Adjemian, Stephane, Houtan Bastani, Michel Juillard, Ferhat Mihoubi, George Perendia, Marco Ratto, and Sebastien Villemot, 2011, “Dynare: Reference Manual, Version 4,” Dynare Working Papers, CEPREMAP, Vol. 1.
Benhabib, Jess, and Roger E. A. Farmer, 1994, “Indeterminacy and Increasing Returns,” Journal of Economic Theory, Vol. 63, pp. 19–46.
Blanchard, Olivier, and Jordi Gali, 2008, “Labor Markets and Monetary Policy: A New-Keynesian Model with Unemployement,” MIT Department of Economics Working Paper, Vol. No. 06-22.
Blanchard, Olivier J., and Danny Quah, 1989, “The Dynamic Effects of Aggegrate Demand and Supply Disturbances,” The American Economic Review, Vol. 79, pp. 655–673.
Blanchard, Olivier J., and Danny Quah, and Lawrence H. Summers, “Hysterisis and the European Unemployment Problem,” 1986, in “NBER Macroeconomics Annual,” Vol. 1 (National Bureau of Economic Research), pp. 15–90.
Blanchard, Olivier J., and Danny Quah, and Lawrence H. Summers, 1987, “Hysterisis in Unemployment,” European Economic Review, Vol. 31, pp. 288–295.
Blundell, Richard, and Thomas H. MaCurdy, 1999, “Labor Supply: A Review of Alternative Approaches,” Handbook of Labor Economics, Vol. 3, pp. 1559–1695.
Evans, George W., and Gary Ramey, 2006, “Adaptive Expectations, Underparameterization and the Lucas Critique,” Journal of Monetary Economics, Vol. 53, pp. 249–264.
Evans, George W., and Gary Ramey, and Seppo Honkapohja, 1993, “Adaptive forecasts, hysteresis and endogenous fluctuations,” Federal Reserve Bank of San Francisco Economic Review, Vol. 1, pp. 3–13.
Evans, George W., and Gary Ramey, and Seppo Honkapohja, 2000, “Expectations and the Stability Problem for Optimal Monetary Policies.” University of Oregon, mimeo.
Farmer, Roger, Carine Nourry, and Alain Venditti, 2013, “The Inefficient Markets Hypothesis: Why Financial Markets Do Not Work Well in the Real World,” NBER Working paper 18647.
Farmer, Roger E. A., 2002, “Why Does the Data Reject the Lucas Critique?,” Annales d’Economie et de Statistiques, No. 67-68, pp. 111–129.
Farmer, Roger E A, 2012, “The stock market crash of 2008 caused the Great Recession: Theory and evidence,” Journal of Economic Dynamics & Control, Vol. 36, pp. 693–707.
Farmer, Roger E. A., and Jang Ting Guo, 1994, “Real Business Cycles and the Animal Spirits Hypothesis,” Journal of Economic Theory, Vol. 63, pp. 42–73.
Fernandez-Villaverde, Jesus, and Juan Rubio-Ramirez, 2005, “Comparing Dynamic Equilibrium Models to Data: A Bayesian Approach,” Journal of Econometrics, Vol. 123, pp. 891–910.
Fernandez-Villaverde, Jesus, and Juan Rubio-Ramirez, 2005, “Estimating Dynamic Equilibrium Economies: Linear Versus Non-Linear Likelihood,” Journal of Applied Econometrics, Vol. 20, pp. 891–910.
Galí, Jordi, Frank Smets, and Rafael Wouters, 2012, “Slow Recoveries: A Structural Interpretation,” Journal of Money, Credit and Banking, Vol. 44 (2), pp. 9–30.
Hall, Robert E., 2005, “Employment Fluctuations with Equilibrium Wage Stickiness,” American Economic Review, Vol. 95, No. 1 (March), pp. 50–65.
Justiniano, Alejandro, Giorgio E. Primiceri, and Andrea Tambalotti, 2010, “Investment Shocks and Business Cycles,” Journal of Monetary Economics, Vol. 57, pp. 132–145.
Klump, Rainer, Peter McAdam, and Alpo Willman, 2007, “Factor Substitution and Factor-Augmenting Technical Progress in the United States: a Normalized Supply-Side System Approach,” The Review of Economics and Statistics, Vol. 89(1), pp. 183–192.
Koopman, Siem Jan, 1997, “Exact Initial Kalman Filtering and Smoothing for Nonstationary Time Series Models,” Journal of the American Statistical Association, Vol. 92, No. 440 (Dec., 1997), pp. 1630–1638.
