Great Depressions from a Neoclassical Perspective Kaiji Chen University of Oslo October 22, 2008 1 Review of Last Class • Model with indivisible labor, either working for fixed hours or not. - allow social planner to choose the fraction of agents to work each period. — social planner also provide full insurance against unemployment risk. - we shows that the decision variables for the social planner are the same as for a divisible labor model, though the marginal disutility for labor is linear. — Frisch elasticity of labor supply is maximized in this model, while in the standard model it is one. 2 • The model generated fluctuation of labor input very close to the data, through fluctuations in employment rather than fluctuations in hours per employed worker. • When agents are ex-ante heterogeneous, and there is no full insurance for unemployment risks, the aggregate elasticity of labor supply depend on the distribution of reservation wage. — Aggregate elasticity of labor supply tends to be large where is a concentration of reservation wage. 3 Roadmap of this Class • Great Depression of the Twentieth Century: An Overview • Great Depression Methodology — Growth Accounting — Dynamic General Equilibrium Model 4 1. GREAT DEPRESSION IN THE 20TH CENTURY 1 Great Depression in the 20th Century 5 1. GREAT DEPRESSION IN THE 20TH CENTURY United States: Real GDP per Working-Age Person 800 50,-,-,-,-,-,-,-,-,-,-, 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 year 6 1. GREAT DEPRESSION IN THE 20TH CENTURY Digression: Economic Growth • Model so far does not display long-run growth, since the economy converges to to is steady state. • Data do. • Partly due to population growth, but even GDP per capita (or per working age person) grows at a positive rate. 7 1. GREAT DEPRESSION IN THE 20TH CENTURY • Assume working-age population (and labor force) grows at a constant gross growth rate r\. Nt = rtNo = rt where No = 1 is the size of labor force at period 0. • Labor augmenting technoligical process. Assume that production function is given by Yt = ztKf^Ht) where 7 is the long-run growth rate of technology, Ht = htN is aggregate hours worked, yt = Yt/Nt is output per working age person. zt is country-specific productivity parameter that varies over time. 8 1. GREAT DEPRESSION IN THE 20TH CENTURY Balanced Growth Path • Balanced growth path is an equilibrium or social planner allocation where all per capita variables grow at a constant rate, with the exception of market hours per working age person, h, which is constant. • Easy to show that the constant growth rate has to be 7. • Define trend level of output and output per working age population as Y = 7tNtY0 9 1. GREAT DEPRESSION IN THE 20TH CENTURY Definitions of Great Depressions • A large negative deviation from trend (or balanced) growth. • Twentieth century U.S. macro data are very close to a balanced growth path, with the exception of Great Depression and the subsequent World War II built-up. • Trend growth rate is set to be two percent per year (7 = 1.02), the long run growth rate of output per working-age person in the United States during the twentieth century. 10 1. GREAT DEPRESSION IN THE 20TH CENTURY United States: Real GDP per Working-Age Person 800 50,-,-,-,-,-,-,-,-,-,-, 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 year 11 1. GREAT DEPRESSION IN THE 20TH CENTURY_ Conditions for a negative deviation from trend to be a great depression • It must be a sufficiently large deviation. - A great depression is a deviation of at least 20 percent below trend level. • The deviation must occur rapidly. — Detrended output perworking age person must fall at least 15 percent within the first decade of depreassion. 12 1. GREAT DEPRESSION IN THE 20TH CENTURY • A time period D = [to,ti] is a great depression if there is some year t in D such that 7 0 1 < -0.20. there is some to < t < to + 10 such that 7 0 1 < -0.15 • We do not require that an economy return to the original trend path at the end of a depression. — We would however expect the productivity factor and eventually the economy itself to gorw at the trend rate. • For the starting year of a depression to, we identify the trend level y/to with the observed level y/1 . 