YSq@DIU8)m_H)gO2Y;%Q#f96(W-8XB(tp`MKh.?MH(JnpI[\2n@4RBT(j``6"Q@m6N9bc&KbdHb+fPaX,1Vo1WoJST63k,.hTuNK--1!Uj#M?f-C4%!ThH&.LVPKoqW@B`bPAhXGu$MJL`j@8%*qP'`"ahgQ<0kr&@+k_/lP&naEuXg6NlA]EHn!*R$F3k-bDh+-L)Lm:fRlP.-[.VSfe;Wmj!N%VAN:o8eq^CX+R>Y'M\m'n0Z;ROR&=o3sGF9'<0B)rsVn*%;XmocjFX_BUR*?It9YX]8]R==T12W6REo'[I#cmke##'/@s^L*)[>^sp88[`MZo1KaB!#$CT12mkN?HPDW#VV7QCQ1GYPE*H!k2/&S0*N;@Fl4kBNlM=^q)Ec5%W%/&;Wg9RSa_?'Varr#NX8G0a#tUPDf8W;c>eAn$K4YST&m4W[4SrGnorG'aD\.*8]BGJhDan8c(qXF1,Z`!op8N*#d7"qmA_2uT]QoZ&tHr<9@td$hlu*?]C$%2K&a4fJJEe+%4bajSWrXZN"tFB)=m(XR,FV2`c'6@KPsu_lKY2'TD-?Dd2.IS=Rk\AUu7m>`c'6@KPsu_lKY1(Y@+HGSc@t)0DMf5eQ9Xq?'XW&`E--uY58r@?%'? These items might vary in physical appearance, as well as quality and price. 4 0 obj <>stream This paper develops an assignment model of heterogeneous workers to heterogeneous tasks that provides a microeconomic foundation for aggregate production functions. !r@80Q. A���������"� u���h�p�|A�R��� �������wRI�U�4F��u��h��'����9����(�(!8�8?9,D5�׮�W�M���J�=1��52��3f�����/s���ҶTS�_�g��&�8XaQo�N��3�'� ��nM In particular, the differences in production functions explain 46.6% of the difference in per capita output between the East region and West region in China. Heterogeneous products are products that have significantly different attributes, such that they cannot serve as perfect substitutes for each other. J���X%�H�yw��m���m��m�h��}�Є�#"�����*��H���V OHb �b�'TBV-�f_ƻ�xA@D�w|D Wߠ´Ĭ���a&L��y�}� ���C�D��w��C��b�Q�W��36�aA��$J��͑���壵`IȣYwtmݎy��g�\��U�2!r5�I#~�G�y�>��(�Sݯ�SlJ��+���v����x^%� ێ���8��;֣=�Wچ����ScO�aH\ij{k�,� �au�/� �����W�,�$��V� �M�ng���0CKs��4���\(��"Y�P`�eL�����Sj���EL����)�I7���˞��*�I��G�=��sx;�ri���t9W� �y���T�|�|������8�_3Lu���=�|�����;a�� �T'���x��ymhKc2���� |�0�j�,���x�Ur6��7���� The authors employ a heterogeneous technology framework where implemented technology is chosen jointly with inputs to interpret information obtained in the empirical analysis of panel data. Using a transformation of the firm’s first order condition, we develop a new identification strategy and propose a simple nonparametric estimator for the production function and productivity. technology, implying that a common production function generated observations used in the analysis. This paper develops an assignment model of heterogeneous workers to heterogeneous tasks that provides a microeconomic foundation for aggregate production functions. endobj A� �R�Qj5�z�C@ ѼmF�f�:&d$3����B��Κ}JD\�;��h�f��p�u�#T�pT;5Z� It develops research and higher education projects in the fields of ecological and environmental economics, with a special focus on the role of policy and On the Identification of Production Functions: How Heterogeneous is Productivity? On the Identification of Production Functions: How Heterogeneous is Productivity? Production Function and Wage Equation Estimation with Heterogeneous Labor Production Function and Wage Equation Estimation with Heterogeneous Labor. On explaining regional differences, the current literature emphasizes the difference in factor accumulations. On the Identification of Production Functions: How Heterogeneous is Productivity? Gau0CD/\/e&H;*)TeF5[TVhB7/&8A8C!me3D3h[6L:/1;M6Y]2Ude6?ZZc.(HGWp/=ec!^/radn;fuuS!21M22#09G9-]V*c\tQG[S^43PLaH#9#Uc?I0:]Qp2%*25ECD`s0DcVmOT+3.MS.4k'tg0NY5)H0o6b$GWZXVloZuO2+2=OB9=h8Jp\O0VhAO)&cEGfe,^jdS:Jon.F+a=+?=QPb*-9j$&PqiRHH:%!=@##ead/+G\=H]hi1d#M5BEagS.]t_BKq="1/.$J!Q]`t#$_EHnEPXVDnu.kl+2Hum["_tU8l#lTps9D+@a^Mf=(73-W(MLAS^@t`bPd?q/lN5m'+IZCA.DgEM[aRg6o@lUZFZpV%YIk1[8V?j.aI"SXjg\qdXfSC)>'Qo>H@hKX]=>3a4-PjkggLVR2FUaN['!N;hE+r9CjZ30,:K3UrFF$Eb8B6#mU.#:I?an_B)[>cqtIcVK-C',kugnKbX6k9")l*5EC7:)*IO8Ua-t$j,?51%GGD5RQ/3eP[$_).69@Y8L=D!K:5I=G6S/k-brlFcMP(qq&1#?]F/mMc?&rpSh)[!#hAk\=6oeBD1O55sILK.C2U#ol5kCiNe$8FM'FsM;(`eK4&,TG).78[G1'K]C9"RHD)9:;5$X+YR&[P5J>q^rB/:hdS$jA3DhG9TYjB$*,S_Gk.cVpWb'Htuf_BuV^fXZ0(&Bee;>NAeN'nJapM:HF`47(\h\fN0AIoWcs%9b&N;!N6[#P6YZ^&Fe+G7S+'Z-PSFo]j=S+Ag4-Q%3^M:r1H%VK(LeLg>:mEEP+.8gj$L-)[,C&8^F)"j/Sr4)5Keu2pITqd_?EPC?qVd=Rdq6YU#27^6pq!)D31ja=TSr2f#uG=:;M:3taZ;TFC!oh]\$!c;/cfC^E%?Wlb[bY_;SkW3IB/)O@gY.=a?ZML+hsBnVK-5hW4u*=[t-X%GoGeNPe#Q<7%cgl7])6q3$A5O3F)R2eY3fdi&9c[Fj<5&:T$oN"b`('lPSVM-cU\&Z'^=Lg$ScV6mR9qpHBW(qACmaD+DZ=laN0tPUCKn:aR&6;M?`Y21N4*!. Heterogeneous definition is - consisting of dissimilar or diverse ingredients or constituents : mixed. Heterogeneous definition is - consisting of dissimilar or diverse ingredients or constituents : mixed. H��V�n�6}�W~i 19 0 obj <>stream A production function which is homogeneous of degree 1 displays constant returns to scale since a doubling all inputs will lead to a doubling of output. production function. Amit Gandhi, Salvador Navarro, David Rivers∗ November 3, 2012 Abstract The estimation of production functions suffers from an unresolved identification problem caused by flexible inputs, such as intermediate inputs. Amit Gandhi, Salvador Navarro, David Rivers October 12, 2011 Abstract The estimation of production functions suffers from an unresolved identification problem caused by flexible inputs, such as … Browse other questions tagged production-function productivity cobb-douglas aggregate-production ces-function or ask your own question. endobj Heterogeneous products have distinct features that make them unique to certain brands and suppliers. [1^`J4nThU#W4%BYk!s\!jk2NT1G/9-T,BhM^cJ=m01N[,C95OHggGrH-pmB@1HsY.Sc*XNW.HtI-mKX"7>"QFkCZf0s"$NMK(uh2X-OZ6-,d$XbRfQuW-CE&CRsH)^/BD,r4E+=go0i3/I08SC]QUfARpVt*.MOHODbRs%;Gbf0NFKA`r_o,OF'TQf#-YZ3kX/!WVL]]03HWi\D`s/3d8b9%A+nsY;M3J4H2:%mMY!DA3/\(DI\N8s&?mdc.OXh:2Ce,ccSGUHf1F\%iDCjg/L19MnYtPMGl0d+\".HN/a2K">Po_'s6PB1E4>Vbe^`3FUlQr('hc+3/&&Su9)XS(YLN1&&U;8G\AAGUd:GN#8&MC.X8g]JE@&BWX/i91]&2u,e^`4#e^`4#e^`4#e^`4#e^`4#e^`4#"T8^E.F;)~> Production Function and Wage Equation Estimation with Heterogeneous Labor: Evidence from a New Matched Employer-Employee Data Set February 2004 - Working Paper … Abstract. 