How should be treated the interaction terms with state variables in the translog production function?

[Rodrigo Remedio]

In the context of the control functions approach for the estimation of production functions (like Olley-Pakes, Levinsoh-Petrin and Wooldridge, to name a few) and under the translog especification, how the interaction terms with state variables, such capital and labor, for example, should be treated? As a state or flexible input?

[Phil Bromiley]

You'll get a better answer if you follow the FAQ on asking questions - provide Stata code in code delimiters, Stata output, and sample data using dataex.

This is not a microeconomics list so you'll also do better if you explain your problem in terms that don't assume we've read specific economics papers. For example, state or flexible input may have meaning in your literature, but they are not Stata terms in this context.

[Jeff Wooldridge]

Rodrigo, this is a good question. I'm not sure you can trick the new user-written command -prodest- into estimating a model with interactions between the state and flexible inputs. But I know what I would do in the context of my 2009 Economics Letters paper:

http://ac.els-cdn.com.proxy1.cl.msu....23fb5412530e76

In my notation, simply add w(i,t)*x(i,t) to both equations (2.10) and (2.11). In (2.10), the interaction is exogenous, just as are w(i,t) and x(i,t) separately. Therefore, just add all interactions that you include to the IV list for (2.10). For (2.11), w(i,t)*x(i,t) will be endogenous because w(i,t) is endogenous. But this is easy to solve, too: just include w(i,t-1)*x(i,t) among the list of instruments, along with x(i,t), w(i,t-1), x(i,t-1) and how ever many lags you want to include as IVs (probably not many).

By the way, this will sound immodest, but your extension to the basic model with only level effects further illustrates a benefit of my method of moments approach. I think this extension would be quite tricky using Olley-Pakes or Levinsohn-Petrin. Maybe you can contact Gabriele Rovigatti, who wrote the -prodest- command and posts on Statalist sometimes.

Jeff

[Rodrigo Remedio]

Dear Jeff,

Thanks for your answer, it's very much appreciated. In fact, it was precisely answer I was wondering to get, as we are working with your GMM approach.

I'll follow your suggestions and post here the code, as in the future someone else maybe be interested in it too.

Best regards,

Rodrigo

[Jeff Wooldridge]

Rodrigo, that would be much appreciated. I believe many people would find that extension useful.

[Gabriele Rovigatti]

Dear Rodrigo, Dear Jeff,

sorry for the delayed answer - I missed this post: yesterday only I was suggested to have a look by another prodest user (thanks Claudia Demmer).

Regarding the topic, I agree with Jeff on the two main points raised in the discussion:

a) It is tricky - when not impossible or wrong - to approach a translog PF with the usual OP and LP methods, because it is not clear whether the free/state interactions have to be considered state or free once completed the first stage. Indeed, to the best of my knowledge the control function approach with translog production functions are limited to the ACF-corrected case (like in DeLoecker and Warzynski, AER 2012), which does not pose a similar issue.

b) It is possible to approach the problem with a slight modification of Jeff's GMM model. Indeed, I played a little bit with prodest code and I came out with a version which actually implements Jeff's suggestion. Below you can find the results of the plain and translog wrdg methods on the example dataset provided with prodest.

At the moment I don't have time to go through the helpfile, clean the code and check all results in order to issue a new official version of the command on SSC (I am defending my thesis next week); however, I am pretty confident that it properly works and I am available to send the augmented code around via email, would you need that.

I hope that it can help,

Gabriele


Plain WRDG

wrdg productivity estimator                     Cobb-Douglas PF

Dependent variable: value added                 Number of obs      =      2544
Group variable (id): id                         Number of groups   =       497
Time variable (t): year
                                                Obs per group: min =         1
                                                               avg =       5.1
                                                               max =        11

------------------------------------------------------------------------------
       log_y |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    log_lab1 |   .2122377   .0128492    16.52   0.000     .1870537    .2374217
    log_lab2 |   .1895564    .011018    17.20   0.000     .1679615    .2111513
       log_k |   .1536604   .0283321     5.42   0.000     .0981305    .2091903
------------------------------------------------------------------------------
Hansen's J = 11.50
Hansen's J p-value = 0.00

Translog WRDG

wrdg productivity estimator                     translog PF

Dependent variable: value added                 Number of obs      =      2544
Group variable (id): id                         Number of groups   =       497
Time variable (t): year
                                                Obs per group: min =         1
                                                               avg =       5.1
                                                               max =        11

------------------------------------------------------------------------------
       log_y |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    log_lab1 |     .56204   .0835301     6.73   0.000      .398324     .725756
    log_lab2 |   .4964897   .0675471     7.35   0.000     .3640997    .6288796
       log_k |   .2389529   .0591643     4.04   0.000      .122993    .3549129
------------------------------------------------------------------------------