DOCSLIB.ORG

On the Identification of Production Functions: How Heterogeneous Is

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
On the Identification of Production Functions: How Heterogeneous Is On the Identification of Production Functions: How Heterogeneous is Productivity? Amit Gandhi, Salvador Navarro, David Rivers∗ May 30, 2016 Abstract We show that the “proxy variable” approaches for estimating production functions generi- cally suffer from a fundamental identification problem in the presence of a flexible input that satisfies the “proxy variable” assumptions for invertibility, such as intermediate inputs. We provide a formal proof of nonparametric non-identification, and illustrate that the source of under-identification is the flexible input elasticity. Using a transformation of the firm’s first order condition, we develop a new nonparametric identification strategy that addresses this problem, as well as a simple corresponding estimator for the production function. We show that the alternative of approximating the effects of intermediate inputs using a value-added production function cannot generally be used to identify features of interest from the gross output production function. 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. ∗We would like to thank Dan Ackerberg, Richard Blundell, Juan Esteban Carranza, Allan Collard-Wexler, Ulrich Doraszelski, Steven Durlauf, Jeremy Fox, Silvia Goncalves, Phil Haile, Joel Horowitz, Jean-Francois Houde, Au- reo de Paula, Amil Petrin, Mark Roberts, Nicolas Roys, Chad Syverson, Chris Taber, Quang Vuong, and especially Tim Conley for helpful discussions. This paper has also benefited from detailed comments by the editor and three anonymous referees. We would also like to thank Amil Petrin and David Greenstreet for helping us to obtain the Colombian and Chilean data respectively. Navarro and Rivers acknowledge support from the Social Sciences and Humanities Research Council of Canada. This paper previously circulated under the name “Identification of Produc- tion Functions using Restrictions from Economic Theory.” First draft: May 2006. Amit Gandhi is at the University of Wisconsin-Madison, E-mail: [email protected]. Salvador Navarro is at the University of Western Ontario, E-mail: [email protected]. David Rivers is at the University of Western Ontario, E-mail: [email protected]. 1 1 Introduction The identification and estimation of production functions using data on firm inputs and output is among the oldest empirical problems in economics. A key challenge for identification arises because firms optimally choose their inputs as a function of their productivity, but productivity is unobserved by the econometrician in the data. This gives rise to a classic simultaneity problem that was first articulated by Marschak and Andrews (1944) and has come to be known in the production function literature as “transmission bias”. In their influential review of the state of the literature nearly 50 years later, Griliches and Mairesse (1998) (henceforth GM) concluded that the “search for identification” for the production function remained a fundamentally open problem.1 Resolving this identification problem is critical to measuring productivity with plant level production data, which has become increasingly available for many countries, and which motivates a variety of industry equilibrium models based on patterns of productivity heterogeneity found in this data.2 In this paper we examine the identification foundations of the “proxy variable” approach for estimating production functions pioneered by Olley and Pakes (1996) and further developed by Levinsohn and Petrin (2003)/Ackerberg, Caves, and Frazer (2015)/Wooldridge (2009) (henceforth OP, LP, ACF and Wooldridge, respectively). Despite the immense popularity of the method in the applied productivity literature, a fundamental question has remained unexplored: does the proxy variable technique solve the identification problem of transmission bias? That is, is the production function in fact identified from panel data on inputs and output under the structural assumptions that the proxy variable technique places on the data? To date there has been no formal demonstration of identification in this literature. On the other hand, there have been various red flags concerning the identification foundations for this class of estimators (see Bond and Söderbom, 2005 and ACF). However, no clear conclusion regarding non-identification of the model as a whole 1In particular, the standard econometric solutions to correct the transmission bias, i.e., using firm fixed effects or instrumental variables, have proven to be both theoretically problematic and unsatisfactory in practice (see e.g., GM and Ackerberg et al., 2007 for a review and Section 7 of this paper for a discussion). 2Among these patterns are the general understanding that even narrowly defined industries exhibit “massive” unex- plained productivity dispersion (Dhrymes, 1991; Bartelsman and Doms, 2000; Syverson, 2004; Collard-Wexler, 2010; Fox and Smeets, 2011), and that productivity is closely related to other dimensions of firm-level heterogeneity, such as importing (Kasahara and Rodrigue, 2008), exporting (Bernard and Jensen, 1995, Bernard and Jensen, 1999, Bernard et al., 2003), wages (Baily, Hulten, and Campbell, 1992), etc. See Syverson (2011) for a review of this literature. 