Federal Reserve Bank of Minneapolis Quarerly Review Vol. 3, No., November 2007, pp. 6 44 Modeling Grea Depressions: The Depression in Finland in he 990s Juan Carlos Conesa Associae Professor Universia Auònoma de Barcelona Timohy J. Kehoe Professor Universiy of Minnesoa and Consulan Research Deparmen Federal Reserve Bank of Minneapolis Kim J. Ruhl Assisan Professor Universiy of Texas a Ausin Absrac This aricle is a primer on he grea depressions mehodology developed by Cole and Ohanian (999, 2007) and Kehoe and Presco (2002, 2007). We use growh accouning and simple dynamic general equilibrium models o sudy he depression ha occurred in Finland in he early 990s. We find ha he sharp drop in real GDP over he period 990 93 was driven by a combinaion of a drop in oal facor produciviy (TFP) during 990 92 and of increases in axes on labor and consumpion and increases in governmen consumpion during 989 94, which drove down hours worked in Finland. We aemp o endogenize he drop in TFP in varians of he model wih an invesmen secor and wih erms-of-rade shocks bu are unsuccessful. The views expressed herein are hose of he auhors and no necessarily hose of he Federal
FEDERAL RESERVE BANK OF MINNEAPOLIS QR Modeling Grea Depressions: The Depression in Finland in he 990s* Juan Carlos Conesa Timohy J. Kehoe Kim J. Ruhl Associae Professor Professor Assisan Professor Universia Auònoma de Barcelona Universiy of Minnesoa Universiy of Texas a Ausin and Consulan Research Deparmen Federal Reserve Bank of Minneapolis The general equilibrium growh model is he workhorse of modern economics. I is he acceped paradigm for sudying mos macroeconomic phenomena, including business cycles, ax policy, moneary policy, and growh. The collecion of papers edied by Kehoe and Presco (2002, 2007) and earlier work by Cole and Ohanian (999) break he aboo agains using he general equilibrium growh model o sudy grea depressions like ha in he Unied Saes in he 930s. This aricle is inended as a primer on he grea depressions mehodology. If oupu is significanly above rend, he economy is in a boom. If i is significanly below rend, he economy is in a depression. Trend is defined relaive o he average growh rae of he indusrial leader. We use a rend growh rae of 2 percen per year because his rae is he secular growh rae of he U.S. economy in he 20h cenury. In he 2s cenury, i is possible ha he European Union or China will become he indusrial leader, and i will be appropriae o define he rend growh rae relaive o ha economy raher han o he U.S. economy. A grea depression, according o Kehoe and Presco (2002, 2007), is a paricular episode of a negaive deviaion from rend saisfying he following hree condiions:. I mus be a sufficienly large deviaion. Kehoe and Presco require ha he deviaion mus be a leas 20 percen below rend. 2. The deviaion mus occur rapidly. Kehoe and Presco require ha derended oupu per working-age person mus fall a leas 5 percen wihin he firs decade of he depression. 3. The deviaion mus be susained. Kehoe and Presco require ha oupu per working-age person should no grow a he rend growh rae of 2 percen during any decade during he depression. Figure displays he evoluion of oupu per workingage person in he Unied Saes for more han 00 years, relaive o a 2 percen rend. The U.S. Grea Depression of he 930s can easily be idenified from his figure. Grea depressions are no a relic of he pas, however, *Originally published in a slighly differen form in Grea Depressions of he Twenieh Cenury (Minneapolis: Federal Reserve Bank of Minneapolis, 2007), pp. 427 75. Conesa graefully acknowledges he suppor of he Barcelona Economics Program of CREA, he Miniserio de Educación y Ciencia under gran SEJ2006-03879, and he Generalia de Caalunya under gran 2005SGR00447. Kehoe and Ruhl graefully acknowledge he suppor of he Naional Science Foundaion under gran SES-0536970. We hank John Dalon, Mark Gibson, and Kevin Wiseman for excellen research assisance. The daa and compuer programs used in he analysis presened here are available on-line a www.greadepressionsbook.com. 6
Modeling Grea Depressions Juan Carlos Conesa, Timohy J. Kehoe, Kim J. Ruhl Figure Real GDP per Working-Age Person in he Unied Saes, 900 2005 Index (900 = 00),600 Figure 2 Real GDP per Working-Age Person in Finland, 900 2005 Index (900 = 00),600 800 800 400 GDP Trend 400 GDP Trend 200 200 00 00 50 900 920 940 960 980 2000 50 900 920 940 960 980 2000 and, unless we undersand heir causes, we canno rule ou heir happening again. Argenina, Brazil, Chile, and Mexico had depressions during he 980s ha were comparable in magniude o hose in Canada, France, Germany, and he Unied Saes in he inerwar period. In recen imes, New Zealand and Swizerland rich, democraic counries wih marke economies have experienced grea depressions. In he 990s, wo counries, Finland and Japan, experienced no-quie-grea depressions. The case of Japan has been analyzed in Hayashi and Presco (2002, 2007). In his aricle, we analyze he experience of Finland. We rely on growh accouning o decompose changes in oupu ino hree porions: he firs due o changes in inpus of labor, he second due o changes in inpus of capial, and he hird due o he changes in efficiency wih which hese facors are used, measured as oal facor produciviy (TFP). We hen use simple applied dynamic general equilibrium models o idenify and quanify he sources of hese movemens. We analyze he sandard neoclassical growh model and hen provide hree exensions: a model wih disorionary axes and governmen consumpion, a wo-secor model wih invesmen specific echnological change, and an open economy model wih erms-of-rade changes. An imporan feaure of our analysis is ha, given ha we provide a baery of models for analysis, we have o provide explici ways of making he daa and he model oucomes comparable. The heory used will guide he measuremen in he daa, and he discussion of how o do ha in a consisen way is a useful conribuion on is own. The Finnish Experience in he 990s Finland has experienced specacular growh during he pas cenury. Figure 2 displays daa on real GDP per working-age person (5 64 years) over he period 900 2005. Noice how growh in Finland, which has averaged 2.4 percen per year, has consisenly ousripped he rend growh of 2 percen per year of he Unied Saes during mos of he cenury depiced in Figure. The major inerrupions o his growh in Finland have been he Firs World War during 94 8, he wo wars wih he Sovie Union 940 45, and wo economic depressions one in he 930s and he oher in he 990s. Figure 3 provides a comparison of he depression ha began in 929 wih he one ha began in 990. Neiher episode mees he Kehoe and Presco (2002, 2007) crieria for a grea depression because real GDP per working-age person derended by 2 percen per year did no fall by 20 percen. Finnish economiss like Kiander and Varia (996) refer o boh episodes as grea depressions, however, and noe ha he episode in he 990s was he more severe of he wo. In Figure 3, i is clear ha Finnish economic performance, measured in erms of real GDP per work- 7
