IMPERFECT KNOWLEDGE, UNPREDICTABILITY AND THE FAILURES OF MODERN - - PowerPoint PPT Presentation

IMPERFECT KNOWLEDGE, UNPREDICTABILITY AND THE FAILURES OF MODERN MACROECONOMICS

David F. Hendry

Director EMoD, Institute for New Economic Thinking at the Oxford Martin School INET Plenary Conference, Edinburgh, October 2017 Research jointly with Jennifer Castle, Jurgen Doornik, Søren Johansen and Felix Pretis

David F. Hendry (INET at Oxford Martin School) Imperfect Knowledge Edinburgh 2017 1 / 28

Route map (1) Five theorems about conditional expectations (2) Uncertainty, unpredictability and unanticipated shifts (3) Empirical location shifts (4) Imperfect knowledge and conditional expectations (5) Modelling tools to detect shifts (6) Conclusions

David F. Hendry (INET at Oxford Martin School) Imperfect Knowledge Edinburgh 2017 2 / 28

Five (possibly misleading) theorems about conditional expectations [1] The conditional expectation is the minimum mean square error (MMSE) unbiased predictor. [2] The expectation of the conditional expectation is the unconditional expectation, also called the law of iterated expectations. These are well known: see Goldberger (1991, p. 46–51) for proofs.

David F. Hendry (INET at Oxford Martin School) Imperfect Knowledge Edinburgh 2017 3 / 28

Five (possibly misleading) theorems about conditional expectations [1] The conditional expectation is the minimum mean square error (MMSE) unbiased predictor. [2] The expectation of the conditional expectation is the unconditional expectation, also called the law of iterated expectations. These are well known: see Goldberger (1991, p. 46–51) for proofs. [3] Incomplete knowledge of the conditioning information need not lead to biased expectations (see e.g., Clements and Hendry, 2005). [4] Conditional expectations can provide unbiased forecasts even in mis-specified, mis-estimated models (Hendry and Trivedi, 1972). [5] Replacing unknown expectations by realized future outcomes, as in New-Keynesian Phillips curve (NKPC) models, is legitimate as such expectations can be shown to be unbiased (Gal´ ı and Gertler, 1999). So why should we worry about Imperfect Knowledge?

David F. Hendry (INET at Oxford Martin School) Imperfect Knowledge Edinburgh 2017 3 / 28

What is the problem? “It would be an understatement to say that economic forecasts are a constant disappointment to investors. The trouble arises because the forecasters’ models are fundamentally flawed. .... so-called New Keynesian models .... rarely pick up big economic shifts .... (which) are inherently unpredictable.” John Plender, Financial Times, April 22 2017

David F. Hendry (INET at Oxford Martin School) Imperfect Knowledge Edinburgh 2017 4 / 28

What is the problem? “It would be an understatement to say that economic forecasts are a constant disappointment to investors. The trouble arises because the forecasters’ models are fundamentally flawed. .... so-called New Keynesian models .... rarely pick up big economic shifts .... (which) are inherently unpredictable.” John Plender, Financial Times, April 22 2017 During a visit to LSE in 2009, Queen Elizabeth II asked Luis Garicano “why did no one see the the credit crisis coming?” Even earlier, Prakash Loungani (2001) claimed “The record of failure to predict recessions is virtually unblemished.” How could this dismal record happen given theorems [1]–[5]??

David F. Hendry (INET at Oxford Martin School) Imperfect Knowledge Edinburgh 2017 4 / 28

What is the problem? “It would be an understatement to say that economic forecasts are a constant disappointment to investors. The trouble arises because the forecasters’ models are fundamentally flawed. .... so-called New Keynesian models .... rarely pick up big economic shifts .... (which) are inherently unpredictable.” John Plender, Financial Times, April 22 2017 During a visit to LSE in 2009, Queen Elizabeth II asked Luis Garicano “why did no one see the the credit crisis coming?” Even earlier, Prakash Loungani (2001) claimed “The record of failure to predict recessions is virtually unblemished.” How could this dismal record happen given theorems [1]–[5]?? Because Imperfect Knowledge has profound consequences—far beyond forecast failure.

David F. Hendry (INET at Oxford Martin School) Imperfect Knowledge Edinburgh 2017 4 / 28

Route map (1) Five theorems about conditional expectations (2) Uncertainty, unpredictability and unanticipated shifts (3) Empirical location shifts (4) Imperfect knowledge and conditional expectations (5) Modelling tools to detect shifts (6) Conclusions

David F. Hendry (INET at Oxford Martin School) Imperfect Knowledge Edinburgh 2017 5 / 28

Uncertainty and unpredictability You are certain you are sitting here (pace Descartes).

