The assignment problem is a special type of linear programming problem and it is sub class of transportation problem. Assignment problems are defined with two sets of inputs i.e. set of resources and set of demands. Hungarian algorithm is able to solve assignment problems with precisely defined demands and resources.Nowadays, many organizations and competition companies consider markets of their products. They use many salespersons to improve their organizations marketing. Salespersons travel form one city to another city for their markets. There are some problems in travelling which salespeople should go which city in minimum cost. So, travelling assignment problem is a main process for many business functions. Mie Mie Aung | Yin Yin Cho | Khin Htay | Khin Soe Myint "Minimization of Assignment Problems" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd26712.pdfPaper URL: https://www.ijtsrd.com/computer-science/other/26712/minimization-of-assignment-problems/mie-mie-aung
Stochastic Order Level Inventory Model with Inventory Returns and Special Salestheijes
This article deals with a single period inventory model with inventory returns and special sales. The demand is assumed to occur in a uniform pattern during a planning period say, tp. Both non-deteriorating items and deteriorating items are considered for the discussion
The reference of this book is from Dominick Salvatore's Managerial Economics. It is in chapter 8 with the following topic: Linear Programming, Production process, Feasible region, Optimal solution, Objective function, Inequality constraints, Nonnegativity constraints, Decision variables, Binding constraints, Slack variable, Simplex method, Primal problem, Dual problem, Shadow price, Duality theorem and Logistic management.
Phương pháp chữa nói lắp toàn diện được Echo Việt nam www.echovietnam.org dịch từ quyển sách Comprehensive Stuttering Therapy và phát hành dưới sự cho phép của tác giả Phillip J. Roberts. Đây là một trong nhiều tài liệu miễn phí hỗ trợ cho người nói lắp Việt Nam. Mọi việc trích dẫn từ sách này phải ghi rõ xuất xứ của quyển sách. Mọi yêu cầu phát hành lại, in lại… phải được sự chấp thuận của Echo Việt Nam, đại diện là người sáng lập Trương Minh Sử Nhiên.
Tài liệu này tuyệt đối không được sử dụng với mục đích thương mại dưới mọi hình thức.
Đại diện, nhóm Echo Việt Nam, tôi xin chúc các bạn sớm thành công trong việc giao tiếp công chúng và đời thường. Thành công sẽ không là xa với nếu ai kiên trì tìm kiếm nó.
Tôi cũng xin gửi lời cảm ơn đến tác giả Phillip J. Roberts, đã cho phép, tôi, tổ chức Echo Việt nam được phép dịch và phát hành để phục vụ rộng rãi cho cộng đồng nói lắp Việt nam.
Sài Gòn, tháng 10 năm 2009
Người sáng lập Echo Việt nam
Trương Minh Sử Nhiên
tmsnhien@gmail.com
The assignment problem is a special type of linear programming problem and it is sub class of transportation problem. Assignment problems are defined with two sets of inputs i.e. set of resources and set of demands. Hungarian algorithm is able to solve assignment problems with precisely defined demands and resources.Nowadays, many organizations and competition companies consider markets of their products. They use many salespersons to improve their organizations marketing. Salespersons travel form one city to another city for their markets. There are some problems in travelling which salespeople should go which city in minimum cost. So, travelling assignment problem is a main process for many business functions. Mie Mie Aung | Yin Yin Cho | Khin Htay | Khin Soe Myint "Minimization of Assignment Problems" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd26712.pdfPaper URL: https://www.ijtsrd.com/computer-science/other/26712/minimization-of-assignment-problems/mie-mie-aung
Stochastic Order Level Inventory Model with Inventory Returns and Special Salestheijes
This article deals with a single period inventory model with inventory returns and special sales. The demand is assumed to occur in a uniform pattern during a planning period say, tp. Both non-deteriorating items and deteriorating items are considered for the discussion
The reference of this book is from Dominick Salvatore's Managerial Economics. It is in chapter 8 with the following topic: Linear Programming, Production process, Feasible region, Optimal solution, Objective function, Inequality constraints, Nonnegativity constraints, Decision variables, Binding constraints, Slack variable, Simplex method, Primal problem, Dual problem, Shadow price, Duality theorem and Logistic management.