FEDERAL RESERVE BANK OF MINNEAPOLIS QR Figure 3 Derended Real GDP per Working-Age Person in Finland During he Depressions of he 930s and he 990s Index (T 0 = 00) 05 00 95 90 85 80 930s (T 0 = 928) 990s (T 0 = 989) 0 2 3 4 5 6 7 8 9 0 T 0 ing-age person, was worse in he 990s han i was in he 930s: by 993, he rough of he depression of he 990s, derended real GDP per working-age person had fallen by 8.5 percen, compared wih a fall of only 4.3 percen by 932, he rough of he depression of he 930s. Alhough he Finnish depression of he 990s is no a grea depression according o he Kehoe-Presco crieria, i comes close, and his aricle uses i as a case sudy for he grea depressions mehodology of Kehoe and Presco (2002, 2007). Our analysis shows ha he sharp drop in real GDP over he period 990 93 was driven by a combinaion of a drop in TFP during 990 92 and of an increase in axes on labor income and on consumpion during 989 94, which drove down hours worked in Finland. Our resuls are in accord wih hose of Böckerman and Kiander (2002b) and Kiander and Varia (996), who characerize he causes of he Finnish depression as a combinaion of bad luck, bad banking, and bad policy. The bad luck refers o he 989 9 collapse of he Sovie Union, Finland s principal rading parner in 989; he bad banking refers o he banking crisis in Finland in 99 94; and he bad policy refers o Finnish labor marke policies, in paricular, he sharp increase in labor income axes. Gorodnichenko, Mendoza, and Tesar (2007) also focus on he banking crisis and decline in rade wih he Sovie Union as he shocks ha generaed he depression in Finland. Oher references for economic developmens in Finland in he 990s include Böckerman and Kiander (2002a), Kiander (2004), and Koskela and Uusialo (2004). Our conclusion ha he drop in TFP and he increases in axes and governmen consumpion, when inroduced ino he model, can accoun for he Finnish depression of he 990s leaves much room for fuure research. The base case model ha we presen akes he flucuaions in TFP as exogenous. A more successful analysis would model TFP flucuaions as endogenous. In such an analysis, he banking crisis and he collapse in rade wih he Sovie Union he bad luck and bad banking of Kiander and Varia (996) would probably play crucial roles. In he analysis presened here, in boh he model wih invesmen and he model wih rade, a porion of he flucuaions in TFP is endogenous. These models are no successful in capuring he TFP flucuaions observed in he daa, however. In fac, we show ha in each model he endogenous porion of TFP moves in he wrong direcion ha is, i acually increases during he depression. In a more successful model in which TFP flucuaions are endogenous, he crucial elemens ha drive he fall in TFP 990 92 may involve he flucuaions in he relaive price of invesmen and he erms of rade, bu hese wo feaures alone are no enough. The analysis in his aricle indicaes some of he difficulies ha a more successful analysis will have o overcome. The Dynamic General Equilibrium Model This secion presens he simple dynamic general equilibrium model ha serves as he base case in our analysis of he Finnish economy. The model feaures a represenaive household ha chooses pahs of consumpion, leisure, and invesmen in order o maximize uiliy. The household maximizes he uiliy funcion ( ) () log C + ( )log hn L = T 0 subjec o a sequence of budge consrains, (2) C + K+ = w L + + r K, nonnegaiviy consrains on C and I = K+ ( ) K, and a consrain on he iniial sock of capial, K T0. In he uiliy funcion, he parameer, 0 < <, is he discoun facor and he parameer, 0 < <, is he 8
Modeling Grea Depressions Juan Carlos Conesa, Timohy J. Kehoe, Kim J. Ruhl consumpion share. Boh need o be calibraed. C is consumpion, K is he capial sock, L is hours worked, w is he wage rae, r is he renal rae, and, 0 < <, is he depreciaion rae. The oal number of hours available for work is hn, where N is he working-age populaion and h is he number of hours available for marke work. We specify h as 00 hours per week. One period of ime is one year. Firms operae in a perfecly compeiive marke, using a consan reurns o scale echnology, which we assume o be Cobb-Douglas: =, (3) Y A K L where Y denoes oal oupu, A is oal facor produciviy (TFP), and, 0 < <, is he capial share. The condiions ha firms earn zero profis and minimize coss provide expressions for he facor prices: (4) w = ( ) A K L =. (5) r A K L The curren period s oupu is divided beween consumpion and invesmen. The feasibiliy consrain is + (6) C + K ( ) K = A K L. The Daa To perform he growh accouning, we use naional accouns daa and labor force surveys. For Finland, we use naional accouns daa consruced using he Unied Naions Sysem of Naional Accouns (SNA93), downloaded from SourceOECD, and daa on hours worked per worker, employmen raes, and working-age populaion from he corresponding Labor Force Surveys, also available in he Groningen Growh and Developmen Cener daabase. The sandard growh accouning is done by he use of an aggregae producion funcion, which is of he Cobb-Douglas form (3). In erms of daa, we need measures of oupu and he capial sock a consan prices and of hours worked. We need o ake a sand on wha daa caegories we should be including as invesmen. We consider he raw measuremen of hours worked we use in our analysis as less problemaic, alhough alernaively we could choose o weigh hours by some measuremen of efficiency unis of labor. We also need o calibrae he capial share,. In he base case model, we assume a closed economy wihou a governmen or a foreign secor, and hence he feasibiliy condiion is given