This paper develops a new threshold autoregressive model which contains two threshold variables. The recent past has seen an increased interest in piecewise linear real exchange rate models. 345 0 obj <>stream 0000004353 00000 n <<6DF469E0975A0C4FA967FF77C0A294B1>]/Prev 146469>> 4An empirical example of the Model (1) is Tiao and Tsay’s (1994) four-regime TAR model Difficulties in model specification. Chen " Conditional Markov Chain and its Application in Economic Time Series Analysis." 0000036766 00000 n 0000014471 00000 n 0000013707 00000 n Despite this popularity, there is only a small Econometrics Syllabus Linear Regression Panel Data Models Probit and Logit Models Bivariate Probit and Logit Models Multinomial Probit and Logit Models Ordered Probit and Logit Models Limited Dependent Variable Models Count 0000005020 00000 n 0000004760 00000 n 0000007378 00000 n straints. 0000005694 00000 n A likelihood ratio test is proposed to determine the number of regimes in the model. 0000012901 00000 n 0000030479 00000 n 0000005561 00000 n 0000002848 00000 n 0000004487 00000 n 0000056327 00000 n ���k����-D���7"Wp�A���C�ї�/^�ż?0�m�N$B8��}��P����a\(����m�wBK�����k�'U9�X��O�M|]&�7����?��r�\b�(�B��,�{��'l}��]+�A۶�.�p�nR�U̔��,�=-��`GqS�Y�.�Tϝ�+�=�K1�����!�5̪�?Fʹ�M��ä3���F�T��z��ӤH��_��]'����oΩd����.�vܩj}\��}i�r9+I�CL��J����0�H�`�\�+���-0ED��Vs�j%�MK?�"�����%��()� ��A�M�A�F��g���>ւ0�r�qC�@d�����?�:Z�|�o������x�D�����Խ��m��c�o�R� 0000022969 00000 n 0000022257 00000 n 256 0 obj <> endobj e䥈��G��UGK���k�g�w��N�w�ݙ���ݛ�˗�$g����g�(�A�H$�x���X4e�ǫW���>�ymϊ�Qn�ء���鿾뮔���>*^o;2p$5H$�W/��N��PxN��>o�ܩ�3�M��(&,!24$���EDXL�B���zghd�B�9y~�B��;�T*D� ���z�"��a�a Ia����\��_���%R"j8E��P�)j���Qo�Q3�Ի�KQ~�(�A�Gj��Z/~+�MM�,���E����*tP��(I�X%����%(15�RS��rE�m�x���M���"yM�#�������t�4�]�̽����lȡג_�1�sh���a+�2Y������0"z��O��H�7D�� 1ľ`j�xn!o0ģ��x����I��5H�;��'*Do���1{��ͪ\}z:���}��]�� o�������x�4-�;� h���qS�v����2��/�Q/�S|�������lixQz3?�-��Fd���I�\�& �_��4o�C�;�1��.�N����r�K���������ӢY��G�Yc.�����!�#�>���hå�UܷGk/_��,2�xy��+;� �h�d��~Cć���N�:�. 0000049843 00000 n 0000003680 00000 n It contains data on West German fixed investment, disposable income and consumption expenditures in billions of DM from 1960Q1 to 1982Q4. 0000055432 00000 n endstream endobj 257 0 obj <>]>>/PageLayout/SinglePage/PageMode/UseOutlines/Pages 253 0 R/Type/Catalog>> endobj 258 0 obj <> endobj 259 0 obj <> endobj 260 0 obj <>/Border[0 0 0]/C[0 1 1]/H/I/Rect[85.464 780.996 216.318 789.108]/Subtype/Link/Type/Annot>> endobj 261 0 obj <> endobj 262 0 obj <> endobj 263 0 obj <> endobj 264 0 obj <> endobj 265 0 obj <> endobj 266 0 obj <> endobj 267 0 obj <> endobj 268 0 obj <> endobj 269 0 obj <> endobj 270 0 obj <> endobj 271 0 obj <> endobj 272 0 obj <> endobj 273 0 obj <> endobj 274 0 obj <> endobj 275 0 obj <> endobj 276 0 obj <> endobj 277 0 obj <> endobj 278 0 obj <> endobj 279 0 obj <> endobj 280 0 obj <> endobj 281 0 obj <>/ExtGState<>/Font<>/ProcSet[/PDF/Text]>> endobj 282 0 obj <> endobj 283 0 obj <> endobj 284 0 obj <> endobj 285 0 obj <> endobj 286 0 obj <> endobj 287 0 obj <> endobj 288 0 obj [/ICCBased 320 0 R] endobj 289 0 obj <> endobj 290 0 obj <> endobj 291 0 obj <>stream 0000003506 00000 n The main reason to learn Stan is to fit models that are difficult to fit using other software. 0000056478 00000 n 0000005151 00000 n 0000035428 00000 n xref 2012, Econometric Review,with T. Chong and H.Q. Inference in TAR Models. For example, if (1 )= 2 = (3), the model will have two regimes only. 0000058473 00000 n 0000003432 00000 n 0��@�?