Phương pháp chữa nói lắp toàn diện được Echo Việt nam www.echovietnam.org dịch từ quyển sách Comprehensive Stuttering Therapy và phát hành dưới sự cho phép của tác giả Phillip J. Roberts. Đây là một trong nhiều tài liệu miễn phí hỗ trợ cho người nói lắp Việt Nam. Mọi việc trích dẫn từ sách này phải ghi rõ xuất xứ của quyển sách. Mọi yêu cầu phát hành lại, in lại… phải được sự chấp thuận của Echo Việt Nam, đại diện là người sáng lập Trương Minh Sử Nhiên.
Tài liệu này tuyệt đối không được sử dụng với mục đích thương mại dưới mọi hình thức.
Đại diện, nhóm Echo Việt Nam, tôi xin chúc các bạn sớm thành công trong việc giao tiếp công chúng và đời thường. Thành công sẽ không là xa với nếu ai kiên trì tìm kiếm nó.
Tôi cũng xin gửi lời cảm ơn đến tác giả Phillip J. Roberts, đã cho phép, tôi, tổ chức Echo Việt nam được phép dịch và phát hành để phục vụ rộng rãi cho cộng đồng nói lắp Việt nam.
Sài Gòn, tháng 10 năm 2009
Người sáng lập Echo Việt nam
Trương Minh Sử Nhiên
tmsnhien@gmail.com
Phương pháp tự điều trị cho người nói lắp được Echo Việt nam www.echovietnam.org dịch từ quyển sách Self Therapy for stutterers của tác giả MALCOLM FRASER và phát hành dưới sự cho phép của tổ chức www.stutteringhelps.org. Đây là một trong nhiều tài liệu miễn phí hỗ trợ cho người nói lắp Việt Nam. Mọi việc trích dẫn từ sách này phải ghi rõ xuất xứ của quyển sách. Mọi yêu cầu phát hành lại, in lại… phải được sự chấp thuận của Echo Việt Nam, đại diện là người sáng lập Trương Minh Sử Nhiên.
Tài liệu này tuyệt đối không được sử dụng với mục đích thương mại dưới mọi hình thức.
Đại diện, nhóm Echo Việt Nam, tôi xin chúc các bạn sớm thành công trong việc giao tiếp công chúng và đời thường. Thành công sẽ không là xa với nếu ai kiên trì tìm kiếm nó.
Tôi cũng xin gửi lời cảm ơn đến tổ chức Stuttering Helps, đã cho phép, tôi, tổ chức Echo Việt nam được phép dịch và phát hành để phục vụ rộng rãi cho cộng đồng nói lắp Việt nam.
Sài Gòn, 22 tháng 10 năm 2010
Người sáng lập Echo Việt nam
Trương Minh Sử Nhiên
tmsnhien@gmail.com
Productivity and GDP per capita growth: A long-term perspective, Bergeaud, Ce...Soledad Zignago
Gilbert Cette's slides at the Secular Stagnation and Growth Measurement Conference, Banque de France, January 16, 2017, with Antonin Bergeaud & Remy Lecat https://www.banque-france.fr/stagnation-seculaire-et-mesure-de-la-croissance-conference-organisee-par-la-banque-de-france-et-le
Design of Scalable FFT architecture for Advanced Wireless Communication Stand...IOSRJECE
Now a day’s numerous wireless communication standards have raised additional stringent requirements on each throughput and flexibility for FFT computation. Advanced wireless systems support multiple standards to satisfy the demands of user application necessities. A wireless system whereas supporting multiple standards should also satisfy performance necessities of these supported standards. Meeting performance requirements of multiple standards is a challenge while designing a system. Fast Fourier transformations, a kernel processing task in communication systems, are studied intensively for efficient software and hardware implementations. To design an efficient system, it's necessary to efficiently design its performance critical component. each system must meet stringent design parameters like high speed, low power, low area, low cost, high flexibility and high scalability, designing FFT processor to support multiple wireless standards whereas meeting the above such performance necessities is a difficult task. This paper proposed a highly efficient scalable architecture, software tools design, and design implementation. The reconstruction of the FFT computation flow is design into a scalable structure. The FFT can be easily expanded for any-point FFT computation. The various parameters satisfied the conditions, gives proper and efficient outputs as compare to other platforms.