by equaion (6), which can be wrien as (7) C + I = Y. There are several alernaive sraegies for maching up objecs in he model wih hose in he daa. One sraegy is o ignore he governmen and he foreign secor. When following ha sraegy, C corresponds o Privae Consumpion in he naional accouns, and I corresponds o Privae Gross Capial Formaion. Oupu is hen he sum of hese wo caegories. Noice ha his sraegy leaves a sizable fracion of GDP ou of he analysis. Anoher se of sraegies which are followed by he papers in Kehoe and Presco (2002, 2007) sar by defining Y o be GDP, and hen allocae he caegories ha are no explicily considered in he analysis, Governmen Consumpion and Ne Expors, o eiher consumpion or invesmen. The mos frequenly followed sraegy in Kehoe and Presco (2002, 2007) is o allocae boh caegories o consumpion. Hayashi and Presco (2002, 2007) follow an alernaive sraegy of allocaing Governmen Consumpion o consumpion bu Ne Expors o invesmen, since ne expors resul in he accumulaion of capial abroad. Consisen wih his sraegy, Hayashi and Presco definey o be gross naional produc (GNP), raher han GDP. Recall ha GNP adds he foreign income of domesic residens o GDP and subracs he income wihin he counry of foreign residens. A his poin, hese alernaive sraegies for maching up objecs in he model wih hose in he daa seem somewha arbirary. In pracice, if one of he sraegies produces very differen resuls from anoher one, i is probably bes o develop a model, along wih a corresponding accouning procedure, ha explicily akes ino accoun governmen consumpion and/or ne expors. We do his laer in he aricle. Even hough we do no do so in his aricle, i is worh menioning ha some researchers have found i convenien o consider durable goods consumpion as invesmen. Such an alernaive sraegy requires us o impue services from durable goods as oupu. (See, for example, Hansen and Presco 995.) The variables in he feasibiliy consrain (6) are inerpreed as physical unis of a homogeneous good, 9
FEDERAL RESERVE BANK OF MINNEAPOLIS QR wih unis measured in values a base period prices. Consequenly, we wan o measure oupu and invesmen a consan prices. The mos sraighforward procedure is o deflae boh consumpion and invesmen wih he same deflaor, he GDP deflaor. I is imporan o undersand ha, in he naional accouns, his is no he way consan price measures are consruced. There, invesmen a consan prices is deflaed wih a differen price deflaor han is consumpion. In fac, Finnish daa show a declining rend in he price of invesmen relaive o consumpion. In our base case, his declining relaive price shows up as capial augmening echnological progress ha ranslaes ino higher TFP, while he capial sock is measured in unis of forgone consumpion. I is also worh noing ha increases in he qualiy of labor, human capial accumulaion, and so on would also show up here as increasing TFP. Laer, we explore an alernaive model in which capial goods are differen from consumpion goods and can have differen prices. In our analysis, we rea he real variables from he naional accouns as hough all are measured in prices of he same base period. We laer discuss he case where hey are chain-weighed quaniy indexes. Sandard naional accouns, such as hose of Finland, do no repor a series for he capial sock, so we have o consruc such a series using he daa on invesmen. We consruc his series using he law of moion for capial in he model, (8) K+ = ( ) K + I. This commonly used procedure for calculaing a capial sock is referred o as he perpeual invenory mehod. The inpus necessary o consruc he capial sock series are a capial sock a he beginning of he invesmen series and a value for he consan depreciaion rae,. The value of is chosen o be consisen wih he average raio of depreciaion o GDP observed in he daa over he daa period used for calibraion purposes. For Finland, we find ha he raio of depreciaion o GDP over he period 980 2005 is (9) 2005 K = 0. 693. = 980 26 Y Wihou explici daa on he capial sock a he beginning of he invesmen series, we have o adop a more or less arbirary rule. One rule he one ha we use in his aricle is ha he capial-oupu raio of he iniial period should mach he average capial-oupu raio over some reference period. Here we choose he capial sock so ha he capial-oupu raio in 960 maches is average over 96 70: (0) K Y 960 960 970 K =. = 96 0 Y The sysem of equaions (8) (0) allows us o use daa on invesmen, I, o solve for he sequence of capial socks and for he depreciaion rae,. There are 27 unknowns: K 980,, and K 98, K 982,, K 2005, in 27 equaions: 25 equaions (8), where = 980, 98,, 2004, (9), and (0). Solving his sysem of equaions, we obain he sequence of capial socks and a calibraed value for depreciaion, = 0.0556. An alernaive rule o (0) is o choose he iniial capial sock so ha, when we compue he capial sock in he subsequen period using equaion (8), is growh rae maches he average growh rae of some number of subsequen periods. If he iniial dae for he invesmen series is far removed from he period of ime in which we are ineresed, hese differen rules have lile percepible effec on our resuls. In our case, we sar our model in 980, 20 years afer he beginning of our capial sock series. Wih he depreciaion rae ha we calibrae, his implies ha almos 70 percen of he 960 capial sock has depreciaed away by he ime he model sars in 980, 0. 685 = ( 0. 0556) 20. By 989, he year before he sar of he depression, his number rises o more han 80 percen. The las ingredien we need o perform our growh accouning decomposiion is o assign a value for he capial share,. We can direcly measure from he daa, bu we need o make some adjusmens. If we are using naional accouning daa under SNA93, as we are in he case of Finland, he income definiion of GDP is he sum of hree caegories: Compensaion of Employees, Ne Taxes on Producion and Impors, and Gross Operaing Surplus and Mixed Income. The las caegory is a residual caegory. As Gollin (2002) argues, defining he labor income share as he raio of wages and salaries o GDP a facor prices (excluding indirec axes) is a bad idea. The problem is ha some paymens o labor are o self-employed workers and o unremuneraed family workers. Furhermore, he fracion of GDP ha goes o such workers varies widely from counry 20
