Forecasting Global Recessions in a GVAR Model of Actual and Expected Output in the G7

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1 Forecasting Global Recessions in a GVAR Model of Actual and Expected Output in the G Tony Garratt, Kevin Lee and Kalvinder Shields Ron Smith Conference London, June Lee (Ron Smith Conference) G Recessions London, June /

2 Motivation This paper considers two aspects of forecasting business cycles highlighted since the financial crisis of : First, given the global reach of the slowdown, we investigate the importance of incorporating cross-country interactions in a forecasting model. Second, we acknowledge the potential role of confidence and pessimism in initiating and propagating business cycle dynamics and the contribution of expectations data, obtained directly from surveys, to the calculation of output forecasts. We look at point forecasts and density forecasts judged in standard statistical terms and also forecast probabilities of recessionary events and the use of forecasts in decision-making. The modelling framework is a multi-country Global Vector Autoregressive (GVAR) model of actual and expected outputs in each country. Lee (Ron Smith Conference) G Recessions London, June /

3 Motivation (cont.) Related literature on global business cycles: large-scale structural econometric systems; e.g. the United Nations Project LINK, or the IMF s multi-regional model MULTIMOD - not easy to isolate the contribution of the global effects in these models more statistical, dynamic factor models identifying global, nation-specific and idiosyncratic shocks; e.g. Kose et al. (JIE, 8) - not typically used in forecasting potential role of confidence and expectation formation in Akerlof and Shiller s animal spirits, for example, and in the analyses of information rigidities in Barsky and Sims (AER, ), Blanchard et al (AER, ), and Coibion and Gorodnichenko (JPE, ). Garratt, Lee and Shields () [GLS] use the same GVAR model estimating a variance-based measure of the persistent effect of shocks: dynamic effects of shocks are complex and prolonged mainly because of the cross-country interactions. a decomposition shows global and national influences are split :, and sentiment and fundamentals split :. Lee (Ron Smith Conference) G Recessions London, June /

4 Motivation (cont.) This paper focuses on forecasting performance: judged by statistical criteria, nowcasts and forecasts are considerably enhanced by taking into account international links and the information available in survey data. relating to economic significance, both the expectations data and the international interactions are important in calculating density forecasts, in forecasting the occurrence of recessionary events defined at the national and G-wide levels and, judged through a fair bet exercise, in decision-making based on forecasts. The remainder of the talk: describe our modelling framework; use of density and probability forecasts in model evaluation using statistical and economic criteria, including the fair bet evaluation; forecasting exercise for the G economies over 99q-q Lee (Ron Smith Conference) G Recessions London, June /

5 Modelling Framework Assume that actual output is first-difference stationary and that expectational errors are stationary. Then we can write t y i,t t y i,t p tyi,t e ty i,t = G i + G ik t k y i,t k t k y i,t t k y tyi,t+ e tyi,t e i,t k e t k y i,t k k= t k yi,t+ k e t k yi,t k e () explaining actual growth measured with a one-period delay, and survey measures of nowcast growth and one-period-ahead growth. This model can be rewritten as (p + )-order vector autoregressive model in levels; i.e. where y i,t = ( ty i,t, t yi,t e, tyi,t+ e ) p+ y i,t = A i + A ik y i,t k + ε i,t, () k = cointegrating VAR in differences moving average representation in differences Lee (Ron Smith Conference) G Recessions London, June /

6 Modelling Framework (cont.) The VAR can be supplemented with global variables, y t = n j= w j y j,t p+ y i,t = B i + k= p+ B ik y i,t k + k= B ik y t k + ε i,t, () Arranging the country series into a n vector z t = (y,t,..,y n,t) and noting that y i,t = w i z t, the n country models can be stacked: so p+ z t = B + s= p+ B s z t s + z t = (I BW) (B p+ + s= s= B s Wz t s + ɛ t, () (B s + B s W)z t s + ɛ t ) () Lee (Ron Smith Conference) G Recessions London, June /

