Transcript Constructing Leading Economic Indicators using DFMx

Constructing Leading Economic
Indicators for the Philippine Economy
using Dynamic Factor Models
Dennis Mapa, Joselito Magadia, Manuel Leonard Albis
School of Statistics
University of the Philippines, Diliman
13th National Convention on Statistics
October 3-4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
Outline of the Presentation
I.
II.
The GDP and LEIS
Mixed Frequency Models for GDP
a. Model 1: Hybrid DFM-VAR
b. Model 2: DF-Mixed Frequency Model
c. Forecasting Performance
IV. Conclusion
13th National Convention on Statistics
October 3-4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
The Gross Domestic Product
• Gross Domestic Product (GDP), published by the
Philippine Statistics Authority (PSA), is the broadest
measure of the overall economic activity
• The official GDP estimates are released by the PSA about
60 days after the reference quarter for the 1st, 2nd and 3rd
Quarters and 30 days after for the 4th Quarter
• This delay is the reason why researchers are interested in
alternative methodologies to provide insights on the “real
time economic activity” using economic indicators that
are available at a higher frequency (e.g. monthly, weekly,
daily) than the quarterly GDP
13th National Convention on Statistics
October 3-4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
The Leading Economic Indicator
• A timely assessment on the movements of the GDP is
important to be able to guide policy makers to come up
with appropriate policies to mitigate, say the impact of a
shock
• Leading Economic Indicator System (LEIS), developed
jointly by the PSA and the National Economic and
Development Authority (NEDA)
• It provides a one-quarter-ahead forecast of the movement
of the GDP and seeks to answer the question whether the
GDP is expected to go up or go down in the succeeding
quarter
13th National Convention on Statistics
October 3-4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
Challenges Encountered
• Short Time Series Horizon - Practitioners have hundreds
of series at their disposal, although most of them are not
desirably long enough (e.g. 20 to 40 years of quarterly
data)
• Mismatched frequencies of data – Available economic
indicators have different frequencies, i.e. CPI is reported on
a monthly basis, exchange rate reported daily, and GDP
reported quarterly
• Aggregation – How to create a composite index of
economic movement from incomplete and mismatched
frequencies of data?
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October 3-4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
Objectives of Study
• Provide alternative models to temporal aggregation by
proposing a multi-frequency model.
• Specifically, estimate a model with quarterly series on the
left-hand side (GDP growth) and monthly economic
indicators as explanatory variables (right-hand side)
• To develop and evaluate potential models in nowcasting
both the movements and the growth rates of the
country’s GDP:
1. Hybrid Dynamic Factor-Vector AutoRegressive (DFVAR) model
2. Dynamic Factor-Mixed Frequency (DF-MF) model
13th National Convention on Statistics
October 3-4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
Contributions to the LEIS
• Interaction of multi-frequency variables can be
assessed without resorting to data aggregation (e.g.
monthly exports can be used to predict intra-quarter
value of GDP)
• A multi-frequency model can generate monthly
forecasts (nowcast) using monthly economic
variables.
