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["The Solow Model with Technological Progress with L and K"]
["Exogenous Variables",null,null,null,null,"Not using any efficiency workers or other clever solution tricks, just brute force simulation."]
["g",0.01,"labor-augmenting techD",null,null,"In steady state (long run equilibrium) when K/Y constant (this is balanced growth)."]
["n",0.01,"%D population",null,null,"r --> 0 is Cobb Douglas; r = 1 is perfect substitutes (linear isoquants); r --> - inf is perfect complements (L isoquants)"]
["A",1,"technology parameter",null,null,"Run Solver to find steady state."]
["a1",0.3,"productivity of capital",null,"a2",0.7,"productivity of labor"]
["s",0.3,"saving rate",null,"r",0.1,{"$f":"1/(1-rho)","v":{"$error":"#NAME?"}},"elasticity of subsitution"]
["d",0.1,"depreciation "]
["Initial Conditions"]
["initial k",3.7999763397299264,"initial L",1]
[]
[]
["Year","L","K","Y","C","I","depK","DK","%DK","%DY","K/Y","r"]
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{"sheet":"Intro","index":1,"n_rows":41,"n_cols":7,"rows_kept":41,"cut":false,"hidden":false,"merged":[]}
[null,null,null,null,null,null,"Capital.xlsm"]
[null,null,null,null,null,null,"by"]
[null,null,null,null,null,null,"Humberto Barreto"]
[null,null,null,null,null,null,"hbarreto@depauw,edu"]
[null,null,null,null,null,null,"http://www.depauw.edu/learn/econexcel/"]
[]
["This Excel workbook explains key ideas in Piketty's Capital.   -->",null,null,null,null,null,"www.amazon.com/Capital-Twenty-First-Century-Thomas-Piketty/dp/1491591617"]
[]
["It is completely self-contained and all you have to do is read (scrolling down as needed), follow instructions (obey the Click and Change commands), and pay close attention."]
[]
["Software Requirements:"]
[null,"You need Microsoft Excel, Windows version 2007 or greater to get full functionality from this file."]
[null,null,"The file can be opened with Mac Excel, but it uses Visual Basic code that may not be fully supported on a Mac. "]
[]
[null,"You must be sure to Enable Content or the buttons and code in this macro-enabled workbook will not work."]
[]
["Let's see if you are ready to go (click the X to close the window when you are finished watching the video):"]
[null,"Click"]
[]
[null,null,"https://player.vimeo.com/video/238782395"]
["Three bad outcomes and fixes:"]
[null,"1) If the button above does not respond when you click it, please close the workbook and open it again, enabling macros."]
[null,null,"Search \"enable macros\" in Excel's Help for more information on how to do this."]
[null,"2) If the video does not play, check your internet connection. You need to be able to watch the videos because they have explanations and instructions."]
[null,"3) If you are connected to the internet, but get other errors (e.g., \"Sorry. This video does not exist.\"), you will not be able to watch the video in a \"floating window\" above this Excel spreadsheet."]
[null,"As a workaround, click the URL under the button to watch the video in a browser. You can resize and move the Excel and browser windows on your screen to see the video and sheet at the same time."]
[]
["If you watched the video, you are ready to start."]
[null,"You now know that I created this Excel file to make Piketty's argument about inequality accessible to the smart, non-expert reader."]
[]
["As you proceed, the workbook will unfold, displaying new sheets, and I will ask you to click buttons and change things. "]
[null,"You are free to take notes on the sheets or change cells as you desire."]
[null,"You can modify charts or create new ones -- there is nothing special about this workbook, nothing is password protected or otherwise blocked."]
[null,"You cannot really hurt anything -- if something does break, just close the workbook and re-open it. You can also Save As if you want to be extra careful and have an original copy available."]
[null,"If you know Visual Basic, go ahead and look at the code. It is freely available for you to inspect and alter as you wish."]
[]
["I welcome all feedback, positive and negative. Drop me an email and let me know what you think or if you have any questions or suggestions."]
["I really hope this helps.",null,null,null,null,"hbarreto@depauw,edu"]
["Enjoy!"]
[]
[null,"Click"]

{"sheet":"Def","index":2,"n_rows":47,"n_cols":13,"rows_kept":47,"cut":false,"hidden":true,"merged":[]}
["Defining","Let's start with the definition of capital, which is absolutely essential, and consider also exactly what income means."]
["K and Y"]
[null,"For Piketty, wealth and capital are the exact same thing (he should have said this in the first sentence instead of p. 47)."]
[null,"Capital (K) is a stock ($ at a point in time) and income (Y) a flow ($ over a period of time, say a year). "]
[]
[null,"Capital includes ALL non-human assets that can be exchanged (bought and sold or given away, including inheritance)"]
[null,null,"Capital includes all real estate, financial, and industrial assets and, if slavery is legal, the value of the slaves."]
[null,null,"Piketty does not like the phrase \"human capital\" because labor as an asset cannot be traded or passed on (since slavery is everywhere now illegal)."]
[]
[null,"Capital can be measured by directly valuing the asset or by computing the capitalized value of the income stream."]
[null,null,"Capital income ($/yr) = rate of return (%/yr) x capital ($) so if we divide both sides by the rate of return, we get: capital = capital income/rate of return."]
[null,null,"If you own a house that you rent out for $10,000 a year and the rate of return is 5% per year (after maintenance), then your capital (wealth) is $200,000 (that's $10,000/0.05). "]
[]
[null,"Click"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"Unlike capital, income is a flow and it can come from labor (L) as a payment for work."]
[null,null,"They are a lot of different names for labor income, such as wages, salaries, tips, stipends, and so on."]
[]
[null,"But, confusingly, capital can also produce a flow of payments: rents, interest, dividends, and other forms of unearned income."]
[null,null,"Remember that house that you rented out? It's $200,000 value is part of the capital stock, but that annual return of $10,000 is capital income."]
[]
[null,"So income is all of the forms of payments received by owners of productive inputs, which we group into two types: labor income and capital (or non-labor) income."]
[null,null,"Total income = labor income + capital income"]
[]
[null,"Inequality can be measured by the share of output going to labor and capital owners (the functional distribution) or by how much each individual person gets (either as annual income or as wealth)."]
[]
[null,"We are often interested in individual income inequality, but the functional distribution gives us another view -- if K is large, then income inequality is high."]
[null,null,null,null,null,null,null,null,null,null,null,null,"This is a critical connection and we will return to it."]
[]
["Summary:","So, before we move on, this is the takeaway:"]
[null,null,"Capital (K) is wealth, a stock of all tradeable asset values at a point in time."]
[null,null,"Income (Y) is a flow of all payments received by owners of inputs during a period of time (usually a year)."]
[]
[null,"Click"]

{"sheet":"Data","index":3,"n_rows":173,"n_cols":43,"rows_kept":173,"cut":false,"hidden":true,"merged":[]}
["New Data","Piketty's brute force compilation of numbers gives us a view we did not have before."]
[null,null,"He wrote Capital a few years ago and it was translated to English in 2014, from which it became a publishing sensation."]
[null,null,"But he had been working for years on this project, producing papers and working with others to create the data which enabled the inequality argument to move forward."]
[]
["Part I:","Before we see what the data show, there is an important new variable to consider: b (beta).",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Left here in case I need to edit"]
["K/Y = b",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Not showing up correctly on other Excel versions so went with images"]
[null,"While we can track K and Y separately over time, a really clever trick is to divide K by Y. This ratio is b. "]
[null,"b removes the currency units so changes in prices over time and across countries do not matter."]
[null,"Think about it: US national income is roughly almost $20 trillion per year and the capital stock is $80T, so K/Y = 4 years of national ncome."]
[null,"This says that the entire country's stock of wealth can buy 4 years of national income."]
[null,"It sounds a little weird to say it that way, as years of income, but K/Y tells you how intensely capitalized an economy is and, as we will see, this offers a window into inequality."]
[null,"You can also express K/Y in percentage terms, so K/Y = 4 is equal to 400%. We would say that capital is 400% of national income."]
[]
[null,"Below is a graph of the the UK's beta since 1870 and there is a table to the right with the data."]
[null,null,"You can control what is displayed in the chart by selecting the country."]
[null,"Change"]
[null,null,4]
[]
[null,null,null,null,"Change","Set the chart to the UK's b, if needed,"]
[null,null,null,null,null,"then -->",null,"Click",null,null,"https://player.vimeo.com/video/238959182"]
[null,null,null,null,null,null,null,null,null,null,"Click the link above if the button does not work."]
[null,null,null,null,null,null,null,null,null,null,null,"Piketty, Capital, Table S4.5, Private Capital as a % of National of Income"]
[null,null,null,null,null,null,null,null,null,null,null,"Year","USA","Germany","France","UK","Europe"]
[null,null,null,null,null,null,null,null,null,null,null,1870,4.4272347386605411,7.1081706544875507,7.1888489745130437,6.7203658180781707,7.0057951490262553]
[null,null,null,null,null,null,null,null,null,null,null,1880,4.5184487694187192,6.9331387170014702,6.9503778149428079,6.7568649753977565,6.8801271691140116]
[null,null,null,null,null,null,null,null,null,null,null,1890,5.0521643664216001,6.2566424612646321,6.9503778149428079,6.7568649753977565,6.6546284172017325]
[null,null,null,null,null,null,null,null,null,null,null,1900,4.7503513406101217,6.4845256703166019,6.9503778149428079,6.7568649753977565,6.7305894868857221]
[null,null,null,null,null,null,null,null,null,null,null,1910,4.746976882929677,6.4176985611497104,6.7119066553725721,6.7933641327173424,6.640989783079875]
[null,null,null,null,null,null,null,null,null,null,null,1920,4.3436609547792333,3.5467568290874611,2.9067217293956675,2.8771730734861838,3.1102172106564372]
[null,null,null,null,null,null,null,null,null,null,null,1930,5.3660348478623128,3.7901945250413727,3.8420959553881837,3.6118826494158212,3.7480577099484598]
[null,null,null,null,null,null,null,null,null,null,null,1940,3.5027993542478577,2.8686496043480214,2.8420959553881837,2.6118826494158212,2.774209403050675]
[null,null,null,null,null,null,null,null,null,null,null,1950,3.8449814897586494,2.3338421076734823,2.7774701813806999,2.3465922253454585,2.4859681714665469]
[null,null,null,null,null,null,null,null,null,null,null,1960,4.0909364582455172,2.9729511961228514,3.2044386481041034,2.8387933008817763,3.0053943817029101]
[null,null,null,null,null,null,null,null,null,null,null,1970,4.0014725114387248,3.1333951636697979,3.6314071148275064,3.330994376418094,3.2224407516040845]
[null,null,null,null,null,null,null,null,null,null,null,1980,4.1750808350237971,3.527987610585547,3.6549359078189552,3.9768982852320516,3.7132925237293679]
[null,null,null,null,null,null,null,null,null,null,null,1990,4.1897823346393901,3.5511652567347562,3.6784647008104043,4.6228021940460087,4.2811873608616722]
[null,null,null,null,null,null,null,null,null,null,null,2000,4.9205117496859803,3.875167699867097,5.0253115465697089,4.9241752340343581,4.9904712456083136]
[null,null,null,null,null,null,null,null,null,null,null,2010,4.3075769382874594,4.1430634981151604,6.0538712541943536,5.2255482740227075,5.5337456325422538]
[null,null,null,null,null,null,null,null,null,null,null,"Source:","http://piketty.pse.ens.fr/en/capital21c2"]
[]
[]
[null,"Notice how the UK had a high K/Y of almost 7 years of national income until 1910 and then it dropped rapidly during World War I."]
