Redistributive Shocks and Productivity Shocks Jos e-V ctor R - PowerPoint PPT Presentation

Redistributive Shocks and Productivity Shocks Jos´ e-V´ ıctor R´ ıos-Rull Raul Santaeulalia-Llopis Penn, CAERP, CEPR, NBER Penn London School of Economics February 5, 2007

Introduction 1 Business Cycle Research (almost) always assumes Cobb-Douglas technology. 2 Which implies constant factor shares. 3 Yet they are not. 4 Does it matter for fluctuations questions? 5 We answer this with a silly theory of factor share movements. Jos´ e-V´ ıctor R´ ıos-Rull, Raul Santaeulalia-Llopis Penn, CAERP Redistributive Shocks and Productivity Shocks LSE 2 / 55

Our thing is to pose not one but two technology shocks 1 The standard technology A multiplicative shock to productivity Y t = e z 0 t K θ t N 1 − θ t Jos´ e-V´ ıctor R´ ıos-Rull, Raul Santaeulalia-Llopis Penn, CAERP Redistributive Shocks and Productivity Shocks LSE 3 / 55

Our thing is to pose not one but two technology shocks 1 The standard technology A multiplicative shock to productivity Y t = e z 0 t K θ t N 1 − θ t 2 We will explore the following technology A shock to factor shares and another to total productivity t K θ − z 2 N 1 − θ + z 2 Y t = e z 1 t t t t Jos´ e-V´ ıctor R´ ıos-Rull, Raul Santaeulalia-Llopis Penn, CAERP Redistributive Shocks and Productivity Shocks LSE 4 / 55

Our Finding is that it matters so much that changes our assessment of previous findings 1 Our process matches both the cyclical behavior of ◮ Solow Residuals ◮ Factor Shares 2 The induced behavior of hours is that it is three (13%) times less volatile than in the standard model, and 13% (2%) than in the data. 3 So the standard claim in the RBC literature that shocks to productivity account for 2/3 of hours volatility is just not right. Agents do not want to move their hours as much. Prices do not induce them to do so. 4 Our findings hold independently of the elasticity of hours. Jos´ e-V´ ıctor R´ ıos-Rull, Raul Santaeulalia-Llopis Penn, CAERP Redistributive Shocks and Productivity Shocks LSE 5 / 55

Literature 1 Cyclical allocation of risk and optimal labor contracts: either Labor share has no information. Gomme and Greenwood (1995) or there are differences in risk attitudes The Boldrin and Horvath (1995) Donaldson, Danthine, and Siconolfi (2005) . 2 Models with occasionally binding capacity constraints. Hansen and Prescott (2005) variable capacity utilization. labor share moves some. 3 Explicit role for markups. Hornstein (1993) Ambler and Cardia (1998) 4 More directly shocks to labor share. Casta˜ neda, D´ ıaz-Gim´ enez, and R´ ıos-Rull (1998) Young (2004). We want to replicate the dynamic patterns of labor share. Jos´ e-V´ ıctor R´ ıos-Rull, Raul Santaeulalia-Llopis Penn, CAERP Redistributive Shocks and Productivity Shocks LSE 6 / 55

0.72 0.71 0.7 0.69 0.68 0.67 0.66 0.65 4 6 8 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 0 2 4 5 5 5 6 6 6 6 6 7 7 7 7 7 8 8 8 8 8 9 9 9 9 9 0 0 0 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 The Labor Share, U.S. 1954.I-2002.IV Jos´ e-V´ ıctor R´ ıos-Rull, Raul Santaeulalia-Llopis Penn, CAERP Redistributive Shocks and Productivity Shocks LSE 7 / 55

0.04 Baseline Labor Share … with Durables … and Government 0.03 Compensation of Employees / GNP 0.02 0.01 0 -0.01 -0.02 -0.03 4 6 8 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 0 2 4 5 5 5 6 6 6 6 6 7 7 7 7 7 8 8 8 8 8 9 9 9 9 9 0 0 0 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 Deviations of Labor Share, Various measures U.S. 1954.I-2002.IV Jos´ e-V´ ıctor R´ ıos-Rull, Raul Santaeulalia-Llopis Penn, CAERP Redistributive Shocks and Productivity Shocks LSE 8 / 55

Properties of Labor Share 1 Labor Share is quite volatile: Table 1 The standard deviation of the baseline definition of labor share is 43% that of output (65% of the variance) and 80% of that of the Solow residual (89% of the variance) 2 Labor Share is countercyclical . Correlatation of -.24. Solow residual -.47. 3 Labor Share is highly persistent . Autocorrelation of .78 4 Labor Share lags output by about a year . Look at phase shift Table 2. 5 Labor Share overshoots . Figure 1 Jos´ e-V´ ıctor R´ ıos-Rull, Raul Santaeulalia-Llopis Penn, CAERP Redistributive Shocks and Productivity Shocks LSE 9 / 55

ρ ( x , s 0 ) σ x σ x /σ GNP ρ ( x , GNP ) ρ ( x t , x t − 1 ) .74 a .85 a GNP 1.59 1.00 1.00 Solow Residual: s 0 .74 a .71 a .85 .53 1.00 -.24 a -.47 a .78 a Baseline Labor Share .68 .43 Note : All variables are logged and HP-filtered. Let a and b denote respective significance at 1 and 5% Table: Standard deviation and correlation with output of Labor Share, U.S. 1954.I-2004.IV Cross-correlation of GNP t with x t − 5 x t − 4 x t − 3 x t − 2 x t − 1 x t x t +1 x t +2 x t +3 x t +4 x t +5 Baseline Labor Share -.20 -.26 -.32 -.34 -.33 -.24 .03 .25 .40 .47 .44 Table: Phase-Shift of the Labor Share, U.S. 1954.I-2004.IV Jos´ e-V´ ıctor R´ ıos-Rull, Raul Santaeulalia-Llopis Penn, CAERP Redistributive Shocks and Productivity Shocks LSE 10 / 55

