{smcl}
{* *! version 1.0.1  06Jun2017}{...}
{* *! version 1.1.1  20Jul2020}{...}

{cmd:help prodest_predict} {right:also see: {helpb prodest}  }
{hline}

{title:Title}

{p 4 16 2}
{cmd:prodest predict} {hline 2} Postestimation tool for prodest{p_end}


{marker predict}{...}
{title:Syntax for predict}

{p 8 16 2}
{cmd:predict} [{newvar}] {ifin} [{cmd:,} {cmdab:resid:uals} {cmdab:exp:onential} {cmdab:par:ameters} {cmdab:omega} {cmdab:mark:ups} {cmdab:input:var(varname)} {cmdab:corr:ected}]

{synoptset 28 tabbed}{...}
{synopthdr :options}
{synoptline}

{syntab:TFP}
{synopt :{opt resid:uals}}stores the residuals (y_it - hat{y}_it) in {newvar}{p_end}
{synopt :{opt exp:onential}}stores the exponentiated residuals in {newvar}{p_end}
{synopt :{opt par:ameters}}returns the estimated input elasticities{p_end}
{synopt :{opt omega}}stores the estimated log(TFP) (phi_it - hat{y}) in {newvar}. Only available after prodest, {opt fsresidual(newvar)}{p_end}

{syntab:Markups}
{synopt :{opt mark:ups}}stores the estimated markups as in De Loecker & Warzynski (AER, 2012) in {newvar}{p_end}
{p2coldent:* {cmdab:input:var(}{opt varname)}}variable input for markups estimation. Mandatory when running {opt markups}{p_end}
{synopt :{opt corr:ected}}markups correction for first-stage residuals. Only available after prodest, {opt fsresidual(newvar)}{p_end}
{synoptline}
{p2colreset}{...}

{title:Options for predict - TFP}

{dlgtab:Cobb-Douglas PF}

{phang}
{opt resid:uals:} log(residuals) values calculated from the log production function as:
omega_it + epsilon_it = y_it - beta_{l} * l - beta_{k} * k

{phang}
{opt exp:onential:} calculated as the exponential of the residuals from the log production function as:
exp(omega_it + epsilon_it) = exp(y_it - beta_{l} * l - beta_{k} * k)

{phang}
{opt par:ameters:} The estimated parameters for free, state and control variables.

{phang}
{opt omega:} Omega calculated as in De Loecker & Warzynski: omega_it = phi_it - hat{y}. Only available after prodest, {opt fsresidual(newvar)} .

{dlgtab:Translog PF}

{phang}
{opt residuals:} log(TFP) values calculated from the log production function as:
omega_it = y_it - beta_{l} * l - beta_{k} * k - beta_{ll} * l^2 - beta_{kk} * k^2 - beta_{lk} * (l * k)

{phang}
{opt exponentials:} TFP values calculated as the exponential of the residuals from the log production function as:
exp(omega_it) = exp(y_it - beta_{l} * l - beta_{k} * k - beta_{ll} * l^2 - beta_{kk} * k^2 - beta_{lk} * (l * k))

{phang}
{opt parameters:} The estimated elasticities for free and state variables. With translog PF, the elasticities (beta) are defined as:
hat(beta)_{l} = E( beta_{l} + 2 beta_{ll} * l + beta_{lk} * k )
hat(beta)_{k} = E( beta_{k} + 2 beta_{kk} * k + beta_{lk} * l )

{phang}
{opt omega:} Omega calculated as in De Loecker & Warzynski: omega_it = phi_it - f(l,k,beta). Only available after prodest, {opt fsresidual(newvar)}.

{title:Options for predict - markups}

{phang}
{opt mark:ups:} markups calculated as in De Loecker & Warzynski (AER, 2012), for each input variable l: markups_{l} = theta_{l} * (alpha_{l})^-1
where theta_{l} = beta_{l} for Cobb-Douglas PFs, theta_{l} = beta_{l} + 2 beta_{ll} * l + beta_{lk} * k for Translog PFs
and alpha_{l} = L / Y is the l input share.