13 1. GREAT DEPRESSION IN THE 20TH CENTURY An overview of great depressions in the twentieth century • 1930s: United States, United Kongdom, Canada, France, Germany • Contemporary: Argentina (1970s and 1980s), Chile and Mexico (1980s), Brazil (1980s and 1990s), New Zealand and Switzerland (1970s, 1980s, and 1990s), Argentina (1998-2002) • Not-quite-great Depressions: Italy (1930s), Finland (1990s), Japan (1990s) 14 1. GREAT DEPRESSION IN THE 20TH CENTURY Figure 1: Detrended output per person during the Great Depression 15 1. GREAT DEPRESSION IN THE 20TH CENTURY Figure 2: Detrended output per working age person during the 1980s in latin America 16 1. GREAT DEPRESSION IN THE 20TH CENTURY Figure 3: Detrended Output per Working-Age Person in New Zealand and Switzerland (1970-2000) 17 2. GREAT DEPRESSION METHODOLOGIES 2 Great Depression Methodologies Growth Accounting • rewrite the production function 1 a log yt = t log 7 +--log zt +--log kt/yt + log ht 1 — a 1 — a where lower case variables denote per working-age person values of a variable. • Along the balanced grwoth path, output per working age person grows at the trend growth rate and each of the remaining three factors are constant. 18 2. GREAT DEPRESSION METHODOLOGIES • Each of the last three factors allows us to examine different set of shocks and changes in policies while studying output. — Constraints imposed upon the way businesses operate, such as a restriction on the adoption of a more efficient production technology, will reduce the productivity factor. — A change in the tax system that makes consumption more expensive in terms of leisure will reduce the balanced growth value of the labor factor. — A change in the tax system that taxes capital income at a higher level will reduce the balanced-growth value of the capital factor. 19 2. GREAT DEPRESSION METHODOLOGIES 20 2. GREAT DEPRESSION METHODOLOGIES Features of U.S. Great Depression • Output fell more than 38% between 1929 and 1933. • By 1939, output remained 11 percent below its 1929 detrended level. • Total factor productivity declines sharply in 1932 ans 1933, falling about 12 percent and 14 percent, respectively, below their 1929 detrended level. • After 1933, TFP rose quickly relative to trend and returned to trend by 1936. 21 2. GREAT DEPRESSION METHODOLOGIES • Total hours plummeted more than 30 percent between 1929 and 1933, and remained 22 percent below their detrended 1929 level at the end of the decade. 22 2. GREAT DEPRESSION METHODOLOGIES Neoclassical Growth Model • Can neoclassical theory account for the Great Depression in the United States? — both the downturn in output between 1929 and 1933 and the recovery between 1934 and 1939. • We introduce trend growth in technology and population in our model. • We take the path of productivity factor as exogenous. • Comparing results of the model with the data, we can identify features of the U.S. Great Depression that need further analysis. 23 2. GREAT DEPRESSION METHODOLOGIES Social Planner's Problem oo r max E0^2 ßtNt [log ct + V log(1 - ht)] {ct,ht,kt+1\t=0 t=0 subject to ct where ct = N"? ht = :Nt, kt+i = Nt+1, and the mean value of z is 1. Ht (1 - S) Kt + ztKf^Ht)1 ^ 0? ht 2 [0? 1] and Ko given (1 - p) + pzt-1 + "t?"t~N (0,a2 Kt Nt Nt N t+1 (2) (3) 24 2. GREAT DEPRESSION METHODOLOGIES • Intratemporal optimality condition zt (1 - a) (Kt/Ht)ajt(1~a) 1 - ht ct • Intertemporal optimality condition 1 = ßEt c+- (l - 5 + zt+iaKt+i1 (-ft+1 Ht+i)1'^ 25 2. GREAT DEPRESSION METHODOLOGIES Detrended variables yt kt Ct 7tNt Yt ltNt Kt 7tNt 7t 26 2. GREAT DEPRESSION METHODOLOGIES Rescaling in detrended variables • Hard to solve for the decision rules numerically in a growing economy. • Want to rewrite the problem in terms of variables that not constantly growing over time, that is in terms of ~ variables. • Note that Kq = kg = kg, since 70 = Nq = 1. • Need to rescale resource constraint and the utility function. 27 2. GREAT DEPRESSION METHODOLOGIES Rescaling of the utility function • With the above utility function we have log ct + V log(1 - ht) = log ct + log 7t + V log(1 - ht) • Can rewrite the lifetime utility of the representative family as Y,PlNt [log ct + V log(1 - ht)] t=0 = Y, ^tNt [log ct + V log(1 - ht)] + E ^tNt log 7t t=0 t=0 • can omit the constant term in utility. 