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il 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 growth economics blog has moved sites click here to find this post at the new site i m prepping for my undergraduate growth course this semester which uses an awesome book by the way we don t require calc from our econ majors at uh so i have to ease them into a few things during the course one of those is using logs to both visualize and then analyze economic growth this post is some notes i started working on to help introduce students to the concepts if you re teaching this might come in handy if you re interested in growth but a little shy about math this might be helpful if you literally have nothing better to do it will kill about 10 minutes and or help put you to sleep we re interested in living standards as measured by real gdp per capita we don t concern ourselves a lot with the absolute value of real gdp per capita as that number depends on exactly how we construct price indices base years etc what we care about is how fast economies grow this is like saying that we don t care whether you start at 150 pounds or 68 kilograms but if your weight grows by 5 per year we know you are going to get fat to visualize those growth rates and to do some crude analysis we invariably plot real gdp per capita in logs when i say log i mean the natural log there are lots of cool explanations of how natural logs work but this post is not one of them for now we re going to take it on faith that natural logs work the way i say they do take the natural log of gdp per capita in each year and graph it against the year itself the figure below for india is an example where real gdp per capita is plotted using the grey line natural logs have a few great properties for our purposes using them means that every step up the y axis is an identical percent change in real gdp per capita going from 7 0 to 7 5 for example is a 65 increase in real gdp per capita going from 7 5 to 8 0 is also a 65 increase in real gdp per capita this is true even though from 7 0 to 7 5 is going from 1 096 to 1 800 in gdp per capita and going from 7 5 to 8 0 is going from 1 800 to 2 980 by plotting things in natural logs we can see the percent increases rather than the absolute increases even more fun is that because of this property we can pick off the average growth rate between two years relatively easily the average growth rate between two years is just the slope of the straight line connecting the two end points in the figure for india i ve overlaid the calculation of the growth rate for several sub periods as well as the average growth rate from 1950 to 2010 from 1950 to 2010 as an example connect the two end points and find the slope of the line you could do this mathematically as follows for the other sub periods you do the same thing just using the end points from those time periods so from 1950 to 1975 growth average 2 0 from 1975 to 1985 if average 3 0 and from 1985 to 2010 it averaged 5 2 why those particular sub periods and not others solely because they looked like obvious break points there is no formula for deciding what sub periods to calculate it just seems intuitive that something different happened around 1985 for example that sets that period apart from the others but you could calculate the growth rate from 1972 to 2003 if you wanted to you want to argue with me that the 1985 to 2010 period should be broken up again into pre 2003 and post 2003 sub periods okay i can t tell you you re wrong the three sub periods i did calculate have the feature that their average growth seems very close to the actual growth that is the actual path of gdp per capita doesn t stray very far from the straight line we used to calculate the average growth from 1950 to 1975 for example what do i mean by very far nothing technical just eye balling it compare those three sub periods though to the whole stretch from 1950 to 2010 we calculate average growth at 2 5 but the straight line that gives us that answer lies well above the actual real gdp per capita for almost the entire period average growth from 1950 to 2010 doesn t give us a very accurate picture of what the growth experience of india was like in history where there really appear to be three separate periods that doesn t mean 2 5 is wrong it is exactly the average growth rate from 1950 to 2010 if you started at real gdp per capita of 798 in 1950 and applied 2 5 growth to that you d end up with which is just rounding error away from the actual value of 3 596 but the path from 1950 to 2010 looks a lot different at 2 5 average growth every year compared to the actual path real gdp per capita followed in india in this time span regardless we ll be interested at times in precisely those periods when the average growth rate is very close to the actual growth rate of real gdp per capita the straight line is close to the gray line 1950 to 1975 as we said or arguably 1985 to 2010 these periods could represent what we ll call balanced growth paths or bgp s we re interested in bgp s because our theories of growth are going to suggest that in the absence of any fundamental change a country will tend to end up on a bgp that is without any major shock to a fundamental characteristic of the economy an economy will tend to have actual growth close to average growth further if we see different bgp s then this indicates that something fundamental did change what the picture from india says is that the period from 1950 to 2010 was not a bgp for india 1950 to 1975 could be one and then in 1975 something fundamental was just different what something was it we cannot tell from this figure we d have to dig into other data on india to decide and our theory might tell us likely candidates to explore in 1985 something again appears to have fundamentally changed as again india switched to what looks like a new bgp and again we d have to explore other data to decide what changed just to be complete what we see in the figure is necessary but not sufficient to establish that india was on a bgp that is there are other conditions that are also necessary to classify a period of time as being on a bgp and there may be other reasons that india was not on a bgp from 1975 to 1985 for example even though actual growth was close to average growth but as a start looking at a figure like this tells us where we should start looking to be even more complete just because most of our theories suggest countries will end up on a bgp in the absence of a major shock doesn t mean they are right our theories could be completely wrong maybe nothing fundamental changed in either 1975 or 1985 and all that happened was that india got really unlucky for a few years perhaps we are making too much of these extended runs of similar growth rates 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 8 replies iq and economic growth posted on january 11 2016 by dvollrath 26 note the growth economics blog has moved sites click here to find this post at the new site i finally got around the writing up a review of hive mind by garett jones short version is that the book is excellent and well worth reading i ll get into more detail below but the book explores the importance of cognitive skills as measured by iq for economic