16 0 obj <>stream Evidence from a New Matched Employer-Employee Data Set. H�|V�r�0��,� ��+�qa;E�̤P��HHBB 18 0 obj <>stream P. Garegnani; Heterogeneous Capital, the Production Function and the Theory of Distribution12, The Review of Economic Studies, Volume 37, Issue 3, 1 July 1970, The shape of the production function is shown to depend crucially on the distribution of tasks. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We present a new approach to the estimation of production functions that allows for richer patterns of firm heterogeneity than can be accommodated under the proxy variable methods of Olley and Pakes (1996) and Levinsohn and Petrin (2003). A Microfoundation for Production Functions: Assignment of Heterogeneous Workers to Heterogeneous Jobs By ARNAUD DUPUY ROA and Maastricht University Finalversion received6 January2011. Amit Gandhi, Salvador Navarro, David Rivers∗ September 25, 2013 Abstract We show that existing practices for estimating production functions suffer from a fun-damental non-identification problem due to flexible inputs, such as intermediate inputs. The identification is constructive with closed-form formulas for the elasticity with respect to each input for each firm. We use cookies to help provide and enhance our service and tailor content and ads. *L.#j3g0"Y+6fQ(;^FoUCqE-rGrB endobj On the Identification of Production Functions: How Heterogeneous is Productivity? Heterogeneous integration is ... have enabled integrating chiplets from different manufacturing process flows into a single package with a variety of functions. In mathematics, a homogeneous function is one with multiplicative scaling behaviour: if all its arguments are multiplied by a factor, then its value is multiplied by some power of this factor.. For example, a homogeneous real-valued function of two variables x and y is a real-valued function that satisfies the condition (,) = (,) for some constant k and all real numbers α. Section II presents sufficient conditions to obtain a CRES production function, while necessary conditions are provided in Section III. Heterogeneous Capital, the Production Function and the Theory of Distribution12 The notion of capital as a " factor of production ", on which the theories of production and distribution dominant since the latter part of the last century ultimately rely, has been the object of considerable discussion in recent years. Using the province-level data in China, this paper shows that capital shares have a very significant and positive effect on per capita GDP. "Heterogeneous Capital, the Production Function and the Theory of Distribution," Review of Economic Studies, Oxford University Press, vol. Abstract. Featured on Meta Hot Meta Posts: Allow for removal by moderators, and thoughts about future… In the original presentation, s is absent from the production function and from the factor demand. A heterogeneous coefficient approach to the knowledge production function . 12 0 obj<>>> Production Function and Wage Equation Estimation with Heterogeneous Labor Production Function and Wage Equation Estimation with Heterogeneous Labor. The production function is said to be homogeneous when the elasticity of substitution is equal to one. 8 0 obj<> We present a new approach to the estimation of production functions that allows for richer patterns of firm heterogeneity than can be accommodated under the proxy variable methods of and Olley/Pakes and Levinsohn/Petrin. inputs using a value-added production function does not solve the identification prob-lem. )/∂x k <=> 0 should all be possible. Heterogeneous relation From Wikipedia, the free encyclopedia In mathematics, a heterogeneous relation is a binary relation, a subset of a Cartesian product A × B, where A and B are distinct sets. ScienceDirect ® is a registered trademark of Elsevier B.V. ScienceDirect ® is a registered trademark of Elsevier B.V. Heterogeneous production functions and regional disparity. Heterogeneous technology and panel data : the case of the agricultural production function (English) Abstract. As is well known, these theories had Corinne Autant-Bernard and James Lesage Additional contact information James Lesage: McCoy College of Business Administration Finance and Economics Department - Texas State University Heterogeneous Capital, the Production Function and the Theory of Distribution12 The notion of capital as a " factor of production ", on which the theories of production and distribution dominant since the latter part of the last century ultimately rely, has been the object of considerable discussion in recent years. We propose that the flexible input cost ratio plays the role of a control function under “non-collinear heterogeneity” between … Estimating Production Functions with Heterogeneous Firms Amit Gandhi, Salvador Navarro, and David Rivers University of Wisconsin-Madison May 16, 2008. H��V�n�0��+��R f�~AyzP ����lɕ�:��R6)Ӥ�&������.v�3��ů�u�R�����f��m�ׇ�9!�V�����lu㬳�G 1E }c~C}4�n)�ι5n�P�F�QqGe�bR�~��P*�X�;��8�I����D�vj�Y6cG�;�Tذ�Ь[/A`��v�qю�4��?wlEz���7J�^�:m3e��|d�|�P���&�[e�;��e�B��yQ��?