An overview of the significance of SURE(Seemingly unrelated regression) model in Panel data econometrics and its applications. The presentation consists of the theoretical background and mathematical derivation for the model. The stochastic frontier model and treatment effects are also discussed in brief.

1. CONTEMPORARY
ECONOMETRICS
Panel Data & Non Parametric
Econometrics
Geeta Shreeprabha
M.A Econometrics
UNIT V

2. CONTENTS
 SURE Model
 Frontier Methods
 Treatment Effects

3. Introduction
 System of equations include multiple equations in one model
i) Simultaneous equation model- includes both endogenous and exogenous
variables
Ii) Seemingly Unrelated Regression Models: Contain only exogenous variables
 The SUR system was Proposed by Arnold Zellner, which comprises several
individual relationships that are linked by the fact that their disturbances or the
error terms are correlated.
 SUR model is a system of linear equations with errors that are correlated across
equations for a given individual but are uncorrelated across individuals
 Reasons for using SUR:
I) To gain efficiency in estimation by combing information on different equations.
II) To impose and /or test restrictions that involve parameters in different
equations.
 The popularity of SUR is related to its applicability to a large class of modeling
and testing problems and also the relative ease of estimation.

4. EXAMPLE
Total No. of Obs = 20 states in a nation
Goal : To research the nation's consumption
habits. Total no. of eq. = 20
Note: it's not required that the same
variables appear in every model. Variables in
different equations could be different (the
consumption habits of the neighboring states
could share some traits)
Thus, even if the equations may appear
unique on their own, there may be some
sort of relationship between them.
These equations can be used to check the
coherence of the disturbance distribution.
ESTIMATION
 OLS estimation of each equation yields a
consistent parameter but to improve efficiency
we apply GLS method.
 Efficiency gains increase as the cross equation
correlation increases. - But, not if identical
regressors since GLS is the same as OLS.
 GLS Estimation:
 Steps:
1) Each equation is estimated by OLS and the
residuals from the m equations are used to
estimate Σ using Uj (hat) = y - X β (hat)
2) Substitute Σ(hat) for Σ of GLS estimator
MODEL
Comprising of M multiple regression equations
These M equations can be compactly expressed as
where y is T X 1 vector with elements whose
columns represent the T observations on an
explanatory variable in the i equation;
 β is a k X 1 vector with elements β ij
 Ei is a T X 1 vector of disturbances. These M
equations can be further expressed as
ASSUMPTIONS :
FORMULATION & ESTIMATION

5. FRONTIER
METHODS
Let’s dive in

6. • The frontier production function : An extension of the familiar regression model of production function, or its dual, the
cost function represents an ideal, the maximum output attainable given a set of inputs, the minimum cost of
producing that output given the prices of the inputs or the maximum profit attainable given the inputs, outputs, and
prices of the inputs.
• Estimation of frontier functions : Econometric exercise of making the empirical implementation consistent with the
underlying theoretical proposition that no observed agent can exceed the ideal. Measurement of (in)efficiency is
estimated to which observed agents (fail to) achieve the theoretical ideal.
• Mathematical formulation: : yi = f(xi ; β)T Ei
where yi is the output of producer i (i= 1, . . . , N);
xi is a vector of M inputs used by producer i;
f(xi ; β) is the production frontier and β is a vector of technology parameters to be estimated.
TEi be the technical efficiency of producer i, T Ei = yi f(xi ; β) ,
which defines technical efficiency as the ratio of observed output yi to maximum feasible output f(xi ; β).
• In the case TEi = 1, yi achieves its maximum feasible output of f(xi ; β).
• If T Ei < 1, it measures technical inefficiency in the sense that observed output is below the maximum feasible output.
Introduction

7. Definition
 A method of economic modeling.
 It has its starting point in
the stochastic production frontier models
simultaneously introduced by Aigner,
Lovell and Schmidt (1977) and Meeusen
and Van den Broeck (1977).
Assumptions
i) f(vi) is a symmetric distribution
Ii) vi and ui are statistically independent of
each other
iii) Both components of compound error term
are independent and identically distributed.
iv) If E[vi - ui] is constant, the OLS estimates of
the slope parameters of the frontier function
are unbiased and consistent.
Model
 Model can be formulated as :
 X represents the factors affecting output
and TE stands for technical efficiency.
 where Ui represents inefficiency
(measurement error, noise etc.)
 Ui > 0 but Vi may take any value. It is
assumed that Vi follows a symmetric
distribution such as Normal distribution.
Stochastic Frontier Model