2 has been reached either. Without an answer to this basic question, it is unclear how to interpret the vast body of empirical results regarding patterns of productivity which rely on the proxy approach for the measurement of productivity. Our first main result is a negative one. We show that the model structure underlying the proxy variable technique does not identify the production function (and hence productivity) in the pres- ence of a flexible input that satisfies the conditions for invertibility invoked in this literature. We establish this result under the LP/Wooldridge approach that uses intermediate inputs as a flexi- ble input that satisfies the proxy variable assumption of being monotone (and hence invertible) in productivity. Under this structure we show how to construct a continuum of observationally equiv- alent production functions that cannot be distinguished from the true production function in the data. We also show that similar non-identification problems arise under the original OP strategy of using investment as the proxy variable.3 Our second contribution is to show that the exact source of this non-identification is the flexible input elasticity for inputs satisfying the proxy variable assumption. The flexible input elasticity defines a partial differential equation on the production function. As we show, if this elasticity were known, then it could be integrated up to nonparametrically identify the part of the production function that depends on the flexible input. We then show that the proxy variable structure is sufficient to nonparametrically identify the remainder of the production function. These results taken together formalize the empirical content of the proxy variable structure that is widely used in applied work - the model is identified up to the flexible input elasticity, but fails to identify the flexible input elasticity itself. Our third contribution is that we present a new empirical strategy that nonparametrically iden- tifies the flexible input elasticity, and hence solves for the missing source of identification for the production function within the proxy variable structure. The key to our approach is that we build on a key economic assumption of the proxy variable structure - that the firm optimally chooses intermediate inputs in response to its realized productivity. Whereas the proxy variable literature 3We do not emphasize OP as the leading case because the applied literature has largely adopted the use of interme- diate inputs as the proxy variable due to the prevalence of zeroes in investment, which was the original motivation for LP. Nevertheless we show that resorting to OP does not solve the non-identification problem we pose for LP. 3 has used this assumption to “invert” and replace for productivity using intermediate inputs, we go further and exploit the nonparametric structural link between the production function and the firm’s first order condition for intermediate inputs. This link allows for a nonparametric regression of the intermediate input’s revenue share on all inputs (labor, capital, and intermediate inputs) to identify the flexible input elasticity. This is a nonparametric analogue of the familiar parametric insight that revenue shares directly identify the intermediate input coefficient in a Cobb-Douglas setting (e.g., Klein, 1953 and Solow, 1957). Our key innovation is that we show that the information in the first order condition can be used in a completely nonparametric way, i.e., without making functional form assumptions on the production function. Our results thus show how this “share regression” can be combined with the remaining content of the proxy variable structure to nonparametrically identify the production function as a whole. This identification strategy - regressing revenue shares on inputs to identify the flexible input elasticity, solving the partial differential equation, and integrating this into the proxy variable struc- ture to identify the remainder of the production function - gives rise to a natural two-step estimator in which a flexible parametric approximation to different components of the production function is estimated in each stage. We present a computationally straightforward implementation of this
Load more

Recommended publications
  • MA Macroeconomics 10. Growth Accounting
    MA Macroeconomics 10. Growth Accounting Karl Whelan School of Economics, UCD Autumn 2014 Karl Whelan (UCD) Growth Accounting Autumn 2014 1 / 20 Growth Accounting The final part of this course will focus on \growth theory." This branch of macroeconomics concerns itself with what happens over long periods of time. We will discuss the factors that determine the growth rate of the economy over the long run and what can policy measures do to affect it. This is closely related to the crucial question of what makes some countries rich and others poor. We will begin by covering \growth accounting" { a technique for explaining the factors that determine growth. Karl Whelan (UCD) Growth Accounting Autumn 2014 2 / 20 Production Functions We assume output is determined by an aggregate production function technology depending on the total amount of labour and capital. For example, consider the Cobb-Douglas production function: α β Yt = At Kt Lt where Kt is capital input and Lt is labour input. An increase in At results in higher output without having to raise inputs. Macroeconomists usually call increases in At \technological progress" and often refer to this as the \technology" term. At is simply a measure of productive efficiency and it may go up or down for all sorts of reasons, e.g. with the imposition or elimination of government regulations. Because an increase in At increases the productiveness of the other factors, it is also sometimes known as Total Factor Productivity (TFP). Karl Whelan (UCD) Growth Accounting Autumn 2014 3 / 20 Productivity Growth Output per worker is often labelled productivity by economists with increases in output per worker called productivity growth.