[null,"It was low, roughly 3 years of national income, from post-WWI to the 1960s."]
[null,"But since the 1960s, K/Y has been rising pretty steadily."]
[]
[null,"So, with respect to b, the historical record for the UK shows that there are three parts:"]
[null,"1) K/Y was pretty high up to 1914, then 2) it dropped like a stone and stayed low during the WWI-Great Depression-WWII, and, finally, 3) K/Y has been rising ever since."]
[]
["Transition:","Having covered K/Y, we are ready to discuss income inequality."]
[]
[]
["Part II:","In addition to detailed compilations of data on capital stocks and income flows, Piketty also collects data on income and wealth inequality."]
["Top 10%","He uses tax returns to get data on the very rich -- a substantial improvement on survey data (such as the Current Population Survey) which cannot capture the highest tail of the distribution."]
[null,"Piketty is not a fan of the Gini coefficient (see p. 266 of Capital), preferring instead a simpler percentile measure: the share going to the top-most percentage in the distribution."]
[]
[null,"The chart below plots the share of income going to the Top 10% (or top decile) of the income distribution in the UK."]
[null,null,"It shows that, in 1900, the richest 10% got almost half of national income. This is a pretty unequal.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Source:","http://piketty.pse.ens.fr/en/capital21c2",null,null,null,null,null,null,null,"Not used in macro for chart, but left here to keep table intact"]
[null,null,"Income equality (at least as measured by what the Top 10% get) improved over the 20th century and by the late 1970s, the Top 10% got just over a quarter of all income.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Added #N/A to pretty up chart"]
[null,null,"But since then, inequality has steadily risen.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Piketty, Table S9.2, UK",null,null,null,null,"Piketty, Table S8.1, France",null,null,null,null,null,null,null,"Piketty, Table S8.2, USA"]
[null,null,null,null,null,null,null,null,null,null,null,3,null,1,null,null,null,null,null,null,"Top 10%","Top 1%","Top 0,1%",null,null,"Top 10% income share ","Top 1% income share ","Top 0,1% income share ","Top 10% wage share","Top 1% wage share",null,null,null,"Top 10% income share ","Top 10%-5% income share ","Top 5%-1% income share ","Top 1% income share ","Top 0,1% income share ","Top 10% income share (excl. capital gains)","Top 1% income share (excl. capital gains)","Top 0,1% income share (excl. capital gains)","Top 10% wage share","Top 1% wage share"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1900,0.47075372340425531,0.21893033472803347,0.11075000000000002,null,1900,0.45500000000000002,{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},null,null,1900,0.40500000000000003,{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},0.40280054307578378,{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"}]
[null,null,null,null,null,null,null,null,null,null,null,"Change","Select combinations of countries and percentiles to display.",null,null,null,null,null,null,1901,{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},null,1901,{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},null,null,1901,{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1902,{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},null,1902,{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},null,null,1902,{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"}]
[null,null,null,null,null,null,null,null,null,null,null,"Data are to the right.",null,null,null,null,null,null,null,1903,{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},null,1903,{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},null,null,1903,{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1904,{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},null,1904,{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},null,null,1904,{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"}]
[null,null,null,null,null,null,null,null,null,null,null,"For more inequality data (more countries, more years, more variables), visit",null,null,null,null,null,null,null,1905,{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},null,1905,0.45500000000000002,{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},null,null,1905,{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"}]
[null,null,null,null,null,null,null,null,null,null,null,"http://wid.world/",null,null,null,null,null,null,null,1906,{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},null,1906,{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},null,null,1906,{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1907,{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},null,1907,{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},null,null,1907,{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1908,0.4625936170212766,0.21748033472803346,0.10930000000000001,null,1908,0.45500000000000002,{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},null,null,1908,{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1909,0.46765851063829794,0.21838033472803348,0.11020000000000001,null,1909,0.46,{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},null,null,1909,{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1910,0.47103510638297869,0.21898033472803347,0.1108,null,1910,0.46500000000000002,0.20499999999999999,9.5000000000000001E-2,0.26410165641219768,5.9031025333934756E-2,null,null,1910,0.4057850620067644,9.886691093573842E-2,0.12921815107102597,0.1777,8.9200000000000002E-2,0.40358134160090198,0.1777,8.9200000000000002E-2,0.27200569423044457,8.2305160599571714E-2]
[null,null,"If we adjust the y axis of the chart when plotting the UK's Top 10% share, we can make the visual message louder -- and connect it to beta!",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1911,0.47159787234042555,0.21908033472803348,0.11090000000000001,null,1911,0.46750000000000003,0.20749999999999999,9.7500000000000003E-2,0.26552155779075787,5.9750915886787617E-2,null,null,1911,0.40795442502818491,9.9395462232243478E-2,0.12990896279594141,0.17865,8.77E-2,0.40573892333709138,0.17865,8.77E-2,0.27335293907860958,8.2745171306209842E-2]
[null,null,null,"The chart below plots the same data as the one above (when set to UK Top 10%), but  the min and max of the y axis have been set to 0.25 and 0.5, respectively.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1912,0.47159787234042555,0.21908033472803348,0.11090000000000001,null,1912,0.46310416666666665,0.20787499999999998,9.7225000000000006E-2,0.26302489786678945,5.9858899469715544E-2,null,null,1912,0.41132264656144313,0.10021610766629085,0.13098153889515224,0.18012500000000001,8.6849999999999997E-2,0.40908885287485913,0.18012500000000001,8.6849999999999997E-2,0.2754447139744447,8.3428345824411124E-2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1913,0.48003936170212763,0.22058033472803346,0.1124,null,1913,0.47000000000000003,0.21,0.1,0.26694145916931805,6.0470806439640486E-2,null,null,1913,0.41012378804960548,9.9924013528748579E-2,0.13059977452085689,0.17960000000000001,8.6199999999999999E-2,0.40789650507328079,0.17960000000000001,8.6199999999999999E-2,0.27470018392677459,8.3185182012847955E-2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1914,0.45640319148936165,0.21479246861924683,0.10710000000000001,null,1914,0.45870833333333327,0.20824999999999999,9.6950000000000008E-2,0.26052823794282109,5.7966883052643477E-2,null,null,1914,0.41469086809470129,0.10103675310033819,0.13205411499436306,0.18160000000000001,8.5999999999999993E-2,0.41243878241262688,0.18160000000000001,8.5999999999999993E-2,0.27753648887027987,8.4111520342612406E-2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1915,0.45977978723404256,0.21544769874476985,0.10769999999999999,null,1915,0.39671666666666661,0.18309999999999998,7.9000000000000001E-2,0.22531941675912329,4.7724784090943682E-2,null,null,1915,0.40144633596392332,9.7809808342728261E-2,0.12783652762119507,0.17579999999999998,9.2200000000000004E-2,0.39926617812852311,0.17579999999999998,9.2200000000000004E-2,0.2693112045341145,8.1425139186295487E-2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1916,0.44852446808510638,0.2121715481171548,0.1047,null,1916,0.44741666666666657,0.20649999999999999,9.3900000000000011E-2,0.25411501671632419,4.8462959665646468E-2,null,null,1916,0.44095157835400228,0.10743500563697855,0.14041657271702371,0.19309999999999999,0.1051,0.43855687711386704,0.1857,9.8699999999999996E-2,0.29384524229543524,8.6010513918629544E-2]
[null,null,null,null,null,null,null,null,null,null,null,"Now we see three parts:",null,null,null,null,null,null,null,1917,0.3973127659574468,0.19895774058577403,9.2600000000000002E-2,null,1917,0.4352833333333333,0.2009,8.8900000000000007E-2,0.247223762025712,4.5850404827256053E-2,null,null,1917,0.40509999999999996,9.8699999999999968E-2,0.12900000000000003,0.17739999999999997,8.4000000000000005E-2,0.40289999999999998,0.17600000000000002,8.3599999999999994E-2,0.27158024848891871,8.1517773019271947E-2]
[null,null,null,null,null,null,null,null,null,null,null,"1) High inequality in the early years of the 20th century.",null,null,null,null,null,null,null,1918,0.37030000000000002,0.19239999999999999,8.6800000000000002E-2,null,1918,0.38891666666666663,0.17949999999999999,7.6700000000000004E-2,0.22088932445801546,4.7688141694835554E-2,null,null,1918,0.40110000000000001,0.10620000000000002,0.13529999999999998,0.15960000000000002,6.7199999999999996E-2,0.39899999999999997,0.1588,6.7400000000000002E-2,0.26914499664204161,7.3551263383297635E-2]
[null,null,null,null,null,null,null,null,null,null,null,"2) Falling and low inequality in the middle of the century.",null,null,null,null,null,null,null,1919,0.38729999999999998,0.19589999999999999,8.9800000000000005E-2,null,1919,0.42249999999999999,0.19500000000000001,8.2599999999999993E-2,0.21464864997456531,5.615146312252331E-2,null,null,1919,0.4032,0.10149999999999998,0.13760000000000003,0.1641,6.6299999999999998E-2,0.39479999999999998,0.15869999999999998,6.4500000000000002E-2,0.26652241773002017,7.3504946466809398E-2]
