Costs of Business Cycles Empirical Evidence

Transcription

1 Costs of Business Cycles Empirical Evidence Petr Sedláček Bonn University Summer Term / 48

2 Background and some empirical evidence Seminal contribution by, Lucas (2003) Empirical evidence on the link between volatility and growth/levels Barlevy (2005) 2 / 48

3 Thought experiment Welfare loss of fluctuations 3 / 48

4 Thought experiment Welfare loss of fluctuations macro born as a response to the Great Recession (Lucas, 2003) the hope being to prevent economic fluctuations Lucas argues welfare gains can be reaped mainly from long-run policies, rather than from eliminating short-run fluctuations 4 / 48

5 Thought experiment Welfare loss of fluctuations Thought experiment What would the welfare effect be if all consumption variability could be eliminated? 5 / 48

6 Thought experiment Welfare loss of fluctuations Simple model consider a single consumer his consumption stream c t = A exp{µt} exp{ 0.5σ 2 }ɛ t, log(ɛ t ) N(0, σ 2 ) E[exp{ 0.5σ 2 }ɛ t ] = 1 mean consumption at t is A exp{µt} 6 / 48

7 Thought experiment Welfare loss of fluctuations Simple model preferences over consumption paths [ ] E β t c1 γ t 1 γ t=0 β is the subjective discount factor γ is the coefficient of risk aversion prefer a deterministic consumption path to a risky path with the same mean 7 / 48

8 Thought experiment Welfare loss of fluctuations Quantifying the welfare loss of fluctuations 8 / 48

9 Thought experiment Welfare loss of fluctuations Quantifying the welfare loss quantify the loss due to fluctuations by compensation λ E [ t=0 ] t (1 + λ)c1 γ t β = 1 γ t=0 λ 0.5γσ 2 t (A exp{µt})1 γ β 1 γ 9 / 48

10 Thought experiment Welfare loss of fluctuations Welfare loss of fluctuations estimate of σ 2 deviations of log real per capita consumption around a linear trend for the U.S. between estimates of γ in macro they range between 1 and 4 assuming log utility we get an welfare loss of λ 0.5(0.032) 2 = / 48

11 Thought experiment Welfare loss of fluctuations Welfare loss of fluctuations the gains from eliminating fluctuations are trivially small especially compared to the welfare gains of increasing growth later research focused on several missing dimensions in Lucas example a link between volatility and growth/levels heterogeneity preferences 11 / 48

12 Data and regression analysis Results Volatility and investment 12 / 48

13 Data and regression analysis Results Volatility and investment traditionally, growth and business cycle theory is separate however, there are several reasons why they could be connected irreversible investment decisions high-risk-high-return vs. low-risk-low return technologies precautionary savings motives 13 / 48

14 Data and regression analysis Results Volatility and investment this paper conducts an empirical analysis of the volatility-growth relationship using cross-country data with 92 countries (and an OECD subset) evidence for a negative relationship 14 / 48

15 Data and regression analysis Results Volatility and investment Data and regression analysis 15 / 48

16 Data and regression analysis Results Volatility and investment Data 1st sample: 92 countries, nd sample: 24 OECD countries, / 48

17 Data and regression analysis Results Volatility and investment Data 1140 Simple correlation THE AMERICAN of ECONOMIC volatility REVIEW and growth DECEMBER BWA OAN HKR*g MLT JPN LSO CYP THA NGRC MW SYR Y NOR?- AUT ITA%IS6R DZA :3SWEt NX SRS DOM'JORIR GB%S&3"$ HUS TGO 0 CHE N4 L EL Z NYlE N SWZ TTO c: GTM JAM CD1 INrIPL pewi UGA IRO >: XG ~~~~St~ BGD SERY AFG ZAR NER SON NIC GHA LBR GUY ZMB MOZ Standard Deviation of Output Growth FIGURE 1. SIMPLE CORRELATION OF GROWTH AND VOLATILITY 17 / 48