    [Show full text]
  • Measuring the “Ideas” Production Function
    1%(5 :25.,1* 3$3(5 6(5,(6 0($685,1* 7+( ³,'($6´ 352'8&7,21 )81&7,21 (9,'(1&( )520 ,17(51$7,21$/ 3$7(17 287387 0LKDHO ( 3RUWHU 6RWW 6WHUQ :RUNLQJ 3DSHU KWWSZZZQEHURUJSDSHUVZ 1$7,21$/ %85($8 2) (&2120,& 5(6($5&+ 0DVVDKXVHWWV $YHQXH &DPEULGJH6 0$ 6HSWHPEHU :HWKDQN-RVKXD*DQV&KDG-RQHV6DP.RUWXP3DXO5RPHUDQGVHPLQDUSDUWLLSDQWVDWWKH1%(5 6XPPHU,QVWLWXWHIRUKHOSIXORPPHQWV-HII)XUPDQ,ULQHX&DUYDOKRDQG*UHJ%RQGSURYLGHGH[HSWLRQDO UHVHDUKDVVLVWDQH7KHDXWKRUVDNQRZOHGJHWKHILQDQLDOVXSSRUWRIWKH&RXQLORQ&RPSHWLWLYHQHVV7KH YLHZVH[SUHVVHGKHUHLQDUHWKRVHRIWKHDXWKRUVDQGQRWQHHVVDULO\WKRVHRIWKH1DWLRQDO%XUHDXRI(RQRPL 5HVHDUK E\0LKDHO(3RUWHUDQG6RWW6WHUQ$OOULJKWVUHVHUYHG6KRUWVHWLRQVRIWH[WQRWWRH[HHGWZR SDUDJUDSKVPD\EHTXRWHGZLWKRXWH[SOLLWSHUPLVVLRQSURYLGHGWKDWIXOOUHGLWLQOXGLQJQRWLHLVJLYHQ WRWKHVRXUH 0HDVXULQJ WKH ³,GHDV´ 3URGXWLRQ )XQWLRQ (YLGHQH IURP ,QWHUQDWLRQDO 3DWHQW 2XWSXW 0LKDHO ( 3RUWHU DQG 6RWW 6WHUQ 1%(5 :RUNLQJ 3DSHU 1R 6HSWHPEHU -(/ 1R 26 26 2 $%675$&7 7KLV SDSHU HVWLPDWHV WKH SDUDPHWHUV RI WKH ³LGHDV´ SURGXWLRQ IXQWLRQ HQWUDO WR UHHQW PRGHOV RI HRQRPL JURZWK :H GR VR E\ HYDOXDWLQJ WKH GHWHUPLQDQWV RI ³LQWHUQDWLRQDO´ SDWHQWLQJ UDWHV DURVV WKH 2(&'6 ZKHUH DQ LQWHUQDWLRQDO SDWHQW LV RQH JUDQWHG E\ WKH 86 SDWHQW RIILH WR D IRUHLJQ HVWDEOLVKPHQW 7DNLQJ DGYDQWDJH RI YDULDWLRQ LQ WKH IORZ RI LGHDV SURGXHG E\ GLIIHUHQW RXQWULHV RYHU WLPH6 ZH SURYLGH HYLGHQH IRU WKUHH PDLQ ILQGLQJV )LUVW6 DW WKH OHYHO RI WKH SURGXWLRQ RI LQWHUQDWLRQDO SDWHQWV6 RXQWU\OHYHO 5>' SURGXWLYLW\ LQUHDVHV SURSRUWLRQDOO\ ZLWK WKH VWRN RI LGHDV DOUHDG\ GLVRYHUHG6 D NH\ SDUDPHWUL UHVWULWLRQ DVVRLDWHG
    [Show full text]
  • ECON3102-005 Chapter 4: Firm Behavior
    ECON3102-005 Chapter 4: Firm Behavior Neha Bairoliya Spring 2014 • The representative firm demands labor and supplies consumption goods. Review and Introduction • The representative consumer supplies labor and demands consumption goods. Review and Introduction • The representative consumer supplies labor and demands consumption goods. • The representative firm demands labor and supplies consumption goods. • Production Function Y = zF (K; Nd ) • Because this is a one-period model, we treat K as a fixed input. In the SR, firms cannot vary their capital input. • z is called the total factor productivity, as an increase in z makes both K and Nd more productive. • Y is output of consumption goods. The Representative Firm • Assume a representative firm