[null,null,null,null,null,null,null,null,null,null,null,"3) Rising inequality at the end.",null,null,null,null,null,null,null,1920,0.40755000000000002,0.18552552301255229,8.0299999999999996E-2,null,1920,0.39590000000000003,0.17949999999999999,7.6299999999999993E-2,0.22088932445801546,5.738194892005332E-2,null,null,1920,0.3901,0.10689999999999998,0.13489999999999999,0.14829999999999999,5.3600000000000002E-2,0.38100000000000001,0.14460000000000001,5.3699999999999998E-2,0.2579053727333781,6.6974261241970007E-2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1921,0.40805000000000002,0.18607154811715482,8.0799999999999997E-2,null,1921,0.39700000000000002,0.17319999999999999,7.2300000000000003E-2,0.2149069191008699,5.227398897757201E-2,null,null,1921,0.43180000000000002,0.12379999999999999,0.15160000000000001,0.15640000000000001,5.5999999999999994E-2,0.42859999999999998,0.1547,5.5999999999999994E-2,0.28762793373628831,7.1652269807280497E-2]
[null,null,null,null,null,null,null,null,null,null,null,"Look familiar?",null,null,null,null,null,null,null,1922,0.41795000000000004,0.1968828451882845,9.0700000000000003E-2,null,1922,0.41539999999999999,0.1787,7.2599999999999998E-2,0.23466965376970642,5.9108215169161663E-2,null,null,1922,0.43719999999999998,0.11779999999999997,0.14880000000000002,0.17059999999999997,6.6400000000000001E-2,0.42950000000000005,0.16289999999999999,6.1699999999999998E-2,0.28818991493172158,7.545025695931476E-2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1923,0.42015000000000002,0.19928535564853553,9.2899999999999996E-2,null,1923,0.43540000000000001,0.18909999999999999,7.6100000000000001E-2,0.24502587478969037,6.475772469757618E-2,null,null,1923,0.41460000000000002,0.1168,0.1414,0.15640000000000001,5.91E-2,0.40590000000000004,0.14990000000000001,5.5E-2,0.2734535191403627,6.9429057815845824E-2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1924,0.41775000000000007,0.19666443514644349,9.0500000000000011E-2,null,1924,0.4214,0.17960000000000001,7.0499999999999993E-2,0.24013862054598054,6.1313199858694364E-2,null,null,1924,0.44409999999999994,0.12299999999999997,0.14689999999999998,0.17420000000000002,6.7900000000000002E-2,0.43259999999999998,0.16320000000000001,6.1399999999999996E-2,0.27012562793821354,7.558920770877943E-2]
[null,null,null,"Lesson:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1925,0.41515000000000002,0.19382510460251043,8.7899999999999992E-2,null,1925,0.44069999999999998,0.18160000000000001,7.0699999999999999E-2,0.25341905582222501,6.8478525228788806E-2,null,null,1925,0.46350000000000002,0.11340000000000003,0.1477,0.2024,8.5199999999999998E-2,0.44170000000000004,0.17600000000000002,6.7500000000000004E-2,0.27580788224759345,8.1517773019271947E-2]
[null,null,null,"This direct measure of income inequality tracks the K/Y ratio story pretty well.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1926,0.41395000000000004,0.19251464435146443,8.6699999999999999E-2,null,1926,0.42060000000000003,0.1782,6.9800000000000001E-2,0.24094039604396117,6.7998868052389957E-2,null,null,1926,0.45710000000000001,0.11100000000000002,0.14699999999999999,0.1991,8.4600000000000009E-2,0.44069999999999998,0.18010000000000001,7.0699999999999999E-2,0.27518345869711214,8.3416766595289071E-2]
[null,null,null,"High, then falling, but more recently rising again.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1927,0.41215000000000002,0.19054895397489538,8.4900000000000003E-2,null,1927,0.42950000000000005,0.17449999999999999,6.8699999999999997E-2,0.26546135541419291,7.3915457672393672E-2,null,null,1927,0.4667,0.10980000000000004,0.14659999999999995,0.21030000000000001,9.2499999999999999E-2,0.44670000000000004,0.18679999999999999,7.4700000000000003E-2,0.27893000000000001,8.6519999999999986E-2]
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["Transition:","Having explored the historical record of K/Y (Part I) and the Top 10% (Part II), we are poised to make a critical connection.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1929,0.41054999999999997,0.18880167364016737,8.3299999999999999E-2,null,1929,0.41590000000000005,0.16149999999999998,6.25E-2,0.26458318104148654,7.1086079531965773E-2,null,null,1929,0.46710000000000002,0.10230000000000004,0.14129999999999995,0.2235,0.1091,0.43759999999999999,0.18420000000000003,7.6200000000000004E-2,0.29243999999999998,8.6709999999999995E-2]
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["Part III:","You may have noticed that the U-shape in the chart above of the UK's Top 10% income share looks similar to that of the UK's K/Y ratio.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1931,0.39895000000000003,0.17613389121338913,7.17E-2,null,1931,0.41119999999999995,0.14630000000000001,5.3699999999999998E-2,0.27174881792185696,7.0208940070841386E-2,null,null,1931,0.44540000000000002,0.1331,0.1573,0.155,5.8899999999999994E-2,0.44400000000000001,0.1527,5.6799999999999996E-2,0.29338999999999998,8.4680000000000005E-2]
["b<->Top 10%","Piketty never draws a double-Y chart like the one below, but it clearly connects K/Y and income inequality.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1932,0.39594999999999997,0.17285774058577405,6.8699999999999997E-2,null,1932,0.43439999999999995,0.14800000000000002,5.2199999999999996E-2,0.2813191738828022,7.1070680041821432E-2,null,null,1932,0.4637,0.13699999999999996,0.1711,0.15560000000000002,5.9699999999999996E-2,0.46299999999999997,0.15479999999999999,5.9000000000000004E-2,0.30280000000000001,8.2899999999999988E-2]
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[null,"Notice how high K/Y at the beginning and end of the 20the century is associated with high income inequality.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1934,0.39505000000000001,0.17187489539748954,6.7799999999999999E-2,null,1934,0.46009999999999995,0.15279999999999999,5.3099999999999994E-2,0.26835849991694366,6.7108979680893827E-2,null,null,1934,0.45779999999999998,0.1207,0.17310000000000003,0.16399999999999998,6.13E-2,0.45159999999999995,0.15869999999999998,5.8200000000000002E-2,0.29766999999999999,8.3070000000000005E-2]
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[null,"This is no coincidence.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1936,0.39755000000000001,0.17460502092050209,7.0300000000000001E-2,null,1936,0.441,0.1474,5.1699999999999996E-2,0.24145278829160777,6.1073428152681498E-2,null,null,1936,0.46590000000000004,0.11950000000000002,0.15350000000000003,0.19289999999999999,7.5700000000000003E-2,0.44770000000000004,0.1764,6.6900000000000001E-2,0.29694999999999999,8.5969999999999991E-2]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1938,0.38329999999999997,0.16944904458598728,6.5700000000000008E-2,null,1938,0.42520000000000002,0.14269999999999999,5.0499999999999996E-2,0.24503682591239323,6.0359150910564797E-2,null,null,1938,0.44069999999999998,0.1273,0.15590000000000001,0.1575,5.8799999999999998E-2,0.43,0.14730000000000001,5.16E-2,0.29833999999999999,8.1270000000000009E-2]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1941,0.35189999999999999,0.14189904458598726,0.05,null,1941,0.38700000000000001,0.1288,4.2699999999999995E-2,0.22302269903127042,5.0936480250208319E-2,null,null,1941,0.41930000000000001,0.11940000000000001,0.14199999999999999,0.15789999999999998,5.8099999999999999E-2,0.41020000000000001,0.15010000000000001,5.2900000000000003E-2,0.29333999999999999,8.1110000000000002E-2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1942,0.3407,0.13207229299363057,4.4400000000000002E-2,null,1942,0.35039999999999999,0.1153,3.6400000000000002E-2,0.22193062982056108,4.8667474275091938E-2,null,null,1942,0.36130000000000001,0.10330000000000002,0.1237,0.1343,4.8099999999999997E-2,0.35489999999999999,0.12909999999999999,4.4800000000000006E-2,0.27079999999999999,7.2120000000000004E-2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1943,0.33649999999999997,0.12838726114649682,4.2300000000000004E-2,null,1943,0.3226,0.1013,3.0099999999999998E-2,0.22590987779712618,4.6647669918068166E-2,null,null,1943,0.33689999999999998,9.6099999999999991E-2,0.11769999999999997,0.1231,4.2599999999999999E-2,0.32669999999999999,0.1148,3.78E-2,0.25879000000000002,6.4240000000000005E-2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1944,0.33449999999999996,0.12663248407643313,4.1299999999999996E-2,null,1944,0.29420000000000002,8.3699999999999997E-2,2.3199999999999998E-2,0.22954335414728622,5.1542692723447178E-2,null,null,1944,0.3251,9.7399999999999987E-2,0.1149,0.1128,3.7599999999999995E-2,0.3155,0.10539999999999999,3.3300000000000003E-2,0.24609000000000003,5.5640000000000002E-2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1945,0.33649999999999997,0.12838726114649682,4.2300000000000004E-2,null,1945,0.29699999999999999,7.5399999999999995E-2,1.9599999999999999E-2,0.24115695507050983,5.9403434524724623E-2,null,null,1945,0.34420000000000001,9.6300000000000024E-2,0.12269999999999999,0.12520000000000001,4.1599999999999998E-2,0.32640000000000002,0.11070000000000001,3.32E-2,0.24045000000000002,5.7259999999999998E-2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1946,0.34149999999999997,0.13277420382165606,4.4800000000000006E-2,null,1946,0.32869999999999999,9.2200000000000004E-2,2.6099999999999998E-2,0.26941143255511002,6.5731856679198439E-2,null,null,1946,0.36700000000000005,9.9300000000000027E-2,0.13489999999999999,0.1328,4.3899999999999995E-2,0.34619999999999995,0.1176,3.4300000000000004E-2,0.25103999999999999,6.3979999999999995E-2]
