BUSINESS CYCLES AND ASSET MARKETS
Lecturer: Dr. James Graham
Email: james.a.graham@sydney.edu.au Office: Social Sciences Building, Room 537
Office Hours: 4-5pm Thursday via Zoom
1
COURSE CONTENTS
In this class we will be studying:
• Macroeconomic models of economic fluctuations (i.e. business cycles)
• Economic motivations for asset holding and asset trade
• Frameworks for analysing interactions between the real economy and asset prices • Models of asset pricing
• Empirical methods in macroeconomics and finance
• How to interpret macro-financial data
• The macroeconomic and financial implications of government policy
2
PRIOR PREPARATION
• Prerequisites: ECOS2001 and ECOS2002
• Micro: utility theory, consumer optimisation, production function, profit maximization, neoclassical equilibrium etc (ECON1001 and ECOS2001)
• Finance: No prerequisite, but some background may be an advantage
• Math/Statistics/Econometrics:
• Basic calculus (e.g. differentiation), functions and equations, logarithmic rules • Basic regression analysis (OLS, t-ratios, F-stat)
• Excel or another simple statistical software
3
ASSESSMENT
Weight
25% Friday 4th June (Week 13), 5pm
25% Tuesday 27th April (Week 8), during class
50% June Exam Period Total 100%
Asssessment Items
Written Report (1500 Words)
Midterm Exam (1.5 hours)
Due Date
Final Exam (2 hours)
4
TEXT AND READINGS
No single textbook, but various readings. No need to purchase textbooks. Check e-course readings on the library website. Some readings will also be posted to the Canvas course website
Key References
• Sanjay K. Chugh (2015), Modern Macroeconomics, MIT Press
• William A. Lord (2002), Household Dynamics: Economic Growth and Policy, Oxford University
Press
• Various journal and policy articles in economics
See Canvas/Library eReserve for more details
5
LECTURE 1:
BUSINESS CYCLE CONCEPTS AND MEASUREMENTS
BUSINESS CYCLE:
1) CONCEPTS AND MEASUREMENTS
What is the business cycle?
• Fluctuations in aggregate economic activities • Focus on short-run to medium-run changes
• Classical cycles vs. Growth cycles
• Recurrent but not ‘periodic’
• Some predictable while others are more random
• Shocks (impulses) and propagation to be identified
6
A STYLIZED ILLUSTRATION OF THE BUSINESS CYCLE
7
RECESSIONS IN AUSTRALIA
Why use the log of GDP?
500
400
300
200
13.00 12.75 12.50 12.25 12.00 11.75 11.50 11.25 11.00
Australia Real GDP
Australia Real GDP (in logarithm)
100
1960 1970 1980 1990 2000 2010 2020
1960 1970 1980 1990 2000 2010 2020 8
$Billions
Log($Billions)
RECESSIONS IN AUSTRALIA
Australia Real GDP with Recession Dates
13.00 12.75 12.50 12.25 12.00 11.75 11.50 11.25 11.00
1960 1970
1980 1990 2000 2010 2020
9
Log($Billions)
TAKING LOGS AND GROWTH RATES
• Letyt berealGDPattimet
• Let ∆yt be the growth rate of y (in percent) between dates t − 1 and t
∆yt = yt − yt−1 yt−1
∆yt= yt −1 yt−1
log(1 + ∆yt) = log(yt) − log(yt−1) • Note that log(1+x) ≈ x if x is close to zero, so
∆yt ≈ log(yt) − log(yt−1)
• Plotting the log of GDP makes it easier to identify growth rates • In a log GDP plot, the slope determines the growth rate
10
APPROXIMATE GROWTH RATES IN AUSTRALIAN GDP
13.00 12.75 12.50 12.25 12.00 11.75 11.50 11.25 11.00
1960 1970 1980
1990 2000 2010 2020
Growth Rate ≈ 4%
Australia Real GDP (in logarithm)
Growth Rate ≈ 3%
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Log($Billions)
CLASSICAL CYCLES
1) Classical Business Cycles
• Burns and Mitchell (1946), researchers at the National Bureau of Economic Research (NBER) in the US, defined business cycles as follows:
“Business cycles are a type of fluctuation found in the aggregate economic activity of nations that organize their work mainly in business enterprises: a cycle consists of expansions occurring at about the same time in many economic activities, followed by similarly general recessions, contractions, and revivals which merge into the expansion phase of the next cycle; in duration business cycles vary from more than one year to ten or twelve years …”
https://www.nber.org/cycles/recessions_faq.html
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CLASSICAL CYCLES: CONCEPT
According to Burns and Mitchell (1946):
Business cycles are not defined as fluctuations in real GDP but as fluctuations in an
undefined measure of “aggregate economic activity”. But why not GDP?