David F. Hendry (INET at Oxford Martin School) Imperfect Knowledge Edinburgh 2017 6 / 28

Uncertainty and unpredictability You are certain you are sitting here (pace Descartes). But you are uncertain if my talk will be clear, amusing, or informative. You may be uncertain as to the truth of some statements after my talk.

David F. Hendry (INET at Oxford Martin School) Imperfect Knowledge Edinburgh 2017 6 / 28

Uncertainty and unpredictability You are certain you are sitting here (pace Descartes). But you are uncertain if my talk will be clear, amusing, or informative. You may be uncertain as to the truth of some statements after my talk. Uncertainty abounds, both in the world and in our knowledge thereof. But increased knowledge may help reduce our uncertainty. Unpredictability is irreducible uncertainty. There are three levels of unpredictability, dependent on the state of nature and our knowledge thereof. Some aspects of unpredictability are measurable and quantifiable in reasonable ways: probabilites can be assigned to represent that unpredictability, as in rolling fair dice.

David F. Hendry (INET at Oxford Martin School) Imperfect Knowledge Edinburgh 2017 6 / 28

Uncertainty and unpredictability You are certain you are sitting here (pace Descartes). But you are uncertain if my talk will be clear, amusing, or informative. You may be uncertain as to the truth of some statements after my talk. Uncertainty abounds, both in the world and in our knowledge thereof. But increased knowledge may help reduce our uncertainty. Unpredictability is irreducible uncertainty. There are three levels of unpredictability, dependent on the state of nature and our knowledge thereof. Some aspects of unpredictability are measurable and quantifiable in reasonable ways: probabilites can be assigned to represent that unpredictability, as in rolling fair dice. Some events are so unpredictable that reasonable probabilities cannot be assigned.

David F. Hendry (INET at Oxford Martin School) Imperfect Knowledge Edinburgh 2017 6 / 28

Unpredictability comes in three varieties: (a) intrinsic unpredictability A random variable X is unpredictable with respect to some information I, if knowing I does not change knowledge about X. The distribution DX(X) of X is unaffected by knowing I when

DX|I(X | I) = DX(X).

David F. Hendry (INET at Oxford Martin School) Imperfect Knowledge Edinburgh 2017 7 / 28

Unpredictability comes in three varieties: (a) intrinsic unpredictability A random variable X is unpredictable with respect to some information I, if knowing I does not change knowledge about X. The distribution DX(X) of X is unaffected by knowing I when

DX|I(X | I) = DX(X).

(a) Intrinsic unpredictability occurs in a known distribution: unknown knowns from chance distribution sampling; ‘independent errors’ in statistical theory; random numbers in a simulation... But which draw matters: bet on Red but get Black at Roulette. Called intrinsic unpredictability because it is a property of the random variable.

David F. Hendry (INET at Oxford Martin School) Imperfect Knowledge Edinburgh 2017 7 / 28

Illustrating intrinsic unpredictability

• riginal distribution
• 10
• 8
• 6
• 4
• 2

2 4 6 8 10 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

← 95% between → −2σ and 2σ

X

• riginal distribution

Normal distribution often the basis for probability calculations; ‘random sampling’ from a known distribution underpins much statistical inference: X is example of intrinsic unpredictability.

David F. Hendry (INET at Oxford Martin School) Imperfect Knowledge Edinburgh 2017 8 / 28

(b) Instance unpredictability (b) Instance unpredictability, or known unknowns:

• utliers from a known ‘fat-tailed’ distributions can occur at

unanticipated times, signs, and magnitudes–see Taleb (2007)

fat-tailed distribution Normal distribution

• 10
• 8
• 6
• 4
• 2

2 4 6 8 10 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

← 95% between → −2σ and 2σ

X

fat-tailed distribution Normal distribution

Sometimes observe what are called ‘black swan events’: X shows instance unpredictability–unknown magnitude, sign and timing, but can attach probabilities to such events.

David F. Hendry (INET at Oxford Martin School) Imperfect Knowledge Edinburgh 2017 9 / 28

(c) Extrinsic unpredictability (c) Extrinsic unpredictability or unknown unknowns:

• ccurs from unanticipated shifts of distributions.

Unknown numbers, signs, magnitudes & timings of such shifts. Cannot usually attach probabilities to their occurrence.

David F. Hendry (INET at Oxford Martin School) Imperfect Knowledge Edinburgh 2017 10 / 28

(c) Extrinsic unpredictability (c) Extrinsic unpredictability or unknown unknowns:

• ccurs from unanticipated shifts of distributions.