28 2. GREAT DEPRESSION METHODOLOGIES The Social Planner's Problem max £0 E /^Nt [log c + V log (1 - ht)j subject to = (1 - S) h + ztfefh 1—a t 0; ht 2 [0; 1] and eo given (1 - p) + pzt_i + "t;"t~N (0;a2) (4) (5) (6) 29 2. GREAT DEPRESSION METHODOLOGIES • First order condition with respect to ct, ht, yield Nt At CXi—OL = At (1 - a) ztk%h~t 1 " ht 30 2. GREAT DEPRESSION METHODOLOGIES • Intratemporal optimality condition (1 - a) ztk?hta 1 - ht et • Intertemporal optimality condition 1 „ r 1 ^7 = ßEt J^- (1 - 6 + zt+1ef+1h-+1) • A balanced growth path is a situation where lct,ct,yt) are constant. 31 2. GREAT DEPRESSION METHODOLOGIES The representative firm's problem in decentralized economy max ztKf {^Ht)1 " - wtH - rtK • First order condition wt = zt (1 - a)(Kt/Ht)a7t(1_a) = zt (1 - a) 7t (%t/ht)a rt = ztaK?'1 [7tHt)1_a = zta (fet/h^)a_1 • Along BGP, et is constant. Therefore, rt is constant, while wt grows at a constant rate 7. 32 2. GREAT DEPRESSION METHODOLOGIES • Given our transformation of variables, the intratemporal and intertemporal optimality conditions in the original economy are equivalent to their counterparts in this stationary economy. 33 2. GREAT DEPRESSION METHODOLOGIES Calibration • One period in our model is one year. • Parameters that have a time dimension: 5,/3,7,r • r = 1.01, the long run growth rate of working age population in the U.S. • At the balanced growth path, 7 is equal to the growth rate of outpur per capita. 7 = 1.019,which is the long run average growth rate of GDP per capita in the U.S. • a = 0.33 to match the average capital income share in the U.S. 34 2. GREAT DEPRESSION METHODOLOGIES • V is set to target an average of one-third of their discretionary time working. • To calibrate S, note that at balanced growth path, the law of motion for capital k7T = (1 — S) k + i which implies e k I S = k + 1 - = — + 1 - 777 k K The long run average ratio Kk = 0.076, which yield an annual depreciation rate of 4.68% (or a quarterly rate of 1.17%). 35 2. GREAT DEPRESSION METHODOLOGIES • For ß; Euler Equation at balanced growth path • Capital output ratio is estimated to be 3. This yield an annual (3 = 0.958. • a = 1.7% and p = 0.9 to match the observed standard deviation and serial correlation of total factor productivity. 36 2. GREAT DEPRESSION METHODOLOGIES Model's prediction • Rewrite the social planner's problem as a dynamic programing problem. • Solve the decision rule of this economy numerically and obtain k+l = gk (h; zt) ;Vt = gy (h, zt) .ct = go (ku zA , gy (ku zA ,h = gh (ku zA. • Assume capital stock in 1929 is equal to its steady state value. • Feed in the sequence of observed levels of total factor productivity as measures of the technology shock. 37 2. GREAT DEPRESSION METHODOLOGIES Growth accounting for the United States 140 120 100 80 60 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 38 2. GREAT DEPRESSION METHODOLOGIES Growth accounting for the United States 140 - 120 100 80 60 n-,-,-,-,-,-,-,-,-,-, 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 39 2. GREAT DEPRESSION METHODOLOGIES Growth accounting for the United States 140 120 100 80 60 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 40 2. GREAT DEPRESSION METHODOLOGIES Growth accounting for the United States 140 - 120 60 n-,-,-,-,-,-,-,-,-,-, 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 41 2. GREAT DEPRESSION METHODOLOGIES Conclusion • A simple dynamic general equilibrium model that takes movements in the productivity factor as exogenous can explain most of the 1929-1933 downturn in the United States. — Keynesian analysis stresses declines in inputs of capital and labor as the causes of depressions. • The model over predicts the increase in hours worked during the 1933-1939 recovery. • Need for Further Study 42 2. GREAT DEPRESSION METHODOLOGIES — The decline in productivity during 1929-1933 — The failure of hours worked to recover 1933-1939. 43 2. GREAT DEPRESSION METHODOLOGIES Other Applications of Neoclassical Growth Model • The Japanese lost decade • The Japanese saving rate • The U.S. saving rate 44 2. GREAT DEPRESSION METHODOLOGIES Source: Hayashi and Prescott (2003) 45 2. GREAT DEPRESSION METHODOLOGIES 1961 1966 1971 1976 1901 1996 1991 1996 Figure 3: Saving Tfote: Da;n end the Infinite Hcrizor. Model Source: Chen, Imrohoroglu and Imrohoroglu (2006) 46