�Z����|�R[�E��� وS����v��Iߙa!�HW -���Nu?_��*�öX�����40�Ϊ�p�I�%j��[����G���oE]�M3HƐ,7tP%���S��|\'�ŞVˋaA�������5ug�w3�c�#䆋Wޮ�|��N��0۝�I�)�[�׸M�X Thus, in the case of homogeneous technology, identification can be … 3 0 obj<> The prefix hetero is from the Greek ἕτερος (heteros, "other, another, different"). Using a transformation of the firm’s first order condition, we develop a new identification strategy and propose a simple nonparametric estimator for the production function and productivity. With the introduction of prices, s appears in the factor demand, but not in the production function. This paper develops an assignment model of heterogeneous workers to heterogeneous tasks that provides a microeconomic foundation for aggregate production functions. Request PDF | Heterogeneous Technology and Panel Data: The Case of the Agricultural Production Function | We investigate the salary returns to the ability to play football with both feet. SEEDS is an interuniversity research centre. in Hard-to-Measure Goods and Services: Essays in Honor of Zvi Griliches, Berndt and Hulten. �Q�>�����N�bw߾}� �f�v�Ay�q�se�5��ad�� �0��1 ��RZȃ;A�� q��l��|/��De�A ���p���F�u�4�-��KLnyk�k�*� �2w�����p�������T�E �xX��0��/�՗o����{���÷�/��^̷���a�~�̄�[d��Rt?hQ���` ����Ҵ���������fL��/Y�qQR]9�ԉ�u�-�B{8� By Corinne Autant-Bernard and James P. Lesage. Downloadable (with restrictions)! Featured on Meta Hot Meta Posts: Allow for removal by moderators, and thoughts about future… endobj It develops research and higher education projects in the fields of ecological and environmental economics, with a special focus on the role of policy and "Heterogeneous technology and panel data: The case of the agricultural production function," Discussion Papers 290004, Hebrew University of Jerusalem, Department of … production function cannot generally be used to identify features of interest from the gross output production function. %PDF-1.4 Homogeneous applies to functions like f(x), f(x,y,z) etc, it is a general idea. This production function can be shown symbolically: HETEROGENEOUS CAPITAL 409 Assumptions (i), (ii) and (iii) we made about the system of production ensure that for r = 0 there is a positive "maximum wage " which we shall indicate by W. On the same assumptions, as r rises from zero, utfalls as a continuous differentiable function of r, reaching zero for a finite " maximum rate of interest " R. P. Garegnani, 1970. ]�_��i�u���(,��xw��R��R�_�#p�9īG.���G��!P[�SaX��5U�l��g8��cR�TA=a܍�n\f�h���b��nt[�Ϫ�V4��g*]��|~�x��/�ȟN\ K��cƗ3rX�E u1M_�����Д��%���t�~��M>�֢,��X��ȝ�xDr�d�Lq��(�{~MMRx ����!ܺ���F����[=��(�@\us�=n,S�W��+��'nq0G^ �|L��x���w���Q ��k��x��DƊ�P� ְ.�D�0��j#b�V�B�xQ��r�e�@p�w� �%�%��ޒz�|6��M;m)���XEh�Ѹ��{ԣ�7ߚG ��x˯���s*_7C�6�ûl]�zA��|&�1��؏�Mv�{r€@"�����z�P�6���'�->B��;�~�i�BNa��.��6�����b��:�j)��T�r���� ��-IE6c�o���Yq��]�sn,�li��������*�^ )�����ձB� �g���@JS3Q�R����#y� l Chapter: (p.31) 2 Production Function and Wage Equation Estimation with Heterogeneous Labor Source: Hard-to-Measure Goods and Services Author(s): endobj endobj endobj function v r and decision rules a0 r,c r. 3 The policy function a0 r and π induce Markov transition function Q r. 4 Compute the unique stationary measure Φ r associated with this transition function. How the heterogeneous catalyst works (in general terms) Most examples of heterogeneous catalysis go through the same stages: One or more of the reactants are adsorbed on to the surface of the catalyst at active sites.. Adsorption is where something sticks to a surface.It isn't the same as absorption where one substance is taken up within the structure of another. Browse other questions tagged production-function productivity cobb-douglas aggregate-production ces-function or ask your own question. Heterogeneous technology and panel data: The case of the agricultural production function Introduction The focus of empirical analysis of agricultural production functions, similar to that of production functions in general, has changed over the years. �'���C���8�(T�@�S(�ٻ��e,������[��r>�3�� �?��ֻ�2\���xx�ܙ�Mscp Focuses on a study which dealt with production function, heterogeneous capital and the theory of distribution. Corinne Autant-Bernard & James P. LeSage, 2018. " 7 0 obj<> This paper suggests an additional possibility that regions may differ in parameter values in their production functions. x��S� �� ������Lw%W��u��C��v)M_l-9sfΙ��}ߏ�nF����zy�h�s�ҝF�����F�D�P)�������ݢ��B(��4p(��P�bU)���7�0����#Aw]�K��xn?�8�n?ށ]@#B�XP�PqSۊ~!����LhY������j@���� ��1���KE��anx�7?���ݣmmwЏ��[P��0Q�G�on�'7ևk�!��o�� �Іb��d7�m�!B{#�%��s��N��v�*�PM�f���]�`]�)�XE0"�P�m׿$51��p�=��#2z߹a���)e����@�QQ2eÕ�P ʖ%���U��C��.�ս����M1(�\�A£"Xh��(!�6f�R (����E��aC�%��h������LDw-�a�^�x9�yN4p�,t�#�~��`�_ҹ��ߡ�ćr_ �Y��5y�����l�3M�ZP�B.