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Time series and panel data in econometrics
1. Times Series and Panel Data in
Econometrics
By
Ibrahim Nurudeen, PhD
Senior Lecturer, Shehu Shagari
University of Education, Sokoto,
Nigeria
1
2. Secondary Data
Secondary Data are basically, the data which
has already been collected, and it is therefore a
second hand piece of information.
Secondary source of data can be classified in to
• Time Series
• Volatility
&
• Panel Data
2
3. Time Series Analysis
• Time series can be classified in to analysis of time
series in a frequency domain and time series in
time domain.
• Time Series can also be divided in to linear and
non linear modeling approach
• For the sake of this discussion we are going to
discuss linear time series framework in a time
domain.
3
4. Evolution of Linear Time Series
Models
• Linear Regression Model
• Simultaneous Equation Model
• Vector Autoregressive model(VAR)
• Vector Error Correction Models(VECM)
• Structural Vector Autoregressive(SVAR)
• Factor Augmented Vector Autoregressive
model(FAVAR)
• FA-SVAR
• SFA-SVAR
4
6. Linear Regression Model
• Linear regression Model links relationship
between tw o variables called bi-variate or
among morethan two variables called multiple
regression model. Consider equation (1) below:
•
Where yt is the dependent variable and x’s are the
independent variable, and the term et refers to error
or stochastic.
Y
)
1
......(
..........
..........
..........
2
3
1
2
1 t
t e
x
x
y
6
7. Regression Model Assumptions
1. Linearity
2. Homoskedasticity
3. Serial Independence
4. Multicollinearity
5. Normality of the residuals
7
8. Limitations of Regression Models
• Theoretic Models: It is be applied in a situation
where we have an economic theory e.g Philips
Curve, or Okun’s Law
• Single Line Equation
• Static Nature
Due to the above Limitations, simultaneous
equation Modelling Procedure was introduced:
8
9. Simultaneous Equation Models
• Simultaneous Equation models serve the same purpose as
regression model, however, it allows for modelling of an
economy with more than one equation simultaneously. In
other word, sometimes there is need to study
interdependences among several dependent variables, in
this case, regression model can not help us. For example
economic analysis suggests that, price and quantity are
determined simultaneously, and therefore a full market
model is not captured in a single model. Equations (2) to
(4), gives a clear picture of simultaneous equation
example
•
9
12. Uses of Regression and Simultaneous
Equation Models
• Impact Analysis
• Forecasting of Series
12
13. Vector Autoregression
Due to limitations found in regression and SEM,
Christopher Sims(1980), came up with a different
modelling procedure, where each variable is treated
as endogenous variable and their historical
components as exogenous variables
Advantages
Atheoretic
Dyanamism/Historical Component
All variables in the system are treated as
endogenous variables
Impact Analysis
Structural Analysis
Forecasting of future through IRF and FEVD 13
14. Vector Autoregressive Model
• To understand the application of a VAR model,
Consider equation(5) below
)
5
......(
..........
.
..........
2
2
1
1
0 t
p
t
p
t
t
t e
w
A
w
A
w
A
v
w
14
15. Differenced Vector Autoregressive
Model(DVAR)
• When all the variables are not stable, and co-
integration does not exist among the variables,
then the long VAR in equation (5) above will be
difference t have a short run impact. The
differenced VAR is presented in eqn (6)
)
6
.........(
..........
..........
..........
..........
t
p
t
p u
w
wt
15
16. Vector Error Correction
Model(VECM)
• VECM is applied when all or some of the
variables are not stable/stationary, but co-
integration exist.(Details of stationarity and co-
integration comes later). VECM is presented in
eqn (7) below:
)
7
........(
..........
..........
..........
..........
1
1 et
e
y
y
y p
t
p
t
t
t
16
17. Application of VAR Procedure
• First step: Check the stochastic properties
• Second step: Check Co-integration
• Third Step : Apply VAR/VECM Model
Procedure
• If all variables are stationary at level, apply VAR
• If all variables are not stationary and co-integration
does not exist, apply VAR at fist difference
• If all variables or some of the variables not stationary
but co-integration exist, then apply VECM
17
18. Limitations of VAR
• Limited Number of Variables
• Dimensinality/ Over parameterization
• Loss of Information
18
19. Structural VAR Model
• To avoid the dimensionality problem and the loss of
parameters needed to solve the model, VAR model went
through development, such as SVAR and SVECM, where
structure is imposed on the variables, and that solves the
over-parameterization problem, but the limited information
problem still prevail. Similarly, despites the problems
mentioned, associated with SVAR/SVECM modeling, a
number of studies have applied the methodology for the
analysis of dynamic responses of macroeconomic
variables. These studies include; Blanchard and Qua
(1989), Gali (1992), Attahir (2016), Gottschalk (2001),
Abubakar and Jorthi (2016), Mihov (1998), Perroti
(2004), Kilian (2011), Ouliaris, Pagan and Retrespo
(2016) and Pfaff and Taunus (2008), Blanchard and
Perroti (2002) etc 19
20. SVAR Uses
• For the study of policy Shock/Mistake, e.g
Monetary policy Shock, Fiscal Policy Shock,
Crude oil Shock, exchange rate shock, etc
• Study of disentangled shock
• Study of Structural Parameters
• Study of contemporanoeus responses of series
e,g responses among, money, prices, and output
• Forecasting
20
21. Application of SVAR
• Where eqn(8)is the basic VAR model and eqn(9),
captures both reduced form and structural form
shocks.