Modeling Grea Depressions Juan Carlos Conesa, Timohy J. Kehoe, Kim J. Ruhl o counry. Consequenly, a definiion of labor income based exclusively on he wages and salaries included in Compensaion of Employees will necessarily be misleading. Correcing he bias in he measuremen of facor shares requires consrucing some measure of mixed income of he household secor. The Deailed Tables of he Naional Accouns under SNA93 provide naional accouns disaggregaed by insiuional secors. Using he Household Secor accouns, we measure nonwage income of he household secor as Gross Operaing Surplus and Mixed Income, minus Consumpion of Fixed Capial. We define he labor income share as unambiguous labor income divided by GDP ne of he ambiguous caegories (household ne mixed income and indirec axes): CE () Labor Share =, GDP HNMI NIT where CE is compensaion of employees, HNMI is household ne mixed income, and NIT is ne indirec axes. This procedure is equivalen o spliing he ambiguous caegories beween labor income and capial income in he same proporions as in he res of he economy. Our calculaions produce an average value of he labor income share of 0.640 over he period 980 2005, so ha = 0.3590. Growh Accouning Once we have obained measures for oupu, invesmen, and hours worked, have consruced a capial sock series, and have calibraed a capial share parameer, we compue TFP: (2) A Y = K L. The growh accouning ha we employ is based on ha of Hayashi and Presco (2002, 2007). To moivae his procedure, suppose ha TFP and he working-age populaion grow a consan raes, (3) A = g A + (4) N nn + =, where g is he growh rae of TFP and n is he growh rae of populaion. Then here is a balancedgrowh pah in which oupu per working-age person, Y / N, grows a he rae g and he capial-oupu raio, K / Y, and hours worked per working-age person, L / N, are consan. Tha such a pah is feasible follows from plugging A+ = g A and K+ / N+ = gk / N ino he producion funcion (3), (5) Y N + + = A + K N + + L N + + = ga K L = g Y. N N N Laer, we show ha here is a unique such pah ha saisfies he firs-order condiions for he represenaive household s uiliy maximizaion problem, and he marginal cos pricing condiions (4) and (5). We rewrie he producion funcion as (6) Y N = A K Y L. N Noice ha, in a balanced-growh pah, ( K / Y ) /( ) and L / N are consan, and growh in Y / N is driven /( by growh in A ). To appreciae he usefulness of his decomposiion, consider he daa for he Unied Saes over he period 970 2005 graphed in Figure 4. The U.S. growh pah is close o balanced: he growh /( in Y / N is close o ha in A ), and ( / ) K Y /( ) and L / N are close o consan. To be sure, here are deviaions from balanced-growh behavior. Over he period 983 99, oupu per working-age person Y / N rises faser han does he produciviy facor A/( ),for example, because hours worked per working-age person, L / N, seadily increase. Figure 5 depics he growh accouning for Finland over he same period, 970 2005. A leas hree feaures are worh noing. Firs, growh in real GDP per workingage person in Finland has been rapid over his period, averaging 2.4 percen per year, compared o.7 percen in he Unied Saes. Second, he sharp drop in Y / N from 989 o 992 was driven by boh a fall in he produciviy /( ) facor A and a fall in he labor facor L / N, bu produciviy recovered sharply in 993, and by 993 i was he fall in labor ha accouned for all of he drop in 2
FEDERAL RESERVE BANK OF MINNEAPOLIS QR Figure 4 Growh Accouning for he Unied Saes, 970 2005 Index (970 = 00) 340 300 260 220 80 40 Y / N A /( ) 00 L / N (K / Y) /( ) 60 970 975 980 985 990 995 2000 2005 oupu. Over he enire period 989 93, he fall in hours worked per working-age person of 2.2 percen was far larger han he drop in real GDP per working-age person,.8 percen in raw erms and 8.5 percen derended by 2 percen per year. Third, alhough oupu recovered rapidly saring in 994, labor recovered only parially, and hours worked per working-age person in 2005 were sill 2.5 percen below heir value in 989. These are Figure 5 Growh Accouning for Finland, 970 2005 Index (970 = 00) 340 300 260 220 80 A /( ) Y / N 40 (K / Y) /( ) 00 L / N 60 970 975 980 985 990 995 2000 2005 he feaures of he Finnish daa ha we es our model agains, boh qualiaively and quaniaively. Compuaion of Equilibrium In his secion, we explain how o solve for he model s equilibrium. As we have discussed in he secion eniled The Dynamic General Equilibrium Model, he model feaures a represenaive household ha chooses pahs of consumpion, leisure, and invesmen o maximize uiliy. The pahs of TFP and populaion are exogenously given, and he agen has perfec foresigh over heir values. We sar he model a dae T 0 = 980 and le ime run ou o infiniy. Definiion. Given sequences of produciviy, A, and working-age populaion, N, = T 0, T 0 +,, and he iniial capial sock, K T0, an equilibrium is sequences of wages, w, ineres raes, r, consumpion, C, labor, L, and capial socks, K, such ha. given he wages and ineres raes, he represenaive household chooses consumpion, labor, and capial o maximize he uiliy funcion () subjec o he budge consrains (2), appropriae nonnegaiviy consrains, and he consrain on K T0 ; 2. he wages and ineres raes, ogeher wih he firms choices of labor and capial, saisfy he cos minimizaion and zero profi condiions, (4) and (5); and 3. consumpion, labor, and capial saisfy he feasibiliy condiion (6). We urn hese equilibrium condiions ino a sysem of equaions ha can be solved o find he equilibrium of he model. We begin by aking firs-order condiions of he household s problem of maximizing he uiliy funcion () subjec o he budge consrain (2) o obain = (7) w hn L C (8) C C + = + r. + Combining he household s opimaliy condiions (7) and (8), he firm opimaliy condiions (4) and (5), and he feasibiliy condiion (6), we can specify a sysem of equaions ha can be solved o find he equilibrium of he model. 22
