Skip to content
Start free
Get App

Semi-parametric approaches of measuring productivity

This video explains semiparametric approaches for measuring productivity, focusing on Levinsohn and Petrin's method to address endogeneity in production function estimation.

Key Takeaways

  • Firms adjust inputs in response to productivity shocks, causing simultaneity and endogeneity in production function estimation.
  • Semiparametric approaches like Levinsohn and Petrin's method use intermediate inputs as proxies to correct endogeneity bias.
  • Levinsohn and Petrin's framework is an extension of Olley and Pakes and is preferred due to smoother response of intermediate inputs.
  • Correcting for endogeneity is crucial for unbiased and consistent productivity measurement in econometric production analysis.
  • The method involves a two-stage estimation process to separate productivity shocks from input decisions.

What the video covers

  • The video continues the discussion on productivity analysis using parametric and semiparametric approaches.
  • It highlights the complexity of production processes and how firms adjust inputs to maximize output and minimize costs.
  • The simultaneity problem arises because firms' input decisions respond to unobserved productivity shocks, causing endogeneity in production function estimation.
  • Semiparametric methods aim to correct this endogeneity by using instrumental variables or proxies.
  • Two key literatures are discussed: Olley and Pakes (1996) and Levinsohn and Petrin, with focus on the latter's value-added production function estimation.
  • Levinsohn and Petrin use intermediate inputs as proxies for productivity shocks, which respond more smoothly than investment proxies used by Olley and Pakes.
  • The video explains how productivity shocks can be internal (R&D, innovation) or external (automation, AI) and how firms systematically respond to these.
  • The framework involves two stages of estimation to correct for simultaneity and endogeneity in production function models.
  • The approach improves estimation accuracy by addressing bias caused by correlation between explanatory variables and error terms.
  • The video also briefly mentions the use of Stata code for implementing these semiparametric estimation methods.

Chapters

  1. 00:00Introduction to Semiparametric Productivity Estimation
  2. 02:00Complexities in Production Function Estimation
  3. 03:32Olley and Pakes vs Levinsohn and Petrin Frameworks
  4. 04:59Impact of Technology and Productivity Shocks
  5. 06:30Using Intermediate Inputs to Address Endogeneity
  6. 08:03Data Considerations and Proxy Variables
  7. 09:25Mathematical Framework and Model Specification
  8. 15:36Summary and Implementation Notes

Answers

Questions about this video

What is the main problem addressed by semiparametric approaches in productivity measurement?

Semiparametric approaches address the endogeneity problem caused by simultaneity, where firms' input decisions respond to unobserved productivity shocks, biasing production function estimates.

How do Levinsohn and Petrin improve upon Olley and Pakes' method?

Levinsohn and Petrin use intermediate inputs as proxies for productivity shocks, which respond more smoothly and frequently than investment proxies used by Olley and Pakes, improving estimation accuracy.

Why is correcting for endogeneity important in production function estimation?

Correcting for endogeneity is crucial because correlation between explanatory variables and error terms leads to biased and inconsistent estimates of productivity, undermining the validity of econometric analysis.