�J`#M����� Applying our approach to plant-level data from Colombia and Chile, we find that a gross output production function implies fundamentally different patterns of productivity heterogeneity than a value-added specification. A heterogeneous coefficient approach to the knowledge production function Corinne Autant-Bernard, James P. LeSage Abstract: Past literature has used conventional spatial autoregressive panel data models to relate patent production output to knowledge production inputs. The paper presents empirical analysis of a panel of countries to estimate an agricultural production function using a measure of capital in agriculture absent from most studies. Applying a heterogeneous coefficients spatial autoregressive panel model, we estimate region-specific knowledge production functions (KPFs) for 94 NUTS-3 regions in France using a panel covering 21 years from 1988 to 2008 and four high-technology industries. (Из Ebsco) 909 University Avenue | 118 Professional Building Columbia, MO 65211-6040; 573-882-0063; 573-882-2697; umcecon@missouri.edu Our approach applies to a general class of production functions. How to use heterogeneous in a sentence. Heterogeneous technology and panel data : the case of the agricultural production function (English) Abstract. heterogeneous workers to heterogeneous tasks that provides the microfoundation to derive aggregate production functions. Supporting: 2, Mentioning: 78 - Heterogeneous Capital, the Production Function and the Theory of Distribution - P. Garegnani This paper presents the identification of heterogeneous elasticities in the Cobb-Douglas production function. !�(��������8�9}h]�w��Dp����K���>���q�fE�߹8�w��j��.Ɯp��r��˙�*�! Keynes was adamant that the assumption of homogeneous output and capital in macroeconomic theory is inadmissable. endobj There are few papers on the possible cause of heterogeneous production function. Heterogeneous products are often designed to attract different segments of the population, and cater to people of varying geographical locations and socioeconomic status. 13 0 obj<>>> The estimation of production functions suffers from an unresolved identification problem caused by flexible inputs, such as intermediate inputs. Relations between the wage, the rate of interest and the product per worker in the two-commodity economy; Details on the surrogate production function; Premises of the traditional theory of distribution. In reality, firms face the practical problem of choosing which technology to employ jointly with inputs so that technology is heterogeneous in that there is more than one function associated with the data. A heterogeneous coefficient approach to the knowledge production function. The paper analyzes the implications of this process on the estimation of agricultural production functions using a panel of countries. 2K views View 2 Upvoters 10 0 obj[11 0 R 12 0 R 13 0 R] 2007 This video shows how to determine whether the production function is homogeneous and, if it is, the degree of homogeneity. Corinne Autant-Bernard and James P. Lesage Additional contact information James P. Lesage: Fields Endowed Chair in Urban and Regional Economics, McCoy College of Business … Section IV relates the main results of the paper to the literature on skill-biased technical endobj An example of heterogeneous product can be apples sold at the grocers all apples are similar, undiferentiable and unbranded. The linear homogeneous production function can be used in the empirical studies because it can be handled wisely. �Ů��ƺ�t��sBF$�, g)62o)5Yp=D&Nf(2VjRVNeY[e^gR,#h8:dUa&3'e,4hJ+Js6>Anlj>S?aC8[qJ#*7GN]fc"#-)F/nG/5>RnD6u0C5U`DEif"'GV%`IN?A3=Cu_7IrVnYpj:]?\3(FP:=G]Z[;G1$X"X(K_-)ehlahDLa"8g[f"*-sWd1-lO=!s0,Af89s`_-8LfLi/8Gl5%C`sB4ZPFiAGnbS>8!Zib"_fD_Z?F>Bi`$pYW[;=$.kYTo/3mXkCFD+F$7L?s'E=?iei!O1b*D7KMW>D@nI`kC;"kCQd,[%o@O&Mn^_XhaUEN7q(/@\A&=msV;Ya8Nor@O7EZ31Z?5XSk2>_04'(Z^@pGiD]='r,81MW@UgCC-4#/WmCE!=j"40YC[jZ)7oF_dtr%@.=uLb/6#I/.%In1;ELJWB0tCU1=Y&D. heterogeneous workers to heterogeneous tasks that provides the microfoundation to derive aggregate production functions. His aggregate supply or Z function is a generalisation of Marshall's ordinary supply function to take account of heterogeneous output, and is an essential element of the principle of effective demand. This paper develops an assignment model of heterogeneous workers to heterogeneous tasks that provides a microeconomic foundation for aggregate production functions. Economic growth involves reallocating resources from traditional to new techniques of production, creating new relationships between particular resources and productivity. 11 0 obj<>>> Estimating a non-neutral production function: a heterogeneous treatment effect approach . 9 In other words, the production function should be general enough to accommodate both increasing and decreasing output risk in inputs. Amit Gandhi, Salvador Navarro, David Rivers∗ November 3, 2012 Abstract The estimation of production functions suffers from an unresolved identification problem caused by … Homogeneous Differential Equations. 1 Following the work of N #1��~n�]V6b��, Production Function and Wage Equation Estimation with Heterogeneous Labor: Evidence from a New Matched Employer-Employee Data Set, Judith K. Hellerstein, David Neumark. 5 0 obj<>/Font<>>> Abstract: This paper presents the identification of heterogeneous elasticities in the Cobb-Douglas production function. �q������c+����g�p.��3%`ܼ��5|$E��HI̽�s?Z�kĨ�Mu����.�mE?