DESIGN OF DELAY COMPUTATION METHOD FOR CYCLOTOMIC FAST FOURIER TRANSFORMsipij
In this paper the Delay Computation method for Common Sub expression Elimination algorithm is being implemented on Cyclotomic Fast Fourier Transform. The Common Sub Expression Elimination algorithm is combined with the delay computing method and is known as Gate Level Delay Computation with Common Sub expression Elimination Algorithm. Common sub expression elimination is effective
optimization method used to reduce adders in cyclotomic Fourier transform. The delay computing method is based on delay matrix and suitable for implementation with computers. The Gate level delay computation method is used to find critical path delay and it is analyzed on various finite field elements. The presented algorithm is established through a case study in Cyclotomic Fast Fourier Transform over finite field. If Cyclotomic Fast Fourier Transform is implemented directly then the system will have high additive complexities. So by using GLDC-CSE algorithm on cyclotomic fast Fourier transform, the additive
complexities will be reduced and also the area and area delay product will be reduced.
A Sogeti study to which extent it\'s possible to convert function points to COSMIC function points and back. A framework on how to make the transition from FPA to COSMIC as the leading FSMM in the organzition. - Published at the SMEF2007 conference (Rome, May 2007)
A downlink scheduler supporting real time services in LTE cellular networksUniversity of Piraeus
The wide spread of real-time services in wireless networks demands scheduling mechanisms supporting strict Quality of Service (QoS) requirements. Nevertheless, the specifications of the LTE standard for mobile connectivity defined by the 3rd Generation Partnership Project (3GPP) does not impose any specific scheduler for the proper allocation of resources to services. Therefore, several LTE schedulers have been proposed in the literature meeting the QoS requirements of modern services. In this paper a QoS aware scheduler for the LTE downlink is proposed namely the FLS-Advanced (FLSA) aiming at prioritizing real-time traffic. The proposed scheduler has been built on three distinct levels assigning the available radio resources to services according to their requirements. Based on simulation results, the FLSA outperforms in terms of packet loss ratio, attainable throughput and fairness the performance of existing schedulers including PF, MLWDF, EXP/PF, FLS, EXP RULE and LOG RULE.
International Journal of Engineering Inventions (IJEI) provides a multidisciplinary passage for researchers, managers, professionals, practitioners and students around the globe to publish high quality, peer-reviewed articles on all theoretical and empirical aspects of Engineering and Science.
IMPLEMENTATION OF FRACTIONAL ORDER TRANSFER FUNCTION USING LOW COST DSPIAEME Publication
In this paper, different fractional order transfer functions are taken first and discretized them using available methods and filters (i.e. Oustaloup or modified Oustaloup). Coefficients of discretized transfer function are calculated and scaled using Q15 number system to get the coefficients in the range between -1 to 1, and converted into equivalent hexadecimal number. These coefficients are entered into the Micro C code that is generated using filter design tool of Micro C for dsPIC microcontroller. Also the simulation results are validated using EasydsPIC4 development board.
"𝑩𝑬𝑮𝑼𝑵 𝑾𝑰𝑻𝑯 𝑻𝑱 𝑰𝑺 𝑯𝑨𝑳𝑭 𝑫𝑶𝑵𝑬"
𝐓𝐉 𝐂𝐨𝐦𝐬 (𝐓𝐉 𝐂𝐨𝐦𝐦𝐮𝐧𝐢𝐜𝐚𝐭𝐢𝐨𝐧𝐬) is a professional event agency that includes experts in the event-organizing market in Vietnam, Korea, and ASEAN countries. We provide unlimited types of events from Music concerts, Fan meetings, and Culture festivals to Corporate events, Internal company events, Golf tournaments, MICE events, and Exhibitions.
𝐓𝐉 𝐂𝐨𝐦𝐬 provides unlimited package services including such as Event organizing, Event planning, Event production, Manpower, PR marketing, Design 2D/3D, VIP protocols, Interpreter agency, etc.
