MICA-BBVA: a Factor Model of Economic and Financial Indicators for - PowerPoint PPT Presentation

MICA-BBVA: a Factor Model of Economic and Financial Indicators for Short-term GDP Forecasting 6th Colloquium on Modern Tools for Business Cycle Analysis Máximo Camacho and Rafael Doménech Luxembourg, September 29, 2010

Introduction • Early assessment of economic evolution is crucial for governments and central banks, financial institutions, consumers... • Generally accepted: GDP growth rate • But statistical agencies publish GDP with about 1-2 months delay • Typical solution: economic indicators Shorter publication delay • Track GDP economic fluctuations • • In Spain GDP forecasting is specially problematic Long publication delay (1.5 months for Spanish growth rate) • Presence of missing values in the historical time series • Short length of some indicators . • Page 2

Introduction • Distinctive features of our model: Uses enlarged series of GDP growth and additional indicators • • Camacho and Pérez-Quiros (2009) use GDP since 1995 • Camacho and Sancho (2003) use IPI Includes financial indicators • • Camacho and Pérez-Quiros (2009) conclude that they are useless • Wheelock and Wohar (2009): do financial series lead growth rate? • This paper: some financial indicators lead the business cycle Examines forecasting accuracy in pseudo real time • • Replicate the characteristics of real time data publication Page 3

Indicators Effective Publication Data Series Source Sample delay transformation 2Q80- 1.5 Real GDP (GDP) SA, QGR INE 3Q09 months BBVA Feb01- based on Real credit card spending (CCS) 0 months SA, AGR Nov09 Servired & INE Jun86- European Consumer confidence (CC) 0 months SA, L Nov09 Commission BBVA Jan81- 1.5 Real wage income (RWI) AGR based on Oct09 months MEF Jan81- Electricity consumption (EC) MEF 1.5 month SA, TA, AGR Oct09 Jan87- European Industry confidence (IC) 0 months SA, L Nov09 Commission BBVA ERD Jan81- Registered unemployment (U) based on 1 month SA, AGR Oct09 INEM (MEI) Jan81- Social security affiliation (SSA) 1 month SA, AGR MEI Oct09 Bank of Jan81- Real credit to the private sector (RCPS) Spain and 2 months SA, AGR Sep09 INE Bank of Mortgage rate minus 12m Euribor Jan89- Spain & 2 months L Thomson (MR12E) Sep09 Financial Slope of the yield curve Nov87- Thomson 0 months L (SLOPE) Nov09 Financial Bank of Mortgage rate minus 12m Treasury Jan81- Spain & 2 months L Sep09 Thomson bill rate (MR12TBR) Financial Page 4

The model: mixing frequencies Model’s • How to deal with mixing frequencies in Kalman filter? dynamics Series are reduced to monthly indicators • Quarterly flow variable which are I(1) • • Proietti and Moauro (2006): exact filter but nonlinear (implies approximations) • Auroba, Diebold and Scotti (2007): exact filter but at the cost of assuming all the indicators to have a linear trend • Mariano and Murasawa (2003): approximate filter Simple mean approximated by geometric mean • Y * Good approximation of quarterly GDP ( ) if changes in the unobservable • t Y monthly GDP ( ) are small t æ Y + Y + Y ö ÷ ç - - ) 1/3 Y * = 3 t t 1 t 2 » 3 YY Y ( ÷ ç ÷ ç è ø - - t t t 1 t 2 3 Page 5

The model: mixing frequencies Model’s • Accordingly 1 dynamics = + + + ln Y * ( ln Y ln Y ln Y ) ln 3 t t t - 1 t - 2 3 • Quarterly growth rate 1 Y 1 Y 1 Y - - ln Y * - ln Y * = ln t + ln t 1 + ln t 2 - t t 3 3 Y 3 Y 3 Y - - - t 3 t 4 t 5 • Defining: º D y ln Y º - y * ln Y * ln Y - * t t t t t 3 • Hence 1 2 2 1 y * = y + y + y + y + y t t t - 1 t - 2 t - 3 t - 4 3 3 3 3 Page 6

The model: state space representation Model’s • There is an unobservable common factor that follows an AR(p1) process: dynamics = r + + r + x x ... x e t 1 t - 1 p 1 t - p 1 t • Monthly GDP growth y = b + y x u y = y y + + y y + e y u d u ... d u t y t t t 1 t - 1 p 2 t - p 2 t • Annual growth rates of hard and levels of soft indicators 11 å = b + z i x u i i = i i + + i i + e i u d u ... d u t i t - j t t 1 t q - p 3 t - p 3 t j = 0 • Financial indicators (in annual growth rates or in levels) may lead the cycle 11 å f z i = b x + u f f f f f f = + + + e u d u ... d u + - t i t h j t t 1 t q - p 3 t - p 3 t j = 0 Page 7

The model: state space representation Model’s • Observation equation (e.g., when p1=p2=p3=1 and h=1): dynamics æ x ö ÷ ç t + 1 ÷ ç ÷ ç x ÷ ç ÷ t ç ÷ ç ÷ ç ÷  b b b b ÷ æ 2 2 öç 2 1 1 2 ÷ ÷ ç ç y y y y b ÷ 0 0  0 1 0 0 ÷ç ç æ ö ÷ x y * ÷ç ç y 3 3 3 3 3 3 3 3 ÷ ÷ ç ÷ ç - t ç t 11 ÷ ÷ ÷ ç ç ç ÷ ÷ ÷ ç ç ÷ ÷ ç y * = b b b ÷ u Z 0   0   0 1 0 ç ÷ ç ÷ ç ÷ ç t ÷ it ÷ i i i ç ÷ ç ÷ ç ÷ ÷ç ç ÷ ç ÷ ç ÷ç Z * b b b 0 0 0 0 1  ç  è ø ÷ ÷ç ç ÷ ft f f f ÷ç ç ÷ ÷ ç ÷ è øç ÷ ç ÷ç y u ÷ ÷ ç t - 5 ÷ ç ÷ ç u i ÷ ç ÷ t ç ÷ ç ÷ ç ÷ f è ç u ø ÷ ÷ ç t ÷ ç Page 8