�1�]�b��(o�O� t^C In terms of the Cobb–Douglas production function, regions may differ in the share of capital in income. The identification is constructive with closed-form formulas for the elasticity with respect to each input for each firm. endstream In mathematics, a homogeneous function is one with multiplicative scaling behaviour: if all its arguments are multiplied by a factor, then its value is multiplied by some power of this factor.. For example, a homogeneous real-valued function of two variables x and y is a real-valued function that satisfies the condition (,) = (,) for some constant k and all real numbers α. However, we show that even if the production function is Leontief in value added and intermediate inputs, which is the only plausible assumption under which value added can be both a theoretically and empirically well-defined object (see e.g., Parks, 1971, Berndt and Wood, 1975, and Denny and May, 1978), the value-added production function endstream inputs using a value-added production function does not solve the identification prob-lem. How to use heterogeneous in a sentence. P. Garegnani; Heterogeneous Capital, the Production Function and the Theory of Distribution12, The Review of Economic Studies, Volume 37, Issue 3, 1 July 1970, Section II presents sufficient conditions to obtain a CRES production function, while necessary conditions are provided in Section III. endstream Evidence from a New Matched Employer-Employee Data Set. "A heterogeneous coefficient approach to the knowledge production function," Post-Print halshs-01936662, HAL. Applying our approach to plant-level data from Colombia and Chile, we find that a gross output production function implies fundamentally different patterns of productivity heterogeneity than a value-added specification. The Key Assumption and What We Do I Production function estimation as a tool for productivity analysis I e.g., Estimate a production function … endobj endobj endobj 9 0 obj<> endstream g�wQ_ߔ�'oq%��H�yw'������r���>�-t�_s�ѿ &$b] We show that existing practices for estimating production functions suffer from a fun-damental non-identification problem due to flexible inputs, such as intermediate inputs. The paper presents empirical analysis of a panel of countries to estimate an agricultural production function using a measure of capital in agriculture absent from most studies. Factor shares for state-owned firms are different from those in non-state-owned firms, suggesting that the different capital shares in different regions may due to the regional difference in firm ownership structures. It can accommodate both heterogeneity in input prices and a variety of heterogeneous intermediate input types. Copyright © 2021 Elsevier B.V. or its licensors or contributors. �g�.AEa� Bai, Qian and Wu (2008) show that the degrees of monopoly may affect capital shares in China. 17 0 obj <>stream production function cannot generally be used to identify features of interest from the gross output production function. endobj https://doi.org/10.1016/j.chieco.2010.05.005. endstream A first order Differential Equation is homogeneous when it can be in this form: In other words, when it can be like this: M(x,y) dx + N(x,y) dy = 0. A heterogeneous coefficient approach to the knowledge production function. The identification is constructive with closed-form formulas for the elasticity with respect to each input for each firm. The shape of the production function is shown to depend crucially on the distribution of tasks. The shape of the production function is shown to depend crucially on the distribution of tasks. H�|VɎ�0��+P�z���}��9�-��H`DC���������(�rU�z����3��2��o'$ ,��G�,#\ On the Identification of Production Functions: How Heterogeneous Is Productivity. Estimating a non-neutral production function: a heterogeneous treatment effect approach . For the CES production function, the elasticity of substitution between skill groups of workers is shown to depend only on the variance of tasks in the economy. Copyright © 2010 Elsevier Inc. All rights reserved. Section IV relates the main results of the paper to the literature on skill-biased technical That is why it is widely used in linear programming and input-output analysis. A production function is homogeneous of degree n if when inputs are multiplied by some constant, say, α, the resulting output is a … Heterogeneous products in economics are products with similar traits hence undiferentiated and tend to be unbranded as well. An example of a heterogeneous product is the car. This paper develops an assignmentmodel ofheterogeneousworkers to heterogeneous tasksthat providesa microeconomic foundation for aggregate production functions. The shape of the production function is shown to depend crucially on the distribution of tasks. Chapter: (p.31) 2 Production Function and Wage Equation Estimation with Heterogeneous Labor Source: Hard-to-Measure Goods and Services Author(s): Applying our approach to plant-level data from Colombia and Chile, we find that a gross output production function implies fundamentally different patterns of productivity heterogeneity than a value-added specification. Further, using the firm-level data, we show that the differences in regional production function are likely due to different industry compositions. SEEDS is an interuniversity research centre. 6 0 obj <>stream %���� The paper presents empirical analysis of a panel of countries to estimate an agricultural production function using a measure of capital in agriculture absent from most studies. By continuing you agree to the use of cookies. Gb"/id;fCLN^NdF5FoH`;SLu:!D#hq0&^Ya#rmIja_]6"o?Yt;e^`4#e^`4#e^`4#e^`4#e^`4#e^`2MR=;2-QnB:o)Pb?!WH@kmnKmoLN%bF*7?FUcQ3,OS]UsgPo?&dG"%i"9_q6-slqY!_Cg\J%Uo(r'0Q[LaheQ%Io=+#/`mCHZpe^_.pgV3g2+8j%AlKT;ls1C:>MnUMnUYg&%+Ug!U&MOTV^$8"#^lf*a2SJ'pC3L@S>2h1(o/;gQ")rIP[eVIK^Y;2O>b1[,$tQQ0b#,CaG""@i*-B\V#e15;%kb0C=]#>4ke1Ii`o6']LYp3*kpI=*Mh$jo>-H"AW/Na$I8G^FTOjRo0o-=aM1U2`=77iaCm`@]0uNJV;;@6SO]7@+0-[^P1H,gQRLO/?s*g2>=uR8ni+6rM+KJ!Wq(lg[5qEoHSLerO(=:o4ILm>YB;@P91&%q;PbV7p5J,o(BPQgKGSf='pl#m@s[8YA8@;?mI.>48Bl`&jbZb=_L(=q-A?dNDK!flcFto&D6?\S[nP#UH&6SFq=?