����) ��� Topics (Cont.) a@>�����e4 �4 �RR�T�6l 0000001171 00000 n 0000002648 00000 n 0000036755 00000 n Some of the common econometric models are: Linear regression; Generalized linear models; Probit; Logit; Tobit; ARIMA; Vector Autoregression; Cointegration; Hazard trailer Model and data. 0000005824 00000 n "Inference in TAR models," Studies in Nonlinear Dynamics and Econometrics, (1997), 2. 2010, Journal of Econometrics Instrumental Variables Regression • Conditions for Valid Instruments: Relevance and Exogeneity • 2SLS estimation: The First and the Second Stage Regression • Tests of Instrumental Validity: F-test and J-test { Gauss Programs and Data Matlab Programs and Data R Programs and Data Link to Abstract and PDF File of Paper . 0000008750 00000 n By invoking Heckscher's (1916) 'commodity points' it has been argued that a threshold autoregressive (TAR) model should be used to study movements in the real exchange rate. 0000004887 00000 n 0000005423 00000 n 0000009256 00000 n 0000022389 00000 n g8/�'7�>X�`{��"���] y�n 0000030198 00000 n Oil market VAR models have become the standard tool for understanding the evolution of the real price of oil and its impact in the macro economy. �"A�H�)�P\\\CC�L �G���V���1�V����f�R7�����^64l�C\���1� �j1M`R`���9� �88��K�J8�ҝl!z@Z�]���3�3�b��'A���@�9�Fq�*N�,B���1��xu�0�'�2p7J0y��|������ �j��A܁�A݂D�F)�l� �� Following Lütkepohl (2007) the VAR model has two lags, i.e. 0000030706 00000 n 0000058249 00000 n startxref 0000022772 00000 n 0000036249 00000 n 0000028976 00000 n 0000053510 00000 n !�$fy@A���>�Ll;��>������/ 0000036849 00000 n 0000003275 00000 n These are linear models with a scalar response, scalar explanatory variables and autoregressive errors. 0000057713 00000 n Today econo-mists refer to models that combine explicit economic theories with statistical models as So it is a nonlinear model. 0000036605 00000 n 4. 0000045115 00000 n For TAR models where more than TWO regimes are considered, this could be onerous to implement in MODEL." 0000009310 00000 n trailer << /Size 268 /Info 226 0 R /Root 228 0 R /Prev 436161 /ID[<19bc1f52a6c1bc666eca7950080a33bc><35c23ce8be1f03216d7de1a15b5a7480>] >> startxref 0 %%EOF 228 0 obj << /Type /Catalog /Pages 222 0 R /AcroForm 229 0 R /Metadata 224 0 R >> endobj 229 0 obj << /Fields [ ] /DR << /Font << /ZaDb 218 0 R /Helv 219 0 R >> /Encoding << /PDFDocEncoding 220 0 R >> >> /DA (/Helv 0 Tf 0 g ) >> endobj 266 0 obj << /S 1370 /V 1533 /Filter /FlateDecode /Length 267 0 R >> stream 0000056694 00000 n 0000054794 00000 n �J�D( 1Q��q��db�� Volatility Models Application in Risk Management 0000005951 00000 n 0000031442 00000 n v) 2 y 01X This book provides a general framework for specifying, estimating and testing time series econometric models. �R������ �jш߿I�n���C�wH'��E�}��#�����1` �a�=�fDC/HMt���1� �wB�&m���h�܃�d��3(y���YP�N��[�!�Rd$������~�6�� �!ˠ1dի�3�Ub� ��uF�[��.�J�}p�:˫�p`�?�2�]]��dh�$~���6��`�ԈDSV ���e������mۓS���+��/�=;?{�uq�ɸ�����yb��zբ�G�%��27�"�8j���Y�eO#���>�ixMs�7m��9d~LܘĤ��^�o�&�=���r����TU�f5�yv�Ҡ����]���_����R[QP}��1ykj����u[㥩�Ҵ,��Z����²r���M~�5��.Gb�G��#cԋ��lʶe�_��S]ʼ���ഝ��4���H�B��r�p�Р�"�W��20}��8{�!�2贲ҌR�僫��r! This literature is enormous, and the papers reviewed here are not an exhaustive list of all applications of the TAR model. 0000034405 00000 n Volatility Models Application in Risk Management Part V Volatility Models As of Feb 14, 2018 Seppo Pynn onen Econometrics II. A���Ύf���7��9?