Full Transcript — Download SRT & Markdown

00:15
Speaker A
Hi, welcome back to the course Applied Production Analysis using MATLAB. Continuing our discussion on productivity analysis, particularly the parametric approaches for estimating productivity. In this session, we'll be covering semiparametric variance of estimating productivity.
00:36
Speaker A
As you know, the production process particularly from a manufacturing or the firm point of view, it involves a very complex decision making. Firms being a profit maximizing entity they try to adjust their input output bundle such a way that the output is maximized and the
00:57
Speaker A
As you know, the production process, particularly from a manufacturing or the firm point of view, involves very complex decision making. Firms, being a profit-maximizing entity, try to adjust their input-output bundle in such a way that the output is maximized and the cost of production is minimized. Many factors, including the level of productivity, are involved in such decision processes. So recently, we have been hearing a lot of cases where MNCs adjust their input-output bundle, particularly the labor bundle, in such a way that it maximizes their profit. Some of them were unfortunately focusing more on capital and sending some set of labor in such a way that they can invest more in positive-involved technologies and focus less on labor.
01:15
Speaker A
that it maximizes their profit were few of them were unfortunately focusing more on capital and sending some set of labor such a way that they can invest more on positive involved in technologies and focus less on the labor
01:39
Speaker A
There was a lot of labor displacement happening in terms of our production process, and so on. So these are the realities from an econometric point of view or from an applied production estimation point of view. Such inherent nature that firms keep creates several complexities in the estimation of production function. In short, profit-maximizing firms may respond to productivity shocks in terms of their adjustment in inputs.
02:00
Speaker A
several complexities in the estimation of production function. In short, profit maximizing firms may respond to productivity shocks in terms of their adjustment in inputs.
02:15
Speaker A
As a result, when you are estimating the production function, it becomes very simultaneous because there are input decisions which are based on the productivity shocks. As a result, we will be unable to identify our production function estimation or production function formula that we are estimating, which will result in simultaneity. From a very econometric point of view, such simultaneity among the variables included in the production function model results in a case where we run into a problem of endogeneity. That means at least one of the explanatory variables that we have included in the model may get correlated with our error term, and as a result, the unbiased nature of our coefficient being estimated as a part of production function estimation or the productivity that we estimate by using such coefficient will become biased.
02:34
Speaker A
function formula that we are estimating which will result in simultaneity and from a very econometric point of view such simultaneity among the variables included in the production function model result in a case where we run into a problem of endogenity. That means at
02:55
Speaker A
So the semiparametric approach tries to address such bias that is happening because of the endogeneity issue, particularly correcting for such endogeneity by including some instruments or following a framework which corrects for such endogeneity happening due to simultaneity. So in this case, we'll be discussing the simultaneity and endogeneity that can happen in the context of production function estimation.
03:12
Speaker A
productivity that we estimate by using such coision will become biased. So separametric approach tries to address such bias that is happening because of the endogenity issue particularly correcting for such endogenity by including some uh instruments or the frame following a
03:32
Speaker A
To address this issue, there are particularly two literatures that have come. One is by Olley and Pakes in the year 1996, followed by Levinsohn and Petrin, which is basically an extension or a modification of the earlier framework proposed by Olley and Pakes. Due to time constraints, we'll be focusing particularly on the latest development in the field of semiparametric approach, that is basically the Levinsohn and Petrin estimation, particularly from a value-added point of view. I'll be showing you the overall framework of such estimation, that is basically stage one and stage two of Levinsohn and Petrin estimation.
03:46
Speaker A
To address this issue there are particularly two literature that has come. One is by Ole Np in the year 1996 followed by Levin and Petrine which is basically an extension or a modification of the earlier framework proposed by
04:02
Speaker A
So as I mentioned, we can have a case where firms respond to the productivity shocks that are happening in the system. That productivity shock can arise due to any internal factor that firms involve in R&D activities, innovation, which will create a productivity change. We can consider it as a productivity shock, or it can happen because of some external factors, particularly investment in new technology that is happening in the global scenario, and automation, AI. Such cases also create our productivity to change over time.
04:22
Speaker A
overall framework of such estimation that is basically stage one and stage two of living in pattern estimation. So as I mentioned we can have a case where firms respond to the productivity shocks that is happening in the system that productivity shock can
04:42
Speaker A
As a result, when there is a positive productivity shock in a firm, firms will react to such positive productivity shocks by increasing the labor intake or the use of inputs. Alternatively, when there is a negative productivity shock happening in period t, in period t + 1, firms may try to reduce their input use and react to the productivity shock that is a negative productivity shock in such a manner. As a result, we can have unobserved productivity shocks entering into the entire data generating process, and the firms, as I mentioned, they respond to such productivity shocks in a very systematic manner, and this will result in simultaneity in the context of estimation point of view. This simultaneity in the estimation of production or in their production function estimation may result in endogeneity.
04:59
Speaker A
