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version to a steady state value the mpk should be roughly a proxy for the return on capital one other rough proxy for that is the earnings yield on the s p 500 which represents how much you get in earnings for buying a unit of capital by purchasing a basket of stocks the figure below which i grabbed from brad delong s site plots this earnings yield from 1880 until today from this it seems to me that the earnings yield has a normal level of about 6 and that while there are sustained deviations from this value it always appears to head back to 6 the first figure shows that mpk has been declining from 1960 until now matching the decline in the earnings yield from rouhgly 1970 until today was the mpk just on walkabout and is coming back to its long run bgp level and no i m not terribly worried about the fact that the mpk is always higher than the earnings yield they are both proxies so the fact they don t agree on levels isn t terribly meaningful the earnings yields suggests that what is abnormal about the figure for mpk is the high values in the 60 s and 70 s not the low values now the s p evidence is consistent with that although the match up is imperfect why was the mpk so high in the 1960 s while the earnings yield didn t rise until the 1970 s regardless in this interpretation the steady state mpk has stayed roughly the same but for some reason we deviated in the 60 s and 70 s to having a high mpk perhaps it was atypical shocks to productivity over and above the regular trend growth rate or atypical shocks to population growth baby boomers and we re now coming back down to normal the caveat here is that the s p earnings yield might be a bad comparison for the mpk but given that the mpk is ex residential housing capital and ex government perhaps not i don t know that there is a way to distinguish between the two stories not without doing more research that i don t have time to do right now without taking a firm stand on this one important point here is that the explanation depends crucially on what you take to be normal and that depends in part on how far back you graph the data the s p data suggests a different story than the mpk series and the mpk series doesn t go back any further because the bls doesn t have the requisite data any further back i guess it is a caution that the starting point of your data series is not necessarily the same thing as the starting point of the economy 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 9 replies do you need more money for economic growth to occur posted on january 15 2016 by dvollrath 20 note the growth economics blog has moved sites click here to find this post at the new site tl dr version no this is another entry to file under notes for undergrads and or explaining things to your neighbor a very common question i get about growth is how does growth occur if there is not any more money in the economy another common question i get is how is it economic growth if spending on one product just replaces spending on another these questions come i think from continued confusion about a nominal versus real gdp b nominal gdp versus the stock of money and c absolute versus relative prices in short things an economist might call money illusion in the defense of students and my neighbors it isn t terribly easy to think in relative prices and real terms when every single transaction you undertake involves absolute dollars let s start with an economy that produces exactly 10 cans of budweiser and nothing else in a year they each sell for 1 meaning that nominal gdp in this economy is 10 for the year what is real gdp well we already really know the answer it s 10 cans of budweiser real gdp is measured in real units that s obvious in this example because the real units are obvious cans of bud to do this more formally we find real gdp by dividing nominal gdp by a price index in this case the price index is easy to figure out it s 1 per can of bud so real gdp is 10 1 per can of bud 10 cans of bud one confusion with real gdp is that the bea and economic textbooks insist on talking about it in terms of dollars that is because the price index they use is not something like 1 per can but is something like 1 37 per 1 of output in 2005 so real gdp is 10 1 37 per 2005 dollar 7 3 units of 2005 dollars which would be reported as 7 3 2005 dollars but despite being reported in terms of dollars real gdp has nothing to do with money i sometimes think that we should save our effort at coming up with good price indices and just use something like the price of a can of bud or a pair of levi 501 jeans as the price deflator in national accounts because then real gdp would be reported in real tangible units and would save us from confusing it with a nominal number for example if the price of a can of bud was 0 50 then real gdp in the us for 2014 would be 17 615 billion 0 50 per can on bud 35 230 cans of bud nominal gdp through q3 2015 is 18 060 so that s real gdp of 36 120 cans of bud a 2 5 increase in real gdp from 2014 i m laboring this point because when it comes to explaining how growth works this confusion between nominal and real concepts becomes a problem let s go back to our simple 10 can economy with a price per can of 1 and see how growth works growth through expanding production of existing products this is the easiest to explain something happens at anheuser busch that lets them produce even more cans of bud with their given inputs perhaps they water it down even more than it already is whatever the reason the economy produces 12 cans of bud this year we know that real gdp went up from 10 cans to 12 cans but let s walk through how to do this calculation using nominal gdp and a price index think of two possibilities nominal gdp stays constant that is nominal gdp is still 10 then it must be that the price of a bud fell to 0 83 the supply curve of bud shifted out and hence the quantity of bud went up and the price of bud went down real gdp is 10 0 83 per can 12 cans of bud for the given flow of money through the economy which does not have any necessary relationship to real gdp the price of a can of bud must adjust to make supply equal demand the price of bud stays constant let each can still be 1 the it must be that nominal gdp is 12 and real gdp is 12 1 per can 12 cans of bud here the supply curve of bud has shifted out but apparently the demand curve shifted out as well leaving the price unchanged and the quantity higher why would this happen who knows and who cares it s possible for a given flow of money through the economy the price of a can of bud must adjust to make supply equal to demand note that it is irrelevant whether nominal gdp goes up or stays constant it could even fall whether nominal gdp rises or not is completely irrelevant to whether real gdp goes up if we could observe the real quantity of cans consumed we wouldn t need nominal gdp at all but we don t actually observe the number of cans of bud consumed all we observe is nominal gdp and the price of a can of bud so when the bea reports a nominal gdp of 10 and a price of 0 83 per can we divide and infer that real gdp is 12 cans of bud if your question now is where people get the extra money to afford 12 cans of bud when their price stays at 1 take a moment to meditate on the equation we