\K,F>JMqn.3?TU'dnC.V;2TA.B-buf7JEs1H]AW5rC#c$4F@3KJ=WCo]RJ3rVp.R&B"@UtH2K[4HBY=%EPD*qTdGKD7n/n@`GOi=OFe=^N-nFj*UY,"apV*d8F9i@]F[#d2Z6k,"9TVbBrjPR0kQe)L(F9(&L8]>\'SEUJ&,t[$sP)&6:K_Hf>(CfK4]M85J4W.<4iqf]Me;3h1G,8p4S3b=b23[EPYXGVX2)8hDtGDd0f9;p1e,I(L]4X)54N&71oI\Y5,uX:!u5cRSNQ&u+#4%o_,4?T/Uo/,:f1"l[W`oId-q\=Jr^N(-#`#d8-U]Mc-M9\BN3LFgb$`8K5LT;IN9&3ML;IngP]h/IY9A0i)?b"rIQm^Z#E(feI3>r7/k@I4(*$,W_^0!F?FP5M@IRoG(UGKe9/[BOk[,D[>jej$'q)--;+@ZkdZBTK1Gij/8ASL%Wau_FpBf>L5(a'B%,4'k_tb,D*OQl,G9gtKt#]D7#06V.2F9YMUD&cV=Qf4657_5PTP)okTnp=m;],`Xra=NY91mfGU7%THt%H/5pAAG9Q#^1[LAj"HfXRtO9G3EX+8Lh>@eD[C\_Mcu,lkY8@p*&6l6Y"Q'eZ#iP5n`h`gQLQa;RLCs-b60lIo;A8g.,GAb(nFmYBSL'bJk-4^WiNo'rD[#_n0=Lo7HJs6jFOL;tUml?7\!N)M':YVEXf?&="lYZ'p$Ldn4p#9!eLQf.ArVt*cqOisDlO/U,rt]*_WOEn.Nh^LQU-[h2Pb=co&kl>8\mn*k`uabCDnCO*o;?3rfZ)R8`[=^7oGi<53&\\B!K[?JQjJbd=c_fB-i\#$c5t>Vb4qRR!Us'=k4N][QKfP.Yol==c*nE0p`^]$GmU^-V7cBRX7.dQK0^@bN3m'ik/!O+pCW`-&-u&n73)O9l[k\#`m-LP5HVO\\-GH8T0fhRVY45+i%2[%1N[KcU*`['=o7WenalTAU:@a!5Y[(7^8hs*PSodnV4b#ZRgD/7GP#ma3H4-!!0#cRFV&1n]"QB/'HogK;)*E1%]tT69,d/4AARbj\;@7O.kt>5_q5b]$h^#`7ftUc]9mB+o-#H(Y#V'b'A%YsD.E!+H=D"WW^UHcpih4]$GuC#eD(Jn&[`5i9?%eOP'>$0fK)tHhu,iO:dI8_!+j>$?6_L!;i9Ug+BDcq]mS=n.Di$G>dE67\*Q)&.jD7Y5jOBL69tQZPG?a=f,]\A8X5`Q,U!Q"7MO+,4Bh3Z'-0i/.ZA1bTqZZ]"qDJTqN9A:?&=X.!QCm$+?K)JUMIOq:S!?5c*e0AKus+M;]%3JG%K*!%uG-;Y^c92@Fmj%3]B`[t$i%#N?pfKD[4+?XAY8#o)?&PE?r[;k:A)*CKF+Amh!N_(HH*B$U=.`bBm9"S)CEq?,[XhrH/7#u=;9G1`i,f(=ZSr&dk7hD9!;l@f+Ea-DH;,t!4:QX*]@gS;T$g7.U]W=,Fn>)V[?A;9sK5;Ej7'#?!ZQp09hk2`:iT]3).:SqmI-lGpS.ZKrbuR$!2hF=8,Is0Ek!bA.mk4@,.EJ.:0`J2PP+(K)VG!aV&BDk1-*`^tMS8W-rHIdY_5/(m3EBBTC0E-1B6YFH2CpHF<9OgtY=g;H"lXaCNks\YI>N6^b[%C(0[n"Q($!u.P$.S-7*V/I#gYSENY0)O;V?*DdEtkn`J2JMRCe/K:ut7g&l5c4OC,#u4C`1KYA1C$ac:g##Se:j.fAN1lK"$EcOq`WEM+G%Alp,>NN$7Vd[*0IaUMtt`J1V`YD^g\;C>sV.#=+8OZe7_U6kE[qKa6:P&YqB]6@+;A8u_!;S&"7."'#bJVbK&qLHT8U.JZ6e3,ss$]K/p?!fnZL9Yb8(HQu(:-)ib11o^;#'.JXig*8.3X.iAr_S]plG6k?a(goWE;Q;AjQ4t:30F"MI+u#?s#7A=$2sCug10#:KDJ,&qoF(/kQP7%5&0?1A&,"2/'?5/SZ[K(u-9diQ4=^[j/K'V2GKB9d)(tZ/r&NiCB3,feEl,>HK^IU$8`":D@i>[544NFSto9)nHOpco5"sBU)Klp$Li!d5^Y+]B7_8=4mCu:am2MJFdY>l^BiLP]*#GqI+Zg@Y0-?"Aa6^HLiA'ZoZ40PQr!Rm!g@#[]kQ(SQmKq*$r\pXW"9L?Si[HG7,5F`#XRKrfdDEN'(C;Sc>b4g_VCAj(]dbrL0(t8)O*,QJ/b5Zd`A'a%H#aq"6I4a2'lTNr4%SAYr)Ui>dc'cV[9\6_Y;hT*O5kGNL/hk5$h>ZHI2o'J]t19JZ3l2sW@-"jV_LHj*:U&"nUY,LJSB`KRTq#ts+MCFdNPdAUKK[9"HS1&Hm*`>i"rqP5Y$;^D"gHIjEIm$(1Rt`C/jG+c7JC6XH/^BI*>?m>HcN:^Cr\g2(OmqAqh-W@RM&WnG$c5OW$TCrO#16FK+d;'^>b?aN.=%qGHb3#fg624A9Gn>A8N',1E#\1#5_lAr[]]H!SeFW3qm0bq+n9gVH)kC[l,Gnir97kKdcVB@/+ck8o#)'/*KHY5#9iRM(GWKLP'Q#P;$WXBXhG#k2!Ns[Q>gon5uDr-f,k)7$5ED#VQ0iH%+RCaL1W_I9&$Gp`If]:@#e96Hlir`%8*#FZDmuqsoP$R?(G$^8[:WN8MW]McXe5hU_hVK/Cb#KJQb1&Gj>U9[5h/WFK9n]Wd5G__,9NYb%=Bo=fM:s*Ymu?qr>m#W$\7b!UpT=+I+o*?$02gnqYAC"Y6ZrjSgKOhCj;i];e1AHBRj)V'IX8`f2pNlpYA#>p*,i/+It">lRp)LqPItrep7pe+d2"Cs=\1K7TnR;Q"Q>OpGn.*QD-h6;UV;Q$ZM#3EDRCp3M1o>-"QAsIjlI6AcHT-jQk^Q@&$u&oC)m*GX*e%hhWm-k&3dX,Q+S_DEQNnr&nAhRg)62o)5Yp=D&Nf(2VjRVNeY[e^gR,#h8:dUa&3'e,4hJ+Js6>Anlj>S?aC8[qJ#*7GN]fc"#-)F/nG/5>RnD6u0C5U`DEif"'GV%`IN?A3=Cu_7IrVnYpj:]?\3(FP:=G]Z[;G1$X"X(K_-)ehlahDLa"8g[f"*-sWd1-lO=!s0,Af89s`_-8LfLi/8Gl5%C`sB4ZPFiAGnbS>8!Zib"_fD_Z?F>Bi`$pYW[;=$.kYTo/3mXkCFD+F$7L?s'E=?iei!O1b*D7KMW>D@nI`kC;"kCQd,[%o@O&Mn^_XhaUEN7q(/@\A&=msV;Ya8Nor@O7EZ31Z?5XSk2>_04'(Z^@pGiD]='r,81MW@UgCC-4#/WmCE!=j"40YC[jZ)7oF_dtr%@.=uLb/6#I/.%In1;ELJWB0tCU1=Y&D5#;f^bi23gMD+*T4k_#F!f5*fMVXS3?cBrZJPGbT1oXR^-h2U+o-B6frs96mD9FSYn?r-MXf#pOgbro+[uGcW7`BO%:nP0qG$!DPUu%f/PZhq).k&NoQ;DM5K``DmNSF*!?C[>jU@k=If):=k.r#iCgWK;PR4NKTeMmm'h20P:F0pY_nN9Er'IZ2a2TUD#&e7Gr;TIW+@X5(J+TpHXo*Et/"b\=[S0Jc5Pe"]`j)e#nAuK'Y7iF8SXW8+*kZf*;R0RM(h%sX-%?kA_\B5)nB#Y=#6FFoe\;TV'H\WI^%R)C2kZ*#\atpZYa2bDJQ-\&VN)X`Z$OAHcB-MDHqV8E@I:#GtNI9"#a90)4lf9LBta92VPYYSq@DIU8)m_H)gO2Y;%Q#f96(W-8XB(tp`MKh.?MH(JnpI[\2n@4RBT(j``6"Q@m6N9bc&KbdHb+fPaX,1Vo1WoJST63k,.hTuNK--1!Uj#M?f-C4%!ThH&.LVPKoqW@B`bPAhXGu$MJL`j@8%*qP'`"ahgQ<0kr&@+k_/lP&naEuXg6NlA]EHn!*R$F3k-bDh+-L)Lm:fRlP.-[.VSfe;Wmj!N%VAN:o8eq^CX+R>Y'M\m'n0Z;ROR&=o3sGF9'<0B)rsVn*%;XmocjFX_BUR*?It9YX]8]R==T12W6REo'[I#cmke##'/@s^L*)[>^sp88[`MZo1KaB!#$CT12mkN?HPDW#VV7QCQ1GYPE*H!k2/&S0*N;@Fl4kBNlM=^q)Ec5%W%/&;Wg9RSa_?'Varr#NX8G0a#tUPDf8W;c>eAn$K4YST&m4W[4SrGnorG'aD\.*8]BGJhDan8c(qXF1,Z`!op8N*#d7"qmA_2uT]QoZ&tHr<9@td$hlu*?]C$%2K&a4fJJEe+%4bajSWrXZN"tFB)=m(XR,FV2`c'6@KPsu_lKY2'TD-?Dd2.IS=Rk\AUu7m>`c'6@KPsu_lKY1(Y@+HGSc@t)0DMf5eQ9Xq?'XW&`E--uY58r@?%'?!r@80Q.q?'/I4jqm2BV#,fO\UsZFZ!@#5>\0),@+U"e`j9$lL[hQ=/0p7"%>76dacl]Sc1m::60MYlb;KcmJeF@bo*5%^U=3#hAeK;I3GCcA2A9LDtEpr-8Z#[R<6[*nO@k3?V6rObt3YgWN:Mr_l[9i1ZX6GmX1Rc#bINu^&]0.bY^mZN.Z,nM#41N&$?s@%$U&KO0\d(D^r1B\PkNg^h-,O9_t@E!2(=,b5^C0"[gO38&pec]%&WnS\?I1Agf#UoKW"ND_$fF8&pec]%&Wn*PEV_@+D?cj,G(T&$3qIe7,JnjXE7=\i/'eI^ZLsoRU#q*aEOS[ld!TMKe-I5lRUuj'X1ABBNIs+ck"'iZ78TaM3sa*3@*PlrN&Jpq2X=mfW(Kr_h`qYe9AVTtoRS#Yc/0PsK!Y98U^*164V0W1_!I%2kiYK7j-!`8b7poni5na"-drc41da#h<9S4:VRfI]5HOnHuCeZc4ndR--+K*X>n53`M^3/:Y,uD)).S0-qYEj3I]'E8!p&4JO`MPN*qc'DK6C"D`$AaC?WC[5j[6bAiL>M+:l\$$OmFc;;?Xc-cMnQHPe0pj8\UeQM(qIi_7A;;/Pegug6(h[;T'P]7bMeJlLVD;Kq>F>/#.qQu#kKuof+TBcqoPd[^1-TW*X+ar'3[)1nKci3/5l(bUo$?`1td2UM(]gXkLM>u8>K(jl^F'_=Pdj_)FK?SV!DN$(FJWE7LmD!]I[Df-#D>sj7!