Concept of a “reference cycle” – measured on the basis of several economic time series,
descriptive evidence, and general business conditions indexes (“coincident indicators”)
Dating of business cycle turning points is based on a mixture of
mechanically applied rules and ad hoc judgments (e.g. NBER’s Business Cycle Dating Committee). Requires careful interpretation of data! https://www.nber.org/research/business-cycle-dating
13
CLASSICAL CYCLES: CONCEPT
• Bry and Boschan (1971) developed a procedure (an algorithm) to identify turning points.
• Following Harding and Pagan (2002) there is a well-known algorithm for quarterly data
known as the BBQ procedure.
How do we identify turning points in the log-level of a series yt?
• A peak at time t occurs if:
• A trough at time t occurs if:
[(yt − yt−2) > 0,(yt − yt−1) > 0],and [(yt+2 − yt) < 0,(yt+1 − yt) < 0]
[(yt − yt−2) < 0,(yt − yt−1) < 0],and [(yt+2 − yt) > 0,(yt+1 − yt) > 0]
Note: An Excel Macro file is available to implement the BBQ (on Canvas)
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BBQ ALGORITHM EXAMPLE: AUSTRALIAN REAL GDP
Australia Real GDP with Recession Dates
13.00 12.75 12.50 12.25 12.00 11.75 11.50 11.25 11.00
1960 1970
1980 1990 2000 2010 2020
15
Log($Billions)
BBQ ALGORITHM EXAMPLE: FINDING A PEAK AND TROUGH
215 210 205 200 195
1988 1989
1990 1991 1992 1993
Australia Real GDP
Peak Trough
16
$Billions
CLASSICAL CYCLES: CONCEPT
• A stylised recession has both duration and amplitude Australia Real GDP
215 210 205 200
195
1988 1989
1990 1991 1992 1993
Amplitude
Duration
17
$Billions
CLASSICAL CYCLES: SUMMARY
In general, classical cycles have the following features:
Recurrent (but not periodic), with aggregate fluctuations comprising of recessions followed by expansions
Co-movements among macroeconomic variables (GDP, GDI, consumption, investment, etc)
“The presence of hills and valleys in a plot of the levels of the seris” (according to Adrian
Pagan)
Requries no detrending (i.e. the removing of a trend) in the data
Classical recession involves an absolute decline in real GDP (typically) for two successive quarters or more
Asymmetry in business cycles: periods of expansion are much longer than periods of recession. (Is this obvious?)
18
GROWTH CYCLES: CONCEPT
2) Growth Cycles
According to Robert Lucas (1977), “aggregate fluctuations around the trend or growth path”
“Refers to the same thing (as Classical cycles) in some detrended series (i.e. trends
removed)”
A growth recession requires a relative decline (i.e. growth can still be positive) in real GDP, but below the long-term growth trend
A complete growth cycle in industralized countries typically takes between 18 months and 8 years, depending on how the trend is defined
No clear asymmetry in growth cycles. (Why might this be?)
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GROWTH CYCLES: CONCEPT
• Think of a time series yt with secular (i.e. uncorrelated) components decomposed as yt = gt + ct
• gt is the growth or trend component
• ct is the cyclical (business cycle) component
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DETRENDING A DATA SERIES: DIFFERENCING
How do we detrend a time series with secular (growth) components?
(1) Difference the series. Let yt be a quarterly time series
Quarterly difference: log yt − log yt−1
Four-quarter ended (year-on-year) difference: log yt − log yt−4
• These methods tend to remove too much information and show short-term volatility. So
not suitable to obtain medium-term movements.
• But, easy and useful to interpret and assess economic conditions.
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DETRENDING A DATA SERIES: DIFFERENCING EMPIRICAL EXAMPLE
Quarterly changes First difference of log GDP
Year-on-year changes Four-quarter ended difference
0.04
0.02
0.00
−0.02 −0.04 −0.06
0.08 0.06 0.04 0.02 0.00
−0.02 −0.04 −0.06
1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 2020
1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 2020
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DETRENDING A DATA SERIES: DETERMINISTIC TRENDS
How do we detrend a time series with secular (growth) components?
(2) Assume a deterministic trend (e.g. linear or quadratic)
• A trend can be linear (i.e. straight line) or a linear function of separate linear and quadratic trends
• ct = yt − gt
• wheregt =α+β·t+γ·t2
• Do the linear or quadratic trends reflect true trends?