technology that is happening in the global scenario and automation AI such cases also create our productivity to change over time. As a result, when there is a positive productivity shock infinity, firms will react react to such positive productivity shocks by increasing the
05:24
Speaker A
So how to address this endogeneity issue in the context of semiparametric production function estimation? So it is basically proposed by Olley and Pakes in the year 1996.
05:41
Speaker A
productivity shock in such a manner. As a result, we can have unobserved productivity shocks entering into the entire data generating process and the forms as I mentioned they respond to such productivity shocks in a very systematic manner and this will result
06:01
Speaker A
So what they use—you have seen in the classic literature on endogeneity and correction error, we use some instruments to account for the endogeneity issue arising in the estimation of the regression function. So in this case, Olley and Pakes claim that in a production framework, investment may respond to our productivity shock, and we can use investment as a proxy for unobserved productivity shock. Alternatively, Levinsohn and Petrin claim that the intermediate inputs may respond to our productivity shocks more smoothly than investment because change in investment involves additional cost, and investment is not something that you can keep changing over a short period of time.
06:20
Speaker A
semiparametric production function estimation. So it is basically proposed by Olay and PEX in the year 1996.
06:30
Speaker A
And they claim that intermediate input is something that immediately responds to any positive or negative productivity shock. They extend the framework of Olley and Pakes by using intermediate inputs as a proxy in place of investment for correcting the unobserved productivity shock and the endogeneity. So here also, from a data point of view, we can use investment as a proxy only for those firms which are reporting investment over the period of time. Most of the cases, net investment that is happening for each firm might not change in a short period of time. As a result, the majority of the firms may report net investment in a particular period as zero.
06:52
Speaker A
framework, investment may respond to our productivity shock and we can use investment as a proxy for unobserved productivity shock. Alternatively, Levenson and Petrine claims that the intermediate inputs may respond to our productivity shocks more smoothly than investment because change in investment
07:16
Speaker A
From a data point of view, Levinsohn and Petrin stands superior in the sense that you get a series of intermediate inputs for almost all the firms, whereas when you are using capital or investment or net investment as a proxy, it is highly likely that you may get zero values for most of the observations, which cannot be used as a proxy for any productivity shocks.
07:23
Speaker A
And they claim that intermediate input is something that immediately respond to any positive or negative productivity show. and they extend the framework of olay and pics by using intermediate inputs as a proxy in place of uh investment for correcting the unobserved
07:45
Speaker A
So we follow a parametric approach in the specification. Here, for example, we have three inputs: labor, capital, and intermediate inputs. We can specify it as Cobb-Douglas functional form. Yt, that is basically the output, as a function of Lt, Kt, Mt, and the bl, bk, and bm are the coefficients associated with labor, capital, and intermediate input. As against our conventional model, here we have two terms in the error term that we are specifying.
08:03
Speaker A
happening for each firm might not change in a short period of time. As a result majority of the firms may report net investment in a particular period as zero. From a data point of view, Levenson and Petrine stands superior in
08:20
Speaker A
And here Wt basically is the parameter that captures any productivity shocks that involve in the production function, and the Et is basically the standard error term. Wt will account for any transmitted productivity component which is considered as a state variable that impacts firm's decision to increase their inputs or achieve a higher level of output. Here we assume the Et that I mentioned is basically the classical error term that we have in a regression function, which we expect to be uncorrelated with any input choices. This is free from any productivity shocks or which has an impact on the input choices of the firm.
08:35
Speaker A
most of the observation which cannot be used as a proxy for any productivity shocks.
08:43
Speaker A
And here we assume that the intermediate inputs Mt depend on firm's Kt and the Wt. So this Kt basically talks about the proportion that may have between capital and labor, and Wt is the process that I was explaining where the firms may choose their level of intermediate inputs based on the level of productivity shock that they are facing. And we can say, as I mentioned, whe—
09:03
Speaker A
a function of lt kt mt and the bl bk and bm are the coicient associated with labor capital and intermediate input as against our conventional model. Here we have two terms in the error term that we are specifying. And
09:25
Speaker A
here WT basically the parameter that capture any productivity shocks that involves in the production function and the ET is basically the standard error term and WT will account for any transmitted productivity component which is considered as a state
09:47
Speaker A
variable that impacts firm's decision to uh increase their inputs or achieve higher level of output and uh here we assume the EAT t that I mentioned it's basically the classical error term that we have it in a regression function which we expect this
10:09
Speaker A
t to be uncorrelated with any input choices this is free from any productivity uh shocks or which has an impact on the input choices of the firm and here we assume that the intermediate inputs MT depends on firms KT and the WT. So
10:29
Speaker A
this KT basically talks about the proportion that may have between capital and labor and WT the process that I was explaining where the firms may choose their level of intermediate inputs based on the level of productivity shock that they are
10:46
Speaker A
facing. And uh we can say as I mentioned when productivity improves firms may use more material inputs and when there is a deterioration in productivity or a negative productivity show they may reduce their use of intermediate input. So we claim this uh
11:06
Speaker A
function that demand for uh factors of production is basically monotonically increasing with respect to WT that is basically the productivity show. As a result, we can express or we can take the inverse demand function to express WT in terms