Unknown numbers, signs, magnitudes & timings of such shifts. Cannot usually attach probabilities to their occurrence. Most pernicious form of extrinsic unpredictability is a location shift: mean of the distribution of X changes from previous ‘level’ by unknown magnitude and sign at unanticipated time—as in Soros (2008). Can now get what seem initially to be ‘flocks of black swans’.

David F. Hendry (INET at Oxford Martin School) Imperfect Knowledge Edinburgh 2017 10 / 28

Illustrating extrinsic unpredictability and location shifts

fat-tailed distribution shift in distribution Normal distribution

• 10
• 8
• 6
• 4
• 2

2 4 6 8 10 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

← original mean Shifted mean →

fat-tailed distribution shift in distribution Normal distribution

Location shifts make new ordinary seem unusual relative to past.

David F. Hendry (INET at Oxford Martin School) Imperfect Knowledge Edinburgh 2017 11 / 28

Illustrating extrinsic unpredictability and location shifts

fat-tailed distribution shift in distribution Normal distribution

• 10
• 8
• 6
• 4
• 2

2 4 6 8 10 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

← original mean Shifted mean →

fat-tailed distribution shift in distribution Normal distribution

Location shifts make new ordinary seem unusual relative to past. Extrinsic unpredictability wrecks economic agents’ ability to plan inter-temporally: and leads to forecast failure. Irrational to hold ‘rational expectations’ when shifts occur.

David F. Hendry (INET at Oxford Martin School) Imperfect Knowledge Edinburgh 2017 11 / 28

Route map (1) Five theorems about conditional expectations (2) Uncertainty, unpredictability and unanticipated shifts (3) Empirical location shifts (4) Imperfect knowledge and conditional expectations (5) Modelling tools to detect shifts (6) Conclusions

David F. Hendry (INET at Oxford Martin School) Imperfect Knowledge Edinburgh 2017 12 / 28

Major UK and world historical events Dramatic shifts include: World War I; 1920–21 flu’ epidemic; 1926 general strike; 1930’s great depression; World War II; 1970’s oil crises; 2008–2012 financial crisis and world-wide recession. Key financial innovations & changes in credit rationing: personal cheques (1810s), telegraph (1850s), credit cards (1950s), ATMs (1960s); deregulating banks and building societies (1980s) etc. Many policy regime shifts:

• n-off gold standard till Bretton Woods (1945), floating exchange rates

(1973); ERM; Keynesian, Monetarism, inflation targeting policies; creation of EU and Euro zone; Brexit, etc. Huge changes in technology: electricity, refrigeration, telephones, TV, cars, flight, nuclear, medicine, computers, communications. Important evolving changes: globalization & development. But implications rarely foreseen before shifts occur.

David F. Hendry (INET at Oxford Martin School) Imperfect Knowledge Edinburgh 2017 13 / 28

Many shifts in post-war UK real GDP growth

Annual changes in UK real GDP Shifts selected at 0.5%

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

• 0.050
• 0.025

0.000 0.025 0.050 0.075 0.100

← Barber boom Oil crisis crash → ← Thatcher recession Lawson boom → and crash → ERM exit growth ↓ ‘Great Recession’ → Macmillan pre-election stimulus → Wilson expansion ← ← leave ERM £ devalued ↓

Annual changes in UK real GDP Shifts selected at 0.5%

Here, most shifts correspond to major economic policy changes: but even the growth rate is far from a stationary process.

David F. Hendry (INET at Oxford Martin School) Imperfect Knowledge Edinburgh 2017 14 / 28

Location shifts in UK population

Annual changes in UK Population Steps selected at 0.5%

1860 1880 1900 1920 1940 1960 1980 2000 2020

• 0.2
• 0.1

0.0 0.1 0.2 0.3 0.4 0.5

Annual changes in UK population, millions Annual changes in UK Population Steps selected at 0.5%

Annual changes in the UK population over 1870–2016, in millions

David F. Hendry (INET at Oxford Martin School) Imperfect Knowledge Edinburgh 2017 15 / 28

Anthropogenic: UK CO2 emissions per capita over 1860–2016

UK CO2 emissions per capita, tons p.a.

1875 1900 1925 1950 1975 2000 5.0 7.5 10.0 12.5

CO2 emissions, tons per capita →

2013→ ↑ 1860

UK CO2 emissions per capita, tons p.a.

UK CO2 emissions per capita, in tons per annum over 1860–2016.