7 Decision-Making and Economic Evaluations The GVAR model can be used - e.g. through simulation - to produce forecasts of the probability of specified events taking place and to make decisions that depend on the events. Write the forecast density Pr(Z T +,T +h Z,T, MT GVAR ) where Z,T = {z, z,...,z T } and denote a recessionary event defined as a outcomes involving z T +, z T +,... by R(Z T +,T +h ). Then probability of recession= R Pr(Z T +,T +h Z,T, M GVAR T ) Z T +,T +h. () In a decision-making context, where an individual s objective function ν(r, R(Z T +,T +h )) depends on the outcome of a choice variable r and the occurrence of the recessionary event, the decision-maker s problem can be written as max r { ν(r, R(Z T +,T +h)) Pr ( Z T +,H Z,T, M GVAR T ) dz T +,T + Lee (Ron Smith Conference) G Recessions London, June / ()

8 Decision-Making and Economic Evaluations (cont.) For example, with the unconditional probability denoted by p, the payout in a symmetric fair bet with stake is s = and p p+ ν(r, R(Z T +,T +h )) is given by W T +h = [ (r T I (R)) + ( r T )( I (R)) ](s ) r T ( I (R)) I (R)( r T ) where I (.) is an indicator function depending on whether the event happens and r T = or depending on whether the decision-maker believes the event will happen based on their forecasting model. An economic evaluation of a model can be based on the sample counterpart of the criterion function evaluated over an out-of-sample evaluation period with the optimal value r t chosen based on forecasts: Ψ T = k T ν(r τ, R(Z τ+,τ+h )), (8) τ=t k Lee (Ron Smith Conference) G Recessions London, June 8 /

9 Forecasting Output and Recession in the G 99q-q Figure : G actual, current survey expectations and one-period-ahead survey expectations on output Comparison of models RW, AR, VAR, GVAR and GVAR Table : RMSE for output growth nowcasts and four-period ahead growth forecasts Table : Log predictive scores Table : Forecasting output drop recessions Table : Forecasting below peak recessions Lee (Ron Smith Conference) G Recessions London, June 9 /

10 ..8. t+yt tyet t yet Canada... t+yt tyet t yet France... 9q 9q q q q q q.8... t+yt tyet t yet Germany. 9q 9q q q q q q q 9q q q q q q t+yt tyet t+yt tyet t yet t yet US Japan. 9q 9q q q q q q t+yt tyet t yet Italy. 9q 9q q q q q q t+yt tyet t yet UK. 9q 9q q q q q q.. 9q 9q q q q q q Figure : Actual, Nowcast and One-Period-Ahead Expected Output

11 Table a: RMSE for Output Growth Nowcasts (Actual RMSE for RW, RatiorelativetoRWforothermodels) RW AR VAR GVAR GVAR Canada France Germany Italy Japan UK US Table b: RMSE for Four-Step-Ahead Output Growth Forecasts (Actual RMSE for RW, RatiorelativetoRWforothermodels) RW AR VAR GVAR GVAR Canada France Germany Italy Japan UK US Notes: RW denotes the random walk model for actual output growth in each country; AR denotes a univariate autoregressive (order ) model of actual output growth in each country; VAR denotes a -variable VAR (order ) model of actual output growth and current and oneperiod ahead survey expectations in each country; GVAR is the global version of AR; and GVAR is the global version of VAR. The denotes that the RMSE is significantly lower than that from the random walk model, working at the % level of significance, and applying the Giocomini-White () test of equal forecast performance

12 Table a: Average Log Predictive Scores for Output Growth Nowcasts (Average Log scores for RW, Scaled difference of log score from RW for other models) RW AR VAR GVAR GVAR Canada France Germany..... Italy Japan UK US Table b: Average Log Predictive Scores for Four-Step-Ahead Output Growth Forecasts (Actual Log scores for RW, Scaled difference of log score from RW for other models) RW AR VAR GVAR GVAR Canada France Germany Italy Japan UK US Notes: See notes to Table. The denotes that the log predictive score is significantly larger than that from the random walk model, working at the % level of significance, and applying the Giocomini-White () test of equal forecast. performance 8

13 VAR GVAR AR GVAR RW ACTUAL Figure : Probability of a Negative Nowcast in / of the G VAR GVAR AR GVAR RW ACTUAL Figure : Probability of 9 period moving average growth < % in / of G

14 VAR GVAR AR GVAR RW ACTUAL Figure : Probability of period T output less than previous peak in / of G VAR GVAR AR GVAR RW ACTUAL Figure : Probability of period T+ output less than previous peak in / of G.