Sports events - Golf competitions/billiards competitions/company sports events: dynamic and challenging
⭐ 𝐅𝐞𝐚𝐭𝐮𝐫𝐞𝐝 𝐩𝐫𝐨𝐣𝐞𝐜𝐭𝐬:
➢ 2024 BAEKHYUN [Lonsdaleite] IN HO CHI MINH
➢ SUPER JUNIOR-L.S.S. THE SHOW : Th3ee Guys in HO CHI MINH
➢FreenBecky 1st Fan Meeting in Vietnam
➢CHILDREN ART EXHIBITION 2024: BEYOND BARRIERS
➢ WOW K-Music Festival 2023
➢ Winner [CROSS] Tour in HCM
➢ Super Show 9 in HCM with Super Junior
➢ HCMC - Gyeongsangbuk-do Culture and Tourism Festival
➢ Korean Vietnam Partnership - Fair with LG
➢ Korean President visits Samsung Electronics R&D Center
➢ Vietnam Food Expo with Lotte Wellfood
"𝐄𝐯𝐞𝐫𝐲 𝐞𝐯𝐞𝐧𝐭 𝐢𝐬 𝐚 𝐬𝐭𝐨𝐫𝐲, 𝐚 𝐬𝐩𝐞𝐜𝐢𝐚𝐥 𝐣𝐨𝐮𝐫𝐧𝐞𝐲. 𝐖𝐞 𝐚𝐥𝐰𝐚𝐲𝐬 𝐛𝐞𝐥𝐢𝐞𝐯𝐞 𝐭𝐡𝐚𝐭 𝐬𝐡𝐨𝐫𝐭𝐥𝐲 𝐲𝐨𝐮 𝐰𝐢𝐥𝐥 𝐛𝐞 𝐚 𝐩𝐚𝐫𝐭 𝐨𝐟 𝐨𝐮𝐫 𝐬𝐭𝐨𝐫𝐢𝐞𝐬."
Improving profitability for small businessBen Wann
In this comprehensive presentation, we will explore strategies and practical tips for enhancing profitability in small businesses. Tailored to meet the unique challenges faced by small enterprises, this session covers various aspects that directly impact the bottom line. Attendees will learn how to optimize operational efficiency, manage expenses, and increase revenue through innovative marketing and customer engagement techniques.
Discover the innovative and creative projects that highlight my journey throu...dylandmeas
Discover the innovative and creative projects that highlight my journey through Full Sail University. Below, you’ll find a collection of my work showcasing my skills and expertise in digital marketing, event planning, and media production.
Business Valuation Principles for EntrepreneursBen Wann
This insightful presentation is designed to equip entrepreneurs with the essential knowledge and tools needed to accurately value their businesses. Understanding business valuation is crucial for making informed decisions, whether you're seeking investment, planning to sell, or simply want to gauge your company's worth.
Personal Brand Statement:
As an Army veteran dedicated to lifelong learning, I bring a disciplined, strategic mindset to my pursuits. I am constantly expanding my knowledge to innovate and lead effectively. My journey is driven by a commitment to excellence, and to make a meaningful impact in the world.
Attending a job Interview for B1 and B2 Englsih learnersErika906060
It is a sample of an interview for a business english class for pre-intermediate and intermediate english students with emphasis on the speking ability.
VAT Registration Outlined In UAE: Benefits and Requirementsuae taxgpt
Vat Registration is a legal obligation for businesses meeting the threshold requirement, helping companies avoid fines and ramifications. Contact now!
https://viralsocialtrends.com/vat-registration-outlined-in-uae/
RMD24 | Debunking the non-endemic revenue myth Marvin Vacquier Droop | First ...BBPMedia1
Marvin neemt je in deze presentatie mee in de voordelen van non-endemic advertising op retail media netwerken. Hij brengt ook de uitdagingen in beeld die de markt op dit moment heeft op het gebied van retail media voor niet-leveranciers.
Retail media wordt gezien als het nieuwe advertising-medium en ook mediabureaus richten massaal retail media-afdelingen op. Merken die niet in de betreffende winkel liggen staan ook nog niet in de rij om op de retail media netwerken te adverteren. Marvin belicht de uitdagingen die er zijn om echt aansluiting te vinden op die markt van non-endemic advertising.
