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# Preparing for Economic Research ECN 297

WFU

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This 4 page Class Notes was uploaded by Sydni D'Amore on Wednesday October 28, 2015. The Class Notes belongs to ECN 297 at Wake Forest University taught by Allin Cottrell in Fall. Since its upload, it has received 13 views. For similar materials see /class/230743/ecn-297-wake-forest-university in Economcs at Wake Forest University.

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Date Created: 10/28/15

Notes on Mankiw Romer and Weil Allin Cottrell September 2003 Here s an exegesis of Section I of the paper by Mankiw Romer and Weil MRW If you can get a good understanding of this section the rest of the paper should be fairly easy On p 409 MRW say We assume a CobbDouglas production function and their rst equation is accordingly YI KI AILI1 0 lt a lt l l A couple of points to note here 9 The repeated I terms do not indicate multiplication by I they are just indicating that output Y capital input K labor input L and the state of technology as it impacts the productivity of labour A are all considered to be functions of time they are all potentially changing over time o The exponents a and l 7 a are both positive fractions and they obviously add up to 1 This is maybe a slightly more complicatedlooking version of something you have seen in micro Let s simplify the production function a little suppressing the Is Y AK L5 What s the marginal product of labor MPL here Basic calculus gives us dY d L5 i AK AK39 eL s 1 6 AK L 9 7 Y dL dL L L The ratio Y L is output per worker also known as the average product of labor or APL Note that if is a positive fraction the MPL is less than the APL In that case the APL will fall as L rises it is being pulled down at the margin And since the MPL is just a constant times the APL it too will fall as L rises So with 0 lt lt l we have positive but diminishing returns to labor A parallel argument shows that 0 lt a lt l is the condition for positive but diminishing returns to capital Now in the MRW version of the equation they in effect put l 7 a What is the signi cance of that Well imagine scaling both inputs capital and labor by a common factor A eg A 2 would indicate a doubling of the inputs What happens to the output We can write the original output as Y0 AKng and the new output as Y1 AAK0 AL0 9 AA XKgA ng AdA sAKng Aa gyo and the ratio Y1 Y0 is then just A H S In that case 9 If a l a scaling of the inputs by A produces an expansion of output by that same factoriconstant returns to scale39 9 if a gt 1 a scaling of the inputs by A produces a greater than proportional increase in outputi increasing returns to scale or economies of scale39 an o ifot lt l we have decreasing returns to scale MRW s writing of the capital and labour exponents as oz and 1 7 oz therefore corresponds to the assumption of constant returns to scale Returning to the text MRW next write down growth equations for labor and the level of technology LI L0equot 2 AI A0egt 3 Here L0 and A0 are just initial values for these variables The idea is that they grow or shrink at continuously compounded rates n and g respectively The magic number 6 2718 the base of natural logarithms achieves the continuous compounding This number has the cool property that d dx 6quot equot The table and graph below illustrate how L and A would behave over time according to these equations withn 003 g 005 andL0 A0100 L I A I 250 1 I 0 100000 100000 1 103045 105127 2 3 106184 110517 109417 116183 10 134986 164872 18 171601 245960 50 11111111 024681012141618 The next step in the argument is passed over fairly quickly The authors note the assumption that a constant fraction of output s is invested39 they de ne k E K AL and y E Y AL39 and they then tell us that the evolution of k over time is given by 151 Syl ng6kl 4 Let s pause on this First a small point of notation the dot indicates a timederivative for any variable x 6 dxdI Since k KAL we can write k7 dkI 7 d KI 7 dz 7EltAltzgtLltzgtgt We want the derivative of k with respect to time We ll have to use the quotient rule for K I A IL I and the product rule for the AILI in the denominator From this point I m going to drop the explicit I s to make the notation less cluttered but of course we have to remember that K A and L are all functions 0 time By the quotient rule 1 dK K dAL 7AL dz AL2 dz and by the product rule 7 1 dK K dL dA 7 AL dz 7 AL2 dz 7 dz 7 1 dK K A dL L dA 7AL dz 7AL ALdz AL dz 7 1 dK 1 dL 7 1 dA K 7 AL dz L dz A dz AL Now consider dKdI the timederivative of the capital stock Since a fraction s of output Y is invested ie used to augment the capital stock the growth of K would equal sY if it were not for depreciation Depreciation wear and tear obsolescence is working to reduce K over time The authors assume this effect is proportional to the size of the capital stock with factor of proportionality 6 Thus dK 7 Y 7 6K dt S Substituting this into the last equation above gives 1 dL 1 dA K 1 k7 Y4K 7 if if 7 ALltS L dtAdt AL kSL5 lLLlLl AL AL Ldt Adt AL ksil ldj5 AL Ldt Adt AL Now cashiny YAL andkKAL toget ldL ldA ksy ZEZE5k Last point dLdl is the simple timederivative of L The proportional rate of change ofL over time is this tim ederivative divided by L But equation 2 implies that this proportional rate is just n That is ldL f E and by the same token l dA 7 A dt T g So nally ksy7ng6k which is MRW s equation 4 MRW give a variant form of this equation Where y is replaced by k ksk 7ng5k It s easy enough to see Where this come from First from the production function 1 Y K AL1 But since y YAL K ltALgt1 a 71 5 yiTiKML 7ltA gt 7k Economics 201 Cottrell Manipulating data with commandline utilities In doing real worldquot data analysis it quite often happens that one can hold of relevant data but not in the exact format that one needs for processing using a program such as gretl or Excel In that case we need to edit the data rst There are various options for doing this You are probably used to editing stuff using a word processor eg MS Word One rst important point to notice is that in editing raw data a word processor is generally not appropriate The data must remain as plain text and must not assume the format of a Word doc which includes formatting codes and a bunch of other stuff The Windows utility known as Wordpad is OK for the purpose so long as you take care to save your edited work as plain text Here though I will talk about another option that can be very useful when the raw data differ in some systematic way from what you want ie where the editing task is to recognize some pattern in the raw data and change it in some speci ed way The option I m talking about is the use of simple command line tools which enable you to modify a text le noninteractively By noninteractively I mean that you don t have to go through the le searching and replacing rather you issue a single command that does all the work for you As a case in point consider the wage data that we downloaded from the Bureau of Labor Statistics website b1 5 gov The le we obtained held monthly wage data from the 1960s to the present It was just what we wanted except thatias I discovered when the dates looked funny in gretliafter the December value labeled M12 for each year there was an M13 value which represented the average value for the year as a whole We wanted just the monthly data so the task in this case was to strip out all lines containing M13 something that is not easy to do with standard SearchandReplace tools The smart utility for this job is a program called grep This program scans a le and either prints only those lines in the le that match a certain pattern or if you add the v think reVerse option prints only those lines that do not match the pattern The command for the BLS task was then grep v M13 b1 stxt gt newtxt Taking this apart the rst bit is grep v M13 that is we re asking grep to give us lines that do not contain M13 The next bit is b1 5 txt the name of the original data le we want scanned The last bit is gt new txt which is composed of two parts the gt symbol calls for redirectioniinstead of sending output to the screen we want it sent to a leiand then we give the name of the le we want created here newtxt Putting it all back together the command is Scan blstxt for lines that do not contain M13 and send the output from this operation to newtxtquot Where to get grep how to install How to open a console Other similar things sed

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