Modeling Grea Depressions Juan Carlos Conesa, Timohy J. Kehoe, Kim J. Ruhl Before explaining how o calculae he whole equilibrium pah, le us explain how o calculae a balancedgrowh pah for his model. Definiion. Suppose ha produciviy, A, grows a he consan rae g and ha working-age populaion grows a he consan rae n, hen a balancedgrowh pah is levels of he wage, w ˆ, he ineres rae, r ˆ, consumpion, C ˆ, labor, L ˆ, he capial sock, K ˆ, and oupu, Y ˆ, T such ha w = g 0 w ˆ, r = r T ˆ, C = ( gn) 0Cˆ, T L = n 0 Lˆ, K gn T = 0 K ˆ, Y gn T = 0 Y ˆ saisfy he condiions for an equilibrium when he iniial capial sock is KT 0 = K ˆ. To solve for he balanced-growh pah, we use (5) and (8) o solve for he capial-oupu raio K ˆ / Y ˆ, Yˆ (9) g = +. Kˆ We hen use (4) and (6) o rewrie (7) as 0 (20) ( ) h N T Lˆ = Kˆ ( gn + ) Yˆ and use his equaion o calculae labor, L ˆ. We can hen use he producion funcion (3) o solve for ˆK and Y ˆ. Using he feasibiliy condiion (6), we can hen solve for C ˆ, and, using he firm opimaliy condiions (4) and (5), we can solve for ŵ and rˆ. We now reurn o he calculaion of he equilibrium pah. Plugging he prices (4) and (5) ino he household s opimaliy condiions (7) and (8), and using he feasibiliy condiion (6), we obain he sysem of equaions = (2) ( ) A K L hn L C (22) C + = ( + A+ K+ L + ) C + (23) C + K ( ) K = A K L. Solving for an equilibrium involves choosing sequences of consumpion, capial socks, and hours worked such ha hese equaions are saisfied, given he iniial condiion K T0 and final condiion, he ransversaliy condiion, (24) lim C K + = 0. In principle, he sysem of equaions ha characerize he equilibrium, (2) (23), involves an infinie number of equaions and unknowns. To make he compuaion of an equilibrium racable, we assume ha he economy converges o he balanced-growh pah a some dae T, which allows us o runcae he sysem of equaions. Using he feasibiliy condiion (6) o solve for C, we can wrie hese equaions as (25) ( ) A K L hn L (26) = A K L K+ + ( ) K, = T, T +,..., T 0 0 + + + + 2 + A K L K + ( ) K A K L K + ( ) K + ( + + + ) = + A K L = T, T +,..., T, 0 0, where KT gnk + = T. We choose T so ha T T0 is large, say 60, so ha we are solving he model over he period 980 2040. We hen consruc he exogenous variables. The exogenous variables A, N for 980 2005 are as hey are in he daa. For 2006 40, we assume ha TFP grows a a consan rae equal o he average growh rae of TFP over he period 980 2005 and ha he working-age populaion grows a he same rae as in 2004 5. These are he growh raes g and n in he specificaion of he balanced-growh pah. Solving he model now consiss of choosing K T0 +, K T0 + 2,, K T and L T0, L T0 +,, L T o solve he sysem of equaions (25) and (26). This sysem of 2( T T0 ) nonlinear equaions in 2( T T0 ) unknowns can be solved relaively quickly using numeri- 23
FEDERAL RESERVE BANK OF MINNEAPOLIS QR cal mehods. A se of MATLAB programs for solving his model are available a www.greadepressionsbook. com. The deails of he programs are available in Appendix A. The soluion of he sysem of equaions (25) and (26) may involve a negaive value of invesmen in some periods. If his is he case, we guess he periods in which invesmen is 0 and replace he corresponding equaion (26) wih he equaion (27) K+ = ( ) K. We follow a guess and verify approach. For our guess ha invesmen in period be 0 o be correc, he condiion corresponding o (8) and (26), (28) + + + + 2 + A K L K + ( ) K A K L K + ( ) K + ( + + + ) + A K L mus hold wih inequaliy.. Calibraion and Resuls for he Base Case Model In addiion o he exogenous pahs for produciviy and populaion, we need o specify he parameers,,, and. We coninue o use he values for and ha we calibraed in he secion eniled The Daa. To calibrae a value for, we use (22) o wrie C + (29) = C + Y K + + Wih values for and, and daa on capial, oupu, and consumpion, we compue for each period and ake he average over 970 80. Tha is, we calibrae household behavior o a period ouside ha in which we are ineresed. We find = 0.9752. The procedure for calibraing is similar. We use (2) o wrie C (30) L =. Y hn L ( ) C L + Using daa on consumpion, hours worked, populaion, and oupu and he value for, we find ha he average. value over 970 80 is = 0.2846. We plo he resuls for he base case model in Figures 6 8. Table compares he growh accouning in he model wih ha in he daa. Here we ake naural logarihms of equaion (6) so ha oupu per working-age person decomposes ino hree addiive facors: Y K L (3) log = log A + log + log. N Y N The numbers repored in Table are average annual changes muliplied by 00, which can be inerpreed as growh raes. Noice ha he model only parially accouns for he fall in oupu during he depression. From 989 o 993, real GDP per working-age person in Finland fell by.8 percen, 8.5 percen when derended by 2 percen per year. In conras, in he model i falls by only.9 percen, 9.4 when derended. Furhermore, he iming is off. Oupu was sill falling in 993 in he daa, whereas i is rising in he model. Noice oo ha he model is able o accoun for only abou one-hird of he fall in hours worked in he daa. The base case numerical experimen is nonsochasic in ha we assume ha households in 980 have perfec foresigh on he evoluion of TFP over he nex 25 years. In he numerical experimen ha we call myopic Figure 6 Base Case Model: Derended Real GDP per Working-Age Person in Finland Index (989 = 00) 30 20 0 00 90 80 70 60 Model wih myopic expecaions Base case model Daa 50 980 985 990 995 2000 2005 24
Modeling Grea Depressions Juan Carlos Conesa, Timohy J. Kehoe, Kim J. Ruhl Figure 7 Base Case Model: Hours Worked per Working-Age Person in Finland Hours per week 30 25 20 5 Model wih myopic expecaions Base case model expecaions, we assume ha households expec TFP in he fuure o grow a he same rae ha i grew over he previous 0 years. We impose hese same condiions on expecaions afer 2005. We assume ha households have perfec foresigh over he evoluion of working-age populaion, however, because hey can observe birh raes and projec hem ino he fuure. This numerical Daa 0 980 985 990 995 2000 2005 Figure 8 Base Case Model: Capial-Oupu Raio in Finland Raio 4.5 4.0 3.5 3.0 2.5 Daa Base case model Model wih myopic expecaions 2.0 980 985 990 995 2000 2005 experimen requires us o solve he model 26 imes, once for each year from 980 o 2005. In 989, for example, households expec TFP o grow forever a he same rae ha i grew over he period 979 89. We compue a perfec foresigh equilibrium for hese expecaions. In 990, households are surprised by a sudden fall in TFP, and hey modify heir expecaions of TFP growh o be ha over he period 980 90. Noice in Figures 6 8 and Table how similar he resuls of he numerical experimen wih myopic expecaions are o hose of he base case, where here is perfec foresigh, especially wih respec o real GDP per working-age