[null,null,null,null,null,null,null,null,null,null,3,null,null,null,null,null,null,null,null,1947,0.33390000000000003,0.126106050955414,4.0999999999999995E-2,null,1947,0.33200000000000002,9.2200000000000004E-2,2.5899999999999999E-2,0.25686020589682357,6.8280875338387476E-2,null,null,1947,0.34350000000000003,9.6700000000000022E-2,0.12719999999999998,0.11960000000000001,3.9199999999999999E-2,0.33020000000000005,0.10949999999999999,3.2400000000000005E-2,0.24969000000000002,6.2740000000000004E-2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1948,0.32909999999999995,0.12189458598726115,3.8599999999999995E-2,null,1948,0.32350000000000001,8.7499999999999994E-2,2.4300000000000002E-2,0.26332640092245169,6.910325844925605E-2,null,null,1948,0.35009999999999997,9.9499999999999991E-2,0.12819999999999998,0.12240000000000001,4.0599999999999997E-2,0.3372,0.11269999999999999,3.44E-2,0.25033,6.2089999999999999E-2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1949,0.32250000000000001,0.11470000000000001,3.4500000000000003E-2,null,1949,0.32200000000000001,9.01E-2,2.6099999999999998E-2,0.24430897923853706,7.0829893997576499E-2,null,null,1949,0.34749999999999998,0.10239999999999999,0.12780000000000002,0.1173,3.8300000000000001E-2,0.33759999999999996,0.10949999999999999,3.3399999999999999E-2,0.25002999999999997,6.1189999999999994E-2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1950,{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},null,1950,0.31969999999999998,8.9800000000000005E-2,2.6000000000000002E-2,0.26979259594807981,6.992564156012461E-2,null,null,1950,0.35560000000000003,0.10030000000000001,0.12710000000000002,0.12820000000000001,4.3899999999999995E-2,0.3387,0.11359999999999999,3.5299999999999998E-2,0.25184000000000001,6.2350000000000003E-2]
[null,null,null,null,null,null,null,null,null,null,"Change","Select the countries above to see how well the K/Y ratio (on the left y axis)",null,null,null,null,null,null,null,1951,0.31670000000000004,0.10890000000000001,3.2099999999999997E-2,null,1951,0.32929999999999998,0.09,2.5499999999999998E-2,0.26824901325476302,6.8955976658126875E-2,null,null,1951,0.3422,0.1002,0.1241,0.11789999999999999,3.8900000000000004E-2,0.32819999999999999,0.1052,3.1200000000000002E-2,0.24706,5.9699999999999996E-2]
[null,null,null,null,null,null,null,null,null,null,null,"matches up to the Top 10% share of income (on the right y axis).",null,null,null,null,null,null,null,1952,0.30980000000000002,0.10199999999999999,2.9500000000000002E-2,null,1952,0.33189999999999997,9.1600000000000001E-2,2.53E-2,0.26688144679963238,7.0338284168112677E-2,null,null,1952,0.33210000000000001,0.1014,0.12280000000000001,0.1079,3.4300000000000004E-2,0.32069999999999999,9.7599999999999992E-2,2.76E-2,0.24424999999999999,5.7419999999999999E-2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1953,0.30499999999999999,9.7200000000000009E-2,2.7699999999999999E-2,null,1953,0.32890000000000003,0.09,2.4799999999999999E-2,0.24877891435876809,6.712431198518426E-2,null,null,1953,0.3231,0.10300000000000001,0.12110000000000001,9.9000000000000005E-2,3.0600000000000002E-2,0.31379999999999997,9.0800000000000006E-2,2.5099999999999997E-2,0.24279000000000001,5.6760000000000005E-2]
[null,"Piketty knows that capital is much more unequally distributed than income so",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1954,0.30630000000000002,9.6699999999999994E-2,2.7200000000000002E-2,null,1954,0.33529999999999999,9.1400000000000009E-2,2.4500000000000001E-2,0.25486636484624331,7.0658470060100009E-2,null,null,1954,0.33640000000000003,0.10339999999999999,0.12530000000000002,0.10769999999999999,3.49E-2,0.32119999999999999,9.3900000000000011E-2,2.5699999999999997E-2,0.24132999999999999,5.6100000000000004E-2]
[null,"economies with high K/Y ratios are likely to also exhibit high income inequality.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1955,0.30259999999999998,9.3000000000000013E-2,2.6499999999999999E-2,null,1955,0.34420000000000001,9.3299999999999994E-2,2.4799999999999999E-2,0.25744179486087559,7.2884429633281372E-2,null,null,1955,0.33939999999999998,0.10339999999999996,0.12540000000000001,0.1106,3.7100000000000001E-2,0.31769999999999998,9.1799999999999993E-2,2.4900000000000002E-2,0.24331999999999998,5.5830000000000005E-2]
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[null,"The claim that high K/Y is associated with high income inequality makes sense because owners of capital get unearned income in addition to labor income.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1957,0.29659999999999997,8.6999999999999994E-2,2.3700000000000002E-2,null,1957,0.34740000000000004,9.3699999999999992E-2,2.4399999999999998E-2,0.26019438610117679,7.6520380706424793E-2,null,null,1957,0.32990000000000003,0.10390000000000001,0.12440000000000001,0.1016,3.1800000000000002E-2,0.31690000000000002,8.9800000000000005E-2,2.3599999999999999E-2,0.24599499999999999,5.4754999999999998E-2]
[null,"Many other factors, however, affect income inequality and the K/Y and Top 10% data for USA and France don't show the connection as clearly.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1958,0.29719999999999996,8.7599999999999997E-2,2.3799999999999998E-2,null,1958,0.34049999999999997,9.01E-2,2.3399999999999997E-2,0.27473669944430612,8.315946730295469E-2,null,null,1958,0.33560000000000001,0.10630000000000002,0.12719999999999998,0.10210000000000001,3.2199999999999999E-2,0.3211,8.8300000000000003E-2,2.29E-2,0.24667999999999998,5.3949999999999998E-2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1959,0.29960000000000003,8.5999999999999993E-2,2.3E-2,null,1959,0.35880000000000001,9.4600000000000004E-2,2.3700000000000002E-2,0.26782111900050182,8.2078233573112003E-2,null,null,1959,0.34,0.1061,0.12740000000000001,0.1065,3.4500000000000003E-2,0.32030000000000003,8.7499999999999994E-2,2.1899999999999999E-2,0.24946499999999999,5.3280000000000001E-2]
[null,"Here's the point: a lot of things affect how income is distributed: politics (tax brackets and deductions), CEO pay, where we are in the business cycle, the stock market's performance, and on and on.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1960,0.30229999999999996,8.8699999999999987E-2,2.4500000000000001E-2,null,1960,0.36109999999999998,9.7100000000000006E-2,2.4500000000000001E-2,0.26404205645175344,8.2887483095291967E-2,null,null,1960,0.33479999999999999,0.10909999999999996,0.12540000000000001,0.1003,3.2500000000000001E-2,0.31659999999999999,8.3599999999999994E-2,2.1000000000000001E-2,0.25225000000000003,5.2610000000000004E-2]
[null,"We do not have an economic theory that directly explains the distribution of income. There are too many contributing factors.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1961,{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},null,1961,0.36820000000000003,9.8800000000000013E-2,2.4799999999999999E-2,0.27405189621225268,7.9443740149753472E-2,null,null,1961,0.34250000000000003,0.1075,0.12859999999999999,0.10640000000000001,3.6499999999999998E-2,0.31900000000000001,8.3400000000000002E-2,2.0499999999999997E-2,0.25212000000000001,5.1970000000000002E-2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1962,0.29370000000000002,8.43E-2,2.29E-2,null,1962,0.35880000000000001,9.4600000000000004E-2,2.3399999999999997E-2,0.27379054764986288,7.7103097556697253E-2,null,null,1962,0.33700000000000002,0.10890000000000004,0.12859999999999999,9.9499999999999991E-2,3.1899999999999998E-2,0.32040000000000002,8.2699999999999996E-2,1.9799999999999998E-2,0.25224000000000002,5.1559999999999995E-2]
["Key Point -->","But we do have a model that explains the K/Y ratio. ",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1963,0.2994,8.4900000000000003E-2,2.23E-2,null,1963,0.36409999999999998,9.4299999999999995E-2,2.29E-2,0.27235402500146666,7.6215996645060471E-2,null,null,1963,0.33779999999999999,0.10940000000000001,0.12920000000000001,9.9199999999999997E-2,3.15E-2,0.3201,8.1600000000000006E-2,1.9599999999999999E-2,0.25187999999999999,5.1379999999999995E-2]
[null,"And we know that when K/Y is high, we are likely to see high income inequality.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1964,0.29909999999999998,8.48E-2,2.2599999999999999E-2,null,1964,0.36840000000000006,9.5600000000000004E-2,2.3E-2,0.28029419066315708,7.7109546316870864E-2,null,null,1964,0.34420000000000001,0.10920000000000002,0.13019999999999998,0.1048,3.3700000000000001E-2,0.31640000000000001,8.0199999999999994E-2,1.9699999999999999E-2,0.25152000000000002,5.1200000000000002E-2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1965,0.29880000000000001,8.5500000000000007E-2,2.2799999999999997E-2,null,1965,0.3715,9.5799999999999996E-2,2.3E-2,0.2817737625591627,7.9427779589206687E-2,null,null,1965,0.3478,0.10900000000000003,0.12989999999999999,0.10890000000000001,3.6600000000000001E-2,0.31519999999999998,8.0700000000000008E-2,2.0400000000000001E-2,0.25248000000000004,5.1379999999999995E-2]
[null,"In fact, Piketty even has a name for societies with high K/Y:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1966,0.28939999999999999,7.9199999999999993E-2,2.0400000000000001E-2,null,1966,0.36460000000000004,9.3599999999999989E-2,2.2599999999999999E-2,0.28387132701586337,8.2225670080660229E-2,null,null,1966,0.3367,0.1075,0.12740000000000001,0.1018,3.39E-2,0.31980000000000003,8.3699999999999997E-2,2.1499999999999998E-2,0.25344,5.1559999999999995E-2]
[null,"PATRIMONIAL CAPITALISM",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1967,0.2878,7.690000000000001E-2,1.9099999999999999E-2,null,1967,0.36210000000000003,9.3599999999999989E-2,2.29E-2,0.28387691370238938,8.0202252250083775E-2,null,null,1967,0.34439999999999998,0.10739999999999998,0.12959999999999999,0.1074,3.6799999999999999E-2,0.32049999999999995,8.43E-2,2.1600000000000001E-2,0.25773000000000001,5.3350000000000002E-2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1968,0.28550000000000003,7.5399999999999995E-2,1.8700000000000001E-2,null,1968,0.34799999999999998,8.77E-2,2.1499999999999998E-2,0.27939224374429572,7.947945119323549E-2,null,null,1968,0.34850000000000003,0.10700000000000003,0.12939999999999999,0.11210000000000001,4.0199999999999993E-2,0.31980000000000003,8.3499999999999991E-2,2.1499999999999998E-2,0.25602000000000003,5.2409999999999998E-2]
[null,"This is a pretty good name: patrimony means inheritance and a society with high K/Y is one with a high capital stock relative to national income.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1969,0.28720000000000001,7.46E-2,1.8500000000000003E-2,null,1969,0.33960000000000001,8.5500000000000007E-2,2.0899999999999998E-2,0.27467721557737834,6.6952509589893655E-2,null,null,1969,0.33929999999999999,0.10850000000000001,0.1273,0.10349999999999999,3.6900000000000002E-2,0.31819999999999998,8.0199999999999994E-2,0.02,0.25707000000000002,5.1879999999999996E-2]