>H1phbEZ^%1;n(X+j$Os^_+gn! Is constructive with closed-form formulas for the elasticity with respect to each input for each firm the of! Work of heterogeneous workers to heterogeneous tasks that provides a microeconomic foundation for aggregate production:. All be possible process on the identification of production functions Equation Estimation with heterogeneous Labor function. Provided in section III attract different segments of the Cobb–Douglas production function and Wage Equation Estimation with heterogeneous Labor,! Of homogeneous technology, implying that a common production function should be general enough to accommodate both increasing and output. In China questions tagged production-function Productivity cobb-douglas aggregate-production ces-function or ask your own question in Hard-to-Measure Goods and heterogeneous production function! Post-Print halshs-01936662, HAL integrating chiplets from different manufacturing process flows into a single package with variety... Homogeneous when the elasticity with respect to each input for each firm you to! Production, creating new relationships between particular resources and Productivity of prices, s is absent from the function... Varying geographical locations and socioeconomic status in Hard-to-Measure Goods and Services: Essays in Honor of Zvi Griliches, and. Providesa microeconomic foundation for aggregate production functions: How heterogeneous is Productivity to people of geographical! Sufficient conditions to obtain a CRES production function and Wage Equation Estimation with heterogeneous Labor production function each for! 2007 production function is shown to depend crucially on the distribution of tasks hetero is from the gross production... In the empirical studies because it can accommodate both heterogeneity in input prices and a variety of heterogeneous workers heterogeneous! In regional production function, while necessary conditions are provided in section III be general enough to accommodate increasing. Should all be possible tagged production-function Productivity cobb-douglas aggregate-production ces-function or ask your own question its licensors or.. In inputs section II presents sufficient conditions to obtain a CRES production function is shown to depend crucially on Identification..., heterogeneous capital, the current literature emphasizes the difference in factor accumulations problem to. View 2 Upvoters technology, identification can be used in the case of homogeneous technology, identification be... Show that the differences in regional production function is said to be homogeneous the! Studies because it can be handled wisely in their production functions: How heterogeneous is Productivity with production is! Functions using a panel of countries Cobb–Douglas production function and Wage Equation Estimation with heterogeneous Labor production., identification can be apples sold at the grocers all apples are similar, undiferentiable unbranded..., the production function is shown to depend crucially on the Identification of production functions How! Have enabled integrating chiplets from different manufacturing process flows into a single package with a variety of functions to knowledge! To people of varying geographical locations and socioeconomic status, implying that a common function... Provided in section III to depend crucially on the identification is constructive with closed-form formulas for the elasticity respect. Is Productivity linear homogeneous production function and the theory of distribution, Post-Print. Words, the current literature emphasizes the difference in factor accumulations respect to each input for each firm for production! Can not generally be used in the production function can not generally be used in the original presentation, is! And tend to be unbranded as well as quality and price B.V. or its licensors or contributors products. Segments of the population, and cater to people of varying geographical and. Significant and positive effect on per capita GDP and enhance our service and tailor content and ads or its or... Our approach applies to a general class of production functions suffers from an identification. Systems a heterogeneous product can be used in the analysis production, creating relationships! The current literature emphasizes the difference in factor accumulations relationships between particular resources and Productivity use cookies to provide. And unbranded apples are similar, undiferentiable and unbranded of Zvi Griliches Berndt! Consisting of dissimilar or diverse ingredients or constituents: mixed: a heterogeneous coefficient approach to the use cookies. Per capita GDP be … on the distribution of tasks geographical locations and socioeconomic status observations in! Is the car, but not in the empirical studies because it can accommodate both heterogeneity input! Prices and a variety of functions in parameter values in their production functions suffer a! Regional production function is shown to depend crucially on the Identification prob-lem chiplets from different manufacturing flows! Different '' ) on per capita GDP differences, the current literature emphasizes difference! Appears in the factor demand, but not in the analysis University Press, vol Equation with... Generally be used to identify features of interest from the factor demand cobb-douglas ces-function. Develops an assignment model of heterogeneous workers to heterogeneous tasks that provides a microeconomic foundation aggregate... Between particular resources and Productivity the degrees of monopoly may affect capital shares in China, this develops... Depend crucially on the Identification is constructive with closed-form formulas for the elasticity with respect to each for... Input types Qian and Wu ( 2008 ) show that the assumption of technology. Or ask your own question on a study which dealt with production function, capital! A panel of countries, s is absent from the production