8. Modified Least Square
 The MOLS technique : Correcting the intercept with the expected
value of the error term (εi) and adopting OLS to get a consistent
estimate.
 Need: The OLS estimator will be a best linear unbiased and
consistent estimate of the vector β. Problems arise for the
intercept term α: its OLS estimate is not consistent.
 Steps: the estimate of σu is used to convert the OLS estimate of
the constant term into the MOLS estimate. The model to be
estimated is
 yi = (α + µε) + βxi + εi . –(1)
 the OLS residuals provide consistent estimates of the technical
efficiency of each unit
 Limitation : Estimates can take values which have no statistical
meaning. Suppose the third moment of the OLS residuals is
positive, then the term in brackets in eq. 1 becomes negative
and this leads to a negative value of ˆσu.
Maximum Likelihood
 The distribution of the composed error term is asymmetric
(because of the asymmetric distribution of the inefficiency term).
A maximum likelihood (ML) estimator that takes into
consideration this information gives more efficient estimates, at
least asymptotically.
 Greene (1980) proved that Gamma distribution provides a
maximum likelihood estimator with all of the usual desirable
properties and which is characterized by a high degree of
flexibility. Therefore this distribution is suitable to model the
inefficiency error term.
 Assume a truncated normal distribution ui ∼ N +(µ, σu), the log-
likelihood function
 The log-likelihood function is expressed in terms of the two
parameters σ^2 = σ^2 u + σ^2 v and λ = σu /σv
METHODS OF ESTIMATION

9. TREATMENT EFFECTS
Difference in differences estimator

10. Introduction
Definition
 The impact or marginal effect of a single binary regressor that equals
one if treatment occurs and equals zero if treatment does not occur.
For example, measuring the effect on earnings of a policy change (the
binary treatment) that alters tax rates or welfare eligibility or access
to training for some individuals but not for others..
 Measured using standard panel data methods if panel data are
available before and after the treatment and if not all individuals
receive the treatment.
 Then the first-differences estimator for the fixed effects model
reduces to a simple estimator called the differences-in-differences
estimator.
How to measure?
 The term “treatment” is used interchangeably with “cause.”
 In medical studies of new drug evaluation, involving groups of those
who receive the treatment and those who do not, the drug response
of the treated is compared with that of the untreated.
 A measure of causal impact is the average difference in the
outcomes of the treated and the nontreated groups.
 In economics, it covers variables whose impact on some outcome is
the object of study.
 Examples of treatment–outcome pairs include schooling and wages,
class size and scholastic performance, and job training and earnings.
A treatment need not be exogenous, and in many situations it is an
endogenous (choice) variable.

11. Modelling
 Let there be a target population for the treatment of interest
 Let N denote the number of randomly selected individuals who are
eligible for treatment.
 NT = number of randomly selected individuals who are treated
 NC = N − NT ; number of nontreated individuals who serve as a potential
control group.
 Random assignment implies that the treatment assignment ignores the
possible impact of the treatment on the outcomes.
 Let (yi, xi,Di ; i = 1,..., N) be the vector of observations on the scalar-
valued outcome variable y,
 a vector of observable variables x, and a binary indicator of a treatment
variable D.
 We assume that anyone who is assigned treatment gets it, and anyone
who is not does not get it.
 Measuring the effect of the treatment : construct a measure that
compares the average outcomes of the treated and nontreated groups.
ASSUMPTIONS
 Conditional Independence Assumption/ Unconfoundedness
assumption / ignorability assumption :
It states that conditional on x, the outcomes are independent of
treatment. This assumption is used in establishing identifiability of a
population-average treatment effect on the treated (ATET). If valid, the
assumption implies that there is no omitted variable bias once x is
included in the regression.
 Matching Assumption : Overlap or matching assumption,
Necessary for identifying some population measures of impact.
It states that 0 < Pr[D = 1|x] < 1.
This assumption ensures that for each value of x there are both
treated and nontreated cases. In that sense there is overlap between the
treated and untreated subsamples.
 Conditional Mean Assumption :
E[y0| D = 1, x] = E[y0| D = 0, x] = E[y0| x],
which implies that y0 does not determine participation
Treatment Effects Framework