13th National Convention on Statistics
October 3-4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
II. Mixed Frequency Models
for GDP
13th National Convention on Statistics
October 3-4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
Indicators of Economic Movement
Variable
Gross Domestic Product (Official Seasonally Adjusted Series)
National Government Expenditures
National Government Revenues
Government Spending under GFCE (COE less Interest Payments less
Subsidy)
Public Construction Spending (Infrastructure & other capital outlays + Capital
transfers to LGUs)
Exports
Exchange Rate
Gross International Reserves
Imports
Terms of Trade
Peso/Euro exchange rate
Peso/SGD exchange rate
Peso/yen exchange rate
Remittances (Cash)
13th National Convention on Statistics
October 3-4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
Indicators of Economic Movement
Variable
PSEI
Consumer Price Index
Deposit rate: Savings
Dubai Crude
Libor 3m
M2: Money Supply
Manufacturing: Value of Production Index
Retail Sale: Price of Rice (Regular-milled)
Sibor 3M
Tbill rate:364
Tbill rate: 91
Time deposit rate (Long-term)
Time deposit rate(Short-term)
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October 3-4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
Indicators of Economic Movement
Variable
Visitor arrival
Wholesale Price Index
Meralco Sales
Bank Average Lending Rate
UKB Loans Outstanding
Registered Stock Corporations and Partnership
Business Expectation Survey (Current Quarter)
Business Expectation Survey (Next Quarter)
Consumer Expectation Survey (Current Quarter)
Consumer Expectation Survey (Next Quarter)
13th National Convention on Statistics
October 3-4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
Preliminary Tests:
Unit Root and Seasonality
• Prior to building the models, the time series data are
tested for the presence of unit root/s using the
Augmented Dickey-Fuller and the Dickey-FullerGeneralized Least Squares tests
• For series with seasonality, the corresponding
seasonally-adjusted values may be generated using
the X-13/12 procedure
• Corresponding transformations were applied on the
series if necessary
13th National Convention on Statistics
October 3-4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
Model 1: Hybrid DFM-VAR
13th National Convention on Statistics
October 3-4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
Hybrid Dynamic Factor VAR Model
• The procedure closely follows the approach of Chow
and Choy (2009) in analyzing business cycles in
Singapore that used Principal Components Analysis in
the extraction of the latent dynamic factors
• The Hybrid DFM-VAR model involves a two-step
process:
Step 1: Generate the dynamic factors using Principal
Components Analysis (PCA) – basically to reduce the
dimension of the data
Step2 : Run the Vector AutoRegressive (VAR) Model
using the aggregated factors, additional “stand alone”
variables, and GDP
13th National Convention on Statistics
October 3-4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
Factors and Stand Alone Variables
• The PCA suggested six factors generally named as:
(1) Prices, (2) Exchange Rates, (3) Interbank Offered
Rates, (4) Investments, (5) Trade, (6) Spending
• Three stand-alone variables were selected: (1)
Remittances, (2) Visitors, (3) Business Expectations
Survey outlook
Factor 1
WPI, Price of Dubai Crude, CPI, Price of Rice
Factor 2
Exchange Rates: Yen, Euro, USD, SGD
Factor 3
LIBOR, SIBOR
TBILL 364, TBILL, Short-Term TD Rate, SEC Registered
Corporations, Manufacturing Value of Production Index
Terms of Trade, Exports, Money Supply, Imports, PSEI
Factor 4
Factor 5
Factor 6
National Government Expenditure, Public Construction
Spending Government Spending
13th National Convention on Statistics
October 3-4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
Vector Autoregressive Model
• The approach of Sims (1980) was to view all variables
as endogenous
• Each endogenous variables by regressing its past
values and the past values of the other variables in
the system
• VAR(1)
𝐺𝐷𝑃𝑡 = 𝑎10 + 𝑎11 𝐺𝐷𝑃𝑡−1 + 𝐚12 𝐗 𝑡−1 + 𝑒1𝑡
Model:
𝐗 𝑡 = 𝐚20 + 𝑎21 𝐺𝐷𝑃𝑡−1 + 𝐚22 𝐗 𝑡−1 + 𝑒2𝑡
13th National Convention on Statistics
October 3-4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
Performance of Hybrid DFM-VAR
• Percentage of correctly predicted
