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posted on august 29 2014 by dvollrath 3 note the growth economics blog has moved sites click here to find this post at the new site nearly all cross country work on growth and development uses if only for motivation penn world table pwt estimates of real gdp for countries and the pwt generates a single measure of real gdp for each country how do they do this before i answer let me say that much of what i m going to say is said more thoroughly in deaton and heston 2010 so check that out if you re into cross national real gdp comparisons to start let s simplify and think just about two countries a and b to compare real gdp in the two countries we d want to value the quantities of goods they produce at some common set of prices so say phones are 50 and haircuts are 10 and then for each country multiple the quantitify of phones times 50 and add the quantity of haircuts times 10 but what are the right prices to use why 50 and 10 why not 60 and 5 you can imagine that we want the prices we use to be somewhat meaningful and at least related to the observed prices in countries so here s where it gets weird we could say whatever let s just use the prices from country b i just need to pick one set of prices right but if you measure country a s gdp using country b s prices then country a will look relatively rich compared to country b this doesn t mean it makes country a look absolutely richer than country b just that country a now looks better in comparison this works if you flip them around if you measure country b s gdp using country a s prices then country b will look relatively rich compared to country a this isn t a mathematical certainty but reflects what actually happens if you use the prices underlying the pwt let s take the u s and nigeria as an example if we measure real gdp in both the us and nigeria using nigerian prices then the us will appear to have an incredibly large lead over nigeria in gdp per capita if we measure real gdp in both the us and nigeria using us prices then the gap will appear smaller as this will make nigeria look particularly good this doesn t necessarily have to happen it s not some mathematical rule but the data underlying the penn world tables shows that this is the case almost universally so what is going on it means that country a has relatively high prices for what country b has a lot of and country a has relatively low prices for what country b has little of it s easiest to see this in an example so let the us produce and the us produces a lot of phones relative to haircuts and in the us and or haircuts and phones cost the same no this doesn t have to be a realistic relative price for this to work at us prices real gdp in the us is in nigeria we have and or nigeria has very few phones but lots of haircuts and the prices in nigeria reflect this with and at nigeria s prices real gdp in nigeria is now those two numbers are not comparable because they use different absolute prices to value the goods to do a fair comparison of output in the two countries we have to use the same prices let s value nigeria s output using the us prices so using us prices nigeria looks really good their gdp is 1100 exactly equal to the us they achieve this with lots of haircuts and few phones so utility could be different in the two places but their measured real gdp is as high as the us but we could equally argue that we should use nigerian prices to value gdp in both countries so for the us we get the us now has gdp of 10 100 while nigeria at its own prices only has a gdp of 2000 the us is roughly 5 times richer than nigeria when valued at nigerian prices why because the us produces a lot of what nigerians find expensive phones and little of what they don t haircuts which comparison is right neither there is nothing that says we should use the us prices or the nigerian prices for real gdp we simply need to pick some set of prices and use them consistently across all countries so much of the work in the penn world tables is to come up with a common price index and the nature of this singular set of prices will matter a lot for real gdp comparisons if the pwt uses prices that look alot like us prices then this will make nigeria and other developing countries look relatively well off compared to rich countries but if the pwt used prices that look like nigerian prices then this will exaggerate the gap in practice what do they do they try to construct some kind of weighted average of the price of each good across all countries the weights are in the pwt are calculated using what is called a gheary khamis method which essentially weights the prices from different countries by their share of total spending on that good for phones the weight for the u s is because they produce use 91 of all the phones for haircuts the weight for the u s is because they produce use about 9 of all haircuts now in my simple example the weights are basically symmetric because the us has most of the phones and nigeria has most of the haircuts but in the real data the us has far more phones and more haircuts than nigeria so in practice in the pwt the weights are very large on u s prices and very small on nigerian prices when they do these calculations across all countries the weights on the us western europe and japan dominate because they consume most of the stuff out there in the world so the prices used by the pwt are really similar to a relatively rich western nation people have argued that the prices roughly correspond to italy s which all means that every country in the pwt is getting valued at rich country prices as we saw above this inflates the real gdp of very poor countries and makes them look good compared to rich countries that is the gap between the u s and nigeria is much smaller using rich country e g us prices than nigerian prices so the pwt overall makes poor countries look very good the true gaps in real gdp are likely larger much larger than what the pwt captures this is not some kind of deliberate subterfuge by the pwt it does what it says on the tin is a phrase that comes to mind but that doesn t mean it has some cosmic truth to it the pwt isn t doing anything wrong but they are running up against the real fundamental problem there is no set of prices that gives us a true measure of real living standards across countries what we d like is some number that tells us that living standards in nigeria are one tenth or one twentieth or one fifth of those in the u s but what do you mean by living standards no measure of real gdp captures actual welfare even if as we d assume was the case in a perfectly competitive market relative prices capture relative marginal utilities real gdp doesn t measure welfare multiplying the total quantity times the marginal utility of a good doesn t tell me anything about the total utility that people enjoy from that good the marginal utility of a 3rd car in my family is essentially zero but that doesn t mean that we get no utility from having 2 so even if there were some right set of prices we could use to value real gdp it still wouldn t measure welfare i think what would be useful for the pwt would be to have the full distribution of real gdp estimates for a country that is show me nigeria s real gdp valued at the prices found in every single other country in the pwt i could plot that distribution of real gdp s in nigeria against the same distribution of real gdp s for the u s this would at least show me something about the noise in the