18 Data and regression analysis Results Volatility and investment Regression analysis calculate mean and standard deviation of per capita growth for each country full sample: y i = σ i (1) (7.7) ( 2.3) OECD subsample: y i = σ i (2) (3.7) (0.67) 18 / 48

19 Data and regression analysis Results Volatility and investment Regression analysis control for other important regressors average investment fraction of GDP initial log GDP per capita initial human capital average growth rate of the population also allow for different innovation volatitlity 19 / 48

20 Data and regression analysis Results Volatility and investment Regression analysis y it = λσ i + θx it + ɛ it ɛ it N(0, σ 2 i ) 20 / 48

21 Data and regression analysis Results Volatility and investment Results 21 / 48

22 Data and regression analysis Results Volatility and investment Results 1142 THE AMERICAN ECONOMIC REVIEW DECEMBER 1995 Relationship TABLE 1-RELATIONSHIP between BETWEEN mean MEAN growth GROWTH AND andvolatility volatility (CONDITIONAL ON LEVINE-RENELT VARIABLES) 92-country sample OECD-country sample Independent variable (2,208 observations) (888 observations) Constant (3.72) (5.73) Volatility (a) (-2.61) (-1.92) Average investment share of GDP (7.63) (2.76) Average population growth rate (-0.38) (0.70) Initial human capital (1.18) (2.00) Initial per capita GDP (-3.61) (-5.70) Summary of variance estimates (all variance numbers are multiplied by 1,000): Mean variance Lowest-variance country / 48

23 Data and regression analysis Results Volatility and investment Results Partial correlation of growth and volatility: OECD countries VOL. 85 NO. S RAMEY AND RAMEY: LINK BETWEEN VOLATILITY AND GROWTH JPN CAN FRA ITA USA o?ti ISL GBR 3 NOR SWE AUS BEL PRT w TUR i NZL IL Standard Deviation of Output Growth FIGURE 2. PARTIAL CORRELATION OF GROWTH AND VOLATILITY: OECD COUNTRIES 23 / 48

24 Data and regression analysis Results Volatility and investment Unpredictable changes in growth change specification to get close at the effect of uncertainty include explanatory variables measured at the initial year only include forecasting variables: flexible time trend and lags of GDP population growth in first two years 24 / 48

25 Data and regression analysis Results Volatility and investment Results Relationship between mean growth and unpredictable volatility 25 / 48

26 Data and regression analysis Results Volatility and investment Volatility and investment 26 / 48

27 Data and regression analysis Results Volatility and investment Volatility and investment many theories link volatility and growth via investment robustness: trying different specifications of investment changes little no relationship between investment and volatility 27 / 48

28 Data and regression analysis Results Volatility and investment Volatility and investment Investment and innovation volatility results 28 / 48

29 A counterfactual growth rate Evidence for the U.S. Diminishing returns to investment Barlevy / 48

30 A counterfactual growth rate Evidence for the U.S. Diminishing returns to investment Main idea Barlevy builds a theory linking volatility, investment and growth E[λ] = f (X, σ) average growth is a function of volatility (σ) and observables construct a counterfactual growth rate fix volatility to σ = 0 fix investment/let investment adjust 30 / 48

31 A counterfactual growth rate Evidence for the U.S. Diminishing returns to investment Using Ramey and Ramey Ramey and Ramey estimate the coefficient on volatility around 0.2 output growth volatility in the U.S. is about 2.5 percent eliminating aggregate shocks would lead to a 0.5pp increase in growth 31 / 48

32 A counterfactual growth rate Evidence for the U.S. Diminishing returns to investment Using Lucas according to Lucas an agent is willing to sacrifice 20 percent of consumption for 1 pp increase in growth (when γ = 1) costs of business cycles are at least 10% of consumption per year 32 / 48

33 A counterfactual growth rate Evidence for the U.S. Diminishing returns to investment Reduced-form evidence for the U.S. 33 / 48