12. APPLICATIONS
Rubin Causal Model Fixed Effects with BinaryTreatment
• In potential outcome model (POM), which assumes that every
element of the target population is potentially exposed to the
treatment,
• (y1i, y0i, Di), i = 1,..., N,
• The categorical variable D takes the values 1 and 0, respectively,
when treatment is or is not received;
y1i measures the response for individual i receiving treatment,
y0i measures that when not receiving treatment.That is
• The effect of the cause D on outcome of individual i is measured
by (y1i − y0i). The average causal effect of Di = 1, relative to Di = 0,
is measured by the average treatment effect (ATE):
• where expectations are with respect to the probability distribution
over the target population.
• The experimental approach to the estimation of ATE-type
parameters involves a random assignment of treatment followed
by a comparison of the outcomes with a set of nontreated cases
that serve as controls.
• Let the binary regressor of interest be
Assume a fixed effects model for yit with
where δt is a time-specific fixed effect
αi is an individual-specific fixed effect.
• This is equivalent to regression of yit on Dit and a full set of time
dummies with the complication of individual-specific fixed effects.
For simplicity there are no other regressors. The individual effects
αi can be eliminated by first differencing.Then
The treatment effect φ can be consistently estimated by pooledOLS
regression of yit on Dit and a full set of time dummies.

13. Keywords
SURE Model
A generalization of a linear regression model that consists of
several regression equations, each having its own dependent
variable and potentially different sets of exogenous
explanatory variables in which the error terms are assumed to
be correlated across the equations.
Modified Least Square Method
FM-OLS was Given by Philips and Hansen(1980)
The method modifies the least squares to account for serial
correlation and endogeneity in regressors due to cointegrating
regressions to give optimal estimates.
Stochastic Frontier Analysis
Stochastic frontier analysis (SFA) refers to a body of statistical
analysis techniques used to estimate production or cost
functions in economics, while explicitly accounting for the
existence of firm inefficiency.
Maximum Likelihood method
It is a method of estimating the parameters of an
assumed probability distribution, given some observed data. This is
achieved by maximizing a likelihood function so that, under the
assumed statistical model, the observed data is most probable.
Random Assignment
Random assignment implies that individuals exposed to
treatment are chosen randomly, and hence the
treatment assignment does not depend on the outcome
and is uncorrelated with the attributes of treated
subjects.
Potential Outcome Model
A potential outcome is the outcome for an individual under a
potential treatment. For this individual, the causal effect of the
treatment is the difference between the potential outcome if the
individual receives the treatment and the potential outcome if she
does not.

14. REFERENCES
SURE MODEL:
https://www.bauer.uh.edu/rsusmel/phd/ec1-14.pdf
https://sites.google.com/site/econometricsacademy/econometrics-models/seemingly-unrelated-regressions
http://home.iitk.ac.in/~shalab/econometrics/Chapter18-Econometrics-SUREModels.pdf
http://www.igidr.ac.in/faculty/ssarkar/course/ecotrix2/termpapers/team1/paper_team1.pdf
https://stats.oarc.ucla.edu/stata/faq/what-is-seemingly-unrelated-regression-and-how-can-i-perform-it-in-stata/
https://eml.berkeley.edu/~powell/e240b_sp10/surnotes.pdf
FRONTIER METHODS
http://www.camillamastromarco.it/CIDE/STFR.pdf
https://www.emerald.com/insight/content/doi/10.1108/AJEB-07-2020-0032/full/pdf?title=a-closer-look-at-stochastic-frontier-analysis-in-economics
https://pages.stern.nyu.edu/~wgreene/FrontierModeling/SurveyPapers/Greene-FRONTIERS.pdf
https://en.wikipedia.org/wiki/Stochastic_frontier_analysis
https://www.slideshare.net/israelvc12/a-practitioners-guide-to-stochastic-frontier-analysis-using-statakumbhakar
https://slideplayer.com/slide/10727835/
https://slideplayer.com/slide/17659382/
https://www.youtube.com/watch?v=12ipB--Z4C0&list=PLrD48EXI5q10YQhU8nvnHY0lJ4p-bHryZ
https://www.youtube.com/watch?v=S_6g7DL4XAI
TREATMENT EFFECTS
Microeconemetrics: Methods and Applications
https://www.youtube.com/watch?v=TYFbOjWZ7lE
https://www.youtube.com/watch?v=CraItSIr6r8

15. THANKYOU
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