StockMarketsandtheBusiness Cycle in Germany : Evidence from Spectral Analysis. Seminar Talk SFB Workshop Motzen June 23-25, 2005

Transcription

1 StockMarketsandtheBusiness Cycle in Germany : Evidence from Spectral Analysis Albrecht Ritschl Martin Uebele Seminar Talk SFB Workshop Motzen June 23-25, 2005

2 Motivation There are four estimations for German net national product But they contradict each other Even latest improvements of the statistical material could not solve the problem (Burhop and Wolff, 2005) New approach: financial data and spectral analysis

3 Overview 1. Motivation 2. Status quo 3. The stock market as a benchmark 4. Spectral analysis 5. Results

4 2. Status Quo Latest Evidence Burhop und Wolff (2005) present improved series Burhop und Wolff (2005) Hoffmann (1965), Hoffmann/Müller (1959) Output (new capital stock) Expenditure (new investment series) Output (Industrial production, agricultural output, services) Expenditure (C + I + G + (X-Z)) Income (new capital stock, new return) Income (Wages + capital return) Taxes (indirect taxes added) Taxes (derived from income tax data)

5 2. Status Quo New vs Old Series Output, 1913 prices Expenditure German NNP in billion marks, 1913 prices German NNP in billion marks, 1913 prices 10.8 log Output log Output Corrected 10.8 log Expenditure log Expenditure Corrected le g sca lo 10 le g sca lo Income Taxes German NNP in billion marks, 1913 prices German NNP in billion marks, 1913 prices 10.8 log Income (1965) log Income (1965) Corrected 10.8 log Income (1959) log Income (1959) Corrected le g sca lo 10 le g sca lo

6 2. Status Quo Recent approaches Burhop und Wolff (2002) apply four different detrending techniques to four NNP estimates log-linear piecewise log-linear Hodrick-Prescott Beveridge-Nelson But the resulting business cycles are contradictory Burhop and Wolff (2005) propose an evenly weighted average of their improved estimates

7 2. Status Quo Improvement? Deviation from HP-trend, new series Deviation from HP-trend, old series Output Expenditure Inc ome Ta xe s Output Expenditure Inc ome Ta xe s

8 3. The Stock Market As a Benchmark New Approach Basic idea: Use stock market index as a leading indicator of the business cycle Financial data given in excellent quality, but never used Consumption-based asset pricing model: p t E u ( ct β u ( c + 1 = t t + 1 t ) Price of a stock today equals discounted expected payoff tomorrow times a stochastic discount factor ) x

9 3. The Stock Market As a Benchmark Data 1200 Ronge Eube Ronge (2002) Performance index constructed like the DAX (30 joint stocks firms with highest market value), Eube (1998) Performance Index, 415 joint stock firms in 55 sectors, , 10 railroad companies are missing, Stückzins-Usancen not incorporated

10 4. Spectral Analysis Statistical Approach Describes the cyclical content of a time series Variance decomposed with respect to frequency Portion of variance of two series with the same frequency represents explained variance Advantage: independent of phase shift

11 4. Spectral Analysis The Power Density Spectrum (PSD) The PSD is a summary of the variance in a Power spectral density of a time series series w.r.t. frequency Can be interpreted like a probability density function A peak at ω* = 1.8 means that cycles with a duration of 2π / years for annual data dominate 0 ω ω ω 2 π 1 * ω

12 4. Spectral Analysis The Power Density Spectrum (PSD) The PSD is defined as the Fourier-transformation of the autocovariance sequence γ (k) S yy k = ( ω) = γ ( k) e iωk Area under the spectrum density equals the total variance π π S 2 ( ω) dω = σ y

13 4. Spectral Analysis Multivariate Spectral Analysis Define cross-spectral density by the Fourier-transform of the covariance sequence ρ(k) S xy ( ω) k = = ρ( k) e iωk Obtain complex coherency as Sxy ( ω) Cxy ( ω) =, with0 Cxy ( ω) 1 S ( ω) S ( ω) Calculate the frequency domain analog to R 2 by π π S yy xx π yy ( ω) dω = C ( ω) S ( ω) dω + S ( ω) dω π xy yy π π e

14 4. Spectral Analysis Multivariate Spectral Analysis Obtain the variance of y t explained by x t as the ratio of the two areas The ratio between ω1 and ω2 depicts explained variance at the relevant business cycle frequencies 3-4 years 7-10 years Explained variance S(ω) ω 0 ω 1 ω 2 π

15 4. Spectral Analysis Parametric vs. Nonparametric Spectral Estimation Simplest nonparametric estimator periodogram: only asymptotically unbiased, inconsistent Variance can be decreased by windowing and averaging over subsamples, but resolution decreases by the same factor With N = 45 averaging over sub-samples decreases resolution too much But estimating parameters of a multivariate time series model is possible Spectral density can be obtained from model-parameters

16 4. Spectral Analysis Parametric Estimation Most frequently used in the literature are VAR(p) models (Broersen, 2000) Parameters can be obtained by OLS However, Burg-estimator is less biased than OLS (Trindade, 2000) Burg-estimator minimizes mean of forward-backward coefficients (Burg, 1968) Multivariate version: Nutall-Strand (Strand, 1977)

17 4. Spectral Analysis Stationarity For spectral estimation, models have to be stationary Data have to be detrended without distorting the frequency content Hodrick-Prescott filter: distorts cyclical content and moments (Canova, 1998; Cogley and Nason, 1995; King and Rebelo, 1993) Ravn and Uhlig (1997): use the right λ!