15 Table a: Forecasting Output Drop Recessions ODR, q-q p Hit Rates Kuipers Score RW AR VAR GVAR GVAR RW AR VAR GVAR GVAR Canada % France % (, ).9 (, )..8 Germany % (, ).. Italy % Japan % UK % US % Majority 9% Average % (, ) Table a (cont.): Forecasting Output Drop Recessions ODR, q-q (Actual Return for RW, ImprovementoverRWforothermodels) Returns to Fair Bet (Symmetric) Returns to Fair Bet (Asymmetric) RW AR VAR GVAR GVAR RW AR VAR GVAR GVAR Canada France Germany Italy Japan UK US Majority Average Note: p is the unconditional probability of the event q-q. The figures in parentheses (.,.) below the Kuipers Scores show, respectively, the outcome of the static and dynamic versions 9

16 Table b: Forecasting Output Drop Recessions ODR, q-q p Hit Rates Kuipers Score RW AR VAR GVAR GVAR RW AR VAR GVAR GVAR Canada % (. ).. (. ) France % (, ).8 (, ) Germany % Italy 9% Japan % UK % US % Majority % Average % Table b (cont.): Forecasting Output Drop Recessions ODR, q-q (Actual Return for RW, ImprovementoverRWforothermodels) Returns to Fair Bet (Symmetric) Returns to Fair Bet (Asymmetric) RW AR VAR GVAR GVAR RW AR VAR GVAR GVAR Canada France Germany Italy Japan UK US Majority Average

17 Table a: Forecasting Below Peak Recessions BPR, q-q p Hit Rates Kuipers Score RW AR VAR GVAR GVAR RW AR VAR GVAR GVAR Canada % (, ).8 (, )...8 France % Germany 9% Italy % Japan % UK % US % Majority % Average % Table a (cont.): Forecasting Below Peak Recessions BPR, q-q (Actual Return for RW, ImprovementoverRWforothermodels) Returns to Fair Bet (Symmetric) Returns to Fair Bet (Asymmetric) RW AR VAR GVAR GVAR RW AR VAR GVAR GVAR Canada France Germany Italy Japan UK US Majority Average

18 Table b: Forecasting Below Peak Recessions BPR, q-q p Hit Rates Kuipers Score RW AR VAR GVAR GVAR RW AR VAR GVAR GVAR Canada 9% (, ) France 9% Germany % (, ). (, ). Italy % Japan 9% UK 9% US % Majority 9% Average 8% Table b (cont.): Forecasting Below Peak Recessions BPR, q-q (Actual Return for RW, ImprovementoverRWforothermodels) Returns to Fair Bet (Symmetric) Returns to Fair Bet (Asymmetric) RW AR VAR GVAR GVAR RW AR VAR GVAR GVAR Canada France Germany Italy Japan UK US Majority Average

19 Concluding Comments Four observations: None of the models of G outputs significantly outperform RW based on point forecasts only. But the more elaborate models do relatively well on density forecasts and this translates into better performance on event probability forecasting and, depending on the context, decision-making. In decision-making, the context is obviously important: the low payouts associated with the symmetric fair bet means decisions based on random walk as effective as those based on the more sophisticated model. But the more demanding decision context of the asymmetric fair bet translates into very different returns and a clear advantage for the more sophisticated models. In a simple horse-race, it is more important to include the cross-country interactions than to take into account the survey data results. But inclusion of survey data does improve forecasting performance. Counter-intuitively, since the surveys directly provide nowcasts on output, the contribution of the survey data is on longer-horizon rather than short-horizon forecasts. Lee (Ron Smith Conference) G Recessions London, June /

20 Concluding Comments (cont.) Despite media scepticism, economic models can provide good insights on future output dynamics and recessionary events, especially if they accommodate cross-country output interactions and information contained in surveys. But there is a need for a nuanced approach to representing predictions on output, providing forecasts of the entire range of possible outcomes and the likelihood of recesssionary events, rather than just point forecasts. Lee (Ron Smith Conference) G Recessions London, June /