which owns capital (plant and equipment), hires labor to produce consumption goods. • Because this is a one-period model, we treat K as a fixed input. In the SR, firms cannot vary their capital input. • z is called the total factor productivity, as an increase in z makes both K and Nd more productive. • Y is output of consumption goods. The Representative Firm • Assume a representative firm which owns capital (plant and equipment), hires labor to produce consumption goods. • Production Function Y = zF (K; Nd ) • z is called the total factor productivity, as an increase in z makes both K and Nd more productive. • Y is output of consumption goods. The Representative Firm • Assume a representative firm which owns capital (plant and equipment), hires labor to produce consumption goods. • Production Function Y = zF (K; Nd ) • Because this is a one-period model, we treat K as a fixed input.
    [Show full text]
  • Input Demands
    Economics 326: Input Demands Ethan Kaplan October 24, 2012 Outline 1. Terms 2. Input Demands 1 Terms Labor Productivity: Output per unit of labor. Y (K; L) L What is the labor productivity of the US? Output is rouhgly US$14.7 trillion. The labor force is roughly 153 million people. Therefore, the aggregate labor productivity for the US is: $96; 000 How is this di¤erent from GDP per capita. The main di¤erence is that we are measuring output per work- ing person not output per person living in the US. Marginal Product: The additional output from an addition unit of input: @F = Marginal Product of Labor @L @F = Marginal Product of Capital @K @F = Marginal Product of Land @T Declining Marginal Productivity: We usually assume that the marginal product of an input declines with input usage. Think about farm production. We have land, labor and capital. If we start with 2 people and 40 acres of land and zero capital and we then buy a tractor, output will increase a lot. If we then buy a second tractor, output might increase less than with one tractor because the second trator will probably not be used as often as the …rst. If we then buy a third tractor, the increase in output will be very low. (Show graph). 2 Input Demands The producer solves the pro…t maximization problem choosing the amount of capital and labor to employ. In doing so, the producer derives input demands. These are the analogues of Marshallian Demand in consumer theory. They are a function of prices of inputs and the price of output.
