Econ 501 Fall 2015 Final Examinaion (200 ps) S.L. Parene Neoclassical Growh Model (50 ps) 1. Derive he relaion beween he real ineres rae and he renal price of capial using a no-arbirage argumen under he following scenarios. (Assume capial depreciaes a rae δ) a. Households pay a ax a rae τ k on ne capial income, i.e. he difference beween capial income and capial depreciaion. (10 poins) Savings 1 uni of oupu 1+i omorrow Buying capial 1 uni of oupu one uni of capial omorrow r +1 +(1-δ)- τ k( r +1 -δ) Therefore, i ( 1 k )( r 1 ) b. One uni of oupu can be convered ino q unis of capial in period and one uni of oupu can be convered ino q +1 unis of capial in period +1 where q +1 =(1+γ q )q. (10 poins) Savings 1 uni of oupu 1+i omorrow Buying capial 1 uni of oupu q unis of capial omorrow r +1 q income + (1-δ)q capial lef ha can be convered ino (1-δ)q /q +1. Therefore, ( 1 1 i ) q 1 / q r 1q 1 2. Take he Neoclassical Growh Model wihou any axes or populaion growh given by he 3 equaions below. Describe how you would assign parameer values for β, α, A, δ, θ, and γ A in Sep 4 of he calibraion. Be sure o sae which equilibrium condiions and observaions you would use o assign he value of each parameer. (Noe: you do NOT need o come up wih he parameer values.) (20 Poins) [ln c 0 ln(1 h )] Household Preferences 1 c x Ak [( 1 A) h ] Producion Funcion and Uses of Oupu k 1 (1 ) k x Capial Sock Law of Moion (i) A normailized o 1. (ii) γ A in use bpg ha y grows a 1+ γ A wih US observaion for growh rae fo y. (iii) r k k/y use observaion for capial income share and equilibrium resul ha θ=r k k/y (iv) δ use capial sock law of moion equaion wih observaion for K/Y and X/Y (v) β use FONC beween c +1 and c wih impued i from r +1 =i + δ and growh rae of consumpion (vi) α use FONC beween c and h wih observaion for h, c/y and Profi max condiions w=(1- θ )y/h 1
3. In a home problem se, you used he calibraed neoclassical growh model o deermine he effec of changes in he curren US ax sysem on seady sae hours, capial per person, oupu per person, and consumpion per person (h, k, y and c). One policy change you evaluaed was an eliminaion of he ax on labor income. This policy change was assumed o be revenue neural so ha he eliminaion of he ax on labor income required an increase in he consumpion ax rae o keep governmen expendiures and ransfers unchanged. You found ha h, k, y and c all increased. Give some inuiion for why hese variables increased. (10 poins) Basically, he ransfer is kep he same. If we jus had a saic model, he budge line for he leisure consumpion indifference curve would Tr 1 c be l 1 c. So if you are keeping Tr fixed and eliminaing w (1 h ) w (1 h ) he axh on labor income, his is a pure wealh effec. Causing he household o feel poorer. So hey work more. FONC profi is r=θ(k/h) θ-1 and no arbirage is sill i ( 1 k )( r 1 ), and hence i follows ha r does no change and so k/h does no change. Since h increases, k mus increase, so yo mus increase. C mus also increase for why would you work more and save more if you ae less? BUSINESS CYCLES (90 ps) 1. Business Cycle Regulariies a. Describe he H-P filer being careful o idenify he inpus, he oupus and he manner by which he oupus are deermined in he algorihm. (10 poins) Take real gdp, quarerly daa and hen logs. Find rend which is soluion o following algorihm T T 2 2 ( y ) [( 1 ) ( 1 )] wih 1 1 λ=1600 b. Given he oupus of he filer, explain how o calculae he volailiy measure of a macroeconomic variable x and is co-movemen wih real GDP. (10 poins) volailiy is sandard deviaion of deviaion o rend whereas comovmen is correlaion coefficien. c. Wha are he ineresing business cycle facs wih regard o hese volailiy measures and he co-movemen measures? (5 poins) hours are abou 2/3 as volaile as oupu. Invesmen is mos volaile. Consumpin less. 2. Real Business Cycle Theory. a. Describe how Kydland and Presco (1982) calibrae he law of moion for produciviy shocks in Sep 4 of he calibraion. (5 poins) Solow growh accouning exercise o impue Solow Residuals. Then esimae AR1 for shocks. Then find mean and sandard deviaion/variance of errors. Sandard deviaion is shock componen. 2
b. From Sep 5, wha are he model s successes and failures? Provide some inuiion for hese findings paricularly wih respec o he failures. Use graphs whenever possible. (10 ps) Successes 2/3 of volailiy of oupu. Ges invesmen volailiy being greaer and consumpion being smoohing abou righ. Hours are no volaile enough and correlaion beween produciviy and hours is 1 whereas in dae close o zero. Graphically, he problem is 3. Explain he assumpion of raional expecaions, boh inuiively and mahemaically. Explain he relevance of he raional expecaions assumpion o he Neuraliy of Money Proposiion and he concep of Reverse Causaion. (10 poins) Ra expecions- people use all available informaion ino accoun in forming heir expecaion. Mahemaically, i is condiional expecaion. Neuraliy of money proposiion- change in money supply has no real effecs. Only if you can fool people does i have real effecs, RE means you canno fool people on average. Reverse causaion people anicipae high fuure produciviy and demand more loans, banks reduce excess reserves o mee loan demand, and hus money muliplier increases 4. Wha is a Vecor Auo Regression? Explain why he VAR procedure is ideally suied for quanifying he real and nominal effecs of moneary policy. Wha is he main problem in quanifying hese effecs wihin his VAR approach? (15 ps) Basically, a VAR is a sysem of N-linear equaions where N is he number of variables. In a given linear equaion, a paricular variable is assumed o be a linear funcion of is pas variables as well as a linear funcion of he pas variables of he N-1 oher variables. In each linear equaion, here is also an error or shock erm. I is ideally suied for quanifying he effecs of moneary policy because of he neuraliy of money proposiion. If money has real effecs, i mus be because of surprise changes. This is wha he VAR hopes o idenify, hrough 3