11:25
Speaker A
of our uh MT and KT. Okay. So here we can write WT as a function of KT and MT.
11:40
Speaker A
Productivity the unobserved productivity shocks are expressed as a function of two observed input which can be modled in a empirical setup and also to model this productivity shock process the living and petrin assume that it follows a the productivity shocks
12:02
Speaker A
follows a first order marco process. WT can be writed uh expressed as a uh function of expected value of WT given the values of WT -1 with uh EA T. Here this functional form has uh one deterministic counterpart and the
12:27
Speaker A
stoastic part where Eat T consist of our uh innovation and the productivity that is happening productivity changes that is happening in the system which is uncorrelated with KT but we are not imposing any uncorrelation of that with the labor that we have included in the
12:45
Speaker A
model and that is basically the source of simultaneity problem or the endogenity that we are conceptualizing in a semiparametric framework.
12:55
Speaker A
Moving ahead, we can have two cases where the dependent variable is considered as the value added and alternatively we can consider the dependent variable as the gross revenue.
13:06
Speaker A
So here we'll consider the case of dependent variable as the value added and we see how to correct for endogenity or the simultaneity issue that we are facing and how to estimate productivity or the coicient involved in the
13:19
Speaker A
production function. So V_T is basically the value added that we are expressing as a function of LT labor and capital and productivity shocks and the error term. And here we can express this end term beta 0 and beta kt and the
13:42
Speaker A
productivity shock as ft which is basically a function of kt and mt as beta 0 beta kt omega kt mt.
13:58
Speaker A
So having this functional form we can plug in this into the original functional form for our value added production function. So that gives us V_T beta LT and FT KT MT plus ET. Okay. Now here in this functional form we have a
14:22
Speaker A
specific function that is basically PT KT MT. In Levinson Petrine framework they approximate that as a third order polomial in KT and MT which can be written as this way sum of I up to 3 J 0 up to 3 3 - I delta
14:46
Speaker A
I J KT I MT J. So this is basically a third order polomial in terms of KT and MT and then plugging in that to our original value added function we get V_T equal to delta 0 plus beta LT plus this
15:04
Speaker A
component that basically the third order polomial in KT and MT and the error term here in this case we can estimate the consistent estimate of beta that using oils and also we can yield an estimate of our we can yield an estimate of our
15:33
Speaker A
ft by using oilless. Now moving ahead in the second stage what we get we take the predicted value of our uh ft function that is basically f_t hat which is basically the difference between the predicted value of our value added minus
15:55
Speaker A
beta l hat lt which can be expressed as delta 0 hat plus sum of i 1 0 up to 3 J 0 up to 3 minus I delta I J hat KT I MT J minus beta L hat LT. So this is the
16:19
Speaker A
same function from what we discussed in the last uh slide. And here there can be alternative values for beta. We name it as beta beta particularly for beta k beta k star we name we can compute it uh
16:37
Speaker A
by using this functional form basically wt equal to ct hat minus beta kt beta beta k star kt. So this you can estimate for each time period and here this can be approximate to a functional form where w
17:03
Speaker A
t that is basically the predicted value of productivity shock is as a function of wt minus one that two with square and cube with an error term and uh following that which we can get an estimate of Our productivity shocks
17:25
Speaker A
basically expected value of WT or omega T for the given values of omega T minus 1.
17:36
Speaker A
And the production function residual can be conceptualized as uh e t hat plus uh sit t hat v_t minus beta l hat lt minus beta k* kt minus our expected value of omega t. And here this can be solved by
18:00
Speaker A
minimizing the value of our uh difference between our actual value of value added minus beta lt minus beta k* kt minus expected value of wt². Okay.
18:23
Speaker A
And here in this stage we get an estimate of productivity that is productivity shocks. And this stage we can estimate get a estimate of our beta k which is free from any uh simultaneity bias or endogenity bias. And so looking
18:40
Speaker A
at the entire procedure we followed in the first instance we specifically assume a functional form that is basically value added as a function of labor and capital and that is basically the parametric aspect of this estimation and in order to correct the endogenity
18:58
Speaker A
issue arising due to simultaneity we follow more of a nonparametric framework. So to summarize uh we have two approaches in terms of semiparametric model. The first one is basically the levvenson and petrine and the second one was the earlier case of
19:16
Speaker A
ole and pigs. In case of levenson and petrin we use materials as the proxy for capturing any productivity shocks and in case of ole and pigs we consider investment as a proxy for capturing any productivity show happening in the
19:32
Speaker A
system. From a data point of view leinsson and petrin is superior as a case for it consider only observation which has a material usage greater than zero. That will be the case for almost all firms because material comes as a
19:47
Speaker A
variable component of our production function. But if you had our investment as a proxy as in the case of Olay in PEG we may lose out lot of observation because we are doing a truncation at I equal to zero only observation with a
20:05
Speaker A
nonzero investment will be included in the model and that is the only component of our bias that uh simultaneity correction or the bias happening correction or bias happening due to endogenity.
20:23
Speaker A
So these are the references basically the Olay and PX 1992 paper. Then we have a modification of that by using raw materials or the intermediate input by uh Levvenson and Petri in 2003 and I have also referred to a paper by Petrial
20:41
Speaker A
2004 which uses the same production framework uh by using a STA code and the documentation thereof. Thank you.
Topics:productivity measurementsemiparametric estimationproduction functionendogeneitysimultaneityOlley and PakesLevinsohn and Petrinintermediate inputseconometricsproduction analysis

