Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions
We propose an estimation method for models of conditional moment restrictions, which contain finite dimensional unknown parameters (θ) and infinite dimensional unknown functions (h). Our proposal is to approximate h with a sieve and to estimate θ and the sieve parameters jointly by applying the meth...
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| Veröffentlicht in: | Econometrica 2003-11, Vol.71 (6), p.1795-1843 |
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| container_title | Econometrica |
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| creator | Ai, Chunrong Chen, Xiaohong |
| description | We propose an estimation method for models of conditional moment restrictions, which contain finite dimensional unknown parameters (θ) and infinite dimensional unknown functions (h). Our proposal is to approximate h with a sieve and to estimate θ and the sieve parameters jointly by applying the method of minimum distance. We show that: (i) the sieve estimator of h is consistent with a rate faster than n-1/4 under certain metric; (ii) the estimator of θ is √n consistent and asymptotically normally distributed; (iii) the estimator for the asymptotic covariance of the θ estimator is consistent and easy to compute; and (iv) the optimally weighted minimum distance estimator of θ attains the semiparametric efficiency bound. We illustrate our results with two examples: a partially linear regression with an endogenous nonparametric part, and a partially additive IV regression with a link function. |
| doi_str_mv | 10.1111/1468-0262.00470 |
| format | Article |
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Our proposal is to approximate h with a sieve and to estimate θ and the sieve parameters jointly by applying the method of minimum distance. We show that: (i) the sieve estimator of h is consistent with a rate faster than n-1/4 under certain metric; (ii) the estimator of θ is √n consistent and asymptotically normally distributed; (iii) the estimator for the asymptotic covariance of the θ estimator is consistent and easy to compute; and (iv) the optimally weighted minimum distance estimator of θ attains the semiparametric efficiency bound. 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Our proposal is to approximate h with a sieve and to estimate θ and the sieve parameters jointly by applying the method of minimum distance. We show that: (i) the sieve estimator of h is consistent with a rate faster than n-1/4 under certain metric; (ii) the estimator of θ is √n consistent and asymptotically normally distributed; (iii) the estimator for the asymptotic covariance of the θ estimator is consistent and easy to compute; and (iv) the optimally weighted minimum distance estimator of θ attains the semiparametric efficiency bound. We illustrate our results with two examples: a partially linear regression with an endogenous nonparametric part, and a partially additive IV regression with a link function.</description><subject>Codes</subject><subject>Consistent estimators</subject><subject>continuous updating</subject><subject>Covariance</subject><subject>Data analysis</subject><subject>Econometric models</subject><subject>Econometrics</subject><subject>Economic models</subject><subject>Economics</subject><subject>endogeneity</subject><subject>Estimating techniques</subject><subject>Estimation methods</subject><subject>Estimators</subject><subject>Exact sciences and technology</subject><subject>Fourier series</subject><subject>Instrumental variables estimation</subject><subject>Linear inference, regression</subject><subject>Linear regression</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Power series</subject><subject>Probability and statistics</subject><subject>Regression analysis</subject><subject>Sciences and techniques of general use</subject><subject>Semi-/nonparametric conditional moment restrictions</subject><subject>semiparametric efficiency</subject><subject>sieve minimum distance</subject><subject>Statistics</subject><subject>Studies</subject><subject>Term weighting</subject><issn>0012-9682</issn><issn>1468-0262</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2003</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNqFUE1P2zAYttAm0THOXDhEk8Yt5fVH7OSISvmQGJtQAWkXz3UccEltsFN1_fc4BAHaZa8sWXq-XvtBaA_DGKc5xIyXORBOxgBMwBYavSGf0AgAk7ziJdlGX2JcAECRzgj9mTaN1da4LpvGzi5VZ73LfJP98LVpY7a23X028a62PaHahC978ZWJXbC6B2PPd8o66-6ya_fg_NplJys3kF_R50a10ey-3jtodjKdTc7yi5-n55Oji1yzikLeMKMKQzSBuhRGQUk0GEE4BzKvMZ5jKLTQTLG5KHhBqKE1x5jXFTS1YgXdQQdD7GPwT6v0OLm0UZu2Vc74VZRUiKokUCbht3-EC78K6WdREqBlyVM1SXQ4iHTwMQbTyMeQugkbiUH2bcu-W9l3K1_aTo7vr7EqatU2QTlt47utIBUTvF_PBt3atmbzv1g5ncyOhvj9wbaInQ8fYtPQKtH5QNvYmb9vtAoPkgsqCnl7eSqPK_6b3wgsf9FnNvqmSg</recordid><startdate>200311</startdate><enddate>200311</enddate><creator>Ai, Chunrong</creator><creator>Chen, Xiaohong</creator><general>Blackwell Publishing Ltd</general><general>Econometric Society</general><general>Blackwell</general><scope>BSCLL</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>0-V</scope><scope>3V.</scope><scope>7WY</scope><scope>7WZ</scope><scope>7XB</scope><scope>87Z</scope><scope>88J</scope><scope>8BJ</scope><scope>8FI</scope><scope>8FK</scope><scope>8FL</scope><scope>8G5</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ALSLI</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FQK</scope><scope>FRNLG</scope><scope>FYUFA</scope><scope>F~G</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>JBE</scope><scope>K60</scope><scope>K6~</scope><scope>L.