreased by as much. By 1950, most countres n the world had started the process of 9

10 economc growth. Some of these late starters have elmnated a large fracton of ther ncome gap wth the ndustral leader over ths perod. Growth mracles are a relatvely recent phenomenon and are lmted to countres that were poor at the tme ther mracles began. There seems to be an advantage assocated wth beng a later starter. Late starters typcally have been able to double ther ncomes n far less tme compared to earler starters at comparable startng ncome levels. Let us look at these facts more closely. 2.1 Pre-1700 Stagnaton Pror to 1700, lvng standards were constant over tme and dd not vary much across countres. Fgure 1 plots per capta ncome of the leader country datng back to 2000 B.C. Up untl 1700, the lvng standard of the leader country, or any other country for that matter, dsplayed no secular ncrease. Between 1580 and 1920, the rchest country n the world was the Netherlands; form 1820 to 1890, t was England; and thereafter t has been the Unted States. Durng ths tme, the lvng standard was sgnfcantly above the subsstence level. In 1688, for example, the poorest quarter of the populaton n Englandthe paupers and the cottagers- survved on a consumpton level that was roughly onefourth the natonal average. A few socetes, such as the Roman Empre n the frst century, the Arab Calphates n the tenth century, Chna n the eleventh century, and Inda n the seventeenth century realzed some ncrease n ther per capta ncomes. However, these ncreases were not sustaned. Why these countres were unable to sustan these 10

11 ncreases s an nterestng queston that has receved a good deal of attenton among economc hstorans. We do not take ths queston up n ths book however. Technology was not stagnant over any part of ths perod. Economc hstorans, partcularly, Joel Mokyr (1990), have documented a steady flow of technologcal nnovatons n ths 2000 BC to 1700 AD perod. Yet, these nnovatons dd not translate nto ncreased lvng standards. Instead, they translated nto ncreased populatons; as total output ncreased, the populaton adjusted so as to mantan a constant level of per capta output. Ths s shown n Fgure 2, whch s taken from Robert E. Lucas s 2002 book, Lectures n Economcs. Fgure 2 plots world populaton and world output from 1000 AD to 2000 AD taken from Madson. Up untl 1700, the two curves are ncreasng but parallel, reflectng the constant lvng standard. Fgure 1: The Leader s Per Capta GDP Relatve to Pre-1800 Level bc 1000 bc

12 Fgure 2: World Populaton and Output 2.2 Post-1700 Development and Growth Only after 1700 do we see an ncrease n per capta output n the world. Ths s shown n both Fgures 1 and 2. Fgure 2 makes apparent that total output started to ncrease faster than the rate of populaton growth around then, mplyng an ncrease n the world s lvng standards. Economc growth, that s sustaned ncreases n per capta output, s a very recent hstorcal phenomenon! 12

13 The frst country to experence sustaned ncreases n per capta Dynamc Presentaton of the Evoluton of nternatonal ncomes. Modern technology can be a most useful tool n teachng. Check out ths youtube vdeo by Hans Roslng called 200 Countres, 200 years, and 4 Mnutes- The Joy of Stats. Who s Hans Roslng by the way? Dr. Roslng s a professor of Internatonal Health at Karolnska Insttute n Stockholm. In addton to beng a lcensed physcan, Dr. Roslng holds a Ph.D. and has been actve n researchng malnutrton and dsease outbreak n sub- Sahara Afrca. He s also cofounder of the Gapmnder Foundaton that developed the Trendalyzer software used n the vdeo. output was England- a so called ndustral revoluton. Hstorans date the start of ths growth n per capta output around Over the next 150 years, these ncreases n the leader country were modest n sze and rregular. However, snce 1900, these ncreases have been larger and farly rregular wth per capta ncome doublng roughly every 35 years. Ths s what Smon Kuznets called modern economc growth. Western Europe and the ethnc offshoots of England (.e., the Unted States, Canada, Australa, and New Zealand) were next to experence sustaned ncreases n per capta output. Other countres were much later n ther startng dates. For example, Fgure 3 shows the date at whch economc growth started n Japan, Brazl, and Inda. As can be seen, Inda dd not start to experence ncreases n ts per capta output untl well after Japan s the earlest starter of these three countres shown n Fgure 3, wth a startng date of 1870, nearly 150 years after England. Even wthn a regon there s a great deal of dsparty n startng dates. Fgure 4 shows how very dverse these dates are among Asan countres. Bangladesh s even later than Inda n ts start. Chna starts somewhat earler, around