Koopman, Siem Jan, and James Durbin, 2000, “Fast Filtering And Smoothing For Multuvariate State Space Models,” Journal of Time Series Analysis, Vol. 21, No. 3, pp. 281–296.
Ludvigson, Sidney C., and Martin Lettau, 2004, “Understanding Trend and Cycle in Asset Values: Reevaluating the Wealth Effect on Consumption,” American Economic Review, Vol. 94, No. 1, pp. 277–299.
Mortensen, Dale T., and Eva Nagypal, 2007, “More on Unemployment and Vacancy Fluctuations,” Review of Economic Dynamics, Vol. 10, pp. 327–347.
Nadiri, M. Ishaq, and Ingmar R. Prucha, 1997, “Estimation of the Depreciation Rate of Physical and R&D Capital in the U.S. Total Manufacturing Sector,” NBER Working Paper No. 4591.
Nelson, Charles R., and Charles Plosser, 1982, “Trends and random walks in macroeconomic time series: Some evidence and implications,” Journal of Monetary Economics, Vol. 10, pp. 139–162.
Plotnikov, Dmitry, 2012, “Can an RBC model match medium-term business cycle fluctuations in the U.S. data?,” UCLA working paper.
Rogerson, Richard, Robert Shimer, and Randall Wright, 2005, “Search-Theoretic Models of the Labor Market: A Survey,” Journal of Economic Literature, Vol. 43, pp. 959–988.
Shimer, Robert, 2005, “The Cyclical Behavior of Equilibrium Unemployment and Vacancies,” American Economic Review, Vol. 95, No. 1, pp. 25–49.
Sims, Christopher A., 2001, “Solving Linear Rational Expectations Models,” Journal of Computational Economics, Vol. 20, No. 1-2, pp. 1–20.
I wish to thank Ariel Burstein, Francisco Buera, Andrew Atkeson, Pablo Fajgelbaum, Jang-Ting Guo, Lee Ohanian, Aaron Tornell and Pierre-Olivier Weill for their detailed comments as well as participants of the Monetary Economics Proseminar at UCLA, ICD Lunchtime seminar, NBER Summer Institute, Society for Economic Dynamics for their helpful feedback. I am especially thankful to Roger Farmer for his time and invaluable advice.
Galí, Smets and Wouters (2012) uses term “slow recoveries” to emphasize that there was no structural break in the relationship between U.S. GDP and employment in 1990. My model is entirely consistent with this evidence as it can generate both regular and jobless recoveries.
Wealth data for the 1948 recession is not available.
Since each steady state is associated with its own unique unempoyment rate, my model does not contain a natural rate of unemployment. Instead many unemployment rate are sustainable as a long-run equilibria.
Shiller (2000) among others argued that the run-up in housing prices prior to 2005 and the subsequent decline cannot be attributed to any change in fundamentals. Farmer, Nourry and Venditti (2013) argue that most of the stock market movements are due to “animal spirits”.
To my knowledge, very few papers argued in favor of this hypothesis. The major exception since 2000 is the paper by Ball (2009). This paper presents new empirical evidence from 20 countries that supports hysteresis in unemployment.
The multiplicity of steady state equilibria is the key difference between the model in this paper and the previous generation of endogenous business cycles models such as Farmer and Guo (1994) or Benhabib and Farmer (1994). These models exhibit dynamic indeterminacy, but all dynamic paths converge to a single steady state. In contrast, the model I describe here has a continuum of steady states but a unique dynamic path that converges to each of them. In both types of models an independent expectations equation selects an equilibrium in every time period. For more details on comparison and evolution of the concept of indeterminacy see Farmer (2012a).
This assumption has both theoretical and empirical foundations. Theoretically, Farmer (2006) argues that the labor supply curve is missing because factor markets are incomplete. Kocherlakota (2012) refers to this feature as models of “incomplete labor markets.” Empirically, Kocherlakota (2012) argues that labor supply equation is inconsistent with real wage, consumption and employment dynamics after the 2008 recession. In the companion paper to the current one, Plotnikov (2012) argues that the labor supply assumption is the most problematic of all assumptions made in a standard business cycle model. Justiniano, Primiceri and Tambalotti (2010) reach the same conclusion using a different dataset.
Evidence from microeconometrics studies (see Blundell and MaCurdy (1999)) supports a labor supply elasticity that is close to zero.
Equation (10) implicitly makes a strong assumption that all workers are laid off in the end of each period. I intentionally make this assumption to show that the model can generate high persistence in the unemployment rate even without assuming that employment is a state variable. See beginning of the next subsection for further discussion.
Equation (10) also implies that hiring costs are expressed in terms of labor units and not in terms of output as in standard labor search models. This assumption is not essential and is made for simplification.