    [Show full text]
  • 1 Lecture Notes - Production Functions - 1/5/2017 D.A
    1 Lecture Notes - Production Functions - 1/5/2017 D.A. 2 Introduction Production functions are one of the most basic components of economics • They are important in themselves, e.g. • — What is the level of returns to scale? — How do input coeffi cients on capital and labor change over time? — How does adoption of a new technology affect production? — How much heterogeneity is there in measured productivity across firms, and what ex- plains it? — How does the allocation of firm inputs relate to productivity Also can be important as inputs into other interesting questions, e.g. dynamic models of • industry evolution, evaluation of firm conduct (e.g. collusion) For this lecture note, we will work with a simple two input Cobb-Douglas production function • 0 1 2 "i Yi = e Ki Li e where i indexes firms, Ki is units of capital, Li is units of labor, and Yi is units of output. ( 0, 1, 2) are parameters and "i captures unobservables that affects output (e.g. weather, soil quality, management quality) Take natural logs to get: • yi = 0 + 1ki + 2li + "i This can be extended to • — Additional inputs, e.g. R&D (knowledge capital), dummies representing discrete tech- nologies, different types of labor/capital, intermediate inputs. — Later we will see more flexible models yi = f (ki, li; ) + "i yi = f (ki, li,"i; ) (with scalar/monotonic "i) yi = 0 + 1iki + 2ili + "i 3 Endogeneity Issues Problem is that inputs ki, li are typically choice variables of the firm. Typically, these choices • are made to maximize profits, and hence will often depend on unobservables "i.
    [Show full text]
  • The Historical Role of the Production Function in Economics and Business
    American Journal of Business Education – April 2011 Volume 4, Number 4 The Historical Role Of The Production Function In Economics And Business David Gordon, University of Saint Francis, USA Richard Vaughan. University of Saint Francis, USA ABSTRACT The production function explains a basic technological relationship between scarce resources, or inputs, and output. This paper offers a brief overview of the historical significance and operational role of the production function in business and economics. The origin and development of this function over time is initially explored. Several various production functions that have played an important historical role in economics are explained. These consist of some well known functions, such as the Cobb-Douglas, Constant Elasticity of Substitution (CES), and Generalized and Leontief production functions. This paper also covers some relatively newer production functions, such as the Arrow, Chenery, Minhas, and Solow (ACMS) functions, the transcendental logarithmic (translog), and other flexible forms of the production function. Several important characteristics of the production function are also explained in this paper. These would include, but are not limited to, items such as the returns to scale of the function, the separability of the function, the homogeneity of the function, the homotheticity of the function, the output elasticity of factors (inputs), and the degree of input substitutability that each function exhibits. Also explored are some of the duality issues that potentially exist between certain production and cost functions. The information contained in this paper could act as a pedagogical aide in any microeconomics-based course or in a production management class. It could also play a role in certain marketing courses, especially at the graduate level.
    [Show full text]
  • Aggregate Production Functions Are NOT Neoclassical
    Aggregate Production Functions are NOT Neoclassical Stefano Zambelli∗ May 15, 2014 Submitted for presentation at the 55th Trento Conference of the Societa' Italiana degli Economisti. Not to be quoted or reproduced without permission. Abstract The issue of whether production functions are consistent with the neoclassical postulates has been the topic of intensive debates. One of the issues is whether the production of an aggregate economic system can be represented as if it was a simple neoclassical well-behaved production function with inputs the aggregate capital K, homogeneous with output Y , and aggregate labor, L. Standard postulates are those of the marginal productivities - and the associated demand of labor and capital - are negatively related with the factor prices, namely the wage rate and the profit rate. The cases where the neoclassical properties do not hold are often regarded as anomalies. In this paper we use real input-output data and we search for these anomalies. We compute the aggregate values for capital, production and labour. We find that for the dataset considered the neoclassical postulates do not hold. We consider this to be a very robust result. The implication is that standard models relying on the neoclassical aggregate Cobb-Douglas-like production functions do not hold. Keywords: Aggregate Neoclassical Production Function, Cobb-Douglas, CES, Technological Change, Macroeconomics, Growth. JEL classifications: C61, C63, C67, O47 D r a f t ∗Department of Economics and Management, Algorithmic Social Sciences Research Unit (ASSRU - www.assru.economia.unitn.it), University of Trento; via Inama, 5, 38100 Trento, Italy; E-mail: ste- [email protected] 1 1 Introduction It is a widespread practice among most (macro) economists to use the \neoclassical" aggre- gate production function while constructing (macro)economic models.