person. Where here are deviaions beween he resuls wih perfec foresigh and hose wih myopic expecaions, he resuls wih myopic expecaions move he resuls of he model furher from he daa. Noice especially in Figure 7 ha he model wih myopic expecaions fails o capure he fall in hours worked during he depression. This is because of he general equilibrium srucure of he model. The downurn in Table Base Table Case. Experimen Base case for experimen Finland: for Finland: Decomposiion Decomposiion of Average Annual of average Changes annual changes in Real Oupu in per real Working-Age oupu per working-age Person (%) person (%) Model: Model: Myopic Daa Base case expecaions Growh 980 89 change in Y/N 2.92 3.8 3.2 due o TFP 3.3 3.3 3.3 due o K/Y 0.7 0.07 0.08 due o L/N 0.03 0.2 0.6 Crisis 989 93 change in Y/N 3.4 0.48 0.98 due o TFP 0.05 0.05 0.05 due o K/Y 2.77.54.03 due o L/N 5.96 2.08 0. Recovery 993 2005 change in Y/N 3.33 4.09 3.64 due o TFP 4.04 4.04 4.04 due o K/Y.58 0.38 0.34 due o L/N 0.87 0.43 0.06 25
FEDERAL RESERVE BANK OF MINNEAPOLIS QR Finland 989 93 was so shor ha households did no have ime o adjus heir expecaions of TFP downward and kep up levels of invesmen. Consequenly, because he level of he capial sock is higher during he depression in he model wih myopic expecaions han i is in he base case model wih perfec foresigh, real wages, and herefore employmen, are also higher. In experimens wih his sor of model for counries ha experience longer depressions, we have found ha he myopic expecaions model does beer in capuring he fall in invesmen and hours worked. Taxes and he Role of he Governmen Secor In his secion, we inroduce disorionary axes and governmen spending ino our model. We find ha increases in disorionary axes generae large declines in hours worked in Finland. The conclusion agrees wih ha of Böckerman and Kiander (2002a, 2002b) for Finland and is in accord wih he resuls obained by Conesa and Kehoe (2007), Ohanian, Raffo, and Rogerson (2006), and Presco (2002, 2007) for a number of oher counries. Consider an environmen where he governmen levies disorionary axes and uses he proceeds o finance ransfers o he household secor and governmen consumpion. The represenaive household s problem is o maximize uiliy () subjec o he sequence of budge consrains c ( ) + + = ( ) + + ( )( ) (32) + C K + w L k r K T, appropriae nonnegaiviy consrains, and a consrain on he iniial sock of capial, K T0. Here c is he ax rae on consumpion; is he marginal ax rae on labor income; k is he marginal ax rae on capial income; and T is a lump-sum ransfer, which may be posiive or negaive, received from he governmen. Noice ha he inroducion of axes requires us o modify he firsorder condiions (7) and (8) of he represenaive household: (33) (34) C = hn L + C C + = + + c c + ( + ( ) A K L c k ( + ) ( + + )) +. A K L The sequence of governmen budge consrains is (35) C + w L + ( r ) K = G + T, c k where he governmen finances governmen consumpion, G, and ransfers o he household secor T. We modify he feasibiliy consrain (6) o include governmen consumpion: + (36) C + K ( ) K + G = A K L. Definiion. Given sequences of produciviy, A, and working-age populaion, N, consumpion axes, c, labor axes,, capial axes, k, and governmen consumpion, G, = T 0, T 0 +,, and he iniial capial sock, K T0, an equilibrium wih axes and governmen consumpion is sequences of wages, w, ineres raes, r, consumpion, C, labor, L, capial socks, K, and ransfers, T, such ha. given he wages and ineres raes, he represenaive household chooses consumpion, labor, and capial o maximize he uiliy funcion () subjec o he budge consrain (32), appropriae nonnegaiviy consrains, and he consrain on iniial capial K T0 ; 2. he wages and ineres raes, ogeher wih he firms choices of labor and capial, saisfy he cos minimizaion and zero profi condiions, (4) and (5); 3. governmen consumpion and ransfers saisfy he governmen budge consrains (35); and 4. consumpion, labor, and capial saisfy he feasibiliy condiion (36). I is worh poining ou ha here is an equivalence beween his specificaion and one in which governmen ransfers are exogenously given and he governmen balances is budge by selling bonds. In his case, he represenaive household faces he sequence of budge consrains c ( ) + + = ( ) w L (37) + C K+ B + 26
Modeling Grea Depressions Juan Carlos Conesa, Timohy J. Kehoe, Kim J. Ruhl ( ( ))( + ) + + + r K B T, k iniial condiions on capial, K T0, and bonds, B T0, and a consrain of he form B g B, where he consan B > 0 is chosen large enough so ha he consrain never binds in equilibrium excep o preven he household from running Ponzi schemes. The governmen faces he sequence of governmen budge consrains ( + ) + + ( ) c k (38) C + w L + r K B B = G + T + + r B and a consrain ha says ha deb canno ge oo large, (39) lim, C B + 0 which is he ransversaliy condiion from he represenaive household s problem. To be precise abou he equivalence: For any equilibrium in he model wih exogenous ransfers and governmen bonds, T and B, in which B T0 = 0,here is an equilibrium in he model wih endogenous ransfers, T ˆ, and no bonds in which + (40) Tˆ = T + + r B ( r ) B B. k Conversely, for any equilibrium in he model wih endogenous ransfers, T, and no bonds, here is an equilibrium in he model wih exogenous ransfers and governmen bonds, T ˆ, and B ˆ, in which ˆT = T and B ˆ = 0. Noice ha here are acually infiniely many combinaions of ransfers and bonds ha have he same values of all of he oher variables in equilibrium as he model wih endogenous ransfers and no bonds. Unless here is some reason o model governmen deb or o fix ransfers, we herefore use he specificaion wih endogenous ransfers and no bonds. If uiliy is separable beween he consumpion-leisure bundle and public goods and services, he disincion beween public goods and services and governmen consumpion ha is no valued by he household is inconsequenial excep for welfare measuremen. The disincion beween governmen consumpion and ransfers is more involved, however. We explore he imporance of his disincion in he nex secion. Calibraion and Resuls for he Model wih Taxes and Governmen Spending To obain esimaes of he sequences of effecive ax raes c,, and k, we use daa on aggregae ax collecions from is main sources individual and household income axes, corporae income axes, sales