14 As a result of these dfferent startng dates, dfferences n lvng standards wdened between countres, especally between 1750 and In 1950, for example, the average country n Afrca was 1/12 th as rch as the Unted States n terms of per capta output. Sub-Sahara Afrca countres tend to be even poorer. In 1950, the poorest countres n sub- Sahara Afrca had a per capta output around 3 to 4 percent of the US level. In 2000, these dfferences were even larger, wth the poorest of these countres havng a lvng standard whch s below 2 percent of the US level. Fgure 3: Dfferent Startng Dates 32,000 16,000 8,000 4,000 Leader Japan 2,000 Brazl 1,000 Inda Fgure 5 presents the tme path of per capta output relatve to the leader grouped by regons of the world, and thus provdes a more comprehensve pcture of the evoluton of nternatonal ncomes snce In general, Latn Amerca started modern economc 14

15 growth n the frst part of the twenteth century. For Asa, the approxmate start of modern economc growth s the mddle of the twenteth century. For Afrca, modern economc growth has yet to start; although per capta ncome has ncreased n many Afrcan natons, snce 1960, the ncreases have been rregular, and clearly less than the ncreases n the leader, the Unted States. Interestngly enough, t s only after 1950 that the path of Asa and Afrca dverge. Fgure 4: Dfferent Startng Dates for Selected Asan Countres 1 Japan 1/2 Tawan Korea 1/4 1/8 Chna Indonesa 1/16 Inda 1/32 Bangladesh 1/ Fgure 6 gves a more complete pcture of today s dsparty n per capta ncome levels. Fgure 6 shows a bar graph depctng the number of countres wth 1995 per capta GDP wthn a gven range of the leader. These ranges or bns are [1, 1/2], [1/2, 1/4], [1/4, 1/8], [1/8, 1/16], and [1/16, 1/32], and [1/32, 0]. The data s taken from the Penn World Tables. In 1995, there were more extremely poor countres, countres n the [1/32,0] bn than n rch countres, countres n the [1,1/2] bn. 15

16 Fgure 5: Evoluton of Internatonal Income Levels (Fracton of Leader) West ern Europe 1/2 Lat n Amerca 1/4 A s a 1/8 Af rca 1/

17 Number of Countres Fgure 6: Dstrbuton of Countres' Per Capta Income Relatve to U.S.: /32 to 1/16 1/16 to 1/8 1/8 to 1/4 1/4 to 1/2 1/2 to 1 Fracton of U.S. Level Some countres and regons have dramatcally reduced ther ncome gap wth the leader subsequent to startng modern economc growth. Ths s apparent n Fgure 5. For example, n the postwar perod, Western Europe managed to elmnate much of ts ncome gap wth the Unted States, the leader snce Asa s another regon that has been catchng up to the leader n the postwar perod. Chna and Inda, whch dd not begn to experence ncreases n per capta GDP untl well after 1950, have elmnated some part of ther gap wth the Unted States snce Chna n 1980 was at 5 percent of the US level. In 2000, t was at 10 percent. Inda n 17