movement of GDP (seasonally adjusted):
77%
• Mean Error in Forecasting GDP growth
(seasonally adjusted): 0.38 percentage
point
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October 3-4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
Model 2: DF-Mixed
Frequency Model
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The DF-Mixed Frequency Model
• The procedure closely follows the approach of Gerlach and
Yiu (2004) in nowcasting the GDP of Hong Kong
• The DFM-Mixed Frequency model involves a three-step
process:
Step 1: Determine the potential variable groupings using
PCA
Step 2: Extract the dynamic factors from each of the
variable groupings using State-Space DFM
Step 3: Estimate a State-Space Time Varying Model for
GDP
13th National Convention on Statistics
October 3-4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
State-Space Model
• The extraction of the latent dynamic factors and the
prediction of GDP was done using the State-Space model
• The State-space model (Kalman 1960) is a general timeseries model for expressing dynamic systems that involve
unobserved state variables
• A state-space model consists of two equations:
– Measurement Equation: Describes the relation between
observed variables (data) and unobserved state variables
– Transition Equation: Describes the dynamics of the
state variables; it has the form of a first-order difference
equation in the state vector
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October 3-4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
State-Space Model:
Dynamic-Factor Model
𝑦1𝑡
𝑦2𝑡
𝑐𝑡
𝑧1𝑡
𝑧2𝑡
Measurement Equation
𝑐𝑡
𝛾1 1 0 𝑧
=
1𝑡 , 𝑦𝑡 = 𝐻𝑡 𝛽𝑡
𝛾2 0 1 𝑧
2𝑡
Transition Equation
𝑐𝑡−1
𝑣𝑡
𝜙1 0 0
= 0 𝛼1 0 𝑧1,𝑡−1 + 𝑒1𝑡 , 𝛽𝑡 =
𝑒2𝑡
0
0 𝛼2 𝑧2,𝑡−1
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October 3-4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
State-Space Model:
Time-Varying-Parameter Model
Measurement Equation
𝐺𝐷𝑃𝑡 = 𝐹1𝑡
𝜙1 0
𝛽1𝑡
𝛽2𝑡 = 0 𝜙2
…
⋮ ⋮
𝛽𝑘𝑡
0 0
𝐹2𝑡
… 𝐹𝑘𝑡
𝛽1𝑡
𝛽2𝑡
+ 𝑒𝑡 , 𝑦𝑡 = 𝑥𝑡 𝛽𝑡 + 𝑒𝑡
⋮
𝛽𝑘𝑡
Transition Equation
𝑣1𝑡
… 0 𝛽1,𝑡−1
𝑣2𝑡
… 0 𝛽2,𝑡−1
+ ⋮ , 𝛽𝑡 = 𝜇 + 𝐹𝛽𝑡−1 + 𝑣𝑡
⋱
⋮
⋮
𝑣𝑘𝑡
… 𝜙𝑘 𝛽𝑘,𝑡−1
13th National Convention on Statistics
October 3-4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
Predicting GDP Growth
Month
QTR
2001Q1
2001Q2
2001Q3
2001Q4
Seasonally
Adjusted
GDP
0.3
1.2
1.2
0.3
2001JAN
Data Conversion 2001FEB
2001MAR
2001APR
GDP growth
rates are treated 2001MAY
2001JUN
as a monthly
2001JUL
series with
2001AUG
missing
2001SEP
observations
2001OCT
2001NOV
2001DEC
13th National Convention on Statistics
October 3-4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
Seasonally
Adjusted
GDP
.
.
0.3
.
.
1.2
.
.
1.2
.
.
0.3
The Kalman Filter
Algorithm will
estimated the missing
GDP values from the
dynamic factors and
stand-alone variables
The estimated model is
also used in forecasting
Performance of DF-Mixed Frequency
• Percentage of correctly predicted
movement of GDP (seasonally adjusted):
94%
• Mean Error in Forecasting GDP growth
(seasonally adjusted): 0.59 percentage
point
13th National Convention on Statistics
October 3-4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
Conclusions
• This paper proposes models in nowcasting the movement and
growth rates of the country’s quarterly Gross Domestic Product
(GDP) using 32 monthly variables and 1 quarterly indicator, in
addition to the one- and two-factor DF model
• The DF-VAR and DF-MF are alternative models to the usual
time series econometric models used in forecasting GDP growth
rates utilizing temporal aggregation
• The assessment of the models, in terms of the percentage of
correctly tracking the movement of the GDP, suggests that
hybrid models are promising as nowcasting tools and can serve
as alternative (and better) models to the current LEIS used by
the NEDA and PSA.
13th National Convention on Statistics
October 3-4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
Acknowledgements
• The authors acknowledge the support of the National
Economic and Development Authority (NEDA) and the
Bangko Sentral ng Pilipinas (BSP) for this research
• The author is indebted to the research support
provided by the members of the Poverty and Hunger
Research Laboratory of the School of Statistics,
University of the Philippines.
13th National Convention on Statistics
October 3-4, 2016, EDSA Shangri-La Hotel, Mandaluyong City