��.�#����d�J�2�RS�U�*ϬP�����sKT�b8Vzd�E��p;�8�vđ��;�Cb%Y�C�����U* ��C���[���=Fw:5,4#�As�> �S���1��ㅝH��M��E���b;xQ*��^�����U�N�|�vڮZ9�QL_[�K�{��$�E,y�R��'h��,�eݳ��0�濢j��QD��_�rWZ���٘�x�ߦ%�6���1:;�ذ1$rC|�44�Ք\��u]��j��z���,U��"�o�+�=�Q�0Y�$�gw��G�+n_c)eH���n��by}��8��� �s9G �r+�1G�$�=�T\��UE���~Np�b:!Aߣļ�y8L���p$��"��h:Z(E}Hd��� ��;�BX�������#|ͣ��?��"E� �ѪO����(:b��_���4�^ݝ�Қ��PE|�BQ�Tz8g��\6gѢ�5 1 lim wherei i ii ii T X XQ Q T is nonsingular with fixed and finite elements. Threshold autoregressive model (TAR model) has certain characteristics due to which linear models fail to t a nonlinear time series, while the problem of how to nd an appropriate threshold value still attracts many researchers’ attention. 0000056975 00000 n ��jHB:ӭ(}�wH� "!X��g The estimation of the parameters and the covariance matrix of a simple VAR model is straightforward. ���ΰ �39�f�2��_La; �j��P����OG�F���kj�`�MD~���#� �2��^�۹�:�l��z|}���*�e�!�x�u���>��,"��0V�35�i�I�͞�r�E�aYK\Ё.>�\t�Nb`��H��8L8�#fx�3��� ��a`�� z�UHOg`� 0000002641 00000 n 0000013375 00000 n 0000008002 00000 n 0000004220 00000 n hތWXSW�=1��F�x,�س�1UFK}��ڊ�AmѪTQ��b�7!$�!��^ 0000045511 00000 n Downloadable! 0�&���!�=����UVЕU��:僡� �S�1FX�R�H5�:�d���c�X�Yu�ZT� \� :�f��E�*U��C�) �Xç(�4-q��,\�/p��N���� ��9�[��H;o 70���ųq����. ])�:��7��.����V��Vm�[���WT�N6����15�˘8$6wi�rOS���JR �0�� 3�����4����Y��c����B��H�qqKK�066�� 0000001266 00000 n Like other forms of statistical analysis, badly specified econometric models may show a spurious correlation where two variables are correlated but causally unrelated. 0000057811 00000 n 2, issue 1, 1-16 Abstract: A distribution theory is developed for least-squares estimates of the threshold in Threshold Autoregressive (TAR) models. "On the issue of functional form choice in hedonic price functions: Further evidence," with John Halstead and Rachel Bouvier, Environmental Management (1997), 21, 759-765. 0000022742 00000 n 0000005284 00000 n 2011, Journal of Applied Econometrics,with P. Wang" Common breaks in means and variances for panel data." 0000047756 00000 n I hope this helps-Ken econometrics and economics literatures which either con-tribute to the theory of TAR estimation and inference, or report a substantive application of a TAR model to eco-nomics. 0000020517 00000 n This is a Ph.D. level Econometrics course taught using Stata, R, and SAS. 0000002884 00000 n 0000057534 00000 n Econometrics may use standard statistical models to study economic questions, but most often they are with observational data, rather than in controlled experiments. In statistics, Self-Exciting Threshold AutoRegressive (SETAR) models are typically applied to time series data as an extension of autoregressive models, in order to allow for higher degree of flexibility in model parameters through a regime switching behaviour. 0000001417 00000 n 0000006842 00000 n 0000027766 00000 n 0000048770 00000 n Finding these approximations requires a specification step, in which one restricts attention to a class of candidate functions believed to contain … %PDF-1.4 %���� the discrete switch with a smoother (first order continuous) transition between models in the example. Estimation. This paper examines the problems of fitting TAR models to real exchange rates. 