and excise axes, payroll axes, and so on and classify hem according o he ax caegories we have in our analysis: consumpion ax, labor income ax, and capial income ax. We follow he mehodology of Mendoza, Razin, and Tesar (994), wih wo major differences. Firs, since we aribue a fracion of households nonwage income o labor income, we ake ha ino accoun when defining he relevan ax base in he daa. Second, we se he income ax raes, and k, equal o heir effecive marginal raes, as opposed o effecive average raes. We focus on marginal raher han average effecive ax raes because, given our heoreical framework, he relevan household decisions are aken a he margin as in (33) and (34). Noice ha, wih our specificaion of ransfers, if he marginal ax rae is higher han he corresponding average rae, hen we are specifying a progressive income ax wih a consan marginal ax rae. In principle, we need o adjus our income ax esimaes using esimaed effecive income ax funcions wih disaggregaed daa, as in Conesa and Kehoe (2007). In his aricle, we simply follow Presco (2002, 2007) for he U.S. case in muliplying average income axes by a facor of.6 o obain marginal ax raes. An explici procedure for calculaing he ax raes for Finland is presened in Appendix B. These ax raes are graphed in Figure 9. We are sill lef wih he nonrivial issue of allocaing governmen revenues beween governmen consumpion and ransfers. We run numerical experimens of he model under wo differen specificaions, following Conesa and Kehoe (2007). In he firs specificaion, we assume ha all governmen revenues are given as a lump-sum rebae o households. In oher words, we se G = 0 in (35) and (36). This specificaion implies ha all governmen revenues go o ransfers o he households, such as pensions or unemploymen subsidies, or o purchases of goods and services ha would oherwise be provided privaely, such as educaion or healh care. Our alernaive specificaion goes o he oher exreme and assumes ha governmen consumpion in he naional accouns is wased or ha i produced a public good ha eners he households uiliy funcion separably. For example, 27
FEDERAL RESERVE BANK OF MINNEAPOLIS QR Figure 9 Tax Raes in Finland Percen 80 Figure 0 Governmen Consumpion in Finland Percen of GDP 26 70 60 Labor income ax 24 50 40 Consumpion ax 30 20 Capial income ax 0 970 975 980 985 990 995 2000 2005 22 20 8 980 985 990 995 2000 2005 we could specify uiliy as (4) ( log C + ( ) hn L = T 0 + log G ). Figure 0 shows he daa for he evoluion of governmen consumpion in Finland. In he numerical experimens, we assume ha governmen spending grows by he facor gn over he period 2006 40 so ha we can assume he equilibrium converges o a balanced-growh pah. In he daa, governmen consumpion grows faser han his over he period 980 2005. If we projec governmen consumpion as growing a his faser rae ino he fuure, however, i evenually becomes larger han he economy can feasibly supply. The reason for his is easily seen in Figure 0. If we exrapolae he growh in governmen consumpion as a percenage of GDP, governmen consumpion evenually becomes more han 00 percen of GDP. To exogenously se he produciviy series, we modify equaion (2), (42) A C + I = K L, where C + I is real GDP a facor prices in he daa. When we repor he conribuion of TFP o growh, however, we calculae TFP as convenionally measured, (43) Aˆ where Yˆ = K L (44) Ŷ = + C I c ( T ) +, is real GDP a marke prices of he base year T. For he Finnish daa ha we use, T = 2000. We run hree numerical experimens wih axes: one for each of he wo alernaive specificaions of governmen spending and a hird in which we mainain ax raes consan a heir average 970 80 and all governmen revenues are ransferred o he household. The presence of disorionary axes requires us o recalibrae he household uiliy funcion parameers and. In he experimen wih consan ax raes and all governmen revenue ransferred, we calibrae =.003 and = 0.4638; in he model wih axes and all governmen revenue ransferred, =.0049 and = 0.4649; and, in he model wih axes and governmen consumpion, = 0.9948 and = 0.3856. Noice ha he calibraed values of in he firs wo experimens are greaer han, which makes he represenaive household s objecive funcion () infinie in an economy in which consumpion and leisure do no converge o 0 sufficienly rapidly. 28
Modeling Grea Depressions Juan Carlos Conesa, Timohy J. Kehoe, Kim J. Ruhl Figure 2 Model wih Governmen Secor: Hours Worked per Working-Age Person in Finland Hours per week 30 Model wih axes and governmen 25 20 5 0 980 985 990 995 2000 2005 To avoid his problem in hese wo numerical experimens, we se, more or less arbirarily, = 0.9990. There are a number of reasons for he high calibraed value of in a model wih axes where all governmen revenues are ransferred o consumers. The ax on capial lowers he afer-ax ineres rae in he firs-order condiion (34), bu he growh rae of consumpion says he same as in he model wihou axes. Noice ha, in he experimen where we do no ransfer all ax revenues o households and we ake governmen consumpion ou of C in (34), he growh rae of consumpion falls sufficienly for he calibraed value of o be less han. Noice ha he conribuion of TFP in he growh accouning differs beween he model and he daa because of he difference beween he produciviy facor ha we exogenously fix, A, and TFP, A ˆ, which depends on endogenously deermined consumpion, C. Figures 3 and Table 2 presen he resuls of he hree numerical experimens wih axes and governmen spending. I is worh menioning ha invesmen is equal o 0 and he inequaliy consrain (28) holds in 994 in boh he model wih axes and all governmen revenue ransferred and in he model wih axes and governmen consumpion. As we have seen in he secion eniled Calibraion and Resuls for he Base Case Model, he base case model does no accoun for he sharp fall in hours worked 989 94. As Figure 2 shows, he inroducion of disorionary axes in our analysis helps in accouning for his feaure of he daa. If anyhing, he model overesimaes he fall in hours worked. Conesa and Kehoe (2007) show ha alernaive uiliy funcions wih lower corresponding labor supply elasiciies can produce a lower response of hours worked o changes Daa Model wih consan axes Model wih axes Figure Model wih Governmen Secor: Derended Real GDP per Working-Age Person in Finland Index (989 = 00) 30 Figure 3 Model wih Governmen Secor: Capial-Oupu Raio in Finland Raio 4.5 20 0 00 90 80 70 60 Model wih axes and governmen Model wih consan axes Daa Model wih axes 4.0 3.5 3.0 2.5 2.0 Model wih axes and governmen Model wih axes Daa Model wih consan axes 50 980 985 990 995 2000 2005.5 980 985 990 995 2000 2005 29