The world of search engine optimization (SEO) is buzzing with discussions after Google confirmed that around 2,500 leaked internal documents related to its Search feature are indeed authentic. The revelation has sparked significant concerns within the SEO community. The leaked documents were initially reported by SEO experts Rand Fishkin and Mike King, igniting widespread analysis and discourse. For More Info:- https://news.arihantwebtech.com/search-disrupted-googles-leaked-documents-rock-the-seo-world/
3.0 Project 2_ Developing My Brand Identity Kit.pptxtanyjahb
A personal brand exploration presentation summarizes an individual's unique qualities and goals, covering strengths, values, passions, and target audience. It helps individuals understand what makes them stand out, their desired image, and how they aim to achieve it.
What is the TDS Return Filing Due Date for FY 2024-25.pdfseoforlegalpillers
It is crucial for the taxpayers to understand about the TDS Return Filing Due Date, so that they can fulfill your TDS obligations efficiently. Taxpayers can avoid penalties by sticking to the deadlines and by accurate filing of TDS. Timely filing of TDS will make sure about the availability of tax credits. You can also seek the professional guidance of experts like Legal Pillers for timely filing of the TDS Return.
3. Outline Introduction Malmquist TFP index and panel data Calculating TFP change using DEA frontiers Calculating TFP change using SFA frontiers Measuring TFP change: conclusions Summary of methods 3 ECON377/477 Topic 5.4
4. Introduction In this part, we consider the case where we have access to better data In particular, we assume we have data on a sample of firms in periods s and t that are sufficient to obtain an estimate of the production technology in these two periods We can then calculate the required distances directly and relax a number of the assumptions made to construct the TFP index numbers In particular, we need no longer assume all firms are operating on the surface of the production technology (are technically efficient) ECON377/477 Topic 5.4 4
5. Introduction We no longer have the situation where the ratio of the distance functions provides a measure of TFP change that is identical to technical change (TC) (i.e. frontier shift), as was the case in earlier parts of this topic Thus, when panel data are available, we can obtain a measure of TFP change that has two components: a TC component a TE change component ECON377/477 Topic 5.4 5
6. Introduction The remainder of this part is organised as follows The Malmquist TFP index is briefly described Then, we describe how to calculate these indices using DEA-like methods Next, we describe the calculation of these indices using the SFA methods We then refer to detailed application of some of these methods in CROB Finally, we make some brief concluding comments ECON377/477 Topic 5.4 6
7. Malmquist TFP index and panel data Malmquist TFP change measures can be decomposed into various components, including TC and TE change These measures could be calculated using distances measured relative to DEA frontiers The Malmquist TFP index measures the TFP change between two data points by calculating the ratio of the distances of each data point relative to a common technology ECON377/477 Topic 5.4 7
8. Malmquist TFP index and panel data If the period t technology is used as the reference technology, the Malmquist (output-orientated) TFP change index between period s and period t is defined as: Alternatively, if the period s reference technology is used, it is defined as: ECON377/477 Topic 5.4 8
9. Malmquist TFP index and panel data The notation represents the distance from the period t observation to the period s technology A value of mo greater than one indicates positive TFP growth from period s to period t while a value less than one indicates a TFP decline These period s and period t indices are only equivalent if the technology is Hicks output-neutral It is Hicks output-neutral if the output distance functions may be represented as for all t ECON377/477 Topic 5.4 9
10. Malmquist TFP index and panel data The Malmquist TFP index is often defined as the geometric mean of the two indices with period s and period t technology: The distance functions can be rearranged to show that it equates to the product of a technical efficiency change index and an index of TC: TE change TC ECON377/477 Topic 5.4 10
11. Malmquist TFP index and panel data The ratio outside the square brackets in the second equation on the previous slide measures the change in the output-oriented measure of Farrell technical efficiency between periods s and t The remaining part of the index in this equation is a measure of TC: the geometric mean of the shift in technology between the two periods, evaluated at xt and xs ECON377/477 Topic 5.4 11
12.
