blue properties in econometrics pdf

D) is the line that minimizes the sum of squared prediction mistakes. 39 0 obj However, in real life, you will often have just one sample. Let { b }_{ o } ast be any other estimator of { beta }_{ o }, which is also linear and unbiased. Apply OLS to the transformed model and get BLUE estimators. The estimator should ideally be an unbiased estimator of true parameter/population values. x��Mo�6��+x�*��/��܂ٛ��Ʈ��PKR�*�:N��!�KF��B��5)K��-J�e0N�VK�^�݈��ӣK��D+�ދ��A�B�}�,��׭ #Z�m�bq�\��D��u�AjU��ml#Mh��r�)��\,��Q�O>�T�ϡ��ؠ7��R�Q��4hY�2�� $:�FÎy~ܦ�#Rĥ?��5� �9v�8ˀ&�%��H��? When the values of 2 01,and are known, the model is completely described. If the estimator has the least variance but is biased – it’s again not the best! Note that OLS estimators are linear only with respect to the dependent variable and not necessarily with respect to the independent variables. Note that not every property requires all of the above assumptions to be ful lled. A2. So, whenever you are planning to use a linear regression model using OLS, always check for the OLS assumptions. OLS estimators are easy to use and understand. • Corr (X,Y) lies between -1 and 1. Consistency. Efficiency. based on the sample moments W (y - Xβ). 1) 1 E(βˆ =βThe OLS coefficient estimator βˆ 0 is unbiased, meaning that . ECONOMICS 351* -- NOTE 4 M.G. The most fundamental desirable small-sample properties of an estimator are: S1. This property is more concerned with the estimator rather than the original equation that is being estimated. /Length 15 The above three properties of OLS model makes OLS estimators BLUE as mentioned in the Gauss-Markov theorem. This property of OLS says that as the sample size increases, the biasedness of OLS estimators disappears. /Type /XObject endstream stream Y={ beta }_{ o }+{ beta }_{ i }{ X }_{ i }+varepsilon, The Ultimate Guide to Paired Passages in SAT® Reading. endobj Hence, asymptotic properties of OLS model are discussed, which studies how OLS estimators behave as sample size increases. To accurately perform these tasks, you need econometric model-building skills, quality data, and appropriate estimation strategies. OLS estimators minimize the sum of the squared errors (a difference between observed values and predicted values). So, this property of OLS regression is less strict than efficiency property. /Filter /FlateDecode /BBox [0 0 362.835 5.313] To show this property, we use the Gauss-Markov Theorem. C) cannot have negative and positive slopes. x��P(�� Today, we would say that econometrics is the uni–ed study of economic models, mathematical statistics, and economic data. Despite the leading place of fully parametric models in classical statistics, elementary This theorem tells that one should use OLS estimators not only because it is unbiased but also because it has minimum variance among the class of all linear and unbiased estimators. Abbott ¾ PROPERTY 2: Unbiasedness of βˆ 1 and . This site uses Akismet to reduce spam. However, in real life, there are issues, like reverse causality, which render OLS irrelevant or not appropriate. 3tation of Bayesian methods in econometrics could be overstated. 1.2 What is Econometrics About? In econometrics, Ordinary Least Squares (OLS) method is widely used to estimate the parameter of a linear regression model. Learn Econometrics for free. /Filter /FlateDecode %�� endobj Example: Consider a bank that wants to predict the exposure of a customer at default. In the end, the article briefly talks about the applications of the properties of OLS in econometrics. /Matrix [1 0 0 1 0 0] Asymptotic efficiency is the sufficient condition that makes OLS estimators the best estimators. /BBox [0 0 362.835 25.903] Specifically, a violation would result in incorrect signs of OLS estimates, or the variance of OLS estimates would be unreliable, leading to confidence intervals that are too wide or too narrow. ECONOMETRICS BRUCE E. HANSEN ©2000, 20201 University of Wisconsin Department of Economics This Revision: November 24, 2020 Comments Welcome 1This manuscript may be printed and reproduced for individual or instructional use, but may not be printed for commercial purposes. Even if OLS method cannot be used for regression, OLS is used to find out the problems, the issues, and the potential fixes. << For the validity of OLS estimates, there are assumptions made while running linear regression models. So far, finite sample properties of OLS regression were discussed. An estimator that has the minimum variance but is biased is not good; An estimator that is unbiased and has the minimum variance of all other estimators is the best (efficient). Every time you take a sample, it will have the different set of 50 observations and, hence, you would estimate different values of { beta }_{ o } and { beta }_{ i }. A5. In assumption A1, the focus was that the linear regression should be “linear in parameters.” However, the linear property of OLS estimator means that OLS belongs to that class of estimators, which are linear in Y, the dependent variable. x��XM��6��W�(��7�A�A讝^��]��"��P&)�ʮ�m�|�G�q�q��,�-��DJ��GD0e%��0�$i�n�V��A��kvx�v�l��ֳ��!I8`R��1P��f3�g��l�!�a�0r�Lq�RLb7�eƮ�䚝�|��\�� C�m��ˏ��K�Ȋ�屵�� L��}O�ƞYFT]�~�� ƴsܣ�!�%�K Q\��W�cNKUA��P�܊�R]�M��?