227 0 obj << /Linearized 1 /O 230 /H [ 1417 1231 ] /L 440831 /E 57887 /N 29 /T 436172 >> endobj xref 227 41 0000000016 00000 n Econometrics | Chapter 3 | Multiple Linear Regression Model | Shalabh, IIT Kanpur 2 iii) 2 yXX 01 2 is linear in parameters 01 2,and but it is nonlinear is variables X. The empirical results show that the model confidence sets imply economically large and time-varying uncertainty about expected utility 0000030309 00000 n 0000055080 00000 n Hey, I would like to estimate a threshold autoregressive model with SAS software, but I do not know if it is possible to estimate it? 0000021207 00000 n Z�6�)(Z~@��_�w�{�h����� W��ڮ���| Simultaneous autoregressive (SAR) models have been extensively used for the analysis of spatial data in areas as diverse as demography, economy and geography. ���%K������ԗ��9w�ܙ�r���L��n��ei����'�{d�r-la��nB�*�|����ߊ�a�+�#��)T| QE��$��i&�j�y�%/�bF_�� " The Theory and Applications of TAR Model with two Threshold Variables." -�+Z�U���|�����, �,��9�I�㬊�LˣS��[]�\Ϋ���r��B�����*7���u���my�ʈB��l��rcc� ����A3�ӥ��l`��O�bU���i/ N�Ra�e`�8���A�q�B� �#l ��9< gy8E�1ȂE��yL��- ��&\�π�;L��.$X��ejF}5�e�ǯ�jHhL�(�Wh�wx� 0000036648 00000 n In this, the design of observational studies in econometrics is similar to the design of studies in other observational disciplines, such as astronomy, epidemiology, sociology and political science. 0000003951 00000 n Many of these papers are themselves highly cited. 0000022359 00000 n 0000002625 00000 n Using R, the former can be computed as 1 (residual deviance)=(null deviance), where residual deviance is the value of the likelihood function of the tted model, and null deviance is the value of the The finite-sample performance of the estimators is evaluated and an empirical application is provided. 256 90 0000003552 00000 n "Inference in TAR models" Studies in Nonlinear Dynamics and Econometrics (1997) Program and Data Files This program replicates the empirical work reported in the above paper. 0000046693 00000 n h�b``a`�������7�A��b�,7�8��~����T!cR[���7������\@ѥ��Ԭ�N5/���;� E uu Iii iiT where ii is the variance of disturbances in 0000006275 00000 n 0000057192 00000 n The models can be thought of in terms of extension of autoregressive models discussed above, allowing for changes in the model parameters according to the value of weakly exogenous transition variable z t. For tests of TAR models vs STAR models, see Gao, Ling and … 0000021852 00000 n 0000057620 00000 n 0000032911 00000 n 0000003818 00000 n 0000011629 00000 n A distribution theory is developed for least squares estimates of the threshold in threshold autoregressive (TAR) models. 0000006084 00000 n 0000031103 00000 n 0000055974 00000 n The founding members of the Cowles Commission defined econometrics as: “a branch of economics in which economic theory and statistical method are fused in the analysis of numerical and institutional data” [Hood and Koopmans (1953, p. xv)]. The Econometrics of Oil Market VAR Models * ... models, let alone the basis for the sometimes divergent conclusions reached in the literature. A distribution theory is developed for least-squares estimates of the threshold in Threshold Autoregressive (TAR) models. ... TAR Models. 0000028247 00000 n 0000053359 00000 n �=��>��Q1�z�]Fu2�g5`����2&:eG ��w�Twq���鮛�3sI������'��߸�R����ߌWkPSg�brb����=/�V�n�e��u�֪�lK���]�J� �@n9'� �"� ��"wP�}�����۩���aھa?vf�C�-���Ι���%������ϙ��B�����ރ-�����hS�s�ثL�l��;H��ٔ�\PVTVȴ�R���ՙ8%Z�mD��������I4��p(o�t:�й��)x���Rހ��`ހx��:Y������B���)��� H������y���f���� ʼ��Ӎ�#���C���B*��>���6�G~�o��[x�`������5iG�x����Zb���An� "ɘf�lϱd^�oC�&�$)z}� �����}�{�T�'CK��8�.