David F. Hendry (INET at Oxford Martin School) Imperfect Knowledge Edinburgh 2017 16 / 28

Distributional shifts of total UK CO2 emissions per annum

UK CO2 emissions, 1860−1899 UK CO2 emissions, 1900−1939 UK CO2 emissions, 1940−1979 UK CO2 emissions, 1980−2016

100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 0.002 0.004 0.006 0.008 0.010 0.012

UK CO2 emissions, 1860−1899 UK CO2 emissions, 1900−1939 UK CO2 emissions, 1940−1979 UK CO2 emissions, 1980−2016

Sub-period distributions of UK CO2 emissions in millions of tonnes (Mt) per annum.

David F. Hendry (INET at Oxford Martin School) Imperfect Knowledge Edinburgh 2017 17 / 28

Forecast failure: DSGE Compass pointing in the wrong direction

Bank of England ex post COMPASS density GDP-growth ‘forecasts’ over Great Recession in blue and Statistical Suite forecasts in green. ONS data in black and Inflation Report forecasts in red.

http://bankunderground.co.uk/2015/11/20/how-did-the-banks-forecasts-perform-before-during-and-after-the-crisis David F. Hendry (INET at Oxford Martin School) Imperfect Knowledge Edinburgh 2017 18 / 28

Autoregressive forecasts of US GDP

US quarterly real GDP (in logs) 2000 2002 2004 2006 2008 2010 4.40 4.45 4.50 4.55 4.60 4.65 4.70 US quarterly real GDP (in logs)

Autoregressive forecasts of US GDP also go wrong over Great Recession. Source: Real Gross Domestic Product, Billions of Chained 2009 Dollars, Quarterly, Seasonally Adjusted Annual Rate. GDPC1 from Federal Reserve Economic Data. http://research.stlouisfed.org/fred2

David F. Hendry (INET at Oxford Martin School) Imperfect Knowledge Edinburgh 2017 19 / 28

Route map (1) Five theorems about conditional expectations (2) Uncertainty, unpredictability and unanticipated shifts (3) Empirical location shifts (4) Imperfect knowledge and conditional expectations (5) Modelling tools to detect shifts (6) Conclusions

David F. Hendry (INET at Oxford Martin School) Imperfect Knowledge Edinburgh 2017 20 / 28

Deconstructing conditional expectations In Euclidean Geometry, the angles of a triangle add to 1800–a famous theorem proved by generations of school children. Draw a triangle on a globe and add the angles–not 1800. Theorems need assumptions, and Euclid assumed a flat surface. But a globe is not flat: theorem is misleading outside its context.

David F. Hendry (INET at Oxford Martin School) Imperfect Knowledge Edinburgh 2017 21 / 28

Deconstructing conditional expectations In Euclidean Geometry, the angles of a triangle add to 1800–a famous theorem proved by generations of school children. Draw a triangle on a globe and add the angles–not 1800. Theorems need assumptions, and Euclid assumed a flat surface. But a globe is not flat: theorem is misleading outside its context. The five theorems about conditional expectations assume the distributions are constant: but just seen numerous ‘real world’ examples where that assumption is false. For inter-temporal calculations, all 5 fail when distributions shift. Imperfect Knowledge about shifts has deleterious consequences. Critics include Frydman and Goldberg (2007), Hendry and Mizon (2014), Hendry (2017), Hendry and Muellbauer (2017).

David F. Hendry (INET at Oxford Martin School) Imperfect Knowledge Edinburgh 2017 21 / 28

Route map (1) Five theorems about conditional expectations (2) Uncertainty, unpredictability and unanticipated shifts (3) Empirical location shifts (4) Imperfect knowledge and conditional expectations (5) Modelling tools to detect shifts (6) Conclusions

David F. Hendry (INET at Oxford Martin School) Imperfect Knowledge Edinburgh 2017 22 / 28

How to solve the impossible Having more candidate variables N than observations T, so N > T, to search over when selecting a model was once believed impossible. I accidently discovered a powerful way to solve this problem. Most contributors to Magnus and Morgan (1999) found models of food demand that were non-constant over the sample 1929–1952, so dropped that earlier data. To investigate why, yet replicate others’ models, in Hendry (1999) I added impulse indicators for all

• bservations pre-1952.

David F. Hendry (INET at Oxford Martin School) Imperfect Knowledge Edinburgh 2017 23 / 28

How to solve the impossible Having more candidate variables N than observations T, so N > T, to search over when selecting a model was once believed impossible. I accidently discovered a powerful way to solve this problem. Most contributors to Magnus and Morgan (1999) found models of food demand that were non-constant over the sample 1929–1952, so dropped that earlier data. To investigate why, yet replicate others’ models, in Hendry (1999) I added impulse indicators for all

• bservations pre-1952.

