The Young, the Old, and the Restless: Demographics and Business Cycle Volatility. Nir Jaimovich and Henry Siu

Transcription

1 The Young, the Old, and the Restless: Demographics and Business Cycle Volatility Nir Jaimovich and Henry Siu

2 What is the role of demographic change in explaining changes in business cycle volatility? Since the mid-1980s the U.S. and other industrialized countries have undergone a substantial decline in business cycle volatility. (The great moderation). There was also a run-up in volatility in the mid-1960s. Document important differences in the responsiveness of labor market activity to the business cycle for individuals of different ages. Use data for G7 countries to identify the effect of workforce age composition on business cycle volatility. Write a variant of the standard RBC model that emphasizes the role of age as determining an individual s labor market experience. Variation in age composition leads to variation in macroeconomic volatility.

3 A first look at US data h i HP cycle t = β 0 + β 1 yt + β 2 h Agg t ) Cyclical volatility is defined as var (ĥi t + β 3 h Agg t 1 + εi t

4 A first look at Japanese data

5 What about all G7 countries?

6 Timing of Demographic Change varies across countries I

7 Timing of Demographic Change varies across countries 2

8 Demographics and Business Cycle volatility I

9 Demographics and Business Cycle volatility II

10 Estimating the effect of age composition on Business cycle volatility I σ it = α i + β t + γshare it + ɛ it

11 Estimating the effect of age composition on Business cycle volatility II

12 Looking at the entire age distribution

13 A back of the envelope calculation Volatility peaks in 1978 when the year old labor force share was 38.5% By 1999 the year old labor force share had gone down to 27.1%. The OLS estimates predict a drop in the volatility of output of = During the same time period cyclical volatility falls from to So changes in age composition account for about 1/3 of the moderation.

14 Modelling the Great Moderation Goal: to construct a RBC model that generates age-group differences in the cyclical volatility of hours worked. Differences accross age groups can arise from: Differences in Preferences (Labor Supply) Differences in factors relating to Technology (Labor Demand) Model with two age groups. Young workers (15-29) are inexperienced while all old workers (30+) are experienced. Production exhibits capital-experience complementarity so that differences in the cyclical demand for experienced and inexperienced labor can take place.

15 Production Function Y t = [ ] µ (A t H Y t ) σ + (1 µ) [λk ρ t + (1 λ) (A th Ot ) ρ ] σ 1 σ ρ Labor-Augmenting technology follows a deterministic growth path with persistent transitory shocks: A t = exp (gt + z t ) z t = φz t 1 + ε t, 0 < φ < 1, var (ε) = σ 2 ε Following Krusell et. al (2000) production exhibits capital-experience complementarity when σ > ρ. Firms rent capital, and young and old worker s time from perfectly competitive factor markets to maximize profits. Optimality then entails equating factor prices with marginal revenue products.

16 Households The representative household s date t problem is to maximize: E t j=t subject to { [ β j t s Y ] N 1+θ Y Y j log C Y j ψ Y 1 + θ Y + (1 s Y ) [ N 1+θ O Oj log C Oj ψ O 1 + θ O s Y C Y j+(1 s Y ) C Oj+ K j+1 = (1 δ) K j+r j Kj+s Y W Y jn Y j+(1 s Y ) W OjN Oj Optimality in this setup entails: C Y t = C Ot = C t The optimal condition for hours worked are given by: W Y t = ψ Y C t N θ Y Y t W Ot = ψ O C t N θ O Ot ]}

17 Structural Estimation of σ First order condition with respect to the demand for H Y t W Y t = Yt 1 σ µa σ t H σ 1 Y t write this in logged first differenced form: log W Y t = a 0 + (σ 1) log (H Y t /Y t ) + σu t Multiply both sides by H Y t log LI Y t = a 0 + σ log (H Y t ) + (1 σ) log Y t + σu t Estimate this equation by restricted least squares

18 Structural Estimation of ρ First order condition with respect to the demand for H Ot W Ot = Y 1 σ t (1 µ) [λk ρ t + (1 λ) (A th Ot ) ρ ] σ ρ ρ write this in logged first differenced form: ( ) QOt log = a 2 + ρ log (H Ot /K t ) + ρu t Q Kt Estimate this equation by restricted least squares. (1 λ) A ρ t Hρ 1 Ot They use Ramey-Shapiro dates and lagged birth rates to instrument their regressors. ˆρ = 0.12 (0.31) and ˆσ = 0.62 (0.2).

19 Calibration I β = δ = θ Y = θ O = 0 household members have Rogerson-Hansen preferences. µ and λ are set to match the income shares of Q K = 0.37 and Q O = 0.47.

20 Calibration II Given values for {σ, ρ, µ, λ} and data on output and factor inputs, they back out {A t }. φ = 0.93, σ ε = and σ ε = S Y = 0.35 matches the share of young individuals in N Yss and N Oss are set to match the ratio of young to old hours worked and H ss = 0.3 In the postmoderation period s Y = 0.27 and N Oss is increased by 12%.

21 Results

22 Some observations Not enough heterogeneity. Might be important to model the participation margin. Labor Supply considerations are important and vary across the life cycle.