[null,"This capital will be passed on and inherited and Piketty goes on another data-gathering binge to show how wealth is incredibly unequally distributed.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1970,0.28820000000000001,7.0499999999999993E-2,1.6399999999999998E-2,null,1970,0.33140000000000003,8.3299999999999999E-2,2.0199999999999999E-2,0.27410292793828789,6.5200467998614092E-2,null,null,1970,0.32630000000000003,0.10970000000000002,0.1263,9.0299999999999991E-2,2.7799999999999998E-2,0.31509999999999999,7.8E-2,1.9400000000000001E-2,0.25669000000000003,5.1330000000000001E-2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1971,0.29289999999999999,7.0199999999999999E-2,1.67E-2,null,1971,0.33350000000000002,8.4700000000000011E-2,2.07E-2,0.27807889716647394,6.6427697327113372E-2,null,null,1971,0.33340000000000003,0.11080000000000002,0.12860000000000002,9.4E-2,2.9900000000000003E-2,0.3175,7.7899999999999997E-2,1.9099999999999999E-2,0.25670999999999999,5.1820000000000005E-2]
[null,"We will not pursue that aspect of Piketty's work here, instead let's end this section on data by really reinforcing exactly what high K/Y means.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1972,0.28899999999999998,6.9400000000000003E-2,1.61E-2,null,1972,0.33030000000000004,8.5199999999999998E-2,2.1099999999999997E-2,0.27281991631829094,6.4386194221864992E-2,null,null,1972,0.33590000000000003,0.11070000000000003,0.1288,9.64E-2,3.1300000000000001E-2,0.31620000000000004,7.7499999999999999E-2,1.9199999999999998E-2,0.25811000000000001,5.3230000000000006E-2]
[]
[null,"Click",null,null,"https://player.vimeo.com/video/238606237",null,null,null,null,null,null,null,null,null,null,null,null,null,null,1973,0.28309999999999996,6.9900000000000004E-2,1.6799999999999999E-2,null,1973,0.33899999999999997,8.8699999999999987E-2,2.2599999999999999E-2,0.27225309516111407,6.8689692969455873E-2,null,null,1973,0.33329999999999999,0.11119999999999998,0.1305,9.1600000000000001E-2,2.76E-2,0.31850000000000001,7.7399999999999997E-2,1.89E-2,0.26140999999999998,5.4219999999999997E-2]
[null,null,null,null,"Click the link above if the button does not work.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,1974,0.28100000000000003,6.54E-2,1.5800000000000002E-2,null,1974,0.33329999999999999,8.5000000000000006E-2,2.0899999999999998E-2,0.26433490253079089,6.3320886634117279E-2,null,null,1974,0.33310000000000001,0.11190000000000001,0.13,9.1199999999999989E-2,2.7300000000000001E-2,0.3236,8.1199999999999994E-2,2.1099999999999997E-2,0.26613999999999999,5.6639999999999996E-2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1975,0.2782,6.0999999999999999E-2,1.3999999999999999E-2,null,1975,0.33409999999999995,8.48E-2,2.0799999999999999E-2,0.26928385225974633,6.4422834714858962E-2,null,null,1975,0.33429999999999999,0.11449999999999999,0.13110000000000002,8.8699999999999987E-2,2.5600000000000001E-2,0.32619999999999999,8.0100000000000005E-2,2.0400000000000001E-2,0.26463999999999999,5.6399999999999999E-2]
[null,"Those elite British nobles inherited the estate and live off of their capital income in high style.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1976,0.27889999999999998,5.8899999999999994E-2,1.3000000000000001E-2,null,1976,0.33189999999999997,8.4399999999999989E-2,2.0799999999999999E-2,0.2632603096205422,5.9988316205953421E-2,null,null,1976,0.33409999999999995,0.11439999999999997,0.13109999999999999,8.8599999999999998E-2,2.5899999999999999E-2,0.32420000000000004,7.8899999999999998E-2,2.0199999999999999E-2,0.26655999999999996,5.7350000000000005E-2]
[null,"The workers (of which there are many, many more of than the idle rich) have only their labor income.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1977,0.27960000000000002,5.9299999999999999E-2,1.2699999999999999E-2,null,1977,0.31679999999999997,7.7899999999999997E-2,1.9400000000000001E-2,0.26100898070204237,5.7882852252210001E-2,null,null,1977,0.33579999999999999,0.11459999999999998,0.13090000000000002,9.0299999999999991E-2,2.7099999999999999E-2,0.32429999999999998,7.9000000000000001E-2,2.0400000000000001E-2,0.26937,5.8560000000000001E-2]
[null,"The gap between rich and poor, upstairs and downstairs is a chasm.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1978,0.27779999999999999,5.7200000000000001E-2,1.24E-2,null,1978,0.31379999999999997,7.8E-2,1.9299999999999998E-2,0.25957678355501812,5.742291414752116E-2,null,null,1978,0.33490000000000003,0.11450000000000003,0.13089999999999999,8.9499999999999996E-2,2.6499999999999999E-2,0.32439999999999997,7.9500000000000001E-2,2.0799999999999999E-2,0.27431,6.0560000000000003E-2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1979,0.28370000000000001,5.9299999999999999E-2,1.3000000000000001E-2,null,1979,0.31030000000000002,7.8200000000000006E-2,1.9699999999999999E-2,0.25766975191563612,5.6751574235642213E-2,null,null,1979,0.34210000000000002,0.11280000000000001,0.12969999999999998,9.9600000000000008E-2,3.44E-2,0.32350000000000001,8.0299999999999996E-2,2.1600000000000001E-2,0.27631,6.2169999999999996E-2]
[null,"Think Downton Abbey when you see values of K/Y of 7 or 8 years of national income.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1980,{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},null,1980,0.30690000000000001,7.6299999999999993E-2,1.9099999999999999E-2,0.26173008137943532,5.8248031799074541E-2,null,null,1980,0.34630000000000005,0.11460000000000001,0.13150000000000003,0.1002,3.4099999999999998E-2,0.32869999999999999,8.1799999999999998E-2,2.23E-2,0.28061000000000003,6.4250000000000002E-2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1981,0.31030000000000002,6.6699999999999995E-2,1.5300000000000001E-2,null,1981,0.30730000000000002,7.5499999999999998E-2,1.89E-2,0.26000988081638454,5.8325735001967957E-2,null,null,1981,0.34539999999999998,0.115,0.13019999999999998,0.1002,3.5699999999999996E-2,0.32719999999999999,8.0299999999999996E-2,2.23E-2,0.28143999999999997,6.4250000000000002E-2]
["Summary:","This sheet explains Piketty's data contribution.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1982,0.31230000000000002,6.8499999999999991E-2,1.61E-2,null,1982,0.29930000000000001,7.0699999999999999E-2,1.72E-2,0.2567958730344046,5.802659403372977E-2,null,null,1982,0.3533,0.115,0.13029999999999997,0.10800000000000001,4.1799999999999997E-2,0.3322,8.3900000000000002E-2,2.4500000000000001E-2,0.28549000000000002,6.6720000000000002E-2]
[null,"He and his colleagues amassed very long series of K and Y for several countries.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1983,0.31759999999999999,6.83E-2,1.5800000000000002E-2,null,1983,0.30430000000000001,6.9900000000000004E-2,1.6299999999999999E-2,0.25988979253948691,5.9086298604435032E-2,null,null,1983,0.36380000000000001,0.11530000000000001,0.13290000000000002,0.11560000000000001,4.6199999999999998E-2,0.33689999999999998,8.5900000000000004E-2,2.6099999999999998E-2,0.29086000000000001,6.9550000000000001E-2]
[null,"They also created data sets on income that include the ultra-rich, using tax records and other sources.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1984,0.32520000000000004,7.1599999999999997E-2,1.67E-2,null,1984,0.30519999999999997,7.0300000000000001E-2,1.6500000000000001E-2,0.25916495187614086,5.7228371743320822E-2,null,null,1984,0.3674,0.11450000000000003,0.13299999999999998,0.11990000000000001,4.9800000000000004E-2,0.33950000000000002,8.8900000000000007E-2,2.8300000000000002E-2,0.29609999999999997,7.2679999999999995E-2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1985,0.32650000000000001,7.400000000000001E-2,1.8200000000000001E-2,null,1985,0.3105,7.2000000000000008E-2,1.7000000000000001E-2,0.26363838158890651,6.0671273459979413E-2,null,null,1985,0.37560000000000004,0.11440000000000002,0.13450000000000001,0.12670000000000001,5.3200000000000004E-2,0.34250000000000003,9.0899999999999995E-2,2.9100000000000001E-2,0.2974,7.2759999999999991E-2]
[null,"There are three parts to the story here:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1986,0.32939999999999997,7.5499999999999998E-2,1.8600000000000002E-2,null,1986,0.31390000000000001,7.4400000000000008E-2,1.8100000000000002E-2,0.26376420515989468,5.9137904879638555E-2,null,null,1986,0.40630000000000005,0.11140000000000004,0.13569999999999999,0.15920000000000001,7.400000000000001E-2,0.34570000000000001,9.1300000000000006E-2,2.87E-2,0.29943000000000003,7.3259999999999992E-2]
["Part I:","The K/Y ratio, more simply known as b, is a key variable. It expresses the intensity of the presence of capital in terms of the number of years of national income.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1987,0.33270000000000005,7.7800000000000008E-2,1.9606761565836305E-2,null,1987,0.31730000000000003,7.7499999999999999E-2,1.9799999999999998E-2,0.26253273276890821,5.7361899605891796E-2,null,null,1987,0.38250000000000001,0.11710000000000001,0.13879999999999998,0.12659999999999999,4.9000000000000002E-2,0.36479999999999996,0.1075,3.73E-2,0.30589,8.1530000000000005E-2]
["K/Y = b","b of 7 or 8 are extremely high, while 2 or 3 are quite low.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1988,0.34210000000000002,8.6300000000000002E-2,2.332740213523132E-2,null,1988,0.32090000000000002,7.9199999999999993E-2,2.06E-2,0.26422281720557161,5.8404126328832767E-2,null,null,1988,0.40630000000000005,0.11340000000000003,0.13799999999999998,0.15490000000000001,6.8000000000000005E-2,0.38630000000000003,0.13170000000000001,5.21E-2,0.31945000000000001,9.3850000000000003E-2]
[null,"The data for the UK and other European countries show a U-shape: K/Y was high, then fell, but has been rising again.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1989,0.34149999999999997,8.6699999999999999E-2,2.3502491103202849E-2,null,1989,0.32420000000000004,8.2100000000000006E-2,2.2000000000000002E-2,0.26147618576745285,5.7705689988801642E-2,null,null,1989,0.40079999999999999,0.11529999999999997,0.1406,0.1449,0.06,0.38469999999999999,0.12609999999999999,4.7400000000000005E-2,0.31529000000000001,8.6940000000000003E-2]