• In order t impose restrictions on A or B matrix,
the following ways can be used
)
9
.......(
..........
..........
..........
..........
..........
)
8
..(
..........
..........
..........
..........
..........
)
(
t
t
Be
AU
et
Y
L
A
21
22. Ways of Imposing Restrictions on
SVAR Model
• Recursive Way, Sims(1980)
• World Restriction
• Based on Economic Theory
• Sign Restrictions
• Restriction based on DSGE
• Restriction based n Hetroskedasticity
However, the restriction period can be either
short run or long run
22
23. FAVAR Model
• Sequel to the limitation observed in SVAR
modeling, Stock and Watson (2005) extended
the methodology to factor augmentation. Here,
the procedure allowed the use of large
macroeconomic variables, and few factors will be
extracted from such large data set. This model can
accomodate 100 variables and above. And it
solves problem of limited information found in
SVAR
23
24. Application of FAVAR
)
11
..(
..........
..........
..........
)
10
.......(
..........
..........
..........
..........
2
1
1
t
t
t
t
t
t
t
j
t
t
v
Y
F
L
Q
Q
Y
F
e
y
f
X
24
25. FA-SVAR & S-FA-VAR & SFA-
SVAR
• In order take care of the criticism that the
estimates from equation 11 lack economic
meaning, the FAVAR of equation 11 could be
extended to include structural identification of
the factors, thus the model becomes FA-SVAR,
and could be specified as below;
et
Y
L
Ay t
t
)
(
2
1
25
26. Univariate Time Series Models
• Autoregressive Model(AR)
• Moving Average(MA)
• Autoregressive Moving Average(ARMA)
• ARIMA(pdq)
p
t
t y
y
0
p
t
t
t u
u
y
1
0
i
t
p
t
t
t y
u
u
y
2
1
1
0
26
27. Volatility Models
Univariate Volatility Models
• ARCH(Engel, 1982)
• GARCH(Bolleslev, 1986)
• Threshold Garch(Zakoain 1990, Glosten,
Jaganathan and Runkle, 1993)
• Other Models include: E-Garch(Nelson, 1991),
I-Garch,O Garch, Go Garch, Aparch etc
p
t
t
t e
h
2
1
0
i
t
j
p
t
t
t h
e
h
2
1
0
1
2
0
t
i
t
j
j
i
t
j
t U
d
B
h
h
27
29. Co-integration Tests
• Co-integrating Regression Durbin
Watson(CRDW)
• Engel Granger(1987) co-integrating Test
• Johansen(1991)
• Peseran, Shin, and Smith Bound testing
approach(1999,2000)
• Narayan K.(2005)
29
30. Procedure for Selecting Co-integration Test
• If all Variables are stationary at Level i.e I(0),
No need for co-integration
• If all Variables are stationary at first difference
i.e I(1), apply Johansen(1991)
• If there is a combination of I(0) and I(1), then
Apply ARDL(Pesaran, Shin, and Smith 1999)
30
31. PANEL DATAANALYSIS
• Panel Regression Model
Where i=1.......N= cross sectional unit
And t=1.....T=Time Series
The assumption of hetrogeneity on alpha can be possible
The common constant is also called pooled regression. It
assumed no differences among the cross sectional
dimensions.
it
it
it e
x
y
it
it
i
it e
x
y
31
32. Panel Models..
• Fixed and Random Effects
In the fixed effect, the constant is treated as group or
country specific
In general we can say in FE, each country differs in its
constant, while RE assumes each country differs in
error term.
Fixed Effect
Random Effect
it
it
it
it e
x
y
it
it
it
i
it e
x
x
v
y
2
2
1
)
(
32
33. Hausman Test (1978)
Hausman Test, 1978
Hausman test is formulated to assist in making a choice
between the fixed and Random effect
Ho: OLS and GLS are consistent, but OLS is inefficient
Ha: OLS is Consistent not GLS
• Panel ARDL
33
35. Unit-root/StationarityTest/Stochastic
Properties
• Levin and Lee(1992)
Assumes: Homogeneus
• Levin Lin and Chu
Assumes: Homogeneity)
• Im, Pesaran and Shin(1997)
Assumes Hetrogeneity and Balanced
• Maddala and Wu(1999):
Asumes Hetrogeneity and Unballanced
• Breitung(2000)
– Extension of LL&LLC, However, added trend which is missing in
their models
• Hadri(2000): Homogeneous, LM test while all above test are T
based test
• Choi(2001)
• Haris and Tzavalis(1999)
35
36. Panel Co-integration Tests
• Mc Coskey and Kao(1999)
• Kao(1998)
• Pedroni(1997,1999,2000)
• Larsson(2001)
• Banerjee, marcellino and osbet(2004)
• Bai and Ng(2004)
• Weterlund,2005a, 2005b)
• Westerlund(2007)
36
37. Alhamdulillahi Rabbil Alameen
• Ibrahim Nurudeen, PhD
Senior Lecturer, Shehu Shagari University of
Education, Sokoto,
Nigeria
37