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DETRENDING A DATA SERIES: LINEAR AND QUADRATIC TRENDS EMPIRICAL EXAMPLES
13.5 Linear Trend Fit To Australian GDP 1.0
13.0 0.8
13.5 Quadratic Trend Fit To Australian GDP 1.0
13.0 0.8
GDP Data Linear Trend
GDP Data Quadratic Trend
12.5
12.0
11.5
11.0
10.5
10.0
1960 1970 1980 1990 2000 2010 2020
0.6
0.4
0.2
0.0
12.5
12.0
11.5
11.0
10.5
0.6
0.4
0.2
0.0
−0.2 −0.2
10.0
1960 1970 1980 1990 2000 2010 2020
Do the trends correctly capture actual recession dates?
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Deviation From Trend
Deviation From Trend
DETRENDING A DATA SERIES: STOCHASTIC TRENDS
How do we detrend a time series with secular (growth) components?
(3) Assume a stochastic trend (i.e. a random trend). Find via a filtering algorithm • The (in)famous Hodrick-Prescott (1997) filter solves a minimization problem:
s.t.
ct = yt − gt
min
{gt}t=1,··· ,T
ct +λ [(gt+1 −gt)−(gt −gt−1)] t=1 t=2
{TT−1 } ∑2∑2
• where λ is a parameter that determines the smoothness of the trend. It reflects the tradeoff between the smoothness of the trend and how closely the trend mimics the actual series.
• Ifwesetλ=0,thengt =yt andsoct =0(Why?)
• Ifwesetλ→∞,thengt−1 =gt =gt+1 =g ̄i.e.alineartrend.
• Rule of thumb: set λ = 1600 for quarterly data. But less agreement about the value of λ for
other data frequencies. E.g. for annual data some suggest λ = 100, others suggest λ = 10.
25
DETRENDING A DATA SERIES: HP FILTER EMPIRICAL EXAMPLES
13.0 12.5 12.0 11.5 11.0
1960 1970 1980
1990 2000
2010 2020
Log of Real GDP and HP Filtered trend GDP
Log Real GDP
HP Trend (λ = 1, 000, 000) HP Trend (λ = 1, 600)
26
DETRENDING A DATA SERIES: HP FILTER EMPIRICAL EXAMPLES
0.02
0.00
−0.02
−0.04
−0.06
1960 1970
1980 1990 2000 2010 2020
HP Filtered cycle for Real GDP Growth Cycle
HP Cycle
Note: A classical recession always implies a growth recession, but the converse is not true. Is there any asymmetry in the growth cycle?
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DETRENDING A DATA SERIES: HP FILTER IS USEFUL
• The growth component computed by the HP-filter is a smooth trend visually similar to the trend that one can obtain with a free-hand drawing
• The HP-filter is consistent with business cycle definition of Lucas (1977) (i.e. growth cycle)
• Extremely popular method for de-trending macroeconomic data, available in most statistical
packages
28
DETRENDING A DATA SERIES: HP FILTER CRITICISMS
• Caution when using the Hodrick-Prescott filter
• Macro-econometrician James Hamilton (among others) strongly recommends against using the
HP Filter
1. The HP filter can produce statistical artifacts in de-trended series that have nothing to do with
the underlying data generating process. Can lead to spurious persistence or co-movement in
data that does not really exist
2. The ‘end point problem’: the HP filter uses data from the future to uncover information about
the trend and cycle today. This can make ex-post trends seem excessively smooth and cycles
excessively large, even though this was not knowable in real-time.
3. The best choice of the smoothing parameter value is disputed. Traditional choice λ = 1600 for
quarterly data is not necessarily optimal if the filter is supposed to best fit the data
29
UNDERSTANDING CYCLICAL PROPERTIES
Let xt and yt be two time series variables (e.g. the stock of money and GDP). We might ask ourselves:
• Are the two variables “related”? (i.e. correlation)
• Is one variable “predicting” the other variable?
• Does one variable “move” more than the other? (i.e. volatility)
30
TIME SERIES (CYCLICAL) RELATIONS
(1) Correlation (or, co-movement for detrended series)
• Measure the degree of synchronisation between any two variables contemporaneously
Remember correlation does not imply causation!
31
CYCLICAL RELATIONS: DEFINITIONS
A macroeconomic variable is:
• Pro-cyclical: if deviations from trend are positively correlated with real GDP deviations from its own trend
• Counter-cyclical: if deviations from trend are negatively correlated with real GDP deviations from its own trend
• Acyclical: if deviations from trend for each variable are not correlated
32
TIME SERIES (CYCLICAL) RELATIONS
(2) Leads and Lags
• Measure the degree of synchronisation between any two variables across time
• We measure these relationships via cross-correlation:
• Corr(xt−j , yt ), where j > 0 indicates a leading variable, j < 0 indicates a lagging variable
33
TIME SERIES (CYCLICAL) RELATIONS
OECD Business Cycle Clock for documenting leading and lagging indicators (https: //www.oecd.org/sdd/leading-indicators/theoecdbusinesscycleclock.htm)
34
TIME SERIES (CYCLICAL) RELATIONS: EXAMPLES
Leading Indicators:
• Stock prices; money growth; interest rate spreads (e.g. 10-year Treasury bill rate minus 90 day Bank bill rate), ...