Get More with the SozAI App

Transcribe recordings, audio files, and YouTube videos — with AI summaries and speaker detection. 30 minutes free.

App Store Google Play
Or transcribe another YouTube video here →

Free tools: TXT to SRT · SRT Validator · Merge SRT · Subtitle to Text · All tools

More from NPTEL-NOC IITM

View All
Topics Covered So Far (Tutorial Summary) — Transcript29:59
Topics Covered So Far (Tutorial Summary) — Transcript
3,350 1 English
An introduction to Parametric approaches of measuring p… — Transcript17:52
An introduction to Parametric approaches of measuring p… — Transcript
3,750 1 English
Bootstrap based bias correction of the Malmquist Produc… — Transcript18:17
Bootstrap based bias correction of the Malmquist Produc… — Transcript
2,160 1 English
Decomposition of Malmquist Productivity Index – Part II — Transcript30:09
Decomposition of Malmquist Productivity Index – Part II — Transcript
3,852 1 English
Decomposition of Malmquist Productivity Index – Part I — Transcript25:52
Decomposition of Malmquist Productivity Index – Part I — Transcript
2,933 1 English
Malmquist Productivity Index: An Introduction — Transcript16:46
Malmquist Productivity Index: An Introduction — Transcript
1,932 1 English
Tornqvist Productivity Index — Transcript18:44
Tornqvist Productivity Index — Transcript
1,709 1 English
Fisher Productivity Index — Transcript19:21
Fisher Productivity Index — Transcript
1,909 1 English
Total factor productivity and The Solow residual — Transcript21:06
Total factor productivity and The Solow residual — Transcript
2,112 1 English
Simar–Wilson Bootstrap Procedures: Algorithms #1 and #2 — Transcript26:43
Simar–Wilson Bootstrap Procedures: Algorithms #1 and #2 — Transcript
3,821 1 English
Bootstrap DEA Models: A Statistical Perspective on Sima… — Transcript27:09
Bootstrap DEA Models: A Statistical Perspective on Sima… — Transcript
4,052 1 English
Limitations of Conventional DEA Model: Bias and Serial … — Transcript14:51
Limitations of Conventional DEA Model: Bias and Serial … — Transcript
1,800 1 English