[null,"It is complicated, however; the USA's pattern is different.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1990,0.36899999999999999,9.8000000000000004E-2,2.8448754448398578E-2,null,1990,0.32640000000000002,8.2299999999999998E-2,2.2000000000000002E-2,0.26245092381306784,5.783611991886508E-2,null,null,1990,0.39979999999999999,0.11569999999999997,0.14080000000000001,0.14330000000000001,5.8200000000000002E-2,0.38840000000000002,0.1298,4.9000000000000002E-2,0.31794,8.993000000000001E-2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1991,0.3765,0.1032,3.0724911032028467E-2,null,1991,0.32439999999999997,7.9699999999999993E-2,2.07E-2,0.25933877810245015,5.6645391914985008E-2,null,null,1991,0.39549999999999996,0.11829999999999999,0.14360000000000001,0.1336,5.1200000000000002E-2,0.38380000000000003,0.1217,4.36E-2,0.31431000000000003,8.5610000000000006E-2]
["Part II:","Instead of using synthetic measures like the Gini Coefficient, Piketty likes the simple Top 10% income share.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1992,0.37640000000000001,9.8599999999999993E-2,2.8711387900355868E-2,null,1992,0.32229999999999998,7.7499999999999999E-2,1.9699999999999999E-2,0.2623607256829722,6.0444302227101773E-2,null,null,1992,0.40820000000000001,0.11760000000000001,0.1439,0.1467,6.0299999999999999E-2,0.3982,0.1348,5.21E-2,0.32450000000000001,9.6259999999999998E-2]
["Top 10%","Using his high-quality data, he finds the same U-shape: worse at the beginning of the 20th century, then better, and now worse again.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1993,0.38340000000000002,0.1036,3.0899999999999997E-2,null,1993,0.32219999999999999,7.6499999999999999E-2,1.9400000000000001E-2,0.25795974078675088,5.8615012428815685E-2,null,null,1993,0.40679999999999999,0.11850000000000001,0.14589999999999997,0.1424,5.7300000000000004E-2,0.39479999999999998,0.12820000000000001,4.7199999999999999E-2,0.31849,9.0540000000000009E-2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1994,0.38329999999999997,0.106,3.1E-2,null,1994,0.32369999999999999,7.7100000000000002E-2,1.9799999999999998E-2,0.25669827177453114,5.7534732465627236E-2,null,null,1994,0.4078,0.11890000000000001,0.14660000000000001,0.14230000000000001,5.7000000000000002E-2,0.39600000000000002,0.1285,4.7E-2,0.31535000000000002,8.72E-2]
["Part III:","This is the crucial logic of Piketty's argument:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1995,0.3851,0.1075,3.2400000000000005E-2,null,1995,0.32409999999999994,7.6999999999999999E-2,1.9599999999999999E-2,0.25378984135827864,5.615605327789927E-2,null,null,1995,0.42109999999999997,0.11890000000000001,0.14989999999999998,0.15229999999999999,6.2100000000000002E-2,0.40539999999999998,0.1353,4.9800000000000004E-2,0.32490999999999998,9.2719999999999997E-2]
["b<->Top 10%","While we don't know the drivers of income inequality, we do know how b is generated.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1996,0.39299999999999996,0.11900000000000001,4.1299999999999996E-2,null,1996,0.32040000000000002,7.7300000000000008E-2,2.0099999999999996E-2,0.25445937317605727,5.6304200517478281E-2,null,null,1996,0.43479999999999996,0.11719999999999996,0.1507,0.16690000000000002,7.2400000000000006E-2,0.41159999999999997,0.1411,5.33E-2,0.33244000000000001,9.8269999999999996E-2]
[null,"Since there is a connection between K/Y and Top 10% income inequality, by knowing where b is headed, we know where inequality is going.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1997,0.38939999999999997,0.1207,4.1500000000000002E-2,null,1997,0.32170000000000004,7.7699999999999991E-2,2.0099999999999996E-2,0.25727665890372192,5.6927581053811335E-2,null,null,1997,0.44640000000000002,0.115,0.1512,0.1802,8.1799999999999998E-2,0.41729999999999995,0.1477,5.8099999999999999E-2,0.33972000000000002,0.10461000000000001]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1998,0.3947,0.12529999999999999,4.4400000000000002E-2,null,1998,0.32590000000000002,7.9399999999999998E-2,2.0899999999999998E-2,0.26063557083221311,5.8173100845207472E-2,null,null,1998,0.45390000000000003,0.11289999999999999,0.15010000000000001,0.19089999999999999,0.09,0.42119999999999996,0.15289999999999998,6.2E-2,0.34433000000000002,0.11005000000000001]
[null,"Piketty is worried about the future because he thinks we could return to a Downton Abbey-like society, with b values of 7 or 8 years of national income.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1999,0.38969999999999999,0.12509999999999999,4.5400000000000003E-2,null,1999,0.33,8.1500000000000003E-2,2.18E-2,0.26391450866716887,5.9711684116932104E-2,null,null,1999,0.4647,0.1125,0.15179999999999999,0.20039999999999999,9.6199999999999994E-2,0.42670000000000002,0.15869999999999998,6.6400000000000001E-2,0.35183999999999999,0.1167]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2000,0.38429999999999997,0.12670000000000001,4.6399999999999997E-2,null,2000,0.33049999999999996,8.2899999999999988E-2,2.2499999999999999E-2,0.26431437913484634,6.0737406298081852E-2,null,null,2000,0.47609999999999997,0.11,0.15090000000000001,0.2152,0.10880000000000001,0.43109999999999998,0.16489999999999999,7.1300000000000002E-2,0.35460999999999998,0.1226]
[null,"In 2010, the USA had a b of 4.3 years of national income (see cell M38).",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2001,0.39329999999999998,0.12710000000000002,4.5100000000000001E-2,null,2001,0.33090000000000003,8.43E-2,2.3300000000000001E-2,0.26463427550898844,6.1763128479231606E-2,null,null,2001,0.44819999999999999,0.11469999999999998,0.15130000000000002,0.1822,8.3699999999999997E-2,0.42229999999999995,0.1537,6.2600000000000003E-2,0.3422,0.10876]
[null,"So that's a perfectly respectable K/Y and everything is fine, right?",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2002,0.38689999999999997,0.12269999999999999,4.2199999999999994E-2,null,2002,0.33030000000000004,8.4600000000000009E-2,2.35E-2,0.26415443094777541,6.1982926089477988E-2,null,null,2002,0.43819999999999998,0.11749999999999999,0.15210000000000001,0.1686,7.3399999999999993E-2,0.42359999999999998,0.14990000000000001,5.9400000000000001E-2,0.33378999999999998,0.10317999999999999]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2003,0.3775,0.12119999999999999,4.2300000000000004E-2,null,2003,0.33110000000000001,8.5500000000000007E-2,2.3700000000000002E-2,0.26479422369605943,6.2642318920217127E-2,null,null,2003,0.44530000000000003,0.11770000000000003,0.15229999999999996,0.17530000000000001,7.8700000000000006E-2,0.42759999999999998,0.15210000000000001,6.1100000000000002E-2,0.33109,0.10215]
[null,"Not so fast. What if we knew K/Y was going to rise?",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2004,0.39539999999999997,0.12890000000000001,4.5700000000000005E-2,null,2004,0.33450000000000002,8.7300000000000003E-2,2.4500000000000001E-2,0.2675133428762666,6.3961104581695363E-2,null,null,2004,0.46399999999999997,0.11449999999999996,0.15200000000000002,0.19750000000000001,9.4600000000000004E-2,0.43640000000000001,0.16339999999999999,6.9000000000000006E-2,0.34183999999999998,0.11044999999999999]
[null,"This, of course, begs questions like these:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2005,0.41619999999999996,0.14249999999999999,5.1900000000000002E-2,null,2005,0.32890000000000003,8.7300000000000003E-2,2.4799999999999999E-2,0.26803479363827831,6.6961104581695366E-2,null,null,2005,0.48330000000000001,0.11170000000000002,0.15239999999999995,0.21920000000000001,0.10980000000000001,0.44939999999999997,0.17679999999999998,7.7600000000000002E-2,0.34651999999999999,0.11434]
[null,"Where does K/Y come from? How is it determined? What influences it and where is headed?",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2006,0.4199,0.1482,5.5500000000000001E-2,null,2006,0.3281,8.9399999999999993E-2,2.6499999999999999E-2,0.26839500088999424,6.9499687853420006E-2,null,null,2006,0.49320000000000003,0.11240000000000001,0.15259999999999999,0.22820000000000001,0.1159,0.45500000000000002,0.18059999999999998,7.9199999999999993E-2,0.35058999999999996,0.11724999999999999]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2007,0.42609999999999998,0.15439999999999998,6.0499999999999998E-2,null,2007,0.33149999999999996,9.2499999999999999E-2,2.7418903803131993E-2,0.27211412007020142,7.177092982596589E-2,null,null,2007,0.49740000000000001,0.11070000000000001,0.15170000000000003,0.23499999999999999,0.12279999999999999,0.45669999999999999,0.18329999999999999,8.1600000000000006E-2,0.35703000000000001,0.12226000000000001]
[null,"This is super-interesting. Let's find out.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2008,0.41676666666666667,0.14713333333333334,5.57E-2,null,2008,0.33030000000000004,8.8000000000000009E-2,2.6085011185682329E-2,0.27215443094777542,6.9473965672270252E-2,null,null,2008,0.48229999999999995,0.11709999999999994,0.15570000000000003,0.20949999999999999,0.10400000000000001,0.45960000000000001,0.1789,7.8200000000000006E-2,0.34856999999999999,0.11376]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2009,0.40429999999999999,0.13880000000000001,5.1100000000000007E-2,null,2009,0.32689999999999997,8.3800000000000013E-2,2.4840044742729307E-2,0.27043531176756819,6.8396799128821004E-2,null,null,2009,0.46500000000000002,0.12390000000000001,0.15989999999999999,0.1812,8.3000000000000004E-2,0.45469999999999999,0.1668,7.0400000000000004E-2,0.33659,0.10238]
["Click",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2010,0.41572222222222227,0.14677777777777778,5.5766666666666666E-2,null,2010,0.32956666666666662,8.8099999999999998E-2,2.6114653243847874E-2,0.27356795426184832,7.1547231542352374E-2,null,null,2010,0.47899999999999998,0.12179999999999999,0.1595,0.19769999999999999,9.5199999999999993E-2,0.46259999999999996,0.17420000000000002,7.4999999999999997E-2,0.34470000000000001,0.10897999999999999]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Source:","http://piketty.pse.ens.fr/en/capital21c2"]

{"sheet":"Algebra","index":4,"n_rows":155,"n_cols":9,"rows_kept":155,"cut":false,"hidden":true,"merged":[[1,0,1,1]]}
["This is from Humberto Barreto, Teaching Macroeconomics with Microsoft Excel, Cambridge University Press, 2015"]
["www.depauw.edu/site/learn/macroexcel/",null,null,"TechProgress.xls"]
[]
["Click"]
[]
["Below is what was displayed in the Piketty's Problem video on the Intro sheet."]
