Transcript Stylised fact or situated messiness? A multilevel country panel

School of Geographical Sciences
Stylised fact or situated messiness? A
multilevel country panel analysis of the
effects of debt on national economic
growth, using Reinhart and Rogoff’s data
Andrew Bell, Ron Johnston and Kelvyn Jones
[email protected]
NCRM Research Methods Festival, July 2014
Outline
•
•
•
•
Reinhart and Rogoff - Growth in a time of debt
Herndon et al’s critique
What is missing?
Our analysis
– Random coefficients model
– Multilevel distributed lag model
Key methodological point
• The world is complex, and needs realistically
complex models to represent it
• Aiming for an average effect, or ‘stylised fact’
can be very misleading when relationships are
heterogeneous over time or space
Growth in a Time of Debt (2010)
• Amer Econ Rev 100(2) 573-78
• Reinhart and Rogoff
argue for a threshold
debt value at 90% of
GDP, after which
growth dramatically
declines in rich
countries.
• Entirely descriptive –
no statistical model
Influence
• A key citation and influence for those in favour
of austerity budgets
– “As Rogoff and Reinhart demonstrate convincingly,
all financial crises ultimately have their origins in
one thing.” (George Osborne, 2010)
– “conclusive empirical evidence that gross debt
…exceeding 90 percent of the economy has a
significant negative effect on economic growth.”
(Paul Ryan, 2013, p78)
Herndon et al’s critique
• Camb J Econ, 2014, 38(2), 257-279
• Find three key flaws
– An excel spreadsheet error deleting five countries
at the top of the alphabet
– Weighting by country, not by country-year
– Exclusion of certain data points
• It seems that the combination of the second
two are what produced the apparent
threshold effect
Herndon et al’s critique
• When corrected,
change is much less
extreme – no threshold
– growth declines
gradually with debt
• But still an apparent
relationship – growth
declines with debt.
Herndon et al’s critique
What is missing?
• ‘Stylised fact’ of a single un-varying effect is