Coincident Indicators:
• New orders, building permits, production, income, consumption, sales, hours workers, ....
Lagging Indicators:
• Inflation, labour costs, loans, consumer credit, unemployment rate, short-term interest rates, ...
35
TIME SERIES PROPERTIES
(3) Variability (a.k.a. volatility)
• Measures the amplitude of deviations from a trend or mean
• Measure variability via the standard deviation of a variable
(4) Persistence
• Measures the time dependence or inertia of a variable
• Measure persistence via the autocorrelation
• Corr(yt,yt−j), where j > 0 or j < 0
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VARIABILITY IN THE US BUSINESS CYCLE
Non-Durable Consumption
Durable Consumption
0.2 0.1 0.0
−0.1
−0.2
0.2 0.1 0.0
−0.1 −0.2 −0.3
0.2 0.1 0.0
−0.1 −0.2 −0.3
−0.3
1950 1960 1970 1980 1990 2000 2010 2020 1950 1960 1970 1980 1990 2000 2010 2020
Residential Investment
Non-Residential Investment
0.2 0.1 0.0
−0.1
−0.2
−0.3
1950 1960 1970 1980 1990 2000 2010 2020 1950 1960 1970 1980 1990 2000 2010 2020
Source: Federal Reserve Economic Database
37
CO-MOVEMENT AND RELATIVE VOLATILITY: EXAMPLES
• Consumption is:
• Pro-cyclical, coincident, and slightly less variable than GDP
GDP Consumption
0.04 0.02 0.00
−0.02 −0.04 −0.06 −0.08 −0.10
1950 1960
1970 1980
1990 2000
2010 2020
Source: Federal Reserve Economic Database
38
Percentage Deviation From Trend
CO-MOVEMENT AND RELATIVE VOLATILITY: EXAMPLES
• Investment is:
• Pro-cyclical, coincident, and more variable than GDP
0.2 0.1 0.0
−0.1
−0.2
1950 1960
1970 1980 1990 2000
2010 2020
GDP Investment
Source: Federal Reserve Economic Database
39
Percentage Deviation From Trend
CO-MOVEMENT AND RELATIVE VOLATILITY: EXAMPLES
• Employment is:
• Pro-cyclical, lagging, and less variable than GDP
GDP
Employment
0.04 0.02 0.00
−0.02
−0.04
−0.06
−0.08
−0.10
−0.12
1950 1960
1970 1980 1990 2000
2010 2020
Source: Federal Reserve Economic Database
40
Percentage Deviation From Trend
ASIDE: HISTORICALLY LARGE DECLINE IN EMPLOYMENT
41
DOCUMENTING BUSINESS CYCLE FACTS
Key facts for industrialized economies
• Magnitude of fluctuations in output and aggregate hours of work are very similar
• Employment fluctuates almost as much as output and total hours of work
• Consumption (of non-durables and services) is smooth and fluctuates less than output
• Investment fluctuates much more than output
• The capital stock fluctuates much less than output and is largely uncorrelated (acyclical) with output
• Productivity is slightly pro-cyclical
• Government expenditure is uncorrelated with output
• Net exports are counter-cyclical
42
DOCUMENTING BUSINESS CYCLE FACTS: EXAMPLES FROM AUSTRALIA
Source: Crosby and Otto (1995). Recommended Reading
43
BUSINESS CYCLES:
USING STATISTICAL MODELS
• What is the Data Generating Process (DGP) that mimics actual real GDP?
• Consider a statistical model (random walk with drift):
yt = μ + ρyt−1 + εt, ρ = 1 where μ and ρ are parameters, and εt is the error term
• Regression the log of real GDP on a constant and lagged log real GDP yields: yt = 0.046 + 0.997yt−1 + εt, R2 = 0.9996
• So the evolution of GDP is indistinguishable from the random walk with drift model
44
BUSINESS CYCLES:
USING A STATISTICAL MODEL
13.00 12.75 12.50 12.25 12.00 11.75 11.50 11.25
Forecasting Australian GDP Using a Random Walk Model
GDP Data
RW Prediction
1960 1970 1980
1990 2000
2010 2020
45