[]
["The model is solved in terms of capital per effective worker (k), not K/Y, but if you can follow the equations below, then you should be able to transform k into K/Y."]
[]
[]
[]
["Welcome (for the last time!) to the Algebra of the Solow Model"]
[]
["As was the case when population growth was added to the model, incorporating technological progress is neither easy nor particularly fun, but it does help you understand the model"]
["and how it is implemented in the EqPath sheet."]
[]
["Each step will be carefully described in this sheet."]
[]
["We get a different result than that obtained from incorporating n -- when we add g, we simply cannot get the standard Dk equation, it is an approximation."]
["If you are one of those people who need to know exactly what is going on, then read on."]
[]
["The Basic Idea"]
["Over time, the number of workers grows at a constant rate, n, and technology improves at a constant rate, g."]
[]
["Therefore, this year’s k, the stock of capital per worker, will change due to FOUR effects:"]
[]
[null,"1) investment – k will grow as more machines are added (from the share of output, s, devoted to making capital goods)"]
[]
[null,"2) depreciation – k will fall as machines wear out and are thrown away (based on d, the rate of depreciation)"]
[]
[null,"3) population growth – k will fall as there are more workers upon which to spread machines around; L grows at constant rate n"]
[]
[null,"4) technological progress – k will fall as improved technology makes it seem that there are (but there aren't, it's imaginary) more workers upon which to spread machines around"]
[null,"This is what we are adding to this model and we are doing it as imaginary workers because we know how to solve models with increasing population."]
[null,"The number of imaginary workers grows at rate g."]
[]
["The standard Dk equation captures the four influences on changes in capital per worker in one single equation that, when set equal to zero, becomes the steady-state (equilibrium) condition for the model:"]
[]
[null,null,null,null,"Equation Editor used throughout; double click an equation to edit it."]
[]
["How does the math work? How is this equation derived?"]
[]
["The algebra below presumes you are familiar with the algebra from the Population.xls workbook."]
[]
["The Solow Model with Constant Technological Progress"]
[]
["What happens to the model when L is growing at a constant rate, n, and we add labor-augmenting technological progress?"]
[]
["We return to the starting point:"]
[]
[]
["We divide both sides of the equation by the number of effective workers in time period t+1:"]
[]
[]
[]
["We assume constant population growth (which equals constant labor force growth since all people are workers), thus, we have, Lt+1 = (1+n)Lt.  "]
[]
["We assume constant technological progress, thus, we have, At+1 = (1+g)At.  "]
[]
["So, we can simply replace the Lt+1 values on the right-hand-side with (1+n)Lt and the At+1 values with (1+g)At:"]
[]
[]
[]
["With the subscripts equal to each other, we can apply the K/AL = k and Y/AL = y substitution:"]
[]
[null,null,null,null,null,null,null,"k and y are now in units of effective workers. This is a critical point that must be remembered."]
[]
["We have to get rid of the 1/(1+n)(1+g) term in front of the kt term to get Dk, but how?"]
[]
["We begin by reorganizing the terms on the right-hand side in anticipation of collecting the kt terms on the right-hand-side:"]
[]
[]
[]
["Now we can combine the two kt terms into one:"]
[]
[]
[]
["We can simplify the expression in the brackets by putting them over their common denominator:"]
[]
[]
[]
["We apply the same nifty algebra trick we used before, adding and subtracting terms that add up to zero from the equation and doing it in a way that gives us the solitary kt term that we seek."]
[]
[]
[null,null,null,null,null,null,null,null,"The trick is that 1 - (1+n)(1+g)/(1+n)(1+g) equals zero (since we are adding and subtracting 1), so we have not changed the equation."]
[]
["Then we multiply through by kt to get the isolated kt that was the reason we went through these steps:"]
[]
[null,null,null,null,null,null,null,null,"That is pretty clever, don't you agree?"]
[]
["We can now move the kt term to the left-hand side and simplify the expression within the brackets on the right-hand side by putting everything over the common denominator:"]
[]
[]
[]
["We have to clean up the numerator on the last term on the right-hand side, being really careful with the signs:"]
[]
[null,null,null,null,null,null,null,null,"Here is where n and g first appear in the steady-state condition, next to d."]
[]
["The left-hand side is now Dk, the ones in the bracket add up to zero so they disappear, and we can pull the minus signs on the remaining terms in front of the bracket like this:"]
[]
[]
[]
["We can simplify a bit by putting the right-hand side over the common denominator, (1 + n)(1 + g):"]
[]
[null,null,null,null,null,"Look at how g acts like n eroding k, but remember that this is NOT REAL, these are imaginary workers."]
[]
["You have to admit we are pretty close to Dk = syt - (d + n + g)kt.  The only thing we need to do is eliminate that (1 + n)(1 + g) term in the denominator and get rid of ng."]
[]
["How do we get the rest of the way?  "]
[]
["Well, it turns out that, strictly speaking, we don't!  Just like when we added population, at the steady-state solution, the (1 + n)(1 + g) term will not matter."]
[]
["Dk = 0 when the numerator is zero, that is, when the sy and (d + n + g + ng)k terms equal each other, no matter the value of the denominator on the right-hand side."]
[]
["In other words, when sy = (d + n + g + ng)k, k will repeat itself endlessly and, thus, will be at its steady-state solution, regardless of the denominator in the right-hand side."]
[]
["The upshot of all of this is that when we are at the steady-state solution, we can safely ignore the (1 + n)(1 + g) term and treat the steady-state condition as simply syt - (d + n + g)kt = 0."]
[]
["What about the ng term? Believe it or not, there is no way to finesse this. It is simply dropped."]
[]
["The rationale behind doing this is that ng will be small because n and g are both small; after all, if n = 0.01 and g = 0.02, then ng = 0.0002. "]
[]
["The work below shows the difference dropping the ng term has on the baseline problem in the EqPath sheet."]
[]
["Exogenous Variables",null,null,null,null,"Solving for steady-state k via analytical methods:"]
["g",0.02,"labor-augmenting tech change"]
["n",0.01,"%D population"]
["A forced equal to 1."]
["a",0.5,"productivity of capital"]
["s",0.3,"rate of saving"]
["d",0.1,"rate of depreciation"]
[]
["Click on the cells in the table to reveal the formulas."]
["The exogenous variable values are those in the green cells above. Change them to see the effect."]
[null,"Steady-state keff"]
["Exact",{"$f":"(B130/(B131+B127+B126+B127*B126))^(1/(1-B129))","v":5.3090955424833819},"Using Dk=sy-(d+n+g+ng)k "]
["Approximate",{"$f":"(B130/(B131+B127+B126))^(1/(1-B129))","v":5.3254437869822473},"Using Dk=sy-(d+n+g)k"]
[]
["Exact - Approximate",{"$f":"B136-B137","v":-1.6348244498865405E-2}]
["% Approx Error",{"$f":"B139/B137","v":-3.0698370225647267E-3},"The difference between Exact and Approximate, where the latter omits the ng term, is very small in typical cases."]
[null,null,"As n and g increase, the approximation error rises."]
[]
[]
["All of the macro textbooks sweep all of this under the rug and just show the standard (approximated) equation:"]
[]
[]
[]
["This allows the professor to say, \"See? If n = g = 0, it's just like the basic model where syt - dkt = 0. So memorize this new equation and you are all set.\""]
[]
["The EqPath sheet gets it exactly right, including the denominator and ng term in the evolution of the model."]
[]
["Now you know what is really going with the Solow Model with population growth and technological progress, instead of merely memorizing a steady-state equation."]
["Q. E. D."]
[]
["Click"]

{"sheet":"Cycle","index":5,"n_rows":101,"n_cols":15,"rows_kept":101,"cut":false,"hidden":true,"merged":[]}
["Flow"]
["Diagram"]
[]
[]
[]
[]
[null,"K (capital), L (labor), Y (output), C (consumption), and I (investment) are tracked each time period. "]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"INITIAL"]
[null,"The picture above may be worth a thousand words -- it expresses the cycle-logic of the Solow Model."]
[null,"Look at it and mentally walk through it. The repetitive behavior, the loop back to the start point, is the key."]
[null,"This is the model Piketty and macroeconomists use to understand economic growth."]
["Key Point -->","The Solow Model determines a steady-state (equilibrium) K/Y ratio."]
[]
["History","This model was first published in 1956 by Robert Solow and it won him a Nobel Prize in Economics."]
[null,"https://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/1987/solow-bio.html"]
[null,"Solow assumed a single composite good that can be consumed or used to make other goods (capital)."]
[null,"This magic stuff can transform itself into consumption goods (such as an apple or clothing) or become machinery."]
[null,"Solow measured everything in units of the composite good. We will assume that the composite good sells for $1/unit."]
[null,"We can then interpret output, consumption, investment, and capital in value (or monetary) terms."]
[]
[null,"Solow solved the model with math, but there is a steep learning curve along that route."]
[null,"There are time subscripts on the variables and it becomes complicated pretty quickly."]
[null,"Click"]
[null,null,null,"You don't actually have to click if you don't want to -- it's the algebra of the model and it will not make a lot of sense to most people."]
[]
[null,"The point of this workbook is that there is another path to understanding the Solow Model."]
[null,"We can simulate the model in Excel and then directly observe the results -- we do not need the math at all to solve and understand the model."]
[null,"Before we can do this, however, we need to make sure we exactly understand how the model functions."]
[]
["Walking","The flow diagram below is the same as the one above, but a new letter, s, has been added and it plays a crucial role. "]
["Through","The picture says that labor and capital produce output according to the production function, f(L,K)."]
[null,"Some of the output is consumed (C) and the rest is added to the existing capital (invested). The curve along the bottom shows that the process is then repeated. "]
[]
[]
[]
[]
[]
[]
[null,"Investment is special because it is tools, plant, and equipment that are used to make other goods."]
[null,"Investment is addition to the capital stock. Investment is literally new K."]
[null,"Investment is a flow (these goods are produced over a period of time) that is added to the existing K stock at the end of the year."]
[null,null,"Y will increase next year when I is added to existing K."]
[]
[null,"A crucial element of the model is the composition of output because the split between C and I determines changes in future output.  "]
["Key Parameter -->","The split is determined by the saving rate (s). This is the percentage, anywhere from 0 to 100%, of output that is saved (not consumed)."]
[null,"Everything that is saved is automatically invested."]
