Introduction to Macroeconomics Martin Ellison Nuffi eld College Michaelmas Term 2018 Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 1 / 39
Macroeconomics is Dynamic Decisions are taken over time t 1 t t+1 Expectations Expectations make economics special Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 2 / 39
Macroeconomics is Stochastic The economy is hit by shocks - Frisch-Slutsky paradigm Impulses Propagation Fluctuations Shocks to: technology monetary policy consumer confidence oil prices exchange rate Microfounded (Lucas) from deep parameters: i) tastes and preferences ii) production technology iii) market structure Decisions have to account for uncertainty Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 3 / 39
Macroeconomics is General Equilibrium Markets are interconnected Income ( ) Labour maximise utility Households Goods Firms maximise profit Expenditure ( ) Need to analyse all markets together Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 4 / 39
Dynamic Stochastic General Equilibrium (DSGE) Work with Frisch-Slutsky paradigm backwards Impulses Propagation Fluctuations What do fluctuations look like? underlying trend business cycle seasonality random fluctuations measurement error Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 5 / 39
Macroeconomic data 10 9 LGNPC96 8 7 1940 1950 1960 1970 1980 1990 2000 2010 2020 10 9 LPCECC96 8 7 1940 1950 1960 1970 1980 1990 2000 2010 2020 Log GNP and non-durable consumption in the US Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 6 / 39
Filtering Hodrick-Prescott filter decomposes data y t into trend τ t and cycle c t y t = τ t + c t Trend should be smooth but follow data closely min {τ t } T t=1 ( T t=1 λ is weighting parameter (y t τ t ) 2 T 1 + λ t=2 λ = 0 means τ t = y t and trend is data λ means 2 τ t = 0 and trend is linear [(τ t+1 τ t ) (τ t τ t 1 )] 2 ) Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 7 / 39
Hodrick-Prescott filter 9.75 9.7 9.65 LGNPC96 LGNPC96( =400) LGNPC96( =800) LGNPC96( =1600) 9.6 9.55 9.5 9.45 9.4 2000 2005 2010 2015 2020 US GNP and Hodrick-Prescott trends Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 8 / 39
Hodrick-Prescott as a band-pass filter λ = 6400 dots; λ = 1600 solid; λ = 400 dashes λ = 1600 defines business cycle as fluctuations less than about 40 quarters Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 9 / 39
Comments on filtering HP is a 2-sided filter that brings future information into the present and so violates informational assumptions of rational expectations Identification of cycles not invariant to filter others may be better Filtering may induce spurious cycles, e.g. linear detrending of a random walk Can remove propagation from a model entirely and still get cycles Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 10 / 39
Long run properties of macroeconomic data 10 9 LGNPC96 LGNPC96( =1600) 8 0.06 7 1940 1950 1960 1970 1980 1990 2000 2010 2020 0.04 0.02 DLGNPC96( =1600) 0 1940 1950 1960 1970 1980 1990 2000 2010 2020 Trend growth in US GNP per capita is approximately constant Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 11 / 39
Long run properties of macroeconomic data 0.75 0.7 0.65 labour share 0.6 1940 1950 1960 1970 1980 1990 2000 2010 2020 0.8 0.6 0.4 0.2 C/Y I/Y 0 1940 1950 1960 1970 1980 1990 2000 2010 2020 Labour share and the Great Ratios in the US are approximately constant Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 12 / 39
Kaldor (1957) facts 1 Output per worker grows at a roughly constant rate 2 Capital per worker grows over time 3 Capital/output ratio is roughly constant 4 Rate of return to capital is constant 5 Shares of capital and labour in net income are nearly constant 6 Real wage grows over time 7 Ratios of consumption and investment to GDP are constant Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 13 / 39