34 A counterfactual growth rate Evidence for the U.S. Diminishing returns to investment Evidence for the U.S. Barlevy extends the evidence for the U.S. divide data into 4-year periods (presidential elections) estimate the same model as Ramey and Ramey quarterly data, 12 4-year periods growth rate in each quarter is a deviation from period mean no need for other explanatory variables 34 / 48

35 A counterfactual growth rate Evidence for the U.S. Diminishing returns to investment Evidence for the U.S. Volatility and growth results, U.S. 35 / 48

36 A counterfactual growth rate Evidence for the U.S. Diminishing returns to investment Estimates using diminishing returns to investment 36 / 48

37 A counterfactual growth rate Evidence for the U.S. Diminishing returns to investment Diminishing returns to investment assume capital production technology Φ(I t /K t ) K t+1 = (1 + Φ(I t /K t ) δ)k t K t+1 = [ Π t s=0 (1 + Φ(I s /K s ) δ) ] K 0 37 / 48

38 A counterfactual growth rate Evidence for the U.S. Diminishing returns to investment Balanced growth path output given by Y t = A t K t investment and consumption shares given by i t = I t /Y t, c t = 1 i t = C t /Y t where C t = c t A t [ Π t s=0 (1 + Φ(I s /K s ) δ) ] K 0 C t = c t A t [ Π t s=0 λ s ] (1 + ɛt )C 0 λ s is the growth rate of the capital stock ɛ t = c t A t /(c 0 A 0 ) 1 is the deviation of consumption from trend C 0 = c 0 A 0 K 0 is the initial consumption level 38 / 48

39 A counterfactual growth rate Evidence for the U.S. Diminishing returns to investment Calculating BC costs assume Φ(I t /K t ) = (I t /K t ) ψ calculate same counterfactual as before 1 + Φ(E[i t A t ]) δ 1 + (E[(λ t 1 + δ) 1/ψ ]) ψ δ need estimate of ψ and λ t 39 / 48

40 A counterfactual growth rate Evidence for the U.S. Diminishing returns to investment Parameter values micro-data gives a range for ψ estimate the distribution of consumption growth using ln C t = ln λ t + ln(1 + ɛ t ) + η t assume a Markov process for A t estimate using maximum likelihood 40 / 48

41 A counterfactual growth rate Evidence for the U.S. Diminishing returns to investment Consumption growth distribution Consumption growth distribution estimates 41 / 48

42 A counterfactual growth rate Evidence for the U.S. Diminishing returns to investment BC costs stabilizing investment at its mean leads to an increase in consumption growth between p.p. according to Lucas calculations, this is a cost of fluctuations of at least 7% of consumption per year 42 / 48

43 A counterfactual growth rate Evidence for the U.S. Diminishing returns to investment Consumption growth distribution Predicted growth rate after stabilization 43 / 48

44 Volatility and the level of GDP 44 / 48

45 Volatility and the level of GDP Link between volatility and levels previous papers have documented a link between volatility and growth the authors develop a theory in which volatility reduces the level of output investigate OECD countries whether such a link exists in the data 45 / 48

46 Volatility and the level of GDP Volatility and the level of GDP 27 OECD countries, y i = βx i + ɛ i y i log average per capita RGDP (in PPP) relative to US X includes average investment share openness output growth rate share of services compare above residuals to volatility of HP-filtered output 46 / 48

47 Volatility and the level of GDP Volatility and the level of GDP Unexplained per capita GDP and volatility UK Level FRA NOR SWE ITA AUT NLD ESP GER AUS BEL JPN DNK CAN NZL IRL CHE HUN GRC ISL PRT LUX FIN MEX TUR POL Volatility 47 / 48

48 Volatility and the level of GDP Volatility and the level of GDP there is a statistically significant negative relationship between volatility and the relative level of GDP an increase in volatility from the lowest (France) to the highest (Poland) implies a reduction in per capita income of 5.6 percentage points! this magnitude is clearly larger than the value put forward by Lucas 48 / 48