Caution: This tutorial is only a guide and should not be adopted in its entirety. Endeavour to consult your tutor and other resource materials for proper guidance!
Introduction
The dissertation
fervor is heating up with the usual twists and turns. In view of these and in
response to readers’ requests, I will be starting a series of lectures on how to run time
series and panel data analyses. These will be in parts and supported with short
video tutorials posted to YouTube (so ensure to hook up to get the hands-on
training). In order not to leave anyone out, these practical lectures will be
carried out using three (3) analytical packages that is common among final-year
students – Stata, EViews and Excel. Also, real country-level and longitudinal data will be used
(but subject to my modifications to prevent unethical conduct from readers).
Lastly, only quantitative research will be addressed.
For time series analysis, the lectures will only cover: data sourcing, model
specification, lag selection, unit root testing, cointegration test, vector
autoregressive model (VAR), autoregressive distributed lag model (ARDL), vector
error correction mechanism (VECM), Granger causality tests, CUSUMSQ test and
other post-estimation tests. While for panel data analysis, the lectures will only cover:
setting up a panel data in Stata and EViews, data sourcing, model
specification, Hausman test, fixed effects (FE) model, random effects (RE)
model and generalised methods of moments (GMM).
So, in order to
get prompt tutorials, the moment I click the “post” button, I will encourage
you to subscribe for these blog posts. Use the “Follow by Email”
menu on my blog https://cruncheconometrix.blogspot.com.ng,
activate the link once you receive the notification in your email (check your
spam box too) and you are good to go! Likewise, follow that up by subscribing
to my YouTube videos for those short hands-on video clips. Click on this link CrunchEconometrix YouTube videos and subscribe!
Data
Sourcing
“I can’t get
data!!!”, “what’s a proxy?”, “I have data but not for all the groups”,“ how do I
go about modeling my theoretical framework?”, “how do I construct my empirical
model?”, “in fact, I’m confused!”…so many questions and believe me the
chattering seems endless. First, I always tell students to relax! Secondly, I
tell them that the moment the research area has been identified, and the topic
streamlined, the next thing to do is to go on data-search. Okay, think about this:
of what use is an empirical research if there is no data (or you have
insufficient data to test your hypothesis)? So before, you proceed to writing
chapter 1 (that is, the study background), make certain that you have the data
handy.
Primary
Data Sources
Regardless of
the field of study or research discipline, primary data gathering requires the
use of questionnaires, interviews, focus group discussions etc. It may require
one of these or a combination of 2 or 3 data-gathering methods. So, if you are using
primary data, ensure to get out these materials and distribute to the
respondents in order to harvest responses within the shortest time frame. Getting
a good number of responses is a precursor to having a quality research and unbiased
results. However, these structured tutorials will not be extended to analysing
primary data….my sincere apologies!
Secondary
Data Sources
Since, research
is not limited to those in the field of economics, it is important that
researchers identify those databases hosting the relevant data required for their
work. As an economist, I will indicate some databases/sources where students
can go source for their data. Here are some which can be
accessed (for macro and micro datasets):
IEA Coal Information
IEA CO2 Emissions from Fuel Combustion
IEA Electricity information
IEA Energy Prices and Taxes
IEA Energy Technology Research and Development
Database
IEA Natural Gas Information
IEA Oil Information
IEA Renewables Information
IEA World Energy Statistics and Balances
ILO Key Indicators of the Labour Market
IMF Balance of Payment Statistics
IMF Direction of Trade Statistics
IMF Government Finance Statistics
IMF International Financial Statistics
IMF World Economic Outlook
OECD Education Statistics
OECD Globalisation
OECD International Development
OECD International Direct Investment Statistics
OECD International Migration Statistics
OECD International Trade by Commodities Statistics
OECD Main Economic Indicators
OECD Main Science and Technology Indicators
OECD National Accounts
OECD Quarterly Labour Force Statistics
OECD Services Statistics
OECD Social Expenditure Database
OECD Structural Analysis
UNIDO Industrial Demand Supply
UNIDO Industrial Statistics
World Bank Global Development Finance
World Bank World Development Indicators
World Bank Africa Development Indicators
Other sources of international data include but not
limited to:
World Bank - http://data.worldbank.org/data-catalog/
International Monetary Fund - http://www.imf.org/external/data.htm#data
United Nations - http://data.un.org/
Data on aid flows complied by OECD - http://www.oecd.org/dac/stats/
NBER data sets - http://www.nber.org/data/
For information from over 256 and regions since 1960,
the accessible databases are:
World Development Indicators
Global Development Finance
The African Development Indicators
Doing Business
Education Statistics
Enterprise Surveys
Gender Statistics
Health Nutrition and Population Statistics
Millennium Development Goals
Worldwide Governance Indicators
Endeavour to
check out those sites that are relevant to your study.