too simplistic
– Why should the effect of debt be the same in
Japan as in the USA?
• Assumption that debt leads to growth and not
vice-versa
Direction of causality
Increase in
Deficit
More govt
borrowing
Interest
rates up
Investors wary of govt
ability to make
repayments
Increase in Debt
Growth reduced
Investor flight
Reduced
government
revenue
Government spends
to stimulate growth
Our reanalysis – 2 parts
• Multilevel model that allows the growth-debt
relationship to vary between countries
(random slopes model)
• Multilevel ‘distributed lag model’ that gives
evidence of direction of causality
– does growth go up after debt, or before?
Random slopes model
𝐺𝑟𝑜𝑤𝑡ℎ𝑖𝑗
= 𝛽0 + 𝛽1 (𝐷𝑒𝑏𝑡𝑖𝑗 −𝐷𝑒𝑏𝑡𝑗 ) + 𝛽2 𝐷𝑒𝑏𝑡𝑗 + 𝛽4 𝑌𝑒𝑎𝑟𝑖𝑗 + [𝑢0𝑗
+ 𝑢1𝑗 (𝐷𝑒𝑏𝑡𝑖𝑗 −𝐷𝑒𝑏𝑡𝑗 ) + 𝑢2𝑗 (𝑌𝑒𝑎𝑟𝑖𝑗 )
+ 𝑒0𝑖𝑗 + 𝑒1𝑖𝑗 (𝐷𝑒𝑏𝑡𝑖𝑗 −𝐷𝑒𝑏𝑡𝑗 ) + 𝑒2𝑖𝑗 (𝑌𝑒𝑎𝑟𝑖𝑗 )]
2
𝑢0𝑗
𝜎𝑢0
𝑢1𝑗 ~𝑁 0, 𝜎𝑢0𝑢1
𝑢2𝑗
𝜎𝑢0𝑢2
2
𝑒0𝑗
𝜎𝑒0
𝑒1𝑗 ~𝑁 0, 𝜎𝑒0𝑒1
𝑒2𝑗
𝜎𝑒0𝑒2
2
𝜎𝑢1
𝜎𝑢1𝑢2
2
𝜎𝑢2
2
𝜎𝑒1
𝜎𝑒1𝑒2
2
𝜎𝑒2
• Run in MLwiN
• Model additionally run using RR’s 4 groupings (instead of a linear
effect) – results substantively similar
Random slopes model
Average effect of debt (within and between
effects separated – see Bell and Jones 2014)
𝐺𝑟𝑜𝑤𝑡ℎ𝑖𝑗
= 𝛽0 + 𝛽1 (𝐷𝑒𝑏𝑡𝑖𝑗 −𝐷𝑒𝑏𝑡𝑗 ) + 𝛽2 𝐷𝑒𝑏𝑡𝑗 + 𝛽4 𝑌𝑒𝑎𝑟𝑖𝑗 + [𝑢0𝑗
+ 𝑢1𝑗 (𝐷𝑒𝑏𝑡𝑖𝑗 −𝐷𝑒𝑏𝑡𝑗 ) + 𝑢2𝑗 (𝑌𝑒𝑎𝑟𝑖𝑗 )
+ 𝑒0𝑖𝑗 + 𝑒1𝑖𝑗 (𝐷𝑒𝑏𝑡𝑖𝑗 −𝐷𝑒𝑏𝑡𝑗 ) + 𝑒2𝑖𝑗 (𝑌𝑒𝑎𝑟𝑖𝑗 )]
2
𝑢0𝑗
𝜎𝑢0
𝑢1𝑗 ~𝑁 0, 𝜎𝑢0𝑢1
𝑢2𝑗
𝜎𝑢0𝑢2
2
𝑒0𝑗
𝜎𝑒0
𝑒1𝑗 ~𝑁 0, 𝜎𝑒0𝑒1
𝑒2𝑗
𝜎𝑒0𝑒2
2
𝜎𝑢1
𝜎𝑢1𝑢2
2
𝜎𝑢2
2
𝜎𝑒1
𝜎𝑒1𝑒2
2
𝜎𝑒2
• Run in MLwiN
• Model additionally run using RR’s 4 groupings (instead of a linear
effect) – results substantively similar
Random slopes model
Average effect of debt (within and between
Varying effects of
effects separated – see Bell and Jones 2014)
debt across countries
𝐺𝑟𝑜𝑤𝑡ℎ𝑖𝑗
= 𝛽0 + 𝛽1 (𝐷𝑒𝑏𝑡𝑖𝑗 −𝐷𝑒𝑏𝑡𝑗 ) + 𝛽2 𝐷𝑒𝑏𝑡𝑗 + 𝛽4 𝑌𝑒𝑎𝑟𝑖𝑗 + [𝑢0𝑗
+ 𝑢1𝑗 (𝐷𝑒𝑏𝑡𝑖𝑗 −𝐷𝑒𝑏𝑡𝑗 ) + 𝑢2𝑗 (𝑌𝑒𝑎𝑟𝑖𝑗 )
+ 𝑒0𝑖𝑗 + 𝑒1𝑖𝑗 (𝐷𝑒𝑏𝑡𝑖𝑗 −𝐷𝑒𝑏𝑡𝑗 ) + 𝑒2𝑖𝑗 (𝑌𝑒𝑎𝑟𝑖𝑗 )]
2
𝑢0𝑗
𝜎𝑢0
𝑢1𝑗 ~𝑁 0, 𝜎𝑢0𝑢1
𝑢2𝑗
𝜎𝑢0𝑢2
2
𝑒0𝑗
𝜎𝑒0
𝑒1𝑗 ~𝑁 0, 𝜎𝑒0𝑒1
𝑒2𝑗
𝜎𝑒0𝑒2
2
𝜎𝑢1
𝜎𝑢1𝑢2
2
𝜎𝑢2
2
𝜎𝑒1
𝜎𝑒1𝑒2
2
𝜎𝑒2
• Run in MLwiN
• Model additionally run using RR’s 4 groupings (instead of a linear