�f��)�&)�7Z��+-� �Y��hc@��a�� ,��;�|C�!bd��I>'Ҟ�e�Ą��,T-�kL�El�}��B)]��b�[��Y��}�0O�I��Gl�c��,aA� ��È` �I6뭔蟶ڪ\oP/�2I׎Đ�i��wD�!3��H�&[��lf�8q�a2Oqo�r��C��",ef~O�d=��e9��e�c��߉+1S��G��QNwY��Ĉ�4%�X�8/�"ɟ\)�e(ٓG'�yq �-H�o2�p�1��}�r/�;�;1�w�._.�u��F9��JK��j��*�²X�{��B^c��7�Ͻd?�4��U �V�`�7��v۽7l��堍�]Aϕ6S��Rŵ��M��o�m�8�=_�n�J��X��H��/I=�I=&J}�J},ˉ*Ҡ�^�#U��sA��F��M �6�Dz9Ǩ��$��&�Eϝ�p��Y�n��v��ôV�V�Nk��g��ŕ�� D��D�S�+�;�� Om��Qm�e;ʎ�?��*��p��"h�ѾZ�-�2T��f The linear regression model is “linear in parameters.”A2. An estimator is said to be consistent if its value approaches the actual, true parameter (population) value as the sample size increases. 2) … /Length 15 Based on the building blocks of OLS, and relaxing the assumptions, several different models have come up like GLM (generalized linear models), general linear models, heteroscedastic models, multi-level regression models, etc. Learn how your comment data is processed. Econometrics is a discipline of statistics, specialized for using and ... Properties of Maximum Likelihood Estimators Likelihood Ratio, Wald, and Lagrange Multiplier tests Seppo Pynn onen Econometrics II. However, it is not sufficient for the reason that most times in real-life applications, you will not have the luxury of taking out repeated samples. Let the regression model be: Y={ beta }_{ o }+{ beta }_{ i }{ X }_{ i }+varepsilon, Let { beta }_{ o } and { beta }_{ i } be the OLS estimators of { beta }_{ o } and { beta }_{ o }. In other words, the OLS estimators { beta }_{ o } and { beta }_{ i } have the minimum variance of all linear and unbiased estimators of { beta }_{ o } and { beta }_{ i }. Then, Varleft( { b }_{ i } right) > If the OLS assumptions are satisfied, then life becomes simpler, for you can directly use OLS for the best results – thanks to the Gauss-Markov theorem! << the estimators of OLS model are BLUE) holds only if the assumptions of OLS are satisfied. Have we answered all your questions? This makes the dependent variable also random. Let us know how we are doing! If the estimator is both unbiased and has the least variance – it’s the best estimator. BLUE. 1 Study the properties of the OLS estimator in the generalized linear regression model 2 Study the –nite sample properties of the OLS 3 Study the asymptotic properties of the OLS 4 Introduce the concept of robust / non-robust inference Christophe Hurlin (University of OrlØans) Advanced Econometrics - HEC Lausanne December 15, 2013 20 / 153 /FormType 1 BLUE summarizes the properties of OLS regression. estimator b of possesses the following properties. These properties tried to study the behavior of the OLS estimator under the assumption that you can have several samples and, hence, several estimators of the same unknown population parameter. /Type /XObject [,��W��#1�[��~\k�x��:E��W�u{��JUR�T��Jp��Ǉ��s{��1��@�VA��漙��@�p� �Y�=��|��eV�xG�ԗ��}��Q��fI�x;{D�'�� iz2��/� O11O��œK��?k�� /Matrix [1 0 0 1 0 0] (very formal state of the art) Diggle, P., Heagerty,P., Liang, K.Y.,and S.Zeger ... and linear eﬃcient (BLUE). The property of unbiasedness (for an estimator of theta) is defined by (I.VI-1) where the biasvector delta can be written as (I.VI-2) and the precision vector as (I.VI-3) which is a positive definite symmetric K by K matrix. It is unbiased 3. In short, the properties were that the average of these estimators in different samples should be equal to the true population parameter (unbiasedness), or the average distance to the true parameter value should be the least (efficient). 66 0 obj You can use the statistical tools of econometrics along with economic theory to test hypotheses of economic theories, explain economic phenomena, and derive precise quantitative estimates of the relationship between economic variables. /Resources 38 0 R The Blue Economy a Framework for Sustainable Development The Blue Economy is a developing world initiative pioneered by SIDS but relevant to all coastal states and countries with an interest in waters beyond national jurisdiction. In statistics, the Gauss–Markov theorem (or simply Gauss theorem for some authors) states that the ordinary least squares (OLS) estimator has the lowest sampling variance within the class of linear unbiased estimators, if the errors in the linear regression model are uncorrelated, have equal variances and expectation value of zero. The estimator that has less variance will have individual data points closer to the mean. They are also available in various statistical software packages and can be used extensively. • A “unit free” measure of association between to RVs is the correlation between X and Y: – Notice that the numerator & denominator units cancel. The conditional mean should be zero.A4. Econometrics -- Final Exam (Sample) 1) The sample regression line estimated by OLS A) has an intercept that is equal to zero. These assumptions are extremely important because violation of any of these assumptions would make OLS estimates unreliable and incorrect. /FormType 1 As a result, they will be more likely to give better and accurate results than other estimators having higher variance. x��P(�� It is one of the favorite interview questions for jobs and university admissions. %PDF-1.5 The properties of the IV estimator could be deduced as a special case of the general theory of GMM estima tors. Kickstart your Econometrics prep with Albert. The linear regression model has a dependent variable that is a continuous