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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

Page 2

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 3

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 4

Indicators

Series

Effective Sample Source Publication delay Data transformation

Real GDP (GDP)

2Q80- 3Q09

INE

1.5 months SA, QGR

Real credit card spending (CCS)

Feb01- Nov09

BBVA based on Servired & INE

0 months SA, AGR

Consumer confidence (CC)

Jun86- Nov09

European Commission

0 months SA, L

Real wage income (RWI)

Jan81- Oct09

BBVA based on MEF

1.5 months AGR

Electricity consumption (EC)

Jan81- Oct09

MEF

1.5 month SA, TA, AGR

Industry confidence (IC)

Jan87- Nov09

European Commission

0 months SA, L

Registered unemployment (U)

Jan81- Oct09

BBVA ERD based on INEM (MEI)

1 month SA, AGR

Social security affiliation (SSA)

Jan81- Oct09

MEI

1 month SA, AGR

Real credit to the private sector (RCPS)

Jan81- Sep09

Bank of Spain and INE

2 months SA, AGR

Mortgage rate minus 12m Euribor (MR12E)

Jan89- Sep09

Bank of Spain & Thomson Financial

2 months L

Slope of the yield curve (SLOPE)

Nov87- Nov09

Thomson Financial

0 months L

Mortgage rate minus 12m Treasury bill rate (MR12TBR)

Jan81- Sep09

Bank of Spain & Thomson Financial

2 months L

Page 5

The model: mixing frequencies

• How to deal with mixing frequencies in Kalman filter?
• 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
• Good approximation of quarterly GDP ( ) if changes in the unobservable

monthly GDP ( ) are small ( )1/3

1 2 * 1 2

3 3 3

t t t t t t t

Y Y Y Y YY Y

• +

+ æ ö ÷ ç = » ÷ ç ÷ ç è ø

* t

Y

t

Y

Model’s dynamics

Page 6

The model: mixing frequencies

• Accordingly
• Quarterly growth rate
• Defining:
• Hence

( )

* 1 2

1 ln ln ln ln ln 3 3

t t t t

Y Y Y Y

• =

+ + +

1 2 * * 3 3 4 5

1 1 1 ln ln ln ln ln 3 3 3

t t t t t t t t

Y Y Y Y Y Y Y Y

• =

+ +

* * * 3

ln ln

t t t

y Y Y - º

• ln

t t

y Y º D

* 1 2 3 4

1 2 2 1 3 3 3 3

t t t t t t

y y y y y y

• =

+ + + +

Model’s dynamics

Page 7

The model: state space representation

• There is an unobservable common factor that follows an AR(p1) process:
• Monthly GDP growth
• Annual growth rates of hard and levels of soft indicators
• Financial indicators (in annual growth rates or in levels) may lead the cycle

1 1 1 1

...

t t p t p t

x x x e r r

• =

+ + +

y t y t t

y x u b = +

1 1 2 2

...

y y y y y y t t p t p t

u d u d u e

• =

+ + +

11 i i t i t j t j

z x u b

• =

= +

å

1 3 3

...

i i i i i i t t q p t p t

u d u d u e

• =

+ + +

11 f i t i t h j t j

z x u b

+ - =

= +

å

1 3 3

...

f f f f f f t t q p t p t

u d u d u e

• =

+ + +

Model’s dynamics

Page 8

The model: state space representation

• Observation equation (e.g., when p1=p2=p3=1 and h=1):

Model’s dynamics

1 * 11 * * 5

2 2 2 1 1 2 1 3 3 3 3 3 3 3 3 1 1

t t y y y y y t t y t it i i i ft f f f y t i t f t

x x x y u Z Z u u u b b b b b b b b b b b

+

• æ

ö ÷ ç ÷ ç ÷ ç ÷ ç ÷ ç ÷ ç ÷ ÷ ç ÷ æ öç ÷ ç ÷ ç ÷ ÷ç ç æ ö ÷ ÷ç ç ÷ ÷ ç ç ç ÷ ÷ ç ç ç ÷ ÷ ç ç ÷ ç ÷ = ç ç ÷ ÷ ç ç ÷ ç ÷ ç ç ÷ ÷ç ç ÷ ç ç ÷ç ç è ø ÷ç ç ÷ç ÷ ç ç ÷ è øç ç ÷ç ç ç ç ç ç ç ç ç è ø ç ç         ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷

Page 9

The model: dealing with missing observations

• Quarterly series are observed once each quarter
• 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)
• 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

Missing

• bservations

*

if observable

• therwise

it it t

Y Y q ì ï ï =í ï ï î

*

if observable

• therwise

it it

H H ì ï ï = í ï ï î

Page 10

Results

• Log likelihood and leads of financial indicators

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. 3150 3155 3160 3165 3170 3175 3 6 9 12 log likelihood (9,9,9,9) (0,0,9,0) (0,0,6,0) (0,0,3,0) (0,0,0,0) (0,0,12,0) (3,3,9,3) (6,6,9,6)

Page 11

Results

Page 12

Results

• Loading factors:

Table 3

GDP CCS CC EC RWI IC U SSA RCPS MR12S SLOPE MR12TBR 0.185 (9.8) 0.038 (2.5) 0.037 (3.6) 0.040 (4.1) 0.045 (13.4) 0.050 (5.7)

• 0.014

(3.2) 0.064 (27.6) 0.019 (3.9)

• 0.018

(2.3) 0.022 (2.3)

• 0.024

(2.3) Factor loadings (t-ratios are in parentheses) measure the correlation between the common factor and each

• f the indicators appearing in columns. See Table 1 for a description of the indicators.

Page 13

Results

• Common factor and Markov-switching

Page 14

Results

• Stylized forecasting procedure

08/15/08-11/15/08 11/15/08-02/15/09 02/15/09-05/15/09

08/15/08 GDP 08.2 11/15/08 GDP 08.3 02/15/09 GDP 08.4 05/15/09 GDP 09.1 08/15/09 GDP 09.2

A M J J A S O N D J F M A M J J A S GDP 08.2 GDP 08.3 GDP 08.4 GDP 09.1 GDP 09.2 GDP 09.3

Backcasts 08.3 Nowcasts 08.4 Forecasts 09.1 Backcasts 08.4 Nowcasts 09.1 Forecasts 09.2 Backcasts 09.1 Nowcasts 09.2 Forecasts 09.3

08/15/08-11/15/08 11/15/08-02/15/09 02/15/09-05/15/09 08/15/08-11/15/08 11/15/08-02/15/09 02/15/09-05/15/09

08/15/08 GDP 08.2 11/15/08 GDP 08.3 02/15/09 GDP 08.4 05/15/09 GDP 09.1 08/15/09 GDP 09.2

A M J J A S O N D J F M A M J J A S A M J J A S O N D J F M A M J J A S GDP 08.2 GDP 08.3 GDP 08.4 GDP 09.1 GDP 09.2 GDP 09.3

Backcasts 08.3 Nowcasts 08.4 Forecasts 09.1 Backcasts 08.3 Nowcasts 08.4 Forecasts 09.1 Backcasts 08.4 Nowcasts 09.1 Forecasts 09.2 Backcasts 08.4 Nowcasts 09.1 Forecasts 09.2 Backcasts 09.1 Nowcasts 09.2 Forecasts 09.3 Backcasts 09.1 Nowcasts 09.2 Forecasts 09.3

Page 15

Results

• Backasts and nowcasts:

Page 16

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

, 1 ,

ˆ ˆ

t t i t MICA t

y y a a y e

• =

+ +

Page 17

Conclusions

• We have proposed an extension of the Stock and Watson (1991) single-index

dynamic factor model for the Spanish quarterly GDP growth.

• The model combines information from real and financial indicators with different

frequencies, short samples and publication lags.

• We find that the common factor reflects the behavior of the Spanish GDP growth

during expansions and contractions very well.

• We show that financial indicators are useful for forecasting output growth

especially when assuming that some financial variables lead the common factor.

• We provide a simulated real-time exercise, showing that the model is a valid tool

to be used for short-term analysis.

• Future extensions:
• Measures of the economic activity at frequencies higher than monthly.
• Models for the aggregate demand components.

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