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Consider a production function to be estimated,

$$(*) y_{it} = \beta_0 +\beta_k k_{it} +\beta_l l_{it} + a_i +\omega_{it} +\varepsilon_{it}$$

where $\omega_{it}=\rho\omega_{i,t-1}+\xi_{it}$. The Blundell-Bond (2000) method involves "$\rho$-differencing" the equation to attain

$$y_{it}-\rho y_{i,t-1} = \beta_0 (1-\rho) +\beta_k(k_{it}-\rho k_{i,t-1})+\beta_l(l_{it}-\rho l_{i,t-1})+a_i(1-\rho) +\xi_{it}+(\varepsilon_{it}-\rho \varepsilon_{i,t-1})$$

$$y_{it} = \rho y_{i,t-1}+ \beta_0 (1-\rho) +\beta_k(k_{it}-\rho k_{i,t-1})+\beta_l(l_{it}-\rho l_{i,t-1})+a_i(1-\rho) +\xi_{it}+(\varepsilon_{it}-\rho \varepsilon_{i,t-1})$$

We are thus in a situation with a lagged dependent variable and fixed effects. This can be estimated by GMM using moments of the form $E[\Delta k_{it-1} (a_i(1-\rho) +\xi_{it}+(\varepsilon_{it}-\rho \varepsilon_{i,t-1}))]=0$

We can also "double-difference" the equation to attain,

$$\Delta y_{it} = \rho \Delta y_{i,t-1} +\beta_k\Delta (k_{it}-\rho k_{i,t-1})+\beta_l\Delta (l_{it}-\rho l_{i,t-1}) +\Delta \xi_{it}+\Delta (\varepsilon_{it}-\rho \varepsilon_{i,t-1})$$

This can be estimated by GMM using moments of the form $E[k_{it-1} (\Delta \xi_{it}+\Delta (\varepsilon_{it}-\rho \varepsilon_{i,t-1}))]=0$

My question is, does a Stata command that exists for GMM estimation of these moments? I know there are many commands for dynamic panel estimation (such as xtdpdsys). But these commands state that the baseline equation (equation * above) does not have an autocorrelated error, which this one does due to the $\omega$. Also, I do not see any specifics in the help files regarding rho-differencing or double differencing. Does this estimation need to be coded by hand in matlab/python? Or by the gmm Stata command?

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  • $\begingroup$ xtdpd or xtabond2? $\endgroup$
    – chan1142
    Jul 5, 2023 at 0:53
  • $\begingroup$ I know these commands exist as well. In the help file I do not see documentation about rho-differencing, double differencing, or the baseline equation having an autocorrelated error. Please let me know if I am overlooking something. $\endgroup$ Jul 5, 2023 at 8:05
  • $\begingroup$ I've just read the BB (2000) paper briefly. I think it's about SYS-GMM. There are two sets of MC - one diff eq + levels IV (they're Section 3.1), and the other levels eq + diff IV (they're Section 3.2). For estimation, see help xtdpdsys or xtabond2. I would be able to help you replicate their results if given the data set. $\endgroup$
    – chan1142
    Jul 5, 2023 at 14:57
  • $\begingroup$ Regarding what you call "rho-differencing", BB's equation (2.3) is derived from (2.1), and is estimated by SYS-GMM (and other methods). I see it as a plain GMM estimation applied to their (2.3) which can be done by xtabond, xtdpdsys, xtdpd, xtabond2, etc. One caveat is the restrictions on the parameters in their equation (2.2). They say that they do minimum distance. (See the paragraph after (2.3).) $\endgroup$
    – chan1142
    Jul 5, 2023 at 15:35
  • $\begingroup$ Regarding the data set, the paper says: "This data was kindly made available to us by Bronwyn Hall". I downloaded one from Bronwyn Hall's website (eml.berkeley.edu/~bhhall/bhdata.html - hmuscln8, 3rd from bottom). I could get only 492 firms, not 509 as written in BB (2000). Please let us know if you can construct the data set used by BB (2000). $\endgroup$
    – chan1142
    Jul 5, 2023 at 15:52

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