effect) – results substantively similar
Random slopes model
Average effect of debt (within and between
Varying effects of
effects separated – see Bell and Jones 2014)
debt across countries
𝐺𝑟𝑜𝑤𝑡ℎ𝑖𝑗
Occasion-level= 𝛽0 + 𝛽1 (𝐷𝑒𝑏𝑡𝑖𝑗 −𝐷𝑒𝑏𝑡𝑗 ) + 𝛽2 𝐷𝑒𝑏𝑡𝑗 + 𝛽4 𝑌𝑒𝑎𝑟𝑖𝑗 + [𝑢0𝑗
variance (that+is,𝑢1𝑗 (𝐷𝑒𝑏𝑡𝑖𝑗 −𝐷𝑒𝑏𝑡𝑗 ) + 𝑢2𝑗 (𝑌𝑒𝑎𝑟𝑖𝑗 )
volatility) varies
+ 𝑒0𝑖𝑗 + 𝑒1𝑖𝑗 (𝐷𝑒𝑏𝑡𝑖𝑗 −𝐷𝑒𝑏𝑡𝑗 ) + 𝑒2𝑖𝑗 (𝑌𝑒𝑎𝑟𝑖𝑗 )]
2
𝑢0𝑗
𝜎𝑢0
with debt
𝑢1𝑗 ~𝑁 0, 𝜎𝑢0𝑢1
𝑢2𝑗
𝜎𝑢0𝑢2
2
𝑒0𝑗
𝜎𝑒0
𝑒1𝑗 ~𝑁 0, 𝜎𝑒0𝑒1
𝑒2𝑗
𝜎𝑒0𝑒2
2
𝜎𝑢1
𝜎𝑢1𝑢2
2
𝜎𝑢2
2
𝜎𝑒1
𝜎𝑒1𝑒2
2
𝜎𝑒2
• Run in MLwiN
• Model additionally run using RR’s 4 groupings (instead of a linear
effect) – results substantively similar
Random slopes model
Average effect of debt (within and between
Varying effects of
effects separated – see Bell and Jones 2014)
debt across countries
𝐺𝑟𝑜𝑤𝑡ℎ𝑖𝑗
Occasion-level= 𝛽0 + 𝛽1 (𝐷𝑒𝑏𝑡𝑖𝑗 −𝐷𝑒𝑏𝑡𝑗 ) + 𝛽2 𝐷𝑒𝑏𝑡𝑗 + 𝛽4 𝑌𝑒𝑎𝑟𝑖𝑗 + [𝑢0𝑗
variance (that+is,𝑢1𝑗 (𝐷𝑒𝑏𝑡𝑖𝑗 −𝐷𝑒𝑏𝑡𝑗 ) + 𝑢2𝑗 (𝑌𝑒𝑎𝑟𝑖𝑗 )
volatility) varies
+ 𝑒0𝑖𝑗 + 𝑒1𝑖𝑗 (𝐷𝑒𝑏𝑡𝑖𝑗 −𝐷𝑒𝑏𝑡𝑗 ) + 𝑒2𝑖𝑗 (𝑌𝑒𝑎𝑟𝑖𝑗 )]
2
𝑢0𝑗
𝜎𝑢0
with debt
Year controlled in all
parts of model
𝑢1𝑗 ~𝑁 0, 𝜎𝑢0𝑢1
𝑢2𝑗
𝜎𝑢0𝑢2
2
𝑒0𝑗
𝜎𝑒0
𝑒1𝑗 ~𝑁 0, 𝜎𝑒0𝑒1
𝑒2𝑗
𝜎𝑒0𝑒2
2
𝜎𝑢1
𝜎𝑢1𝑢2
2
𝜎𝑢2
2
𝜎𝑒1
𝜎𝑒1𝑒2
2
𝜎𝑒2
• Run in MLwiN
• Model additionally run using RR’s 4 groupings (instead of a linear
effect) – results substantively similar
Distributed lag model
• 𝐺𝑟𝑜𝑤𝑡ℎ𝑖𝑗 = 𝛽0 + 𝛽1 (𝐷𝑒𝑏𝑡𝑖−3𝑗 ) + 𝛽2 (∆𝐷𝑒𝑏𝑡𝑖−2𝑗 ) +
𝛽3 (∆𝐷𝑒𝑏𝑡𝑖−1𝑗 ) + 𝛽4 (∆𝐷𝑒𝑏𝑡𝑖𝑗 ) + 𝛽5 (∆𝐷𝑒𝑏𝑡𝑖+1𝑗 ) +
𝛽6 (∆𝐷𝑒𝑏𝑡𝑖+2𝑗 ) + 𝛽7 (∆𝐷𝑒𝑏𝑡𝑖+3𝑗 ) + 𝑒0𝑖𝑗
• Regress multiple leads and lags of
debt on growth
• Can plot these in an ‘impulse
response’ graph
• See whether a change in growth
or a change in debt happens first
From http://www.nextnewdeal.net/rortybomb/guest-post-reinhartrogoff-and-growth-time-debt
Distributed lag model
• 𝐺𝑟𝑜𝑤𝑡ℎ𝑖𝑗 = 𝛽0 + 𝛽1 (𝐷𝑒𝑏𝑡𝑖−3𝑗 ) + 𝛽2 (∆𝐷𝑒𝑏𝑡𝑖−2𝑗 ) +
𝛽3 (∆𝐷𝑒𝑏𝑡𝑖−1𝑗 ) + 𝛽4 (∆𝐷𝑒𝑏𝑡𝑖𝑗 ) + 𝛽5 (∆𝐷𝑒𝑏𝑡𝑖+1𝑗 ) +
𝛽6 (∆𝐷𝑒𝑏𝑡𝑖+2𝑗 ) + 𝛽7 (∆𝐷𝑒𝑏𝑡𝑖+3𝑗 ) + 𝑒0𝑖𝑗
• Dube (2013) – reanalyses RR’s
data, finds evidence direction is
mainly in the direction from
growth to debt, not from debt to
growth
• But is this the same for all
countries?