he srucural shocks. These are differen from he errors (forecas erms) in he VAR as hey forecas errors in each equaion will be correlaed wih he oher forecas errors, or o say his hey will be funcions of he fundamenal shocks o each variable. Tha is he main problem wih his approach- idenifying hese fundamenal shocks. Wihou some addiional resriciions on he sysem, his is no possible. 5. The simples New Keynesian Model is defined by he following hree equaions: (i) i y (ii) y y [ i y ( p p )] 1 1 1 1 ( y y ln (iii) E ) (a) Wha is he name of each of hese hree equaions? (5 poins); Moneary (Taylor) Rule, IS Curve, Phillips Curve. (b) For each equaion, provide a verbal general descripion of how his equaion is derived or arrived a? (10 poins) Moneary rule is assumpion abou way Fed has se money supply policy. IS- FONC wih respec o c +1 and c plus fisher relaion, and goods marke clearing. Phillips Curve- Saggered price seing, Monopolis opimal price seing, HH FONC wih respec o c and h and labor marke clearing. (c) Provide inuiion for why a surprise in moneary policy has a real effec in his model. (10 poins) Firs i increases demand because i will lead o a change in he real ineres rae because no all firms can adjus heir prices by assumpion. This is eviden from he IS curve, paricularly he middle erm. I will increase he GROWTH and DEVELOPMENT (60 poins) 1. Describe he wo main procedures for making inernaional income comparisons? Explain which one produces more accurae comparisons? (10 ps). Exchange rae mehod. Muliply GDP in domesic currency by exchange rae wih US. PPP mehod. Take Nominal indusry sales and divide by indusry price index. Muliply by world price. Do his for all good and sum over all goods. PPP is more accurae because ensures same value is used o weigh quaniy of each good. Exchange rae mehod does no because law of one price fails o hold. 2. Use a graph of per capia oupu (logarihm) agains ime o show he before and afer effecs associaed wih he following changes as prediced by boh he Solow Model wih exogenous echnological change and he Ak Model: (Assume ha prior o he change, he economy is on is balanced growh pah equilibrium.) a. A permanen decline in he feriliy rae. (5 ps.) b. New regulaion imposed on businesses inended o reduce greenhouse gasses (5 ps.) 3. Wha is he difference beween endogenous and exogenous growh heory? Evaluae he abiliy of he branch of he endogenous growh lieraure ha does no assume monopolisic elemens o accoun for he key developmen and growh facs. (10 ps) 4
Endogenous- growh arises wihin model due o decisions of households and firms. Endogenough growh canno accoun for he fac ha growh miracles only happen in he poor and are a recenly new phenomenon. 4. Consider he following version of he Solow growh model expressed in per capia variables: 1 y Ak [( 1 e) h ] c ( 1 s) y ( 1 n) k 1 (1 ) k sy ( 1 1 n) h (1 ) h eh The variable, h, is human capial and i is accumulaed by going o school. The leer e denoes he fracion of ime people are in school in a period and so (1-e) is he fracion of ime hey work. Noe ha his ime spli is reaed as a parameer. Show algebraically how he growh rae of per capia oupu along a balanced growh pah/seady sae depends criically on he value of he parameer ϕ. (10 poins) Divide capial law of moion by k and conclude ha k and y mus grow a same rae in BGP. Take dae +1 and dae raio of producionfuncion o conclude ha growh rae of h is he same as y and k. Finally, divide educaion equaion by h.observe, ha if ϕ=1, here is a BGP growh rae equal o [(1-δ)+e]/(1+n). If ϕ < 1, hen he growh rae for h is a decreasing funcion of h so you can only have a seady sae. Iff ϕ > 1, hen he growh rae for h is an increasing funcion of h. There is no balanced growh pah, as he growh rae exploded as h increases. If 5) Take he Malhus model absen echnological change and capial wih he following birh and deah rae funcions. The moivaion for hese funcions is as follow: The increase in he deah rae a mid-level ranges of consumpion corresponds o when urbanizaion raes firs sar o show a dramaic increase. Ciies, before public saniaion sysems and public healh sysems are pu in place, were very deadly places o live. The rise in he birh rae iniially corresponds o he observaion ha as income sars o increase people have more kids, bu afer a significanly high level of income, people have less children. Birh rae Deah rae 5
C a. Plo he populaion growh rae funcion corresponding o he deah rae and birh rae funcions above (5 ps) b. Find he Seady sae consumpion levels and populaion levels for his economy. (7 ps) c. Thomas Malhus had a very pessimisic view of he condiions of he human race in ha he believed ha any increase in he living sandard due o a sudden decrease in he populaion would be emporary. This is indeed he predicion of he Mahus model we sudied in class. Does he version of he Malhus Model in his quesion make he same predicion? Use graphs in your answer. (8 ps) 6