ll come back to that in a few paragraphs growth through addition of new products this one will stretch the mind a little more but the same principles are going to hold rather than bud watering down their beer even further we re going to introduce a new beer into the market someone and god bless them invents real ale coffee porter in response people with functioning taste buds buy 5 cans of coffee porter and everyone else still buys 5 cans of bud so we ve still only got 10 cans of beer being sold is this economic growth meaning that real gdp is higher it depends on relative prices if those cans of coffee porter are more expensive than cans of bud then this represents real economic growth why because if the relative price of coffee porter is higher than that of bud then the relative marginal utility of coffee porter is higher than that of bud assuming that utility for both has typical properties declining mu then we know the mu of the 5th can of bud is higher than the 10th can and since coffee porter has a higher mu than that it follows that we are better off in utility terms more intuitively if we weren t better off then why were we willing to substitute away from bud even though coffee porter costs more which suggests that if coffee porter and bud sold for the same amount then we aren t any better off in this case it s a perfect substitute and the choice of 5 of each is just random it s the difference in relative prices that a new product introduces that defines it s contribution of real growth so eocnomic growth is just about things getting more expensive no note that i didn t say anything about the absolute price of bud or coffee porter because that is irrelevant for real gdp so long as coffee porter is more expensive than bud we ve experienced real growth that holds if porter costs 2 to bud s 1 or 20 to bud s 10 or 0 02 to bud s 0 01 once we ve established that there is a relative price difference then the same questions about nominal gdp from before come up let s say that we observe that coffee porter costs twice as much as bud how do we calculate real gdp nominal gdp stays constant it must be that bud costs 0 67 and the porter is 1 33 so nominal gdp is 10 multiply it out and you can see it what is real gdp in this case sticking with our standard of using the price of bud real gdp is 10 0 67 per can of bud 15 cans of bud it is as if our economy produced 15 cans of bud where before it only produced 10 there is real gdp growth due to the introduction of coffee porter even though all coffee porter does is replace consumption of bud and total beer drinking stays constant at 10 cans the price of bud stays constant if bud still costs 1 then the porter is 2 so nominal gdp is 15 again just multiply it out what is real gdp 15 1 per can of bud 15 cans of bud real gdp has gone up it is irrelevant what the nominal price of bud is we observe real gdp growth because the introduction of coffee porter introduced a relative price difference notice that if all the bea reports to me is nominal gdp and the price of bud i can infer real gdp regardless of what exactly happens our bud based measure of real gdp goes up to 15 i don t actually have to observe the number of cans purchased this example of adding a new product brings up one issue with price indices which is product replacement if as would be logical if people tasted them the introduction of coffee porter completely eliminated bud from the market then we cannot calculate real gdp there will be no price of bud to divide nominal gdp by and we can t just use the price of coffee porter because yesterday all we had was bud and there was no price for coffee porter one of the reasons we use more sophisticated price indices that combine the price of bud and coffee porter in some way is so that we always have a price index to use but that sophisticated price index by putting things in 2005 dollars or something like that creates confusion between real gdp and nominal gdp always think of real gdp as being cans of bud rather than in dollar terms now if you are still wondering where people get the extra money to buy the coffee porter in this example then the next section is for you where does the extra money come from nowhere there is no extra money nominal gdp is not a measure of how much money we have nominal gdp is the flow of dollars through the economy the stock of money is well a stock in all the examples above what is the stock of money you can t answer that question because i never said anything about it let s say that this economy has a stock of 4 one dollar bills here s the transactions flow in this economy in the initial stage with only 10 can of bud consumed person a starts with the 4 nominal gdp is zero person a buys 4 buds for 4 from person b nominal gdp is 4 person b buys 4 buds for 4 from person c nominal gdp is now 8 person c buys 2 buds for 2 from person d nominal gdp is now 10 person d ends up with 2 and person c with 2 final nominal gdp is 10 then next period we start again only now c and d hold the money stock the money stock is always 4 and it gets turned over and over resulting in 10 of nominal transactions or gdp no it doesn t matter that the circle isn t closed here with different people ending up with the actual dollars real gdp is 10 cans of bud if we have the case where coffee porter gets introduced things look like this person a starts with the 4 nominal gdp is zero person a buys 2 porters for 4 from person b nominal gdp is 4 person b buys 4 buds for 4 from person c nominal gdp is now 8 person c buys 2 porters for 4 from person d nominal gdp is now 12 person d buys 1 bud for 1 and 1 porter for 2 from person e nominal gdp is now 15 person d ends up with 1 and person e with 3 final nominal gdp is 15 no new money is necessary real gdp is 15 cans of bud the same 4 gets recycled over and over again this time used to purchase both buds and porters different people end up with money stock at the end we could easily write out an example where the growth occurred because of just an increase in the number of buds and if you prefer that nominal gdp not increase you can easily go back and work out the same set of transactions lower the absolute prices and get nominal gdp to come out to exactly 10 and yes i made up these examples but i just need to show you that it is possible to get economic growth even though there is no new money in the economy economic growth occurs either because we produce more of existing things or because we introduce new things that that are more valuable than the old things we produced which shows up in relative price differences the level of absolute prices is irrelevant the level of nominal spending is irrelevant the stock of money is irrelevant for any modern economy it is effectively impossible for there to be not enough money to let growth occur the economy as a whole can always turn over the money stock faster to allow for the extra transactions if necessary whether that turnover involves you and means that you can afford to buy some coffee porter is a different question and involves your own productivity and or ownership of a bud or coffee porter producing machine 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 20 replies calculating growth rates posted on january 13 2016 by dvollrath 8 note the 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