18 4. Spectral Analysis Application of filters Modified Baxter-King filter (Woitek, 1996): better properties, still not perfect Baxter-King works well with or without unit root in the data, Hodrick-Prescott creates spurious cycles in difference stationary data (Woitek, 2001) We use both filters to check for robustness

19 Main Findings 1. Nominal series better suited than real series for historical business cycle research 2. Among the nominal series, Income is closest to the benchmark 3. Income contains wages, which match the benchmark surprisingly well

20 Nominal vs Real Series x 10 4 Nominal x 10 4 Real Expenditure nom Income nom Taxes nom Expenditure Income Taxes 4 4 M ark n b ), c es p ri t n u re (c N P M ark n b ), c es p ri (1 N P

21 Nominal vs Real Series, Cycles Nominal Real ṯre fr ti ia e d n H Pṯre m o n fr tio D evia Expenditure nom Income nom Taxes nom Expenditure Income Taxes

22 Two Arguments for Nominal Series 1. The deflator implicitly given by Hoffmann (1965) distorts the cyclical properties of the NNP-series 2. If we deflate the stock price index, we introduce an element that changes the amount of joint variation, but we do not know how much Thus we analyze only nominal series

23 Explained Variance 1 Explained variance Explained variance Expenditure nominal (Burhop 2005) Taxes nominal (Burhop 2005) Explained Variance 3-10 years 46% Explained Variance 3-10 years 46% Explained Variance 7-10 years 25% Explained Variance 7-10 years 18% Cycle Length 7.2 years Cycle Length 6.8 years AR(3), Hodrick-Prescott(6.25), Ronge

24 Explained Variance 1 Explained variance Income nominal (Burhop and Wolff, 2005) Explained Variance 3-10 years Explained Variance 7-10 years Cycle Length 61% 29% 7.2 years AR(3), Hodrick-Prescott(6.25), Ronge

25 Explained Variance of Nominal Series Burhop und Wolff (2005) Hoffmann (1965), Hoffmann/Müller (1959) Expenditure Expenditure Income Taxes Income Taxes HP 3-10 y. 46% 61% 46% 58% 62% 44% HP 7-10 y. 25% 29% 18% 33% 33% 18% BK 3-10 y. 30% 55% 47% 48% 52% 44% BK 7-10 y. 22% 33% 22% 27% 32% 22% AR(3), Hodrick-Prescott (6.25), Baxter-King (K=3, 2-15 y.)

26 Composition of Income NNP = Wages + Capital + Income Foreign Income

27 Composition of Income NNP = Wages + Capital + Income Foreign Income Capital Stock x Rate of Return

28 Cyclical Properties of Return 18 1 Explained variance Rate of Return Explained Variance: 65% Cycle lengt: 7.2 years Hoffmann (1965): assumes constant rate of 6.68% Burhop&Wolff (2005): rate of return from dividends (Donner, 1934) Good performance due to that trick? Then wages will most likely be acyclical

29 Composition of Income NNP = Wages + Capital + Income Foreign Income

30 Cyclical Properties of Wages Wage s hare, Hoffmann (1965), deviations from trend 0.9 Explained variance Wages Explained Variance: 70% Cycle Length: 7.5 years Wages are even closer to the stock market! Indicates well functioning labor markets

31 The Business Cycle (HP-filtered) d n H Pṯre m o n fr tio D evia

32 The Business Cycle (Baxter-King-filtered) d n H Pṯre m o n fr tio D evia

33 Wages (t)/stock Market (t+1) 0.15 Wages Stock Market 0.1 d n H Pṯre m o n fr tio D evia trend

34 Interpretations 0.15 Wages Stock Market 0.1 d n H Pṯre m o n fr tio D evia trend French- German War

35 Gründerzeit/Gründerkrise? 0.15 Gründerzeit Wages Stock Market 0.1 d n H Pṯre m o n fr tio D evia trend French- German War Gründerkrise

36 Great Depression? Gründerzeit Wages Stock Market No Great Depression ; regular cycles d n H Pṯre m o n fr tio D evia trend French- German War Gründerkrise

37 Great Depression? Evidence from Trends Log Trend Growth Wages/Stock Market (Index 1870=1) Trend Component Logs of Wages and Stock Market Trend Growth Wages/Stock Market (Index 1870=1) Trend Component of Wages and Stock Market, (1870=1) Wages HP Wages BK Stock Market HP Stock Market BK Wages HP Wages BK Stock Market HP Stock Market BK e a l c L ogs 1 = x d e In

38 But What About the Real Economy? Is there evidence from real figures? Spree (1978) publishes 18 macro-time series ( ), 13 of which were used to estimate a dynamic factor with Bayesain methods (joint with Samad Sarferaz): REAL Crop net production (Mark, 1913 prices) Sugar consumption (tons) Prussian coal output (tons) Labor productivity coal mining (t/capita) Pig iron production (tons) Number of marriages Yarn production (tons) NOMINAL Gross investment cotton spinning works (Marks, 1913 prices) Wholesale prices crop (index) Profits yarn production (Pfennig/kilo) Wholesale prices industrial raw materials (index) Bill discount rate Hamburg/Berlin (%) Stocks of bills German banks

39 A Factor, the Stock Market and Wages 0.15 Wages Stock Market (shifted) Spree-Factor 0.1 d n H Pṯre m o n fr tio D evia

40 Outlook Work with industrial production series Apply research strategy to data from UK, US Extend the factor model approach Use stock prices and wages to estimate a growth model

41 Explained Variance Capital Stock (Real) Explained variance Explained variance Capital Stock Old Capital Stock New Explained Variance 3-10 years 40% Explained Variance 3-10 years 28% Explained Variance 7-10 years 26% Explained Variance 7-10 years 15% Cycle Length 7.6 years Cycle Length 6.9 years AR(3), Hodrick-Prescott(6.25), Ronge