<blockquote>
  <p>How do we develop concise production functions from a set of equations
  like these?</p>
</blockquote>

<p>It goes the other way around.</p>

<p>VAR's are  a special group of models for time series data, developed mainly for atheoretical forecasting purposes. In a VAR approach we do not assume some structural economic model, we just want to use the past of a variable and its interelations with other variables, to form a good quality predictor (and it is for this reason that when they were first introduced and propagated by Sims,  they created a lot of controversy).</p>

<p>In general, estimating a production function of a single firm using time-series data does not alter the econometric approach described in the answer to your other question, only here the assumption we make is that the unknown parameters refer to a single firm (and not to many firms), and so stay constant across time (and not across firms on the same time period.</p>

<p>A new econometric issue is that with time series data we are forced to deal with the aspect of serial correlation (in a cross-sectional setting, "serial" correlation makes no sense because we can permutate the index without consequences). Serial correlation may emerge in two ways: a) In the regressors  b) in the error term.</p>

<p>A new economic issue in a production function setting is the intertemporal change in Total Factor Productivity.</p>

CC BY-SA 3.0
2018-04-08T01:51:56.023Z
_In general, estimating a production function of a single firm using time-series data does not alter the econometric approach described in the answer to your other question, only here the assumption we make is that the unknown parameters refer to a single firm (and not to many firms), and so stay constant across time (and not across firms on the same time period._ - so we just need to make sure our variables are stationary before estimating a structural equation?
EconJohn
CC BY-SA 3.0
2018-04-08T11:29:04.010Z
@EconJohn Serieal correlation and regressor endogeneity never go away that easily.
Alecos Papadopoulos
CC BY-SA 3.0
2018-04-05T22:11:51.493Z
2018-04-06T01:16:46.797Z
2018-04-06T01:16:46.797Z
Alecos Papadopoulos
<p>A while back I asked <a href="https://economics.stackexchange.com/questions/14551/how-do-we-estimate-production-functions">How do we estimate production functions?</a></p>

<p>The answers given address cases when dealing with cross-sectional data, However most of the data I've been seeing is given by a time series.</p>

<p>For example if we have a (logged) VAR(1) with two variables $x_{t,1}$ and $x_{t,2}$, the appropriate model is:</p>

<p>$$x_{t,1}=\alpha_1+\beta_{11}x_{t-1,1}+\beta_{12}x_{t-1,2}+\mu_{t,1}$$
$$x_{t,2}=\alpha_2+\beta_{21}x_{t-1,2}+\beta_{22}x_{t-1,1}+\mu_{t,2}$$</p>

<p>How do we develop concise production functions from a set of equations like these?</p>

<production-function><applied-econometrics>
Estimating production functions with time series data
EconJohn
# Estimating production functions with time series data

(Asked by: username_0 on 2018-04-05)

A while back I asked [How do we estimate production functions?](https://economics.stackexchange.com/questions/14551/how-do-we-estimate-production-functions)

The answers given address cases when dealing with cross-sectional data, However most of the data I've been seeing is given by a time series.

For example if we have a (logged) VAR(1) with two variables $x\_{t,1}$ and $x\_{t,2}$, the appropriate model is:

$$x\_{t,1}=\alpha\_1+\beta\_{11}x\_{t-1,1}+\beta\_{12}x\_{t-1,2}+\mu\_{t,1}$$
$$x\_{t,2}=\alpha\_2+\beta\_{21}x\_{t-1,2}+\beta\_{22}x\_{t-1,1}+\mu\_{t,2}$$

How do we develop concise production functions from a set of equations like these?

**Tags:** production-function, applied-econometrics

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## 1 answers

### Answer by username_1 on 2018-04-05. Score: 1 | Accepted answer

> How do we develop concise production functions from a set of equations
> like these?

It goes the other way around.

VAR's are a special group of models for time series data, developed mainly for atheoretical forecasting purposes. In a VAR approach we do not assume some structural economic model, we just want to use the past of a variable and its interelations with other variables, to form a good quality predictor (and it is for this reason that when they were first introduced and propagated by Sims, they created a lot of controversy).

In general, estimating a production function of a single firm using time-series data does not alter the econometric approach described in the answer to your other question, only here the assumption we make is that the unknown parameters refer to a single firm (and not to many firms), and so stay constant across time (and not across firms on the same time period.

A new econometric issue is that with time series data we are forced to deal with the aspect of serial correlation (in a cross-sectional setting, "serial" correlation makes no sense because we can permutate the index without consequences). Serial correlation may emerge in two ways: a) In the regressors b) in the error term.

A new economic issue in a production function setting is the intertemporal change in Total Factor Productivity.

> **Comments:**
> **username_0**: _In general, estimating a production function of a single firm using time-series data does not alter the econometric approach described in the answer to your other question, only here the assumption we make is that the unknown parameters refer to a single firm (and not to many firms), and so stay constant across time (and not across firms on the same time period._ - so we just need to make sure our variables are stationary before estimating a structural equation?  
> **username_1**: @EconJohn Serieal correlation and regressor endogeneity never go away that easily.  

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