R: Estimate productivity - Olley-Pakes method

prodestOP {prodest}

R Documentation

Estimate productivity - Olley-Pakes method

Description

The prodestOP() function accepts at least 6 objects (id, time, output, free, state and proxy variables), and returns a prod object of class S4 with three elements: (i) a list of model-related objects, (ii) a list with the data used in the estimation and estimated vectors of first-stage residuals, and (iii) a list with the estimated parameters and their bootstrapped standard errors .

Usage

  prodestOP(Y, fX, sX, pX, idvar, timevar, R = 20, cX = NULL,
            opt = 'optim', theta0 = NULL, cluster = NULL, tol = 1e-100, exit = FALSE)

Arguments

`Y`	the vector of value added log output.
`fX`	the vector/matrix/dataframe of log free variables.
`sX`	the vector/matrix/dataframe of log state variables.
`pX`	the vector/matrix/dataframe of log proxy variables.
`cX`	the vector/matrix/dataframe of control variables. By default `cX= NULL`.
`idvar`	the vector/matrix/dataframe identifying individual panels.
`timevar`	the vector/matrix/dataframe identifying time.
`R`	the number of block bootstrap repetitions to be performed in the standard error estimation. By default `R = 20`.
`opt`	a string with the optimization algorithm to be used during the estimation. By default `opt = 'optim'`.
`theta0`	a vector with the second stage optimization starting points. By default `theta0 = NULL` and the optimization is run starting from the first stage estimated parameters + `N(\mu=0,\sigma=0.01)` noise.
`cluster`	an object of class `"SOCKcluster"` or `"cluster"`. By default `cluster = NULL`.
`tol`	optimizer tolerance. By default `tol = 1e-100`.
`exit`	Indicator for attrition in the data - i.e., if firms exit the market. By default `exit = FALSE`; if `exit = TRUE`, an indicator function for firms whose last appearance is before the last observation's date is generated and used in the second stage. The user can even specify an indicator variable/matrix/dataframe with the exit years.

Details

Consider a Cobb-Douglas production technology for firm i at time t

y_{it} = \alpha + w_{it}\beta + k_{it}\gamma + \omega_{it} + \epsilon_{it}

where y_{it} is the (log) output, w_it a 1xJ vector of (log) free variables, k_it is a 1xK vector of state variables and \epsilon_{it} is a normally distributed idiosyncratic error term. The unobserved technical efficiency parameter \omega_{it} evolves according to a first-order Markov process:

\omega_{it} = E(\omega_{it} | \omega_{it-1}) + u_{it} = g(\omega_{it-1}) + u_{it}

and u_{it} is a random shock component assumed to be uncorrelated with the technical efficiency, the state variables in k_{it} and the lagged free variables w_{it-1}. The OP method relies on the following set of assumptions:

a) i_{it} = i(k_{it},\omega_{it}) - investments are a function of both the state variable and the technical efficiency parameter;
b) i_{it} is strictly monotone in \omega_{it};
c) \omega_{it} is scalar unobservable in i_{it} = i(.) ;
d) the levels of i_{it} and k_{it} are decided at time t-1; the level of the free variable, w_{it}, is decided after the shock u_{it} realizes.

Assumptions a)-d) ensure the invertibility of i_{it} in \omega_{it} and lead to the partially identified model:

y_{it} = \alpha + w_{it}\beta + k_{it}\gamma + h(i_{it}, k_{it}) + \epsilon_{it} = \alpha + w_{it}\beta + \phi(i_{it}, k_{it}) + \epsilon_{it}

which is estimated by a non-parametric approach - First Stage. Exploiting the Markovian nature of the productivity process one can use assumption d) in order to set up the relevant moment conditions and estimate the production function parameters - Second stage. Exploiting the residual e_{it} of:

y_{it} - w_{it}\hat{\beta} = \alpha + k_{it}\gamma + g(\omega_{it-1}, \chi_{it}) + \epsilon_{it}

and g(.) is typically left unspecified and approximated by a n^{th} order polynomial and \chi_{it} is an indicator function for the attrition in the market.

Value

The output of the function prodestOP is a member of the S3 class prod. More precisely, is a list (of length 3) containing the following elements:

Model, a list containing:

method: a string describing the method ('OP').
boot.repetitions: the number of bootstrap repetitions used for standard errors' computation.
elapsed.time: time elapsed during the estimation.
theta0: numeric object with the optimization starting points - second stage.
opt: string with the optimization routine used - 'optim', 'solnp' or 'DEoptim'.
opt.outcome: optimization outcome.
FSbetas: first stage estimated parameters.

Data, a list containing:

Y: the vector of value added log output.
free: the vector/matrix/dataframe of log free variables.
state: the vector/matrix/dataframe of log state variables.
proxy: the vector/matrix/dataframe of log proxy variables.
control: the vector/matrix/dataframe of log control variables.
idvar: the vector/matrix/dataframe identifying individual panels.
timevar: the vector/matrix/dataframe identifying time.
FSresiduals: numeric object with the residuals of the first stage.

Estimates, a list containing:

pars: the vector of estimated coefficients.
std.errors: the vector of bootstrapped standard errors.

Members of class prod have an omega method returning a numeric object with the estimated productivity - that is: \omega_{it} = y_{it} - (\alpha + w_{it}\beta + k_{it}\gamma). FSres method returns a numeric object with the residuals of the first stage regression, while summary, show and coef methods are implemented and work as usual.

Author(s)

Gabriele Rovigatti

References

Olley, S G and Pakes, A (1996). "The dynamics of productivity in the telecommunications equipment industry." Econometrica, 64(6), 1263-1297.

Examples

    require(prodest)

    ## Chilean data on production.The full version is Publicly available at
    ## http://www.ine.cl/canales/chile_estadistico/estadisticas_economicas/industria/
    ## series_estadisticas/series_estadisticas_enia.php

    data(chilean)

    # we fit a model with two free (skilled and unskilled), one state (capital)
    # and one proxy variable (electricity)

    OP.fit <- prodestOP(chilean$Y, fX = cbind(chilean$fX1, chilean$fX2), chilean$sX,
                        chilean$inv, chilean$idvar, chilean$timevar)
    OP.fit.solnp <- prodestOP(chilean$Y, fX = cbind(chilean$fX1, chilean$fX2),
                              chilean$sX, chilean$inv, chilean$idvar,
                              chilean$timevar, opt='solnp')
    OP.fit.control <- prodestOP(chilean$Y, fX = cbind(chilean$fX1, chilean$fX2),
                                chilean$sX, chilean$inv, chilean$idvar,
                                chilean$timevar, cX = chilean$cX)
    OP.fit.attrition <- prodestOP(chilean$Y, fX = cbind(chilean$fX1, chilean$fX2),
                                chilean$sX, chilean$inv, chilean$idvar,
                                chilean$timevar, exit = TRUE)

    # show results
    summary(OP.fit)
    summary(OP.fit.solnp)
    summary(OP.fit.control)

    # show results in .tex tabular format
     printProd(list(OP.fit, OP.fit.solnp, OP.fit.control, OP.fit.attrition))

[Package prodest version 1.0.1 Index]