-</scope><scope>M0C</scope><scope>M0T</scope><scope>M2O</scope><scope>M2R</scope><scope>MBDVC</scope><scope>PADUT</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PYYUZ</scope><scope>Q9U</scope><scope>S0X</scope></search><sort><creationdate>200311</creationdate><title>Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions</title><author>Ai, Chunrong ; Chen, Xiaohong</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c4930-f4ea5e2c20d87ea082c0e726602bd11b105c7c4a4b756523e3d6116d90fda453</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2003</creationdate><topic>Codes</topic><topic>Consistent estimators</topic><topic>continuous updating</topic><topic>Covariance</topic><topic>Data analysis</topic><topic>Econometric models</topic><topic>Econometrics</topic><topic>Economic models</topic><topic>Economics</topic><topic>endogeneity</topic><topic>Estimating techniques</topic><topic>Estimation methods</topic><topic>Estimators</topic><topic>Exact sciences and technology</topic><topic>Fourier series</topic><topic>Instrumental variables estimation</topic><topic>Linear inference, regression</topic><topic>Linear regression</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Power series</topic><topic>Probability and statistics</topic><topic>Regression analysis</topic><topic>Sciences and techniques of general use</topic><topic>Semi-/nonparametric conditional moment restrictions</topic><topic>semiparametric efficiency</topic><topic>sieve minimum distance</topic><topic>Statistics</topic><topic>Studies</topic><topic>Term weighting</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ai, Chunrong</creatorcontrib><creatorcontrib>Chen, Xiaohong</creatorcontrib><collection>Istex</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>ProQuest Social Sciences Premium Collection</collection><collection>ProQuest Central (Corporate)</collection><collection>Access via ABI/INFORM (ProQuest)</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Global (Alumni Edition)</collection><collection>Social Science Database (Alumni Edition)</collection><collection>International Bibliography of the Social Sciences (IBSS)</collection><collection>Hospital Premium Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection (Alumni Edition)</collection><collection>Research Library (Alumni Edition)</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Social Science Premium Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Business Premium Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>International Bibliography of the Social Sciences</collection><collection>Business Premium Collection (Alumni)</collection><collection>Health Research Premium Collection</collection><collection>ABI/INFORM Global (Corporate)</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>International Bibliography of the Social Sciences</collection><collection>ProQuest Business Collection (Alumni Edition)</collection><collection>ProQuest Business Collection</collection><collection>ABI/INFORM Professional Advanced</collection><collection>ABI/INFORM Global</collection><collection>Healthcare Administration Database</collection><collection>Research Library</collection><collection>Social Science Database</collection><collection>Research Library (Corporate)</collection><collection>Research Library China</collection><collection>ProQuest One Business</collection><collection>ProQuest One Business (Alumni)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>ABI/INFORM Collection China</collection><collection>ProQuest Central Basic</collection><collection>SIRS Editorial</collection><jtitle>Econometrica</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ai, Chunrong</au><au>Chen, Xiaohong</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions</atitle><jtitle>Econometrica</jtitle><date>2003-11</date><risdate>2003</risdate><volume>71</volume><issue>6</issue><spage>1795</spage><epage>1843</epage><pages>1795-1843</pages><issn>0012-9682</issn><eissn>1468-0262</eissn><coden>ECMTA7</coden><abstract>We propose an estimation method for models of conditional moment restrictions, which contain finite dimensional unknown parameters (θ) and infinite dimensional unknown functions (h). Our proposal is to approximate h with a sieve and to estimate θ and the sieve parameters jointly by applying the method of minimum distance. We show that: (i) the sieve estimator of h is consistent with a rate faster than n-1/4 under certain metric; (ii) the estimator of θ is √n consistent and asymptotically normally distributed; (iii) the estimator for the asymptotic covariance of the θ estimator is consistent and easy to compute; and (iv) the optimally weighted minimum distance estimator of θ attains the semiparametric efficiency bound. We illustrate our results with two examples: a partially linear regression with an endogenous nonparametric part, and a partially additive IV regression with a link function.</abstract><cop>Oxford, UK and Boston, USA</cop><pub>Blackwell Publishing Ltd</pub><doi>10.1111/1468-0262.00470</doi><tpages>49</tpages></addata></record> |
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| subjects | Codes Consistent estimators continuous updating Covariance Data analysis Econometric models Econometrics Economic models Economics endogeneity Estimating techniques Estimation methods Estimators Exact sciences and technology Fourier series Instrumental variables estimation Linear inference, regression Linear regression Mathematical models Mathematics Power series Probability and statistics Regression analysis Sciences and techniques of general use Semi-/nonparametric conditional moment restrictions semiparametric efficiency sieve minimum distance Statistics Studies Term weighting |
| title | Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions |
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