13. decomposing TE change into scale efficiency and ‘pure’ technical efficiency components (this can only be done when the distance functions are estimated relative to a CRS technologyECON377/477 Topic 5.4 12
14. Malmquist TFP index and panel data The decomposition into scale efficiency involves taking the efficiency change measure and decomposing it into a pure efficiency change component (measured relative to the arguably true VRS frontier), and a scale efficiency component, ECON377/477 Topic 5.4 13
15. Malmquist TFP index and panel data The scale efficiency change component is the geometric mean of two scale efficiency change measures The first is relative to the period t technology and the second is relative to the period s technology Note that the extra subscripts, v and c, relate to the VRS and CRS technologies, respectively Refer to CROB for an evaluation of this method and an alternative approach The returns to scale properties of the technology are very important in TFP measurement ECON377/477 Topic 5.4 14
16. Calculating TFP change using DEA frontiers A number of different methods could be used to estimate a production technology and, hence, measure the distance functions that make up the Malmquist TFP index The most popular method has been the DEA-like LP method, discussed in this section The other main alternative approach is the use of stochastic frontier methods, described in the next section ECON377/477 Topic 5.4 15
17. Calculating TFP change using DEA frontiers Given suitable panel data, we can calculate the distance measures using DEA-like LPs For the i-th firm, four distance functions are calculated to measure the TFP change between two periods This requires solving four LP problems using a CRS technology in the TFP calculations This ensures that TFP change measures satisfy the property that if all inputs are multiplied by the (positive) scalar and all outputs are multiplied by the (non-negative) scalar , the resulting TFP change index will equal / ECON377/477 Topic 5.4 16
18. Calculating TFP change using DEA frontiers The required four LPs are: [dot(qt, xt)] - 1 = max, st -qit + Qt 0 xit - Xt0 0 [dos(qs, xs)] - 1 = max, st -qis+ Qs0 xis – Xs0 0 … ECON377/477 Topic 5.4 17
20. Calculating TFP change using DEA frontiers In the third and fourth LPs, where production points are compared with technologies from different time periods, the parameter need not be greater than or equal to one, as it must be when calculating Farrell output-orientated TEs The s and s are likely to take different values in the above four LPs, which must be solved for each firm in the sample As extra time periods are added, it is necessary to solve an extra three LPs for each firm (to construct a chained index) ECON377/477 Topic 5.4 19
21. Calculating TFP change using DEA frontiers Decomposing technical efficiency change into scale efficiency and ‘pure’ technical efficiency measure requires the solution of two additional LPs (when comparing two production points) These LPs would involve repeating the first two with the convexity restriction (I1 = 1) added to each This provides estimates of distance functions relative to a VRS technology ECON377/477 Topic 5.4 20
22. Calculating TFP change using DEA frontiers CROB (pages 295-300) provide a numerical example of the application of the DEA-like method to construct Malmquist TFP indices, using the DEAP computer program Four distances are calculated for each firm in each year, relative to: the previous period’s CRS DEA frontier the current period’s CRS DEA frontier the next period’s CRS DEA frontier the current period’s VRS frontier ECON377/477 Topic 5.4 21
23. Calculating TFP change using DEA frontiers All indices are calculated relative to the previous year Hence, the output begins with year 2 Five indices are presented for each firm in each year: TE change relative to a CRS technology technological change pure TE change relative to a VRS technology scale efficiency change TFP change ECON377/477 Topic 5.4 22
24. Calculating TFP change using DEA frontiers Summary tables of these indices follow for the different time periods (over all firms) and for the different firms (over all time periods) Note that all indices are equal to one for time period 3 because the data for year 3 are identical to the year 2 data in the example data set used ECON377/477 Topic 5.4 23
25. Calculating TFP change using SFA frontiers The distance measures required for the Malmquist TFP index calculations can also be measured relative to a parametrically estimated technology We focus our attention on the production frontier case, which is a single-output special case of the more general (multi-output) output distance function ECON377/477 Topic 5.4 24
26. Calculating TFP change using SFA frontiers Consider a translog stochastic production frontier defined as: i = 1,2,...,I , t = 1,2,...,T where qit is the output of the i-th firm in the t-th year; xnit denotes the n-th input variable; t is a time trend representing TE; the s are unknown parameters to be estimated; the vits are random errors, and the uits are the technical inefficiency effects ECON377/477 Topic 5.4 25
