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sing jekyll and github on the new site for those that are interested it s built totally on static text files which is something that satisfies my unix lizard brain i m sure that i have screwed something up so if you find yourself unable to read the blog or link to old pages just let me know thanks for reading 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 leave a reply the declining marginal product of capital posted on january 20 2016 by dvollrath 9 note the growth economics blog has moved sites click here to find this post at the new site a few weeks ago i posted about the recent decline in capital per worker in the u s the short summary is that from 2009 2013 capital per worker has been shrinking and this is at odds with most of historical experience this shrinking capital per worker contributes to higher measured productivity growth the illustrious areendam chanda asked in response what the marginal product of capital looked like given the decline in capital per worker in this series this is straightforward to calculate given the bls data and it shows what i think is an interesting pattern first i calculate the mpk as where is capital s share of output if the world is roughly cobb douglas this should describe for us the extra amount of output we could get from one additional unit of capital this is an aggregate concept and doesn t necessarily map to any specific use of capital e g the marginal product of a laptop can be different than the marginal product of a shovel this is the marginal product of dumping an extra unit of homogenous capital into the economy here s the figure showing the time path from 1960 to 2013 in terms of the recent decline in capital per worker the uptick in the actual series black line from 2000 2013 makes some sense declining capital per worker should be associated with a higher return on capital but what appears to be true is that the recent uptick in mpk is driven by a change in capital s share in output i plotted in gray an alternative mpk that assumes capital s share is constant at 0 31 a rough long run average and as you can see this continues the downward trend of the prior decades the uptick is due almost entirely to the increase in capital s share of output what seems far more interesting in this figure is the general drift downward in the mpk since 1960 i can come up with two different interpretations of this which depend a lot on the time frame you consider secular shift in mpk essentially interpret this as evidence of some kind of sustained secular change in the us economy the drift down in the mpk isn t consistent with the us being on a balanced growth path bgp as a quick reminder traditionally a bgp is a situation where gdp per worker is growing at a roughly constant rate the return on capital mpk is constant over time and the share of output going to capital is constant over time and we almost always presume that the us is on a bgp i will be telling my undergrads this in a week or so i m sure almost every growth model is written so that it delivers a bgp eventually because people feel that this represents what we see in the data and when they say bgp in their model they almost always mean that the mpk is constant in a standard solow model the steady state is a bgp and the model tells us what determines the mpk on that bgp where is capital s share of output is population growth is productivity growth is the depreciation rate and is the savings rate note this equation is for the mpk in steady state not necessarily at any given point in time but it is useful for thinking about what might drive the decline in mpk the steady decline in the mpk over time is consistent with declining because capital s marginal product is lower when there are fewer people around declining slower productivity growth and higher more savings in this story we are transitioning from the immediate post war era of relatively rapid population and technological change to a new era of relatively low population and technological growth it s worth remembering here that the mpk is calculated using the bls data which excludes the government sector and the residential housing stock so this represents a decline in the non residential housing mpk return of mpk to long run trend but from a long long term perspective maybe the decline in mpk since 1960 is just a reversion 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 i...
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