Notice that if ρ = 0 both equations reduce to the standard Cobb-Douglas case: income shares of both inputs are constant and equal to a for capital and b for labor.
By definition, the income shares of capital and labor are:
Notice that these shares are not constant in the general CES case (except for the Cobb-Douglas case, ρ = 0) and depend on the current level of income and both inputs. Additionally, the labor income share is affected by the externality in the labor market, Θt and the labor productivity st. This feature of the CES technology can partially explain procyclicality in the labor income share in the data (see previous section). On the other hand, this mechanism is not central to the paper and does not substantially improve the performance of a standard model.,
In contrast, the standard practice in the labor literature is to assume that employment is a state variable (see for example Rogerson, Shimer and Wright (2005)).
Even when the employment level is a state variable, the standard model generates a very low persistence of the unemployment rate. In contrast, my model produces a highly persistent unemployment rate even without this assumption. In general, making employment a state variable will not worsen performance of the model. Farmer (2011a) builds a similar model where employment is a state variable and shows that none of the results depend on this simplification.
Several recent papers pointed out the significance of wealth, in particular stock market and housing wealth, in the consumption decision. Ludvigson and Lettau (2004) pointed out that there is a low frequency relationship between consumption and asset wealth. Farmer (2012b) documented a similar relationship between consumption and S&P 500 index measured in wage units.
The necessity of this condition was first introduced by Muth (1961). There, the author showed that adaptive expectations about output are rational under specific restrictions on the speed of adjustment and on the output process, which, in his model, has to be ARIMA(0,1,1).
The data was constructed as in Farmer (2010). In the next section I present summary statistics and plot these series.
The results of the model are not sensitive to this choice.
Recall that, in contrast to standard models, this steady state does not correspond to the socially optimum steady state. The expression for the socially optimal steady state is given by Equation (18).
Since the matrix F always has a unit eigenvalue, I use the diffuse Kalman filter. Because the state space model (34) is non-stationary, the initial value for the filtering procedure matters. First introduced in Jong (1991) and later developed in Koopman (1997), Koopman and Durbin (2000), the diffuse Kalman filter addresses this problem.
Recall, that if the production technology is CES, the capital share is not constant and depends on the current physical level of output and capital.
Because l* depends on both Г and θ, every time I evaluate the likelihood for a given set of parameters, I choose Г so that Equation (18) is satisfied for the given value of θ and the fixed value of u*. The results of the model do not depend on the value of Г as long as
A rule of thumb that ensures bell-shaped prior distributions with no positive probability mass on either end of the support requires the distance between the prior mean and the closest natural limit to be less than two standard deviations.
The labor share in this case can be calculated as
Recall that Cobb-Douglas case corresponds to ϵk,l = 1 and ρ = 0.
The Monte-Carlo moments I report do not change once the number of simulated samples exceeds 5000. I take R=10000 to eliminate even small changes.
For example, I compare the standard deviation of investment to the Monte-Carlo average of the standard deviations of the simulated investment series.
Because of nonstationarity I cannot take the limit T → ∞, as many summary statistics do not converge. Moreover if some data series are non-stationary, statistics for these series will change over time. However as long as the sample size is fixed, statistics for the data and simulated series are comparable.
Since the long run statistical mean of the employment rate is 0.943, a one percent log-deviation for the employment rate is approximately a 1 percent deviation in terms of the labor force.
I used Dickey-Fuller test with no intercept and no trend since by construction means of all series are zero.
There are two reasons to believe that output in wage units is in fact a random walk. First, consumption and investment together constitute 81 percent of U.S. GDP. Since consumption is a random walk and investment is stationary GDP is likely to be a random walk as well. Second, since labor share in the U.S. data is close to being constant, this implies that the employment rate is roughly proportional to the output in wage units. Since existence of unit root in the unemployment rate is not rejected, it suggests that output in wage units has to have a unit root as well.
Consumption and investment constitute 81 percent of the U.S. GDP.
Intuitively, Г = +∞ corresponds to an infinitely efficient matching function which means all matches are instant or, in other words, the labor market clears instantly.
I defined the employment rate in the data to be one minus the civilian unemployment rate. Real output is defined as real U.S. GDP in chained 2005 U.S. dollars.
To be more precise, in Figure 9 I use output in wage units to identify belief shocks. Since real output is not affected by belief shocks, this procedure is identical to identifying belief shocks from the actual wages.
In the same situation consumption in the RBC model as calibrated in the previous section is almost 60 percent more sensitive.
In contrast to the rest of the IRFs reported, I report the effect on the unemployment rate in percent of the labor force, not as a percent of the steady state value.