The model: dealing with missing observations Missing • Quarterly series are observed once each quarter observations • Some indicators start too late (soft) or end too soon (hard) • We follow Mariano and Murasawa (2003) • Substitute missing values by random draws N(0,1) ì ì Y if observable H if observable ï ï ï ï it it Y * =í H * = í it it ï ï q otherwise 0 otherwise ï î ï î t • While keeping all the matrices conformable, it has no impact on MLE • At each time t, Observed data are used to estimate the state vector • State vector and the idiosyncratic component are used to estimate missing • values Forecasting can be done by adding missing values at the end • Page 9

Results • Log likelihood and leads of financial indicators 3175 (0,0,9,0) 3170 (0,0,6,0) (0,0,12,0) (0,0,0,0) (0,0,3,0) 3165 log likelihood (3,3,9,3) 3160 (6,6,9,6) 3155 (9,9,9,9) 3150 0 3 6 9 12 Figure 1: Financial indicators at time t have been related to the common factor at time t+h. In this figure, the value of h for the slope of the yield curve appears on the horizontal axis and the log likelihood on the vertical axis. Numbers in brackets refer to the values of h for the four financial variables in the following order: (1) credit, (2) spread, (3) slope and (4) the mortgage rate minus 12m Treasury bill rate. Page 10

Page 11 Results

Results • Loading factors: Table 3 GDP CCS CC EC RWI IC U SSA RCPS MR12S SLOPE MR12TBR 0.185 0.038 0.037 0.040 0.045 0.050 -0.014 0.064 0.019 -0.018 0.022 -0.024 (9.8) (2.5) (3.6) (4.1) (13.4) (5.7) (3.2) (27.6) (3.9) (2.3) (2.3) (2.3) Factor loadings ( t -ratios are in parentheses) measure the correlation between the common factor and each of the indicators appearing in columns. See Table 1 for a description of the indicators. Page 12

Results • Common factor and Markov-switching Page 13

Results • Stylized forecasting procedure 08/15/08 08/15/08 11/15/08 11/15/08 02/15/09 02/15/09 05/15/09 05/15/09 08/15/09 08/15/09 GDP 08.2 GDP 08.2 GDP 08.3 GDP 08.3 GDP 08.4 GDP 08.4 GDP 09.1 GDP 09.1 GDP 09.2 GDP 09.2 GDP 08.2 GDP 08.2 GDP 08.3 GDP 08.3 GDP 08.4 GDP 08.4 GDP 09.1 GDP 09.1 GDP 09.2 GDP 09.2 GDP 09.3 GDP 09.3 A A A M M M J J J J J J A A A S S S O O O N N N D D D J J J F F F M M M A A A M M M J J J J J J A A A S S S 08/15/08-11/15/08 08/15/08-11/15/08 08/15/08-11/15/08 11/15/08-02/15/09 11/15/08-02/15/09 11/15/08-02/15/09 02/15/09-05/15/09 02/15/09-05/15/09 02/15/09-05/15/09 Backcasts 08.3 Backcasts 08.3 Backcasts 08.3 Nowcasts 08.4 Nowcasts 08.4 Nowcasts 08.4 Forecasts 09.1 Forecasts 09.1 Forecasts 09.1 Backcasts 08.4 Backcasts 08.4 Backcasts 08.4 Nowcasts 09.1 Nowcasts 09.1 Nowcasts 09.1 Forecasts 09.2 Forecasts 09.2 Forecasts 09.2 Backcasts 09.1 Backcasts 09.1 Backcasts 09.1 Nowcasts 09.2 Nowcasts 09.2 Nowcasts 09.2 Forecasts 09.3 Forecasts 09.3 Forecasts 09.3 Page 14

Page 15 • Backasts and nowcasts: Results

Results • Predictive accuracy: Back Now Fore MSE-MICA 0.1377 0.1938 0.2596 MSE-RW 0.3513 0.3567 0.3605 MSE-MICA/MSE-RW 0.3919 0.5432 0.7201 MSE-AR 0.2069 0.2802 0.3089 MSE-MICA/MSE-AR 0.6652 0.6916 0.8404 Equal predictive accuracy tests DM-RW 0.0001 0.0004 0.0046 DM-AR 0.0002 0.0008 0.0581 MDM-RW 0.0001 0.0004 0.0049 MDM-AR 0.0002 0.0009 0.0590 WSR-RW 0.0000 0.0000 0.0000 WSR-AR 0.0000 0.0000 0.0000 MGN-RW 0.0000 0.0000 0.0000 MGN-AR 0.0000 0.0000 0.0000 MR-RW 0.0000 0.0000 0.0000 MR-AR 0.0000 0.0000 0.0000 Encompassing tests RW/MICA 0.0000 0.0000 0.0000 AR/MICA 0.0000 0.0000 0.0000 ˆ ˆ y - y = a + a y + e t t i , 0 1 t MICA , t Page 16