Labor's Share IRF to (orthogonalized) Labor's Share IRF to (orthogonalized) one S.D. Solow Residual Innovation one S.D. GNP Innovation (% Deviations from Trend) (% Deviations from Trend) 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0 0 -0.1 -0.1 -0.2 -0.2 -0.3 -0.3 0 5 10 15 20 25 30 35 40 45 0 5 10 15 20 25 30 35 40 45 Figure: Labor’s Share IRFs to GNP (left panel) and Solow Residual (right panel) Innovations Jos´ e-V´ ıctor R´ ıos-Rull, Raul Santaeulalia-Llopis Penn, CAERP Redistributive Shocks and Productivity Shocks LSE 11 / 55

The standard specification: Solow residuals as shocks • Linearly detrend variables X t ln X t = χ x + g x t + � x t . y t , � • Apply it to { Y t , K t , N t } yielding { � k t , � n t } . s 0 y t − ζ � • Then define t = � k t − (1 − ζ ) � n t . Jos´ e-V´ ıctor R´ ıos-Rull, Raul Santaeulalia-Llopis Penn, CAERP Redistributive Shocks and Productivity Shocks LSE 12 / 55

A structural interpretation of the Solow residual • With Cobb-Douglas, the Solow residual is the shock to productity: � � 1 − θ = e z 0 � � 1 − θ Y t = e z 0 (1 + λ ) t µ N t (1 + λ ) t µ (1 + η ) t h t t A K θ t A K θ t t λ and η are productivity and population growth rates. A and µ just units parameters. Under CRRA, there is a balanced growth path. Rewrite Y ∗ e � y t = e z 0 t A [ K ∗ e � k t ] θ [ µ h ∗ e � h t ] 1 − θ Y ∗ z 0 y t − θ � k t − (1 − θ ) � y t − θ � k t − (1 − θ ) � = � h t + ln AK ∗ θ ( µ h ∗ ) θ = � h t t • If we use model data (with share parameter θ ), we obtain s 0 y t − θ � k t − (1 − θ ) � h t = z 0 t = � t • Recall: Cobb-Douglas (and competition) imply constant factor shares. Jos´ e-V´ ıctor R´ ıos-Rull, Raul Santaeulalia-Llopis Penn, CAERP Redistributive Shocks and Productivity Shocks LSE 13 / 55

A Structural Interpretation of two shocks: the Redistributive Shock • Define the folliwing residual t = ln Y t − (1 − W t N t ) ln K t − W t N t ln s 1 ln N t = ln Y t − ζ t ln K t − (1 − ζ t ) ln N t Y t Y t • Now Pose � � 1 − θ + z 2 t A K θ − z 2 µ (1 + λ ) t (1 + η ) t h t Y t = e z 1 t t t • Under competitive markets ∂ Y t ∂ N t N t W t N t = (1 − θ ) + z 2 = t Y t Y t So the deviation from mean labor share is THE shock z 2 • t . Jos´ e-V´ ıctor R´ ıos-Rull, Raul Santaeulalia-Llopis Penn, CAERP Redistributive Shocks and Productivity Shocks LSE 14 / 55

A Structural Interpretation: the Multiplicative Shock Detrending � k t � θ − z 2 t � h t � 1 − θ + z 2 t , Y ∗ e � K ∗ e � µ h ∗ e � y t = e z 1 t A Y ∗ = AK ∗ θ ( µ h ∗ ) θ . taking logs and using � K ∗ � z 1 y t − ( θ − z 2 t ) � k t − (1 − θ + z 2 t ) � h t + z 2 t = � t ln µ h ∗ � � K ∗ s 1 t = z 1 t − z 2 • So we have t ln µ h ∗ • Units matter. We choose units in the model so that K ∗ = µ h ∗ and then s 1 t = z 1 • t , so the redistributive shock z 2 has no effects on productivity. Jos´ e-V´ ıctor R´ ıos-Rull, Raul Santaeulalia-Llopis Penn, CAERP Redistributive Shocks and Productivity Shocks LSE 15 / 55

0.06 s 0 s 1 s 1 - s 0 0.04 0.02 0 -0.02 -0.04 -0.06 4 6 8 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 0 2 4 5 5 5 6 6 6 6 6 7 7 7 7 7 8 8 8 8 8 9 9 9 9 9 0 0 0 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 Figure: The two sets of productivity residuals s 0 t and s 1 t , U.S. 1954.I-2004.IV Jos´ e-V´ ıctor R´ ıos-Rull, Raul Santaeulalia-Llopis Penn, CAERP Redistributive Shocks and Productivity Shocks LSE 16 / 55

Let’s estimate processes for the shocks (Full ML) 1 z 0 is an AR(1). ρ 0 = . 954, σ ǫ 0 = . 00668. Standard. (.02, .000) Jos´ e-V´ ıctor R´ ıos-Rull, Raul Santaeulalia-Llopis Penn, CAERP Redistributive Shocks and Productivity Shocks LSE 17 / 55