Note: it is expected that you state your data source in
your thesis/dissertation and the years of coverage say 1980 to 2016, or 1970 to
2015 etc.
What
is a Panel Data?
The panel data
approach pools time series data with cross-sectional data. Depending on the
application, it can comprise a sample of individuals, firms, countries, or
regions over a specific time period. The general structure of such a model
could be expressed as follows:
Yit
= a
+ bXit
+ uit
where uit ~ IID(0, s2),i = 1,2,…,N
individual-level observations, and t
= 1, 2,…,T time series observations.
In this
application, it is assumed that Yit
is a continuous variable. The panel data model is simply where the observations
of each individual, firm or country over time are stacked on top of each
another. This is the standard pooled model where intercepts and slope
coefficients are homogeneous across all N
cross-sections and through all T time
periods. The application of ordinary least squares (OLS) to this model ignores
the temporal and spatial dimension inherent in the data and thus throws away
useful information. It is important to note that the temporal dimension
captures the ‘within’ variation in
the data while the spatial dimension captures the ‘between’ variation in the data. The pooled OLS estimator exploits
both ‘between’ and ‘within’ dimensions of the data but does not do so
efficiently. Thus, in this procedure each observation is given equal weight in
estimation. In addition, the unbiasedness and consistency of the estimator
requires that the explanatory variables are uncorrelated with any omitted
factors. The limitations of OLS in such an application prompted interest in
alternative procedures. There are a number of different panel estimators but
the most popular is the fixed effects (or ‘within’) estimator and this will be
reviewed extensively here. Lastly, the generalized methods of moments (GMM)
estimator will be discussed given its relevance to dynamic panel modelling.
Some Advantages of Panel Data Analysis
Panel data
analysis has quite a number of distinct advantages over time series and cross-section analysis:
· Panel
(or longitudinal) data allows a researcher to analyse a number of important
economic questions not readily answerable by either a cross-section or a
time-series dataset alone.
· The
availability of panel data increases the number of data points available and
reduces collinearity among the explanatory variables thus improving the
efficiency of the econometric estimates.
· Panel
data captures the heterogeneity that is related to the individuals, firms,
states, countries etc. over time.
· By
combining time series of cross-sectional observations, panel data gives “more
informative data, more variability, less collinearity among variables, more
degrees of freedom and more efficiency”.
· Dynamic
effects cannot be estimated using cross-sectional data. Even time series data
are imprecise in this regard as there is generally limited change or variation
in the data to identify such effects. For instance, in estimating a distributed
lag model using only time series data, multicollinearity lowers the precision
of the estimates. Hence, panel data models can provide greater variation in the
explanatory variable for a given year thus reducing the degree of
multicollinearity and improving the precision of the estimates. This clearly
renders panel data better suited to the study of dynamic change However, it
should be emphasised that the estimation procedures required for dynamic models
which include a lagged dependent variable are not straightforward and this
issue is the subject of discussion in later sections.
· Panel
data models can take into account a greater degree of the heterogeneity that
characterize individuals, states, and firms over time.
(Detailed discussion on the rudiments of panel data
analysis will be done in the next tutorial).
(Here is the
link to video clip on converting wide-format data to long-format in Stata).
Model
Framework and Specification
This section
focusses on the theoretical framework and model specification. I will also
touch on description of variables in a model, the a priori expectations and finally, the method of analysis (or the
estimation technique(s) to be used in testing the research hypothesis).
Theoretical Framework
Before you
specify the empirical model, you must
first state the theoretical model. That is, let your readers know where your
empirical model is linked to. The theoretical model is that model supporting
the theory you are using to undertake your research because no research can be
done in isolation without an underlying theory. For instance, if my study is on
the effect of exchange rate on output for 30 countries from 2000 to 2016 (that is, 17years), then I must look for a
suitable theory which I can adapt to my research. Hence, I may decide to use the “monetary model of exchange
rate” which is one of the earliest models used to determine the exchange rate.
It is used as a measure to study the other approaches that are used in
determining exchange rate. The monetary model approach assumes a simple demand
for money curve, the purchasing power parity or the law of one price and a
vertical aggregate supply curve.
The theoretical
framework can be built as follows: (remember that this is just an example, and should not to be copied
literarily!)