[null,"Consider two countries: in A, all output is consumption goods; while B pumps half of its output into Investment, making more machines.  "]
[null,"What do you think will happen over time?"]
[null,"Isn't it obvious that A's economy will remain stagnant (or decline if there is depreciation of capital) while B's will grow?   "]
[null,"After all, B's economy is Investing, that is, adding new plant and equipment, which can be used to make MORE output next year."]
[null,"In the Solow Model, s is given and does not change as the model cranks away and is attracted to its equilibrium position."]
[]
["Stepping","Because the cycle-logic of the Solow Model is so important, let's do one more thing before we reveal the full-scale simulation."]
["Through","We will step through a few years, slowly and carefully following the variables."]
[null,"Output is produced by labor and capital according to this function:"]
[null,"Y = L1/2K1/2"]
[null,"This is called a Cobb-Douglas production function. It says that output is the square root of the number of hours worked times the square root of the number of machines."]
[null,"If you have 4 hours of work and 9 machines, ta da, you get 2 x 3 = 6 units of output."]
[null,"The saving rate, s, is 25% so of the 6 units produced, 1/4 x 6 = 1.5 is saved and then invested (for next year) and the rest, 4.5, is consumed."]
[]
[null,"Begin stepping through the model by clicking the button below. Pay close attention to what happens and how the numbers are being calculated."]
[null,"Click"]
[]
[]
[]
[null,"We will track everything that happens in this table:"]
[null,"Year","L","K","Y","C","I","%DK","%DY","K/Y"]
[null,1,25,100,{"$f":"(C68^0.5)*(D68^0.5)","v":50},{"$f":"(3/4)*E68","v":37.5},{"$f":"(1/4)*E68","v":12.5},null,null,{"$f":"D68/E68","v":2}]
[null,2,25,{"$f":"D68+G68","v":112.5},{"$f":"(C69^0.5)*(D69^0.5)","v":53.033008588991066},{"$f":"(3/4)*E69","v":39.7747564417433},{"$f":"(1/4)*E69","v":13.258252147247767},{"$f":"(D69-D68)/D68","v":0.125},6.0660171779821324E-2,{"$f":"D69/E69","v":2.1213203435596424}]
[null,3,25,{"$f":"D69+G69","v":125.75825214724776},{"$f":"(C70^0.5)*(D70^0.5)","v":56.070993425131981},{"$f":"(3/4)*E70","v":42.053245068848987},{"$f":"(1/4)*E70","v":14.017748356282995},0.11785113019775786,5.7284791434057146E-2,{"$f":"D70/E70","v":2.2428397370052795}]
[null,4,25,{"$f":"D70+G70","v":139.77600050353075},{"$f":"(C71^0.5)*(D71^0.5)","v":59.113450352591236},{"$f":"(3/4)*E71","v":44.335087764443429},{"$f":"(1/4)*E71","v":14.778362588147809},0.11146583319136703,5.4260799418894799E-2,{"$f":"D71/E71","v":2.3645380141036494}]
[]
[]
[null,"After you finish stepping through the model, be sure to explore the cells in the table. Click and inspect the numbers and formulas."]
[null,"Get comfortable with the calculations -- nothing should be a mystery. The mechanics are straightforward even though the solution is not."]
[]
[null,"So this is the basic model. There are a few more bells and whistles (depreciation, population growth and technical progress), but the logic is the same."]
[null,"In fact, this is the workhorse model of modern growth theory and there have been extensions and improvements, but the core of a cyclical process is the same:"]
[null,null,"Inputs make output, which is split into consumption and investment (determined by the saving rate), which is added to previous K, and the process repeats."]
[]
[null,"There is one major idea that remains to be explained: the steady-state (also known as equilibrium)."]
[null,"But instead of doing that here (I'm guessing you were growing tired of clicking the buttons to crank out another year), we will do this on our"]
[null,"full-scale simulation platform."]
[]
["Summary:","We are poised to make the leap!"]
[null,"We know (from the video on the Intro sheet) that Piketty's Problem has two sides:"]
[null,null,"1) He is concerned about income and wealth inequality and wants to figure out how to measure, explain, and control it, but"]
[null,null,"2) The theoretical apparatus on which he relies (the Solow Model) is quite complicated."]
[null,"We know (from the Def and Data sheets) that inequality is influenced by many factors, but a high K/Y is associated with high inequality."]
[null,null,"A high K/Y is 7 or 8 years of national income (from the Understanding Beta video)"]
[null,null,"A high K/Y is the hallmark of Patrimonial Capitalism -- the K stock plays a dominant role and idle rich live off of unearned income a la Downton Abbey."]
[null,"We know that the Solow Model determines K/Y, but this sheet did not explain this because it did not explain how the cyclical process settles down."]
[null,"This sheet did, however, set the table. It emphasized the cyclical nature of the Solow Model's mechanics."]
[null,"With this prep work, we are ready to see the full-scale simulation and understand why Piketty is worried about what the future holds in terms of inequality."]
[]
[null,"Before you click the button, a word of warning: you will be presented with a complicated sheet."]
[null,"Take a moment to scroll around. Click on a few cells to see if they have numbers or formulas."]
[]
[null,"The steady-state is a crucial idea -- it tells us where the economy is tending and, once there, it will remain there. It's just like equilibrium."]
[null,"Enjoy!"]
[null,"Click"]

{"sheet":"Model","index":6,"n_rows":313,"n_cols":17,"rows_kept":313,"cut":false,"hidden":true,"merged":[]}
["Understanding Piketty via Simulation of the Solow Model",null,null,null,null,null,null,null,"Click the links below "]
["Exogenous Parameters",null,null,null,null,null,null,null,"the buttons if needed."]
["a",0.3,"exponent on K",null,null,"Click"]
["g",0.02,"tech progress",null,null,"(in order)","https://player.vimeo.com/video/239720469"]
["n",0.01,"pop growth rate"]
["s",0.25,"saving rate",null,null,null,"https://player.vimeo.com/video/240381464"]
["d",0.02,"depreciation rate"]
[null,null,null,null,null,null,"https://player.vimeo.com/video/240409378"]
[]
[null,null,null,null,null,null,null,null,null,null,null,"Steady-state:"]
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[null,null,null,null,null,null,null,null,null,null,null,"K/Y",null,null,null,"Per person"]
["Year","A","L","K","Y","C","I","depK","DK","%DK","%DY","b","r",null,null,"y = Y/L","%Dy"]
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{"sheet":"Final","index":7,"n_rows":46,"n_cols":10,"rows_kept":46,"cut":false,"hidden":true,"merged":[]}
["Main","Piketty thinks inequality is deeply baked into the DNA of capitalism."]
["Point","But we can get more or less inequality -- it depends on the parameters."]
[null,"Low g and n will produce high K/Y and we will get Patrimonial Capitalism."]
[null,null,"K/Y of 6 or 7 years of national income is high (think Downton Abbey)."]
[null,"A highly capitalized economy is associated with high income inequality."]
[null,null,"Capital is much more unevenly distributed than income so economies"]
[null,null,"with high K/Y will have more income inequality."]
[]
["Loose","r > g --> there is no mechanism that connects r and g so they can be close or far apart. "]
["Ends",null,"Piketty's warning is that r >>> g will produce high levels of income inequality that will destabilize society."]
[null,null,"The global tax on capital proposal is an attempt to close the gap between r and g."]
[]
[null,"Piketty says diffusion of knowledge and education for all tends to reduce inequality, but there are two key, different forces of divergence:"]
[null,null,"1) Labor income is becoming much more unequal, with a few earning superstar amounts and everyone else's earnings stagnant."]
[null,null,"2) High K/Y produces extreme inequality because K is much more unequally distributed than income from labor so a society where capital income is a dominant part of total income will be more unequal."]
[null,null,"Piketty says both of these forces are syncing up and driving massive inequality."]
[null,null,"This Excel file is only about the second of these forces and explains how the long run capital intensiveness of the economy is determined."]
[]
["Piketty v. ","Piketty is too complicated for non-experts. The only thing many Pikettians hear is that r > g so super rich are out of control. But remember:"]
["Pikettians","If something cannot go on forever, it will stop."]
[null,"Piketty knows this and he is not saying that the rich will continue to get an increasing share forever."]
[null,"Marx once said, \"I am not a Marxist.\" One day, Piketty will say \"I am not a Pikettian.\""]
[null,null,"By the way, Marx thought K/Y would rise without bound until there was a revolution."]
[null,null,"He was right that K/Y was rising, but he did not have Piketty's data and he did not understand the Solow Model like you do."]
[]
["The","Of course, there are anti-Pikettians also--there's even a book titled Anti-Piketty -->",null,null,null,null,null,null,null,"www.amazon.com/Anti-Piketty-Capital-21st-Century-Emmanuel-Martin/dp/1944424253"]
["Debate","There are many parts of Piketty's argument that are controversial, but the key variable is undoubtedly g."]
["Key Point -->","No one knows what g will be. No one knows how it is determined."]
[null,"These two are on opposite ends of the spectrum:"]
[null,null,"Pessimism:","Gordon, R. (2016) The Rise and Fall of American Growth"]
[null,null,"Optimism:","Brynjolfsson, E. and A. McAfee (2014) The Second Machine Age"]
[null,"The pessimists say we are in for big trouble, with low g. Gordon says that the outstanding, 2% per year increase in GDP per capita we enjoyed in the 20th century is unlikely to be repeated."]
[null,"By focusing on advances in digitization and artifical intelligence and connectivity, optimists like Brynjolfsson and McAfee argue for a future that is incredibly bright."]
[null,"They think that we are poised on some kind of singularity and are about to break out into a fantastic new world:"]
[null,null,"\"It will make a mockery of all that came before.\"  (Location 1402 in the Kindle edition of The Second Machine Age.)"]
[null,"So who's right? The worriers who can't see how we can keep up the pace of tachnological progress or the dreamers who see a futuristic, sci-fi paradise of technology?"]
[null,"The reason why we get such divergent forecasts and why we cannot answer the question is because we still do not understand growth and development. "]
[null,"We know the market system has something to do with it, but the details remain shrouded in mystery."]
[null,"Adam Smith wrote An Inquiry into the Nature and Causes of the Wealth of Nations in 1776. "]
[null,"He was asking a basic question: Why are some countries rich and others poor?"]
[null,"A few centuries later, the Solow Model helps a little, but we still do not have a complete answer."]
[null,"Figuring out the evolution of a market economy continues to be the most important open problem in economics."]
[]
["Last","Piketty's Capital was translated to English in 2014 and he became a rock star. "]
["Video","He even made it to the Colbert Report! If you are up for one last short video, you can watch him here:"]
[null,"http://www.cc.com/video-clips/e301vf/the-colbert-report-thomas-piketty"]