Short run properties of macroeconomic data Detrended GNP and non-durable consumption 0.06 0.04 LGNPC96(hp) LPCECC96(hp) 0.02 0 0.02 0.04 0.06 0.08 1940 1950 1960 1970 1980 1990 2000 2010 2020 σ Y > σ C ; strong correlation; C leads Y by a quarter or two? Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 14 / 39
Short run properties of macroeconomic data Variable Sd% Cross-correlation of output with: t-3 t-2 t-1 t t+1 t+2 t+3 GNP 1.72 0.38 0.63 0.85 1.00 0.85 0.63 0.38 CND 0.86 0.55 0.68 0.78 0.77 0.64 0.47 0.27 CD 4.96 0.49 0.65 0.75 0.78 0.61 0.38 0.11 I 8.24 0.38 0.59 0.79 0.91 0.76 0.50 0.22 H 1.59 0.30 0.53 0.74 0.86 0.82 0.69 0.52 Ave H 0.63 0.34 0.48 0.63 0.62 0.52 0.37 0.23 L 1.14 0.23 0.46 0.69 0.85 0.86 0.76 0.59 GNP/H 0.90 0.20 0.30 0.33 0.41 0.19 0.00-0.18 Ave W 0.55 0.21 0.14 0.09 0.03-0.07-0.09-0.09 Cyclical behaviour of the US economy 1954-1991 Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 15 / 39
Stylised facts Non-durable consumption less volatile than output Volatility of output and hours similar Employment more volatile than average hours Wages less volatile than productivity Productivity slightly procyclical Wage acyclical Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 16 / 39
Vector autoregressions (VARs) Flexible form that describes wide range of real data sets R t = R 0 + a 11 R t 1 +... + a p1 R t p + b 11 π t 1 +... + b p1 π t p + e 1t π t = π 0 + a 12 R t 1 +... + a p2 R t p + b 12 π t 1 +... + b p2 π t p + e 2t p-th order vector autoregression in interest rate R t and inflation π t Can be estimated by Ordinary Least Squares (OLS) Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 17 / 39
The identification problem VAR residuals and fundamental shocks ( ) ( ) ( ) e1t θ1 θ = 2 u1t ; e 2t θ 3 θ 4 u 2t ( u1t u 2t ) N [ ( 1 0 0; 0 1 )] Problem is that both u 1t and u 2t may affect both e 1t and e 2t Not identified Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 18 / 39
Causal ordering Assume R t reacts to π t with a lag VAR residuals and fundamental shocks ( ) ( ) ( e1t θ1 0 u1t = e 2t θ 3 θ 4 u 2t ) N [ ( σ1 σ 0; 12 σ 12 σ 2 )] Unique identification σ 1 = θ 2 1, σ 12 = θ 1 θ 3, σ 2 = θ 2 3 + θ 2 4 Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 19 / 39
Notes on causal ordering Identified VAR is a structural vector autoregression (SVAR) Ordering could be so π t reacts to R t with a lag not unique Known as Wold decomposition or Choleski ordering Generalisable to more than two variables Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 20 / 39
Impulse response functions Shock to u 2t t R t π t 1 0 0 0 0 θ 4 1 b 11 θ 4 b 12 θ 4 2 a 11 b 11 θ 4 + b 11 b 12 θ 4 + b 21 θ 4 a 12 b 11 θ 4 + b 12 b 12 θ 4 + b 22 θ 4... Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 21 / 39
Sims (1992) Six variable VAR for UK 1965q4 to 1990:12 Causal ordering 1 Short interest rate R 2 Index of foreign exchange value of domestic currency XR 3 Commodity price index PC 4 Monetary aggregate M 5 Consumer price index P 6 Industrial production index Y Innovations only affect variables lower in causal ordering Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 22 / 39
Sims (1992) Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 23 / 39
Christiano, Eichenbaum and Evans (2005) Nine variable VAR for US 1965:3 to 1995:3 Causal ordering 1 Real GDP, real consumption, GDP deflator, real investment, real wage, labour productivity 2 Interest rate 3 Real profit and growth rate of M2 R shocks only affect real profit and M2 R affected by all shocks except real profit and M2 shocks Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 24 / 39
Christiano, Eichenbaum and Evans (2005) Solid lines with plus signs are VAR-based estimates Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 25 / 39