• Use the multilevel logic of
previous model to allow causal
direction to vary by country…
From http://www.nextnewdeal.net/rortybomb/guest-post-reinhartrogoff-and-growth-time-debt
Multilevel distributed lag model
𝐺𝑟𝑜𝑤𝑡ℎ𝑖𝑗
= 𝛽0 + 𝛽1 (𝐷𝑒𝑏𝑡𝑖−3𝑗 ) + 𝛽2 (∆𝐷𝑒𝑏𝑡𝑖−2𝑗 ) + 𝛽3 (∆𝐷𝑒𝑏𝑡𝑖−1𝑗 )
+ 𝛽4 (∆𝐷𝑒𝑏𝑡𝑖𝑗 ) + 𝛽5 (∆𝐷𝑒𝑏𝑡𝑖+1𝑗 ) + 𝛽6 (∆𝐷𝑒𝑏𝑡𝑖+2𝑗 ) + 𝛽7 (∆𝐷𝑒𝑏𝑡𝑖+3𝑗 )
+ 𝛽8 𝑌𝑒𝑎𝑟𝑖𝑗 + [𝑢0𝑗 +𝑢1𝑗 (𝐷𝑒𝑏𝑡𝑖−3𝑗 ) + 𝑢2𝑗 (∆𝐷𝑒𝑏𝑡𝑖−2𝑗 )
+ 𝑢3𝑗 (∆𝐷𝑒𝑏𝑡𝑖−1𝑗 ) + 𝑢4𝑗 (∆𝐷𝑒𝑏𝑡𝑖𝑗 ) + 𝑢5𝑗 (∆𝐷𝑒𝑏𝑡𝑖+1𝑗 )
+ 𝑢6𝑗 (∆𝐷𝑒𝑏𝑡𝑖+2𝑗 ) + 𝑢7𝑗 (∆𝐷𝑒𝑏𝑡𝑖+3𝑗 ) + 𝑢8𝑗 (𝑌𝑒𝑎𝑟𝑖𝑗 ) + 𝑒0𝑖𝑗 ]
2
2
2
2
𝑢0𝑗 ~𝑁 0, 𝜎𝑢0
, 𝑢1𝑗 ~𝑁 0, 𝜎𝑢1
, 𝑢2𝑗 ~𝑁 0, 𝜎𝑢2
, 𝑢3𝑗 ~𝑁 0, 𝜎𝑢3
,
2
2
2
2
𝑢4𝑗 ~𝑁 0, 𝜎𝑢4
, 𝑢5𝑗 ~𝑁 0, 𝜎𝑢5 , 𝑢6𝑗 ~𝑁 0, 𝜎𝑢6 , 𝑢7𝑗 ~𝑁 0, 𝜎𝑢7
,
2
2
𝑢8𝑗 ~𝑁 0, 𝜎𝑢8 , 𝑒0𝑖𝑗 ~𝑁(0, 𝜎𝑒0 ).
Run in Stata using the runmlwin command (code available on request)
Results (1)
Predicted Growth (%GDP)
6
5
4
Greece
Australia
3
Ireland
US
2
UK
Japan
1
0
0
70
140
Debt:GDP ratio
210
• Average effect (the
“stylised fact”) now
not significant
• Lots of variation
between countries
• No evidence of a
relationship
between growth
and debt in the UK
Results (2)
• Higher level-1 variance
at debt ratios greater
than 90%
• Suggests debt is
associated with volatility
in economic growth
Level 1 Variance
12
8
4
0
<30
30-60
60-90
Debt:GDP ratio
90+
Results (3)
In most countries,
a change in debt
occurs after a
change in growth
Suggests low
growth causes
debt, rather than
debt causing
growth.
Some variation –
e.g. less clear
directionality in
Ireland.
Conclusions
• Substantive:
– The relationship between growth and debt is highly
variable;
– The average effect (‘stylised fact’) is not significant,
although volatility in growth does appear to be higher
at debt:GDP ratios over 90%;
– The causal direction is predominantly from growth to
debt, not debt to growth
• Methodological:
– Stylised facts are often too simplistic – the world is
complex and messy, and our statistical models should
aim to reflect that complexity.
For more information
• Bell, A; Johnston, R; Jones K (2014) Stylised fact or situated
messiness? The diverse effects of increasing debt on national
economic growth. Journal of Economic Geography, online,
DOI: 10.1093/jeg/lbu005
• Bell, A and Jones, K (2014) Explaining fixed effects: Random
effects modelling of time-series cross-sectional and panel
data. Political Science Research and Methods, online, DOI:
10.1017/psrm.2014.7
– Paper showing the advantages of using a multilevel/random effects
model, rather than fixed effects models or other alternatives