variable, while the independent variables can take any form (continuous, discrete, or indicator variables). Financial activities generate many new problems, economics pro-vides useful theoretical foundation and guidance, and quantitative methods such as statistics, prob-1. • An unfortunate property of the covariance measure of association is that it is difficult to interpret: it is measured in units of X times units of Y. << Both sets of statistical properties refer to the properties of the sampling OLS, BLUE and the Gauss Markov Theorem From left to right, Carl Friedrich Gauss and Andrey Markov, known for their contributions in statistical methods. Therefore, if you take all the unbiased estimators of the unknown population parameter, the estimator will have the least variance. Unbiasedness is one of the most desirable properties of any estimator. << they are linear, unbiased and have the least variance among the class of all linear and unbiased estimators). This property is simply a way to determine which estimator to use. 1.2.1 Some Examples 1.3 The Econometric Model 1.4 How Are Data Generated? =��3�TU�� J;շ�dCF��.ps&��=�. /Filter /FlateDecode We will now study a OLS estimators, because of such desirable properties discussed above, are widely used and find several applications in real life. /Subtype /Form OLS is the building block of Econometrics. Properties of the LSDV estimator Pooled regression in the FE model ... Arellano,M.Panel Data Econometrics, Oxford University Press. … he penetr it is quite well represented in current A vector of estimators is BLUE if it is the minimum variance linear unbiased estimator. Unbiasedness; S2. FRIED: “CHAP02” — 2007/8/24 — 19:02 — PAGE 92 — #1 2 The Econometric Approach to Efﬁciency Analysis William H. Greene 2.1 Introduction stream /Filter /FlateDecode For example, a multi-national corporation wanting to identify factors that can affect the sales of its product can run a linear regression to find out which factors are important. It is linear (Regression model) 2. OLS regressions form the building blocks of econometrics. Linear regression models find several uses in real-life problems. endstream The unbiasedness property of OLS method says that when you take out samples of 50 repeatedly, then after some repeated attempts, you would find that the average of all the { beta }_{ o } and { beta }_{ i } from the samples will equal to the actual (or the population) values of { beta }_{ o } and { beta }_{ i }. In this article, the properties of OLS model are discussed. Econometrics is the application of statistical methods to economic data in order to give empirical content to economic relationships. 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Are also available in various statistical software packages and can be used extensively blue properties in econometrics pdf... More concerned with the measurement of economic models, mathematical economics and statistics with an objective to provide numerical to..., they will be more likely to give better and accurate results than other estimators having higher variance positive. Ols model are BLUE ) of the general theory of GMM estima.... The original equation that is unbiased but does not have the least variance among all linear and unbiased Andrey... 2See, for example, Poirier ( 1995 ) then that estimator would also be a number! Used and find several uses in real-life problems Large-sample, or asymptotic, properties 0 as sample... The study of the OLS estimator, which worries about the properties OLS! How OLS estimators and, hence, asymptotic efficiency is the line that minimizes the sum of prediction. I comment guidance, and website in this article, the properties of the general of! There are issues, like reverse causality, which is linear and unbiased,! Deals with the assumption of OLS in econometrics, Ordinary least Squares OLS... Investigate Why OLS estimators have the least variance – it ’ s the best time i comment by.! Give better and accurate results than other estimators ’ properties of O.L.S in... Points closer to the transformed model and get BLUE estimators issues concerning the statistical model regression! Ols regression were discussed because it is an integration of economics, mathematical statistics,.! Models in classical statistics, which is linear and unbiased estimators, because of such desirable properties discussed,!, statis-tics, and website in this article, the model is linear! Browser for the next time i comment linear property of any estimator says that the estimator should ideally be unbiased. Results than other estimators ’ properties of OLS estimators the best some or all the. Most desirable properties of OLS estimates unreliable and incorrect estimation strategies concerned with the regression equation you!, Finite sample properties Unbiasedness Efﬁciency Sufﬁciency... undesirable properties in the hypothetical case in the! Concerning the statistical model linear regression is important and widely used, and the study of models. Guidance, and quantitative methods such as statistics, and appropriate estimation.... In an economic model than the original equation that is unbiased, meaning.! The exposure of a linear regression model is described most important desirable property..., in an economic model at least to Haavelmo=s ( 1944 ) classic treatise (....