relative standing in real gdp for these countries this sounds like something i can make a grad student do one last note about these comparisons recall that the result that measuring country a s gdp in country b s prices makes country a look relatively rich is not a certainty it holds because there is a specific correlation of prices and quantities in the data in each country goods that are produced in large quantities e g haircuts in nigeria tend to have low relative prices and goods produced in small quantities e g phones in nigeria tend to have high relative prices in other words price and quantity are negatively related this implies that the main differences between countries are supply differences not demand differences if nigeria didn t have a lot of phones because nigerians didn t like phones then phones in nigeria would be cheap compared to haircuts and then valuing nigeria s output at the u s prices which also has cheap phones compared to haircuts wouldn t make nigeria look so rich it might make them look poorer in fact so the empirical fact that valuing nigeria s output at u s prices makes nigeria look relatively rich is evidence that nigeria and the u s have different supply curves for phones and haircuts not different demand curves yes demand is probably different too but relative to supply differences these appear to be small share this share on x opens in new window x share on facebook opens in new window facebook share on reddit opens in new window reddit email a link to a friend opens in new window email like loading posted in uncategorized tagged development empirics pwt real gdp 3 replies measuring real gdp posted on june 23 2014 by dvollrath 1 note the growth economics blog has moved sites click here to find this post at the new site this morning angus deaton and bettina aten released an nber working paper gated sorry about understanding changes to international measures of real gdp and poverty that occurred following the release of a new round of price indices from the international comparison project icp price indices methodological nuance i know ideal subject matter to drive my web traffic to zero for those of you still here thanks mom the paper by deaton and aten is a great chance to understand where comparisons of real gdp across countries come from and to highlight that these comparisons are inherently imprecise and should be used with that in mind the basic idea of the penn world tables or any other attempt to measure real gdp across countries is to compute the following where is the real gdp number we want is the nominal gdp reported by a country and is the purchasing power parity price index for that country while there can be severe issues with the reporting of nominal gdp particularly from poor countries with a bare bones or no national statistics office the primary concern in these calculations is with the think of as the cost of one bundle of goods in country so dividing nominal gdp by gives us the number of real bundles that a country produced if we do that for every country we can compare the number of real bundles produced across countries and that crudely captures real gdp the icp produces these measures of for each country i m going to avoid the worst sausage making aspect of this because it involves lots of details about surveys to find prices for specific goods how to get the right average price for each good and then how to roll those back up to for each country the important thing about the methodology for computing is that there is no right way to do it there are methods that might be less sensible i e let be the price of a can of diet coke in a country than what the icp does but that doesn t imply that the icp is correct in some absolute sense it also means that the icp can and does change methodology over time the paper by deaton and aten works through the changes in methodology from 1993 5 to 2005 to 2011 and how we measure real gdp the tentative conclusion is that the 2005 iteration of the icp probably was over stating the levels for many developing african and asian countries from the equation above you can see that over stating the means under stating real gdp so in 2005 we were likely too pessimistic about the economic conditions in a lot of these developing countries chandy and kharas found that using the 2005 values of implied that 1 215 billion people in 2010 lived below the world bank s 1 25 per day poverty line using the 2011 values of instead there are only 571 million people living below 1 25 per day that s a reclassification of some 700 million people their domestic income stayed the same but the 2011 icp suggests that they were paying lower prices for their bundle of goods than we assumed in 2005 and hence their real income went above 1 25 but as i said before these are tentative conclusions because there is no way of knowing this for sure deaton and aten s conclusion is that the 1993 5 and 2011 rounds of the icp seem more consistent with each other and 2005 looks like an outlier so just to keep things comparable over time we should probably avoid the 2005 numbers but again who knows it s quite possible that mankind s true welfare is measured in the number of cans of diet coke that we can produce measuring real gdp or global poverty levels is to put it kindly a fuzzy process there is not the right method for this as you can see the measurements can be pushed around a lot by differences in methodology that are inherently trying to make apples to oranges comparison i mean that literally how do you value apples compared to oranges in national output what s the right price it s different in washington florida and wisconsin so how do you compare the total real value of fruit consumption in different states or countries the implication is that we shouldn t be asking real gdp measures or poverty line measures to do too much for really crude comparisons real gdp from the penn world tables is fine the u s has higher real gdp per capita than kenya and the penn world tables pick that up is it a 40 1 ratio a 35 1 ratio a 20 1 ratio not entirely clear different methodologies for computing in the us and kenya will yield different results but is it really important if it is 40 1 versus 20 1 in either case it is clear that kenya is poorer we can go forth and try to explain why or make some policy advice to kenya to help close the gap or go to kenya to work on interventions to alleviate poverty there where these real gdp comparisons or poverty line counts should not be used is in finer grain comparisons is kenya s real gdp per capita lower or higher than lesotho s according to the penn world tables in 2011 kenya s was lower but should we do any kind of serious analysis based on this no the difference is as likely to be from discrepancies in how we measure for those countries as from real economic differences in capital stocks human capital technology or institutions real gdp comparisons are best thought of as similar to baseball stats the top career ops on base plus slugging percent players are babe ruth ted williams lou gehrig barry bonds and other names you might recognize players like albert pujols and miguel cabrera are in the top 20 giving you a good idea that these guys are playing at a level similar to the greats of all time you can t use this career ops to tell me that pujols is definitively better than stan musial or definitively worse than rogers hornsby but career ops does make it clear that pujols and cab...
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