18 1980 was at 6 percent of the US level and subsequently ncreased to 8 percent of the US level n Wth growth there, the lvng standard of the average person lvng n ths world has ncreased both n absolute terms and relatve terms. The catch-up Asa s also due to the growth mracles experenced by Japan, South Korea, Tawan, Hong Kong, and Sngapore. The catch-up between the Unted States and Japan s shown n Fgure 7. It s clear from Fgure 7 that Japan dd not return to ts pre-world War II path. Not all countres have elmnated ther gap wth the leader after startng modern economc growth. Latn Amerca s one regon that has mantaned the same relatve ncome level of 25 percent of the US level over the last century. Sub-Sahara Afrca has not elmnated any of ts gap ether. It has fallen further behnd the leader over the post perod. Most of the countres there have realzed some ncrease n ther lvng standard over ths perod, but lost ground relatve to the Unted States as these ncreases have been smaller than the ones realzed by the Unted States n ths perod. The growth mracles experenced by Japan, South Korea, Tawan, Hong Kong, Sngapore, and most recently Chna n the post 1950 perod are unprecedented. These countres were able to double ther ncomes n a decade or less. In terms of growth rates, these countres per capta GDPs grew on average at more than 6 percent per year. 18

19 Fgure 7: Trends n Output per Capta (1990 $US) U.S. 8 Japan These growth mracles are a recent phenomenon; no country was able to double ts ncome n a decade or less before Addtonally, these mracles are lmted to countres that were poor relatve to the ndustral leader at the tme ther mracles started. We have never observed the leader or a country wth an ncome gap less than one half the leader s, double ts per capta ncome n less than a decade. Ths suggests that there s an advantage assocated wth beng a late starter, somethng noted by Alexander Gerschenkron n Late starters do seem to have an advantage over earler starters. Fgure 8 documents ths general pattern. It plots the number of years t took a country to go form 10 percent to 20 percent of the 1985 US per capta GDP level versus the frst year that the country acheved the 10 percent level per capta GDP was 20,000 n 1990 dollars. The dfference n the length of doublng perod between the set of late starters and the set of 19

20 earler starters s dramatc. For early starters, whch are those achevng 10 percent of the US level before 1950, the medan length of the doublng perod s 45 years. For late starters, defned as those achevng 10 percent of the 1985 US level after 1950, the medan length of the doublng perod s 15 years. The choce of the startng level n unmportant. A smlar pattern emerges when the startng level s fxed at 5 percent or 20 percent of the 1985 US level. Fgure 8: Years for Per Capta Income to Grow from 2000 to 4000 (1990 $US) 80 IRE N.Z. NETH U.K. BEL U.S. AUSTRA AUS FRA DEN SWI CHIL JPN CZE FIN CAN NOR S.A. COL PERU PORT BUL TUR JOR P.R. TAIW III. Concluson Today, huge dsparty characterzes the dstrbuton of nternatonal ncome levels. Three-hundred years ago, ths dsparty was small. We know that the rse n ths dsparty s the result of dfferent countres startng to grow at dfferent dates. Why some 20

21 countres started to grow earler than others s a crtcal queston we shall want to address n the next chapters. Subsequent to startng to grow, the experence of late starters has vared dramatcally. Some countres, especally those located n Asa, have elmnated much of ther gaps wth the early starters. Some countres, partcularly, those located n Central and South Amerca have not elmnated any part of ther gap wth the leaders over the last century. Some of the countres that have elmnated much of ther gap wth the leader were able to double ther ncomes n a decade or less. These growth mracles are a very recent phenomenon and are reserved to poor countres. Ths suggests there s an advantage to beng a late starter. Indeed, analyzng the data over the last three centures, we see that late starters have been able to double ther ncomes n far shorter perods of tme. Of course, not all late starters have bettered early starters n ths regard, but t does suggest a possblty that never exted earler. For sure, there are stll a large number of countres that reman extremely poor today. However, a consequence of the catch-up that has occurred n the post World War II perod, partcularly n Chna and Inda where most of the world s populaton lves, s that the welfare of the average person n the world has ncreased dramatcally over the last 50 years. Ths s shown n Fgure 9, whch s taken from Lucas (2002). Fgure 9 plots the dstrbuton of ncome across people n the world. In contrast to the other fgures n ths chapter, ths fgure does not use the country as the bass for the GDP measurement. The estmates n ths fgure take each country s per capta GDP and multply that number by 21