    [Show full text]
  • Microeconomics (Production, Ch 6)
    Microeconomics (Production, Ch 6) Microeconomics (Production, Ch 6) Lectures 09-10 Feb 06/09 2017 Microeconomics (Production, Ch 6) Production The theory of the firm describes how a firm makes cost- minimizing production decisions and how the firm’s resulting cost varies with its output. The Production Decisions of a Firm The production decisions of firms are analogous to the purchasing decisions of consumers, and can likewise be understood in three steps: 1. Production Technology 2. Cost Constraints 3. Input Choices Microeconomics (Production, Ch 6) 6.1 THE TECHNOLOGY OF PRODUCTION ● factors of production Inputs into the production process (e.g., labor, capital, and materials). The Production Function qFKL= (,) (6.1) ● production function Function showing the highest output that a firm can produce for every specified combination of inputs. Remember the following: Inputs and outputs are flows. Equation (6.1) applies to a given technology. Production functions describe what is technically feasible when the firm operates efficiently. Microeconomics (Production, Ch 6) 6.1 THE TECHNOLOGY OF PRODUCTION The Short Run versus the Long Run ● short run Period of time in which quantities of one or more production factors cannot be changed. ● fixed input Production factor that cannot be varied. ● long run Amount of time needed to make all production inputs variable. Microeconomics (Production, Ch 6) 6.2 PRODUCTION WITH ONE VARIABLE INPUT (LABOR) TABLE 6.1 Production with One Variable Input Amount Amount Total Average Marginal of Labor (L) of Capital (K) Output (q) Product (q/L) Product (∆q/∆L) 0 10 0 — — 1 10 10 10 10 2 10 30 15 20 3 10 60 20 30 4 10 80 20 20 5 10 95 19 15 6 10 108 18 13 7 10 112 16 4 8 10 112 14 0 9 10 108 12 -4 10 10 100 10 -8 Microeconomics (Production, Ch 6) 6.2 PRODUCTION WITH ONE VARIABLE INPUT (LABOR) Average and Marginal Products ● average product Output per unit of a particular input.
    [Show full text]
  • Production Functions and Productivity Slides
    Production Functions and Productivity Paul T. Scott NYU Stern [email protected] PhD Empirical IO Fall 2017 1 / 84 Intro Overview I Brief background on industry dynamics I Methods for estimating production functions: I Olley Pakes (1995) I Ackerberg, Caves, and Frazer (2015) I What production analysis can say about market power: I De Loecker and Warzynski (2012) I These tools are highly relevant outside IO, notably in trade, macro, and development 2 / 84 Intro Some Questions I Role of entry and exit in driving growth? I Impact of events like trade liberalization and deregulation on productivity? I Persistence of productivity within plant/firm? I What are the factors driving plant/firm-level changes in productivity and growth? 3 / 84 Firm size distribution The firm size distribution I A very robust finding: the firm size distribution has a long upper tail. I ... this holds within the vast majority of industries, countries, and after conditioning on observable characteristics. I Typically, the size distribution is approximated with a lognormal or Pareto distribbtion. I Broader theme: almost any variable we look at exhibits tremendous heterogeneity across firms 4 / 84 Firm size distribution Gibrat’s Law: a trivial model of growth and heterogeneity I Gibrat’s law states that if the growth rate of a variable is independent of its size and over time, it will have a log-normal distribution in the long run. I Let Yit denote firm i’s size (employment or output) in year t . Suppose it evolves according to the following process: (Yi,t+1 − Yit )/Yit = εit where εit is i.i.d.
    [Show full text]
  • Chapter 3: National Income (Long-Run Neoclassical Theory)
    Chapter 3: National Income (Long-Run Neoclassical Theory) The economy uses inputs (or factors) of labor (L) and capital (K) to produce the output or GDP (Y). The wage and rent are denoted by W and R, respectively. We want to answer two questions Q1: How to use K and L to produce Y? So where does national income come from? Q2: How are W and R determined? So how is the national income distributed among owners of labor and capital? Mathematically, the production process is captured by the production function of Y = F(K, L) We assume (1) ̅ ̅, so the quantity of both inputs are fixed in long term. (2) Both K and L are fully utilized. So there is no unemployment. Assumptions (1) and (2) imply that_________ (3) Let ( ) ( ) denote the marginal product of labor, ( ) ( ) the marginal product of capital. As K or L rises, Y rises. Mathematically __________ 1 (4) As K or L rises, Y rises but at decreasing rate. This assumption is called decreasing marginal product. Mathematically, __________________. We can draw the graph (Figure 3-3) that represents a typical production function as (5) The production function has the property of constant returns to scale. That is, ( ) (1) So if both inputs are doubled ( =2), the output is doubled as well. A production function with constant returns to scale has the property of (2) This result is called Euler’s theorem. Proof (Optional) 2 (6) The firm is competitive in both output market and input market. In other words, the firm takes the output price (P) and the input prices (W, R) as given.
