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 Jonesandrew.bell@bristol.ac.uk

NCRM Research Methods Festival, July 2014

School of Geographical Sciences

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

Increase in Deficit More govt

borrowingInterest rates up Growth reduced

Government spends to stimulate growth

Reduced government revenueIncrease in Debt

Investors wary of govt ability to make repayments

Investor flight

Direction of causality

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

• Run in MLwiN• Model additionally run using RR’s 4 groupings (instead of a linear

effect) – results substantively similar

Random slopes modelAverage effect of debt (within and between effects separated – see Bell and Jones 2014)

• Run in MLwiN• Model additionally run using RR’s 4 groupings (instead of a linear

effect) – results substantively similar

Random slopes modelAverage effect of debt (within and between effects separated – see Bell and Jones 2014)

Varying effects of debt across countries

• Run in MLwiN• Model additionally run using RR’s 4 groupings (instead of a linear

effect) – results substantively similar

Random slopes modelAverage effect of debt (within and between effects separated – see Bell and Jones 2014)

Varying effects of debt across countries

• Run in MLwiN• Model additionally run using RR’s 4 groupings (instead of a linear

effect) – results substantively similar

Occasion-level variance (that is, volatility) varies with debt

Random slopes modelAverage effect of debt (within and between effects separated – see Bell and Jones 2014)

Varying effects of debt across countries

Occasion-level variance (that is, volatility) varies with debt

Year controlled in all parts of model

• Run in MLwiN• Model additionally run using RR’s 4 groupings (instead of a linear

effect) – results substantively similar

Distributed lag model

h𝐺𝑟𝑜𝑤𝑡 𝑖𝑗=𝛽0+𝛽1(𝐷𝑒𝑏𝑡 ¿¿ 𝑖−3 𝑗 )+𝛽2(∆𝐷𝑒𝑏𝑡 ¿¿ 𝑖−2 𝑗)+𝛽3 (∆𝐷𝑒𝑏𝑡¿¿ 𝑖−1 𝑗)+𝛽4 (∆𝐷𝑒𝑏𝑡 ¿¿ 𝑖𝑗 )+𝛽5(∆𝐷𝑒𝑏𝑡¿¿ 𝑖+1 𝑗 )+𝛽6(∆𝐷𝑒𝑏𝑡¿¿ 𝑖+2 𝑗)+𝛽7(∆𝐷𝑒𝑏𝑡 ¿¿ 𝑖+3 𝑗)+𝑒0 𝑖𝑗 ¿¿¿¿¿ ¿¿From http://www.nextnewdeal.net/rortybomb/guest-post-reinhartrogoff-and-growth-time-debt

• 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

Distributed lag model

h𝐺𝑟𝑜𝑤𝑡 𝑖𝑗=𝛽0+𝛽1(𝐷𝑒𝑏𝑡 ¿¿ 𝑖−3 𝑗 )+𝛽2(∆𝐷𝑒𝑏𝑡 ¿¿ 𝑖−2 𝑗)+𝛽3 (∆𝐷𝑒𝑏𝑡¿¿ 𝑖−1 𝑗)+𝛽4 (∆𝐷𝑒𝑏𝑡 ¿¿ 𝑖𝑗 )+𝛽5(∆𝐷𝑒𝑏𝑡¿¿ 𝑖+1 𝑗 )+𝛽6(∆𝐷𝑒𝑏𝑡¿¿ 𝑖+2 𝑗)+𝛽7(∆𝐷𝑒𝑏𝑡 ¿¿ 𝑖+3 𝑗)+𝑒0 𝑖𝑗 ¿¿¿¿¿ ¿¿From http://www.nextnewdeal.net/rortybomb/guest-post-reinhartrogoff-and-growth-time-debt

• 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…

Multilevel distributed lag model

.

Run in Stata using the runmlwin command (code available on request)

Results (1)

• 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

Australia

Greece

IrelandJapan

UK

US

0

1

2

3

4

5

6

0 70 140 210

Pre

dict

ed G

row

th (%

GD

P)

Debt:GDP ratio

Results (2)

0

4

8

12

<30 30-60 60-90 90+

Leve

l 1 V

aria

nce

Debt:GDP ratio

• Higher level-1 variance at debt ratios greater than 90%

• Suggests debt is associated with volatility in economic growth

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