FEDERAL RESERVE BANK OF MINNEAPOLIS QR Table 2 Table Governmen 2. GovSnmen Secor Experimen secor experimen for Finland: for Finland: Decomposiion Decomposiion of Average of Annual average Changes annual changes in Real Oupu in real per oupu Working-Age per working-age Person (%) person (%) Model: Model: Consan Model: Taxes and Daa axes Taxes governmen Growh 980 89 change in Y/N 2.92 3.2.20.68 due o TFP 3.3 2.95 3.8 3.7 due o K/Y 0.7 0.07 0.54 0.67 due o L/N 0.03 0.0 2.52 2.7 Crisis 989 93 change in Y/N 3.4.6 5.55 5.30 due o TFP 0.05 0.09.5 0.68 due o K/Y 2.77.96 2.80 2.66 due o L/N 5.96 3.03 9.5 8.64 Recovery 993 2005 change in Y/N 3.33 4.00 4.22 4.23 due o TFP 4.04 3.93 3.50 3.69 due o K/Y.58 0.56 2.07 2.0 due o L/N 0.87 0.64 2.80 2.55 in labor and consumpion axes in his sor of model. Ljunge and Ragan (2004) argue ha he responses of labor supply o changes in axes like hose in Finland in he early 990s hey focus on similar changes ha occurred in Sweden a he same ime were large, bu no as large as hose prediced by our logarihmic uiliy funcion (). Furhermore, Ragan (2005) and Rogerson (2007) argue ha much of he revenues from axes on labor in Scandinavia are used o finance subsidies and ransfers o workers, which lower he effecive ax rae on labor. This is a opic ha deserves more research. Figure shows ha he model wih axes also does a beer job han he base case model in accouning for he coninued fall hrough 993 in derended real GDP per working-age person in he daa. Noice ha he specificaion in which governmen consumpion is wased or eners he uiliy funcion separably significanly improves he performance of he model relaive o he specificaion where ax revenues are lump-sum rebaed. In his specificaion, increases in axes generae negaive income effecs ha induce households o provide more labor in he marke han hey would have done if he ax revenues were rebaed. Finally, noice ha he model wih consan axes does no perform beer han he base case model in accouning for he fall in hours or he lengh of he crisis. I is he evoluion of disorionary axes ha improves hese feaures of he model s performance, no heir mere presence in he model. This is because we have calibraed he parameers and so ha he model is consisen wih observed behavior over he period 970 80. To induce households o supply as much work and o inves as much as hey did during 970 80, we have o se and o higher values when here are axes han when here are no axes. Two Secors: Consumpion and Invesmen We have defined invesmen in our growh accouning and base case model o be invesmen in curren prices deflaed by he GDP deflaor. In his secion, we develop an alernaive model in which invesmen is invesmen in curren prices deflaed by he invesmen deflaor. In his model, here is an inraemporal relaive price ha plays a major role, he relaive price of invesmen o consumpion. Figure 4 depics he evoluion of his relaive price over he period 980 2005. As an aside, i is worh noing ha some researchers argue ha he naional accouns do no fully capure he improvemens in qualiy experienced by invesmen goods. (See, for Figure 4 Relaive Price of Invesmen in Finland Index (989 = 00) 0 05 00 95 90 85 80 75 980 985 990 995 2000 2005 30
Modeling Grea Depressions Juan Carlos Conesa, Timohy J. Kehoe, Kim J. Ruhl example, Gordon 990 and, for a more recen conribuion, Cummins and Violane 2002.) We model he invesmen secor in he simples possible way. Le q be he relaive price of invesmen goods o consumpion goods. We assume ha X (45) I = K+ ( ) K =. q Tha is, here is a producion echnology ha ransforms q unis of consumpion goods ino one uni of he invesmen good. This specificaion is similar o ha of Greenwood, Hercowiz, and Krusell (2000) and Rebelo (99). The feasibiliy condiion for he consumpion good secor is (46) C + X = A K L. Combining (45) and (46), we obain (47) C + q I = A K L where, (48) I = K ( ) K, + and he budge consrain of he represenaive household becomes (49) C + q I = w L + r K. The firs-order condiion ha characerizes households consumpion and savings behavior, (8), becomes (50) C C + = A+ K + L + + q + q. The condiion ha characerizes households labor and leisure behavior, (7), says he same. Definiion. Given sequences of produciviy, A, relaive prices of he invesmen good, q, and working-age populaion, N, = T 0, T 0 +,, and he iniial capial sock, K T0, an equilibrium wih a consumpion secor and an invesmen secor is sequences of wages, w, ineres raes, r, consumpion, C, labor, L, invesmen, I, and capial socks, K, such ha. given he wages and ineres raes, he represenaive household chooses consumpion, labor, and capial o maximize he uiliy funcion () subjec o he budge consrains (49), appropriae nonnegaiviy consrains, and he consrain on K T0 ; 2. he wages and ineres raes, ogeher wih he firms choices of labor and capial, saisfy he cos minimizaion and zero profi condiions, (4) and (5); and 3. consumpion, invesmen, labor, and capial saisfy he feasibiliy condiions (46), (47), and (48). Calibraion and Resuls for he Two-Secor Model wih Consumpion and Invesmen The inroducion of he invesmen secor, and he consequen inroducion of he relaive price of he invesmen good, requires ha we make significan adjusmens o he manner in which we mach he model wih he daa. Firs, he numeraire is he consumpion good. As a resul, GDP in he daa mus be deflaed by he consumpion deflaor, raher han he GDP deflaor as in he one-secor environmen. Second, we have o recompue a consisen measure of he capial sock using X (5) K+ = ( ) K +, q where X is invesmen deflaed by he consumpion deflaor. Since he relaive price of invesmen changes every period, here is no mehod ha is exacly equivalen o equaions (8) (0) for choosing he iniial capial sock and he depreciaion rae. Some mehods would ake seriously he vinage naure of our capial sock and counry-specific depreciaion rules. Here we simply se (52) (53) where 2005 q K = 0. 693 = 980 26 Y q K Y 960 960 960 (54) Y = C + q I 970 q K =, = 96 0 Y is GDP in curren prices deflaed by he consumpion good deflaor. 3