{phang}
{cmdab:input:var(}{opt varname)} the l input variable on which to compute markups. It is mandatory when when running prodest predict 
with {opt markups}, and it must match one of the free variables previously specified

{phang}
{opt corr:ected:} Correction of alpha_{l} which accounts for the inclusion of first-stage residuals in output observation. 
markups_corrected_{l} = theta_{l} * ( alpha_{l} * exp(epsilon) )^-1  . Only available after prodest, {opt fsresidual(newvar)}.

{marker examples}{...}
{title:Examples}
{tab}{cmd:. insheet using "https://raw.githubusercontent.com/GabrieleRovigatti/prodest/master/stata/data/prodest.csv", names clear}}
{phang2}{it:({stata "insheet using https://raw.githubusercontent.com/GabrieleRovigatti/prodest/master/stata/data/prodest.csv, names clear":load data})}

{tab}{cmd:. xtset id year, y /* not run */}

{pstd}Levinsohn and Petrin method{p_end}
{tab}{cmd:. prodest log_y, free(log_lab1 log_lab2) state(log_k) proxy(log_materials) va met(lp) opt(dfp) reps(50) id(id) t(year) fsresiduals(fs_lp)}
{phang2}{it:({stata "prodest log_y, free(log_lab1 log_lab2) state(log_k) proxy(log_materials) va met(lp) opt(dfp) reps(50) id(id) t(year) fsres(sf_lp)":click to run})}

{tab}{cmd:. predict lpfit, residuals}
{phang2}{it:({stata "predict lpfit, residuals":click to run})}

{pstd}Ackerberg, Caves and Frazer with translog{p_end}
{tab}{cmd:. prodest log_y, free(log_lab1 log_lab2) state(log_k) proxy(log_materials) va met(lp) acf reps(20) id(id) t(year) translog}
{phang2}{it:({stata "prodest log_y, free(log_lab1 log_lab2) state(log_k) proxy(log_materials) va met(lp) acf reps(20) id(id) t(year) translog":click to run})}

{tab}{cmd:. predict, parameters}
{phang2}{it:({stata "predict, parameters":click to run})}

{title:Authors}

{pstd}Gabriele Rovigatti{p_end}
{pstd}Bank of Italy{p_end}
{pstd}Rome, Italy{p_end}
{pstd}gabriele.rovigatti@gmail.com{p_end}

{pstd}Vincenzo Mollisi{p_end}
{pstd}University of Rome Tor Vergata{p_end}
{pstd}Rome, Italy{p_end}
{pstd}vincenzo.mollisi@gmail.com{p_end}

{title:Also see}

{psee}
Online: {helpb opreg}, {helpb levpet}, {helpb acfest}{p_end}

{phang}
Yasar, M., Raciborski, R. and Poi, B., 2008.
Production function estimation in Stata using the Olley and Pakes method.
The Stata Journal, 8, pp. 221-231.

{phang}
Petrin, A., Poi, B. and Levinsohn, J., 2004.
Production function estimation in Stata using inputs to control for unobservables.
The Stata Journal, 4, pp. 113-123.

{phang}
Manjon, M. and Manez, J., 2016.
Production function estimation in Stata using the Ackerberg-Caves-Frazer method.
The Stata Journal, 16, pp. 900-916.

{phang}
Rovigatti, G., and Mollisi, V., 2018. 
Theory and practice of total-factor productivity estimation: The control function approach using Stata. 
The Stata Journal, 18(3), pp. 618-662.

{phang}
Rovigatti, G., 2020. 
Markup estimation using Stata: the Micro and the Macro approaches. 
Working Paper

{title:Bug Reporting}

{psee}
{opt prodest} is part of an ongoing project. Thus, it might contain errors and malfunctions. Please submit bugs, comments and suggestions via email to:

{pstd}	gabriele.rovigatti@gmail.com

{psee}
Please try to include steps to reproduce issues and possibly the output of the Stata command -creturn list-.