22 the country s populaton. Ths then allows us to determne the number of people n the world wth a certan lvng standard. Thus, Fgure 9 shows the dstrbuton of ncome across people n the world, rather than the dstrbuton across countres. Snce 1960, there has been a large decrease n the number of people wth per capta GDP between $500 and $ US dollars. Yes, there s stll a large number of people lvng n poverty, but the good news s that ths number s fallng. Fgure 9: Dstrbuton of World Income 1960 and

23 References: Alexander Gerschenkron, Economc Backwardness n Hstorcal Perspectve: A Book of Essays. Cambrdge, MA: Belknap Press of Harvard Unversty Press, Lucas, Robert E Lectures on Economc Growth. Cambrdge and London: Harvard Unversty Press. Mokyr, Joel (1990). The Lever of Rches: Technologcal Creatvty and Economc Progress. Oxford: Oxford Unversty Press. Problems: For these problems you wll need to download data from the PWT7.1 data set. The address s 1. Determne the relatonshp between savngs rates and per capta ncomes n 1960 and To do ths, you wll need to download for all countres the varable c and y n both 1960 and 2000 n the PWT7.1. The varable labeled c s the nvestment share of GDP (.e. savngs rate) and the varable labeled y s per capta GDP of a country expressed relatve to the US level n percentage terms. Thus f y=50 n the data, t means that country has a per capta GDP n 1960 that s ½ the US level n that year. Hand n a scatter plot for 1960 and Also calculate and hand n the correlaton coeffcent for savng rates and ncome levels n 1960 and Note: I suggest you download the data n two steps. The frst s for 1960 and the second s for To mport nto an excel fle, you should Select "CSV" and clck on the "Send" button. Once the data s produced for you, copy t wth your browser. Open up excel and paste. Now clck on the data headng and then clck on the Text to Columns opton. On the frst page, make sure delmted opton s checked, then clck the next button. On the next page, check the tab and comma optons. Clck Next and then Clck Fnshed. Repeat ths for the 2000 download. 2: Calbrated Solow Model. Next calculate the average annual populaton growth rate for each country between 1960 and If ether the 1960 or 2000 data s mssng, use the frst the years closest to these years for whch data s avalable. For ths you wll need to download the varable labeled POP n the PWT7.1. Now use the savngs rate for 2000 for each country you mported n Queston 1. Assume all countres have the same deprecaton rate δ=.05, the same rate of exogenous technologcal change, γ=.02, and the same TFP parameter A=1. Use the formula for the rato of the balanced growth path per BGP BGP capta output for the Solow model that we used n the 2/10/2014 class y, t / yus, t, where the comparson s beng made to the US. More specfcally, take the average savngs rate and average annual populaton growth rate for each country and compute ts output per capta relatve to the US level. 23

24 BGP BGP Hand n a scatter plot whch relates Solow relatve GDPs per capta 100 y and y, t / US, t actual relatve 2000 GDPs per capta (.e. y n the data). We multply Solow relatve GDP per capta by 100 so as to put t n percentage terms as s the case wth the varable y. 3. Download the varable y for each country n 1960, 1970, 1980, 1990 and Next, remove from the spreadsheet any country for whch data s mssng n one of these fve years. In dong so, you wll end up wth a balanced panel. a. For each year, calculate the standard devaton of relatve per capta GDP. Hand n a plot of the standard devaton aganst tme. b. For each year, compute the average relatve ncome of the top 5% of the rchest countres n each year. Do ths for the poorest 5% of countres as well. Hand n a plot that shows the rato of the top 5% to bottom 5% aganst tme. c. For each year, calculate the average relatve ncome. Hand n a plot that shows the average n each year. d. For each of the 5 years, calculate the medan relatve ncome. Hand n a plot that shows the medan relatve ncome. Note: You can put the plots for (b), (c) and (d) on one fgure. 4. Now download the varable rgdpch, real per capta GDP (Chan Seres) for all countres n 1960 and For those countres for whch data s avalable n both years, compute the average annual growth rates. a. Hand n a scatter plot of average annual growth rate aganst a country s 1960 the logarthm of per capta GDP. b. Hand n the names of the 10 fastest growng economes over ths tme perod, and the names of the 10 slowest growng economes over ths tme perod. 24