Title PageIntroductionIntroductionProduction and GrowthAugust 24, 20161/91What do we want to explain?2/91The importance of small differencesIDi↵erent growth rates l ead to big di↵erences in income levels3/91RoadmapIAssume you are the presidentIYou want to increase growthIIt’s cost l y !IHow do you do it?IWhat’s the best use of resources?4/91AsimpleproductionmodelINow that we have some data in mind, we want to constru ct amodel that may be consistent with these observationsIA natural place to start is asking “how is output produced?”IWhat are the factors of production? Which ones are wegoing to focus on?IWhat ass ump t i ons do we want to make on a functionalform?IWhat i s the productivity component?IThen, we’ll compare the production model to the dataIThis production model is central to almost everything we’ll do inthis c our se5/91The Production FunctionIGDP is produced using many factors: machines, labor, energy,land, r aw materials, and moreIFocus on: Capital (K) , Labor (N) , and ”Technology” (A)I”Technology”:Ireflects the idea that more productive economies producemore wit h the same K, NIdepends on actual technology, management, efficientallocation of res our ce s, human capital, other institutions,etc.Iwe will see how to read it from existing data... but stillhard to assign exact weights for the di↵erent components ofproductivity6/91The Production FunctionA produ ct i on function “translates” a given level of cap it al , labor, andproductivity into output:Yt= AtF (Kt,Nt)IYtis aggregat e physical out p ut (or GDP/Price index) producedduring period t (a month, quarter, year...)IKtis the stock of capital available duri n g period tINtis the labor input (or total hours of work) during period tIAtis Total Factor Productivity - a variable that capturesproductivity elements we discussedIF (·, ·) is a time-invariant function. Inputs change7/91Marginal ProductsMPN =@Y@N= A@F(K, N)@N⌘ AFNMPK =@Y@K= A@F(K, N)@K⌘ AFK8/91Properties of the production functionHere are four assumptions that we’ll keep throughout our analysis:1. Marginal products are positive: MPN > 0 MPK > 0IEverything else equal, mor e input ! more output2. Diminishing marginal products:@M P N@N=@2Y@N2= A@2F (K, N)@N2= AFNN< 0@M P K@K=@2Y@K2= A@2F (K, N)@K2= AFKK< 09/91Properties of the production functionThe first two properti es result in production functions that have thisgraphical representation:IAssumption 1: positive slopesIAssumption 2: diminishing slopes10 / 91Properties of the production function3. Complementarity:IMore N ! higher mar gi n al product of capital:@M P K@N=@2Y@K@N= A@2F (K, N)@K@N= AFKN> 0IMore K ! hi gher marginal product of labor:@M P N@K=@2Y@N @K= A@2F (K, N)@N @K= AFNK> 0IIntuition: provides competitive forces to balance inputs,towards an optimal ratio of capital to labor11 / 91Properties of the production function4. Constant Returns to Scale (CRS):IDouble the inputs ! double the outputIMore pr eci s el y... if we multiply both K, and N by somefactor >0, we get  times the output:AF (K, N )=AF (K, N)=YIThe rati o of capital to labor be comes the key:KN=KN12 / 91The Cobb-Douglas Production FunctionYt= AtK↵tNt, 0 <↵,<1IHeavily used...ISatisfies the four properties: ↵ +  = 1 for CRTSIElasticities:I✏Y,K=@Y@KKY=@ ln Y@ ln KI↵ is the elasticity of output with respect to capitalI is the elasticity of output with respect to laborIWe’ll derive this later on13 / 91Development AccountingIDoes t h e production model provide a good account for data?IAssume a Cobb-Douglas prod. function AK↵N1↵IDivide by N to make it per-capita:y =YN=AK↵N1↵N= A✓KN◆↵= Ak↵Iy is output per worker, and k ⌘KNis the capital-labor ratioIAssume ↵ =0.333, and A = 1 (normalization)IUse data k for di↵erent countries, and calculate predicteddi↵erences in y across countriesICompare t o actual data on yIDoes t h e model provide a good fit?14 / 91Development AccountingIDoes t h e production model provide a good account for data?IAssume a Cobb-Douglas prod. function AK↵N1↵IDivide by N to make it per-capita:y =YN=AK↵N1↵N= A✓KN◆↵= Ak↵Iy is output per worker, and k ⌘KNis the capital-labor ratioIAssume ↵ =0.333, and A = 1 (normalization)IUse data k for di↵erent countries, and calculate predicteddi↵erences in y across countriesICompare t o actual data on yIDoes t h e model provide a good fit?15 / 91Development Accounting!!IWith our assumptions, the model is inconsistent with the dataIShould we di s mi ss it? Not necessarily... let’s look at a relat e dexercise16 / 91Development AccountingIAllow A (Total Factor Pro du ct i v ity, TFP) to di↵erIUse data on y and k to find the implied di↵erences in A acrosscountries:A =yk↵!!17 / 91The Importance of TFPIWe just learned that TFP (A) is responsible for at least some ofthe obse rved income di↵erences between countriesIHow important? Let’s look at an example (assuming m odelcorrect)yUSyIndia=10.089= 11.24yUSyIndia=AUSAIndiak1/3USk1/3India=3.95 ⇥ 2.8451=log(3.95)log(11.24)+log(2.845)log(11.24)= .57 + .43ITFP is responsible for ⇡ 57% of income di↵er en ce sICapital is responsibl e for ⇡ 43% of income di↵e r en cesIRepeating for di↵erent countries results in di↵erent numbers butA is still important18 / 91Summary of De ve lo p m e nt AccountingIA simple production model allows t o account for s ome fraction ofincome d i↵ er en ce s across countriesIThe large part is due to an “unknown” component that we callTotal Factor Productivity (TFP)IResponsible for at least 50% of income di↵er en ce sIIncludes many dimensions that are crucial for growth (someare easie r to quantify than others)19 / 91...So What’s in TFP?ITechnology, accumulated knowledgeIInstitutions and cult ur eIInfrastructureINatural r e sou rc es, Climate, and GeographyIEfficient allocation of resources (see next slide)20 / 91MisallocationsIRecent studies identified misallocations as q uantitativelyimportantIWhat i s it? Easy to ill u st r ate with our production modelIAssume two firms that have the same production function,same A, and same NIHowever, firm 1 has more capital: K1>K2IImplication MPK1<MPK2(why?)ILet’s r eal l ocate a unit of K from 1 to 2Iwe lose MPK1units of outputIwe gain MPK2units of outputIthe gain is greater than the lossIWe can max output by reallocating K until the marginalproducts are equal21 / 91Misallocations...IThis is not the only way... we