27. Calculating TFP change using SFA frontiers The above model has the time trend, t, interacted with the input variables to allow for non-neutral TC The technical efficiencies of each firm in each year can be predicted using the approach outlined in Topic 4 We obtain the conditional expectation of exp(-uit), given the value of eit= vit - uit These TE predictions are between zero and one, with a value of one indicating full TE ECON377/477 Topic 5.4 26
28. Calculating TFP change using SFA frontiers We can use measures of TE and TC to calculate the Malmquist TFP index via equations (11.4-11.6) in CROB (see next slide) TE change = TEit/TEis The TC index between period s and t for the i-th firm can be calculated directly from the estimated parameters First, the partial derivatives of the production function are evaluated with respect to time using the data for the i-th firm in periods s and t ECON377/477 Topic 5.4 27
29. Malmquist TFP index and panel data From an earlier slide (slide 9), the Malmquist output index equates to the product of a technical efficiency change index and an index of TC: TE change TC CROB, equation (11.4) ECON377/477 Topic 5.4 28
30. Calculating TFP change using SFA frontiers The TC index between the adjacent periods s and t is calculated as the geometric mean of these two partial derivatives When a translog function is involved, this is equivalent to the exponential of the arithmetic mean of the log derivatives, and TC equals: The indices of TE change and TC can then be multiplied together to obtain a Malmquist TFP index ECON377/477 Topic 5.4 29
31. Calculating TFP change using SFA frontiers The above technical change measure involves derivative calculations, which appears to contradict the earlier comments that these indices are derived from distance measures It can be easily shown (for the translog case in which a time trend is used to represent technical change) that the geometric means of the distance ratios in equation (11.6) in CROB are equivalent to the geometric means of the derivative measures ECON377/477 Topic 5.4 30
32. Calculating TFP change using SFA frontiers A criticism of this method is that the TFP index may produce biased measures because the productivity changes due to scale changes are not captured One possible solution to this problem is to impose CRS upon the estimated production technology Another option is to derive a Malmquist TFP decomposition identical to that proposed above, and address the scale issue by including a scale change component in the TFP measure ECON377/477 Topic 5.4 31
33. Calculating TFP change using SFA frontiers Scale change = where , and This scale change index is equal to one if the production technology is CRS, when the scale elasticity ( ) equals one An empirical application to rice production data is provided by CROB (pages 302-309) ECON377/477 Topic 5.4 32
34.
35. It does not assume all firms are fully efficient
36. It does not need to assume a behavioural objective such as cost minimisation or revenue maximisation
37. It permits TFP change to be decomposed into components such as TC, TE change and scale changeECON377/477 Topic 5.4 33
38. Measuring TFP change: conclusions An important advantage of the Tornqvist approach is that it can be calculated using only two data points In contrast, the frontier approach needs a number of firms to be observed in each time period so that the frontier technology in each year can be estimated If one has suitable panel data, the frontier approach provides richer information and makes fewer assumptions ECON377/477 Topic 5.4 34
39. Measuring TFP change: conclusions But if only aggregate time-series data are available, the Tornqvist approach provides useful estimates of TFP change, given that the assumptions specified earlier in the topic notes are reasonable ECON377/477 Topic 5.4 35
40. Summary of methods We have considered four principal methods: Least-squares econometric production models TFP indices (Tornqvist/Fisher) DEA SFA They differ in various ways, as demonstrated in the table on the next slide ECON377/477 Topic 5.4 36
47. the method does not assume a smooth pattern of TCThe principal disadvantage is that it requires both price and quantity information ECON377/477 Topic 5.4 39
48. Summary of methods Both approaches assume that firms are technically efficient, which is unlikely to be true To relax this assumption, frontier methods can be used, assuming panel data are available, to calculate TFP change ECON377/477 Topic 5.4 40
51. does not require the assumption of cost minimisation and revenue maximisation
52. permits TFP to be decomposed into TC and TE changeECON377/477 Topic 5.4 41
53. Summary of methods But an important advantage of the index-number approach is that it only requires two data points, say observations on two firms in one time period or observations on one firm in two time periods The frontier approaches need a number of firms to be observed in each time period so that the frontier technology in each year can be calculated ECON377/477 Topic 5.4 42