�1��-DZy�����S�n�� /p�B�ȋY�� This popularity is due to the fact that they are relatively simple to specify, estimate, and interpret, at least in comparison with many other nonlinear time-series models. A distribution theory is developed for least-squares estimates of the threshold in Threshold Autoregressive (TAR) models. 0000023057 00000 n Theory and Applications of TAR Model with Two Threshold Variables Haiqiang Chen Wang Yanan Institute for Studies in Economics , Xiamen University , Fujian , China , Terence Tai-Leung Chong Department of Economics and Institute of Global Economics and Finance , The Chinese University of Hong Kong , Hong Kong , China Correspondence [email protected] �N<2K�&/��Z45��O��Z�s��M��B��VA�)zS�\�nl����xQ3'���i=ML"��Z��N�r&lM�����)�d(b��b�ힴ:jaPIW�&���@9i��P��ٓ�F,�q�+Xd��S8��#�X휔Aŋ �p��ht ��X��d�5Ô�M����U�0h;+i�a��Q(1 (�"d��4��q/�����!Ɉ�E�+y%��5)w��U�pppl��ht�c���b�ʐoQpU:��ND£�'R-���%Q}��x}���9d�F�ÆN��EGVi�����_V@�jɣ&f�P�M>G��j��F��(�gR�Pܖ|l�����GLLl"\K^��xmU�������.�����L In this case, the chance of staying in either regime is reasonable. topic Re: TAR Models in SAS Forecasting and Econometrics. We find that if we let the threshold effect (the difference in slopes between the two regimes) get small as the sample size increases, then the asymptotic distribution of the threshold estimator is free of nuisance parameters (up to scale). 0000033273 00000 n For this illustration the dataset E1 from Lütkepohl (2007) is used. 0000007841 00000 n tax gap, we develop a model for estimating an important element of the gap --improper claims for the Earned Income Tax Credit EITC). For Y = (y1,..., yT) and Z = (z1,..., zT) with z as a vector of lagged valus of y and possible deterministic terms the least squares estimator of the parameters is ˆA = YZ(ZZ ′) − 1. Threshold Autoregressive (TAR) models are quite popular in the nonlinear time-series literature. 0000028605 00000 n 0000002096 00000 n 0000035504 00000 n 0000038234 00000 n 0000057477 00000 n The purpose of this survey is to provide a guide to this literature.1 Our focus is on the econometric foundations of the analysis of oil market models with The model can be rewritten as y t= 4 j=1 (j) 0 ((j) 0 + p i=1 (j) iy t− +u), (2) 3Restrictions on the structural parameters can be imposed so that there are less than four regimes. Our (econometric model is motivated by the specification developed by Erard and Feinstein (2001) for evaluating the level of non-compliance associated with understated self-employment income from �G�0^dr�1o��WP`�c��X�|�� �un��Fg&���}{��mb (6��" 0 IL�� endstream endobj 267 0 obj 1112 endobj 230 0 obj << /CropBox [ 0 0 504 720 ] /Parent 221 0 R /Contents 241 0 R /Type /Page /Resources << /ExtGState << /GS1 260 0 R >> /ProcSet [ /PDF /Text /ImageB /ImageC /ImageI ] /XObject << /Im1 262 0 R /Xi0 263 0 R >> /Font << /F1 239 0 R /F2 233 0 R /F3 246 0 R /F4 250 0 R /F5 256 0 R >> /Properties << /MC1 265 0 R >> >> /MediaBox [ 0 0 612 792 ] /Rotate 0 >> endobj 231 0 obj << /Type /Encoding /Differences [ 38 /ampersand 40 /parenleft /parenright 44 /comma /hyphen /period /slash /zero /one /two /three /four /five /six /seven /eight /nine /colon /semicolon 63 /question /at /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O /P 82 /R /S /T /U /V /W /X /Y 97 /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p /q /r /s /t /u /v /w /x /y /z 133 /endash 141 /quotedblleft /quotedblright 144 /quoteright 147 /fi /fl 169 /copyright ] >> endobj 232 0 obj << /Subtype /Type1C /Length 8030 /Filter /FlateDecode >> stream Econometrics II Seppo Pynn onen Department of Mathematics and Statistics, University of Vaasa, Finland Spring 2018 Seppo Pynn onen Econometrics II. 0000058156 00000 n 0000037864 00000 n 0000030776 00000 n 0000055496 00000 n We find that if we let the threshold effect (the difference in slopes between the two regimes) become small as the sample size increases, then the asymptotic … 0000057908 00000 n 0000004625 00000 n 0000044640 00000 n 9��d�C�w)�ld In this work we extend this modeling approach from scalar to functional covariates. 0000032622 00000 n 0000026894 00000 n Eu i 0. 0000014098 00000 n 0000058571 00000 n Economist Ronald Coase is widely reported to have said "if you torture the data long enough it will confess". Abstract and PDF File . �dd So it is a linear model iv) 1 0 2 y X is nonlinear in the parameters and variables both. 0000003028 00000 n 0000057485 00000 n 0000004093 00000 n Econometrics | Chapter 18 | SURE Models | Shalabh, IIT Kanpur 3 Treat each of the M equations as the classical regression model and make conventional assumptions for iM 1,2,..., as Xi is fixed. The model confidence set is then applied recursively and, for every month in the out-of-sample period, it identifies the set of models that contains the best model with a given confidence level. n3��n����v������M�#��c��C��v�I:�� 3�J=E�F��z|܅MH�B!��5i椧+���:M�*g�ҩT{�JO@�#��m:����>�7s_���xo[J=��|ܕMH����*+���ΰ%Ak�UNߐ�Z��� 0000022304 00000 n 0000036017 00000 n rank X k ii . 0000050666 00000 n So TAR model makes sense. 0000009219 00000 n 0000013287 00000 n H�b```c``���/@(�����QQp`�K��2�:�5�)�L? 0000021832 00000 n 0000037514 00000 n 0000058064 00000 n 0000009512 00000 n 0000058677 00000 n H���yT�ƫ���v�Y��*�g��{DDu@pas ��L+h��֢�J7��Юh��TD�TA�B"*FD�F&q������h��d��Q��s�}��{?3`8�����xL��.n�����F[��xk�Nٙ�~`��f`g�-��MRZb�e�ȕs��7��" Bruce Hansen () Studies in Nonlinear Dynamics & Econometrics, 1997, vol. 0000029125 00000 n 0 %%EOF The task of econometrics is to specify models m(x, ) and G( ), or F(y|x), that approximate the real mappings set by nature. ���J�6>���5�˒Nd1����i�i6% Warning about TAR You will get very inaccurate or misleading result of (9) if the dummy variable dt has little variation That happens when the frequency of regime-switching is extremely low Plot II displays the ag (or indicator) for regime-switching. Another is squared correlation between^y is (prediceted probability) and observed y is (which have 0/1 values). 0000027382 00000 n models. Binary Dependent Variables: • Linear Probability Model • Probit Model • Logit Model • Ordered Probit Model 5. 0000012352 00000 n %PDF-1.3 %���� Special emphasis is given to estimation by maximum likelihood, but other methods are also discussed, including quasi-maximum likelihood estimation, generalised method of moments estimation, nonparametric estimation and estimation by simulation. 0000058368 00000 n �CPLTx�T�䏍0�ư(#1l���a�7$6�cX$�)1,�J1|��9c��S�-V�a���¥x�@"�$ Ԃ2�-��0J��d��BF�$^��E}�I�����|�ʱ/��?i�)�8�?K��H�t���[L��f��DT����� ]h��u���M�M��YJl�mG��K Ls�n���}��s6���yp?roV;�����Y�7���2��&C�%��yFL�sSu�o� ���5�NS��Y These notes are for a one-day short course in econometrics using Stan. 0000056192 00000 n 0000000016 00000 n Basic models. 0000020843 00000 n One is McFadden measure.
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