development there are several reasons to like it first the book has absolutely no fat on it this is a model of concise explanatory writing most books that try to bring recent research to the public end up bloated not this one five stars for clarity here onto the content there are really two parts to the book first jones establishes that cognitive skills are in fact highly correlated with economic development and a subsidiary part of this is establishing that iq is just one of many ways of measuring cognitive skills i m not going to go into a lot of detail here like i said the book is very lean and you can easily read jones own words on this let me summarize by listing his own five main channels for how iq is related to economic development in italics next to the channel are a few comments of my own on them high iq s are related to higher savings rates but we have evidence that savings rates don t actually vary a whole lot across countries and that what variation there is explains little high iq s are related to more cooperation for my money the most important channel economic development looks a lot like people choosing the cooperate equilibrium in a repeated game high iq may be a marker for people willing to play this move and to play it first and often even though the other players could take advantage of them high iq s are related to market oriented policies perhaps it is that high iq people believe in their own ability to succeed high iq s are related to using team based technologies i think i would lump this in with cooperation people like to conform this isn t about iq itself but if you have lots of high iq people with those other traits then even those without high iq s will try to conform a critical mass of high iq people may be sufficient to reach the good equilibrium let s be clear here about the role of high iq s they are a marker not necessarily a cause of these behaviors and traits jones is clear on this and is not making some strong causal claim rather think of all these traits including high iq scores as a package of traits that tend to come together call these traits cognitive skills as they typically involve some kind of ability to do abstract thinking an interesting note here is that lots of what the labor literature calls non cognitive skills are what i think jones would lump under cognitive skills for example patience is something that some refer to as a non cognitive skill but for jones it is part of the package of abilities that come along with relatively high iq levels the wrong conclusion to draw from jones book is that there is some kind of fixed genetic difference in intelligence across countries that explains why some are rich and some are poor these traits are malleable as evidenced by the flynn effect of rising iq scores over time cognitive skills certainly are related to economic development but they are better seen as a more refined measure of human capital than years of schooling you can invest in cognitive skills the same way that you can invest in years of schooling one possibility might be more extensive pre schooling that teaches those non cognitive skills that are associated with iq by the way feyrer politi and weil have a paper coming out on how iodizing water helped raise iq scores in the us there may be direct public health measures that could materially impact cognitive skills and iq in developing countries the second part of the book delves more specifically into jones research on the returns to iq or cognitive skills namely why is there such a small premium on iq within countries but such a large premium to iq across countries again i m not going to lay into a lot of detail here he does a nice job in the book explaining the theory here let me try to give you the basic intuition high iq places are able to take on fragile production processes where even one mistake ruins the output e g a semiconductor or a hit movie economists often call these o ring processes after the challenger disaster having lots of high iq people means you have lots of high productivity fragile production processes and this creates demand for other non fragile production processes e g retail the high demand for the non fragile process means that wages are relatively high for the low iq people who can work that sector hence there is little difference in wages between the high iq people and the low iq people but the average wage is incredibly high because the economy engages in these productive fragile production processes so high iq countries are very rich compared to low iq countries let me add that this disconnect of the within country return to a trait iq years of education etc and the cross country return to the same trait is littered all over the growth literature sometimes we think about these positive spillovers externalities but for the most part we do not one nice thing about jones book and prior research is that he does think about these things seriously even if you don t buy the first part of the book it is worth reading the second part substitute high skill or high education in everywhere you see high iq and you ll be fine i ll be assigning parts of this to my undergrads this semester it should be a fun day of class 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 26 replies beating a dead robotic horse posted on december 31 2015 by dvollrath 17 note the growth economics blog has moved sites click here to find this post at the new site one of the recurring themes on this blog has been the consequences of robots ai or rapid technological change on labor demand will humans be put out of work by robots and will this mean paradise or destitution i ve generally argued that we should be optimistic about robots and ai and the like but others have made coherent arguments for pessimism i spent a chunk of this week reading over posts both new and old and thinking more about these positions if there is one distinct difference between the robo pessimist and robo optimist view it is almost exclusively down to timing the pessimists are worried that the rapid decline of human labor is occurring now and in many cases has been occurring for a while already the optimists believe that we have time in front of us to sort things out before human labor is replaced en masse brynjolfsson and mcafee s latest is a good example of this robo optimist view they concede that human labor is in danger of being replaced but will there be enough demand especially over the long term for those two types of human labor that which must be done by people and that which can t yet be done by machines there is a real possibility that the answer is no that human labor will in aggregate decline in relevance because of technological progress just as horse labor did earlier if that happens it will raise the specter that the world may not be able to maintain the industrial era s remarkable trajectory of steadily rising employment prospects and wages for a growing population but at the same time they do not think this is imminent but are our interpersonal abilities the only ones that will allow us to stave off economic irrelevance over at least the next decade the answer is almost certainly no that s because recent technological progress while 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