From the
absolute purchasing power parity (P = EP*), the exchange rate is
obtained by dividing the price of the domestic currency by the foreign price
for that domestic currency. That is: Eppp = P/P*. The demand
for money assumption: since real money balance depends on real income, demand
for money is given as Md = kPY, where k is constant and Y is the real income level. Hence, in
equilibrium, money demand (Md) equals money supply (Ms)
and at the point of intersection of the aggregate demand and the aggregate
supply curve:
kPY=Ms
P = Ms/kY
EP* = P
= Ms/kY
and E = Ms/P*kY
From the stated framework, it is theorised that if the money
supply within an economy increases, it will result in appreciation of the
domestic currency. Hence, if it is generalised for the 30 countries in the data, the same assumption must be made, ceteris paribus. Likewise, foreign price level and the output level are
inversely related to the exchange rate. If fixed money supply rises in the
domestic economy, since prices are held constant, excess money supply leads to
higher demand for goods and services within the economy.
Model
Specification
So, having
stated the theoretical framework, I can now go ahead to modify it to suit my
research and form there formulate my empirical model. For instance, in using a
Cobb-Douglas production from the neo-classical growth mode, I will attempt to explain
output growth in the context of capital accumulation, labour and productivity,
usually referred to as technological progress. The Cobb- Douglas production
model is implicitly stated as:
Y
= f(ALβKα) [1]
where, Y is output;
K is capital stock; L is labour and A is productivity of
labour which grows at an exogenous rate. As a result of constant returns to
scale, if all inputs are increased by the same amount, then there would be an
increase in output. The production function,
Y
= KαL1-α [2]
where (1 - a = b) is
mainly used by economists and researchers due to the following reasons:
firstly, there is a constant return to scale and secondly, the two exponents α
and (1 - a),
sum up to one.
Next, is to tie
up the empirical model to the theoretical framework. That is given the
relationship between exchange rate and output, the model is implicitly specified
as:
Yit
= f (Exchrateit, X1it, X2it, …, Xnit) [3]
where Yit
= output (the dependent variable, state the measurement either gross output, or
% of GDP, or growth rate etc.)
Exchrateit
= real exchange rate (main explanatory variable)
X1it,
X2it, …, Xnit = control variables (state their individual
measurements either gross output, or % of GDP, or growth rate etc.)
On the basis of
the theoretical framework and using the Cobb-Douglas production, the explicit
model is stated as:
Yit
= β0 + β1Exchrateit + β2X1it
+ β3X2it + … + βnXnit + uit [4]
where, ut
= white noise error term
A Priori
Expectations
Always know that
the expected a priori is directly
related to what theory says. It is from that you know what signs of the
coefficients are expected from the main regressor and other covariates. For
instance, from the theory, it is expected that currency depreciation will have
a positive impact on domestic output, hence, a negative sign of the coefficient
is expected. That is:
β1
< 0
Therefore, the
expected signs of the control variables must be in line with their respective
theories which must be related to your study.
Estimation
Technique
At this point,
the researcher may not know the exact technique or estimator to adopt between
the fixed-effects within-group (fixed effects model) or the random effects
estimator. The choice between these two is subject to the outcome of the Hausman test.
That is, to determine
which model is the more appropriate to adopt, a statistical test is implemented.
The Hausman test compares the random effects estimator to the ‘within’
estimator. The null hypothesis of the test is that the composite error term is
not correlated with the explanatory variables in the model. If the null is
rejected, then the fixed effects estimator is applicable (i.e., it favours the
fixed effects but only relative to the random effects). The use of the test in
this case is to discriminate between a model where the omitted heterogeneity is
treated as fixed and correlated with the explanatory variables, and a model
where the omitted heterogeneity is treated as random and independent of the
explanatory variables.
Variables, Measurement and Description
Lastly, tabulate
your variables detailing their names, short description, measurement and
sources.
Here’s an
example:
Table xxx: Variables
Description and Measurement
Variables
|
Short
Definition
|
Measurement
|
Source
|
Output
|
World Bank (2016)
|
||
Real exchange
rate
|
World Bank (2016)
|
Source:
Researcher’s compilation (always put this at the bottom
of the Table)
Conclusion
I have taken you
through the steps required on how to source for your data, in addition to a brief on panel data
analysis and its relevance over time series and cross-sectional data. I also briefly explained how to
formulate a theoretical framework, adapting the framework to align with the
research, how to construct the empirical model, stating the expected a priori, having an idea about the
estimation technique with a brief on the Hausman test, tabulating your data
showing the brief description of your variables, their measurements and data
sources.
From next
lecture, I will begin analysing the data using both Stata and EViews analytical
packages. So, endeavour to follow these tutorials by getting the most of it to
ease the dissertation pressure. Make sure you follow me on the next lecture
series which is: Panel Data Analysis (Lecture 2): Setting up panel data model and the
Hausman Test.
If you have any
comments or question in relation to what have been discussed, do
not hesitate to post them in the comment section below….