Christiano, Eichenbaum and Evans (2005) Results suggest that after an expansionary monetary policy shock: 1 output, consumption, and investment respond in a hump-shape, peaking after about one and a half years and returning to pre-shock levels after about three years 2 inflation responds in a hump-shape, peaking after about two years 3 interest rate falls for roughly one year 4 real profits, real wages, and labor productivity rise 5 growth rate of money rises immediately Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 26 / 39
Problems with causal orderings Sims (1992) and Christiano, Eichenbaum and Evans (2005) find prices for a while after an unexpected in R t Could be a cost channel effect (firm borrowing costs rise so they increase prices) but more likely faulty identification Sign restriction VARs designed to rule out such anomalies Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 27 / 39
Mapping all identifications Relationship between residuals and fundamental shocks e 1t = (θ 1 cos λ) u 1t + (θ 1 sin λ) u 2t e 2t = (θ 3 cos λ θ 4 sin λ) u 1t + (θ 3 sin λ + θ 4 cos λ) u 2t λ = 0 recover standard causal ordering ( ) λ = tan 1 θ3 θ4 recovers alternative causal ordering By looking at λ [ π, π] can map all possible identifications Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 28 / 39
Mapping all identifications Matrix form ( e1t e 2t ) ( θ1 0 = θ 3 θ 4 ) ( cos λ sin λ sin λ cos λ ) ( u1t u 2t ) Distribution of residuals ( ) e1t N for all λ [ π, π] e 2t [ ( θ 2 0; 1 θ 1 θ 3 θ 1 θ 3 θ 2 3 + θ 2 4 In linear algebra we are rotating matrices )] Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 29 / 39
Sign restrictions First variable is R t and second variable is inflation π t Standard VAR with causal ordering identifies θ 1, θ 3, θ 4 All possible rotations e 1t = (θ 1 cos λ) u 1t + (θ 1 sin λ) u 2t e 2t = (θ 3 cos λ θ 4 sin λ) u 1t + (θ 3 sin λ + θ 4 cos λ) u 2t Monetary policy shock raises R t and lowers π t Search for rotations that satisfy θ 1 cos λ > 0 θ 3 cos λ θ 4 sin λ < 0 Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 30 / 39
Illustrative example Suppose standard VAR identifies θ 1 = θ 3 = θ 4 = 1 Permissible rotations θ 1 cos λ > 0 θ 3 cos λ θ 4 sin λ < 0 λ is in region [ π 4, π ] 2 Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 31 / 39
Canova (2007) Responses to a US policy shock, 1964:1-2001:10 Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 32 / 39
Canova and Paustian (2010) Sign restrictions Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 33 / 39
Canova and Paustian (2010) Response intervals to monetary shocks Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 34 / 39
Identification using high frequency information ECB monthly press conference January 15, 2009 Traders expect interest rate cut on February 5, 2009 Trichet announces no policy change expected next meeting Traders revise up expectations Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 35 / 39
Rosa (2008) Link Time zero when Trichet starts answering a journalist s question Mid-quote on 3-month Euribor future expiring in March 2009 Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 36 / 39
Kuttner (2001) Spot-month futures rate on day t of month s interpreted as conditional expectation of the average funds rate in month s plus term premium fs,t 0 1 = E t m r i + µ 0 s,t i s Policy surprise measure computed from the 1-day change in the spot-month future rate r t u = m ( f 0 m t s,t fs,t 1 0 ) Policy surprise is proxied by change in futures rate proxy VAR Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 37 / 39
Proxy Correlated with u 1t so E (u 1t z t ) = φ Uncorrelated with u 2t so E (u 2t z t ) = 0 Correlated with both residuals [( ) ] [( ) ( e1t θ1 θ E z e t = E 2 u1t 2t θ 3 θ 4 u 2t ) ] ( θ1 φ (φu 1t + ν t ) = θ 3 φ ) Proxy VAR identified by restriction for known E (e 1t z t ) and E (e 2t z t ) θ 1 = E (e 1tz t ) θ 3 E (e 2t z t ) Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 38 / 39
Kuttner (2001) 1-month response of interest rates to Fed funds surprises Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 39 / 39