    [Show full text]
  • Redalyc.Aggregate Production Functions, Neoclassical Growth
    Estudios de Economía Aplicada ISSN: 1133-3197 [email protected] Asociación Internacional de Economía Aplicada España FELIPE, JESUS; FISHER, FRANKLIN M. Aggregate production functions, neoclassical growth models and the aggregation problem Estudios de Economía Aplicada, vol. 24, núm. 1, abril, 2006, pp. 127-163 Asociación Internacional de Economía Aplicada Valladolid, España Available in: http://www.redalyc.org/articulo.oa?id=30113179006 How to cite Complete issue Scientific Information System More information about this article Network of Scientific Journals from Latin America, the Caribbean, Spain and Portugal Journal's homepage in redalyc.org Non-profit academic project, developed under the open access initiative E STUDIOS DE ECONOMÍA APLICADA VOL. 24-1, 2006. P ÁGS. 127-163 Aggregate production functions, neoclassical growth models and the aggregation problem JESUS FELIPE(*) y FRANKLIN M. FISHER(**) (*) Macroeconomics and Finance Research Division. Economics and Research Department. Asian Development Bank. Manila, Philippines; (**) Massachusetts Institute of Technology. Cambridge, MA 02139-4307 E-mails: (*) [email protected] - (**) ffi [email protected] ABSTRACT Lawrence R. Klein pioneered the work on aggregation, in particular in production functions, in the 1940s. He paved the way for researchers to establish the conditions under which a series of micro production functions can be aggregated so as to yield an aggregate production function. This work is fundamental in order to establish the legitimacy of theoretical (neoclassical) growth models and empirical work in this area (e.g., growth accounting exercises, econometric estimation of aggregate production functions). This is because these models depend on the assumption that the technology of an economy can be represented by an aggregate production function, i.e., that the aggregate production function exists.
    [Show full text]
  • 14.452 Economic Growth: Lectures 5-7, Neoclassical Growth
    14.452 Economic Growth: Lectures 5-7, Neoclassical Growth Daron Acemoglu MIT November 8, 13 & 15, 2018 Daron Acemoglu (MIT) Economic Growth Lectures 5-7 November8,13&15,2018 1/83 Introduction Introduction Foundations of Neoclassical Growth Solow model: constant saving rate. Ramsey or Cass-Koopmans model: differs from the Solow model only because it explicitly models the consumer side and endogenizes savings. This model specifies the preference orderings of individuals and derives their decisions from these preferences. It also Enables better understanding of the factors that affect savings decisions. Enables to discuss the “optimality” of equilibria Clarifies whether the (competitive) equilibria of growth models can be “improved upon”. Beyond its use as a basic growth model, also a workhorse for many areas of macroeconomics. Daron Acemoglu (MIT) Economic Growth Lectures 5-7 November8,13&15,2018 2/83 Introduction Preliminaries Preliminaries Consider an economy consisting of a unit measure of infinitely-lived households. I.e., an uncountable number of households: e.g., the set of households could be represented by the unit interval [0, 1]. H Emphasize that each household is infinitesimal and will have no effect on aggregates. Can alternatively think of as a countable set of the form H = 1, 2, ..., M with M = ¥, without any loss of generality. H f g Advantage of unit measure: averages and aggregates are the same Simpler to have as a finite set in the form 1, 2, ..., M with M large but finite. H f g Acceptable for many models, but with overlapping generations require the set of households to be infinite.
    [Show full text]