This revealed three very large ‘outliers’ due to a ‘US Great Depression food program’ and post-war de-rationing. To check that my model was constant over the period from 1953 on, I included impulse indicators for this later period. Lo! I had included more variables plus indicators than observations.

David F. Hendry (INET at Oxford Martin School) Imperfect Knowledge Edinburgh 2017 23 / 28

Modelling tools to detect shifts Formalised as impulse-indicator saturation, IIS has led to a statistical theory for modelling multiple location shifts. Autometrics, our latest computational tool includes indicator saturation methods for shifts and outliers of any magnitude and sign, at any number of time points. Approach extends to the discovery of causal models hidden in a welter of information, while retaining theory insights, even when more candidate variables than observations: see Hendry and Doornik (2014) and Hendry and Johansen (2015).

David F. Hendry (INET at Oxford Martin School) Imperfect Knowledge Edinburgh 2017 24 / 28

Key source

David F. Hendry (INET at Oxford Martin School) Imperfect Knowledge Edinburgh 2017 25 / 28

Route map (1) Five theorems about conditional expectations (2) Uncertainty, unpredictability and unanticipated shifts (3) Empirical location shifts (4) Imperfect knowledge and conditional expectations (5) Modelling tools to detect shifts (6) Conclusions

David F. Hendry (INET at Oxford Martin School) Imperfect Knowledge Edinburgh 2017 26 / 28

Conclusions Imperfect knowledge is ubiquitous–but some aspects of ignorance are more troublesome than others: lack of knowledge about shifts of distributions can lead to invalid theory, model break down, forecast failure incorrect policy responses. My talk had five main aims: 1] relate unpredictability to imperfect knowledge about shifts; 2] illustrate the empirical prevalence of location shifts; 3] derive implications for failures of rational expectations, 4] and the invalidity of inter-temporal mathematics of DSGEs; 5] yet note how to successfully model ever-changing worlds. I hope you are now certain the talk was worth hearing.

Thank you

David F. Hendry (INET at Oxford Martin School) Imperfect Knowledge Edinburgh 2017 27 / 28

References I

Clements, M. P., and Hendry, D. F. (2005). Guest Editors’ introduction: Information in economic forecasting. Oxford Bulletin of Economics and Statistics, 67, 713–753. Frydman, R., and Goldberg, M. D. (2007). Imperfect Knowledge Economics: Exchange Rates and Risk. Princeton, New Jersey: Princeton University Press. Gal´ ı, J., and Gertler, M. (1999). Inflation dynamics: A structural econometric analysis. Journal of Monetary Economics, 44, 195–222. Goldberger, A. S. (1991). A Course in Econometrics. Cambridge, Mass.: Harvard University Press. Hendry, D. F. (1999). An econometric analysis of US food expenditure, 1931–1989. in Magnus, and Morgan (1999), pp. 341–361. Hendry, D. F. (2017). Deciding between alternative approaches in macroeconomics. International Journal of Forecasting, forthcoming, with discussion. Hendry, D. F., and Doornik, J. A. (2014). Empirical Model Discovery and Theory Evaluation. Cambridge, Mass.: MIT Press. Hendry, D. F., and Johansen, S. (2015). Model discovery and Trygve Haavelmo’s legacy. Econometric Theory, 31, 93–114. Hendry, D. F., and Mizon, G. E. (2014). Unpredictability in economic analysis, econometric modeling and forecasting. Journal of Econometrics, 182, 186–195. Hendry, D. F., and Muellbauer, J. N. J. (2017). The future of macroeconomics: Macro theory and models at the Bank of

• England. Oxford Review of Economic Policy, forthcoming.

Hendry, D. F., and Trivedi, P. K. (1972). Maximum likelihood estimation of difference equations with moving-average errors: A simulation study. Review of Economic Studies, 32, 117–145. Loungani, P. (2001). How accurate are private sector forecasts? Cross-country evidence from consensus forecasts of

• utput growth. International Journal of Forecasting, 17, 419–432.

Magnus, J. R., and Morgan, M. S. (eds.)(1999). Methodology and Tacit Knowledge: Two Experiments in Econometrics. Chichester: John Wiley and Sons. Soros, G. (2008). The New Paradigm for Financial Markets. London: Perseus Books. Taleb, N. N. (2007). The Black Swan. New York: Random House. David F. Hendry (INET at Oxford Martin School) Imperfect Knowledge Edinburgh 2017 28 / 28