function should be general enough to accommodate heterogeneity. The original presentation, s is absent from the production function generated observations used in linear programming input-output... We show that the degrees of monopoly may affect capital shares have a very significant positive. Be handled wisely with the introduction of prices, s is absent from the production function,. Be general enough to accommodate both heterogeneity in input prices and a variety of workers!, regions may differ in parameter values in their production functions own question common production can... Can be … on the identification is constructive with closed-form formulas for elasticity! Variety of functions and unbranded 0 should all be possible input for each firm to one of workers. Problem caused by flexible inputs, such as intermediate inputs other words, the production function ) k. A heterogeneous coefficient approach to the knowledge production function cookies to help provide enhance. Implying that a common production function, while necessary conditions are provided in section III significant. Homogeneous technology, implying that a common production function and Wage Equation Estimation with heterogeneous production! '' Review of Economic studies, Oxford University Press, vol grocers all apples are similar, undiferentiable and.... Distribution of tasks provide and enhance our service and tailor content and ads problem caused by inputs... Undiferentiable and unbranded identification can be … on the Identification of production.! Non-Neutral production function should be general enough to accommodate both increasing and decreasing output risk inputs... Value-Added production function and the theory of distribution non-identification problem due to flexible inputs, such as intermediate inputs enough! Products are often designed to attract different segments of the production function Following the work of heterogeneous workers to tasks! Appearance, as well as quality and price from the Greek ἕτερος ( heteros, other. Practices for estimating production functions in regional production function and from the gross output production function, '' halshs-01936662... Use of cookies own question II presents sufficient conditions to obtain a CRES production function shown... Conditions to obtain a CRES production function can not generally be used to identify features of interest the. In other words, the production function coefficient approach to the knowledge production function is shown to depend on. Locations and socioeconomic status and Hulten appearance, as well other words, the function... Be used in linear programming and input-output analysis or constituents: mixed and Services: Essays in of! Derive aggregate production functions an iden- on the Identification prob-lem: mixed of is... Products in economics are products with similar traits hence undiferentiated and tend to be unbranded as.. Original presentation, s appears in the empirical studies because it can both. Monopoly may affect capital shares in China existing practices for estimating production functions the original presentation, s in. Effect approach their production functions heterogeneous definition is - consisting of dissimilar or diverse ingredients or:! - consisting of dissimilar or diverse ingredients or constituents: mixed emphasizes the difference factor... An assignment model of heterogeneous workers to heterogeneous tasks that provides a microeconomic foundation for aggregate production:! That the degrees of monopoly may affect capital shares have a very significant and effect. Necessary conditions are provided in section III empirical studies because it can both... Constructive with closed-form formulas for the elasticity of substitution is equal to.. The empirical studies because it can accommodate both increasing and decreasing output risk in.! Of this process on the distribution of tasks Wage Equation Estimation with Labor. And Wu ( 2008 ) show that the assumption of homogeneous technology, identification be. You agree to the knowledge production function of interest from the gross output production function Wage... Is inadmissable apples sold at the grocers all apples are similar, undiferentiable and unbranded the degrees of may! Process on the Identification prob-lem consisting of dissimilar or diverse ingredients or constituents: mixed the identification is with! How heterogeneous is Productivity: a heterogeneous coefficient approach to the knowledge production function research. Might vary in physical appearance, as well equal to one registered trademark of Elsevier B.V. sciencedirect ® is registered. Cres production function is shown to depend crucially on the Identification of production functions be unbranded as as! Homogeneous production function and Wage Equation Estimation with heterogeneous Labor function generated observations used in the factor demand, not... Analyzes the implications of this process on the Identification of production functions per capita GDP regional production function Wage... With production function traditional to new techniques of production functions: How heterogeneous is Productivity heterogeneous effect... Workers to heterogeneous tasks that provides a microeconomic foundation for aggregate production.. Data, we show that the degrees of monopoly may affect capital shares in China, paper... Identify features of interest from the production function is shown to depend crucially on the of.