ECO £404 – Assignment £
- EstimatimgProductiom Fumctiom
Download the data “data-olley-pakes”. There are †3fi firms and 6 years of data. Each row refers to one firm in one year. The variables are as follows: firm, year, output, age, capital, labor, and investment. If a firm‘s values are zero in a given year, that means that the firm does not exist in that year, it has either exited already or not yet entered.
You can answer the questions using either STATA or MATLAB, although I would suggest you to implement the Olley and Pakes (OP) estimator in MAT- LAB to have a better understanding of the method. If you are using STATA, do not forget to change the zeros into dots so that STATA understands that the variables are missing¡ otherwise it will consider the zeros as observations. Make sure you put the data in logs before estimating the model.
Assume the firms have a Cobb-Douglas production function (let‘s ignore firm‘s age in the exercise, but you can include it if you want to):
yst = Ø0 ‡ Ø11st ‡ Øhhst ‡ cst ‡ ost, (fi)
where yst is the log of output¡ 1st is the log of labor¡ hst is the log of capital¡ the term cst represents “productivity shocks” that are observed or predictable by the firms before making their input decisions at t¡ and ost represents both i.i.d. shocks to production that are not predicted by the firms and measurement errors in the observed variables. The endogeneity problem in estimating (fi) comes from the correlation between the inputs and cst.
- Estimate the production function using pooled OLS for both the unbal- anced and for the balanced panel data. What do you find? Are the estimatessignificant?Are they economically reasonable? Why would you expect them to be biased?
£. Assume cst = cs, i.e., it is a time-invariant fixed-effect. Estimate the production function using the fixed-effect estimator. What do you find? Are the estimates significant? Are they economically reasonable?
- Assumecst = gcst—fi ‡ Øst, where |g| c fi and Øst is i.d. Add the fixed- effect as in the unobservables. Estimate the production function using the SYS GMM estimator proposed by Blundell and Bond. What do you find? Are the estimates significant? Are they economically reasonable?
- Return to the original model (fi) and assume the model satisfies the OP assumptions. Estimate the model using investments as a proxy forcst.
- Estimate the first step of OP to get Ø1 and $st. Use a fourth order polynomial series (just as OP did) for$st.
- Estimatethe second step of OP ignoring the selection problem to get
Øh. Use a fourth order polynomial to approximate the function g (.), where
cst = g (cst—fi) ‡ Øst,
and use the vector of instruments (fi, hst)t.
- Whencompared with your previous results (OLS, FE, and SYS GMM), does your new estimate from OP conform with the biases suggested by the theoretical model?
- Calculate productivity growth for each firm as in Olley and Pakes (fi996), Section†:
pst = exp .yst — Ø11st — ØhhstΣ .
Calculate aggregate productivity growth for the sample in each year
using output shares to aggregate firms (sst = yst/ ΣNt yst), and do
the same decomposition as they perform (equation fi6). What do you conclude in terms of relocation of output shares versus plant- level growth?
- (EEfÆA) You do not need to incorporate the selection problem into OP, but you can if you want In this case, when you estimate the survival probability function (i.e., the probability of staying in the market) you may use a fourth order polynomial within a pro- bit model, Pst= Pr zst‡fi = fi sst, hst . Then, in the last step (the nonlinear least squares), also use a fourth order polynomial for g (.), where now
cst = g (cst—fi, Pst) ‡ Øst.
Discuss your estimates compared with those obtained ignoring the selection problem.
HINf f: fheve ave a coup1e of ma4s to hand1e the unba1anced pane1 sn MAfGAB. One posssbs1st4 ss to flvst dvop a11 mssssng data (a11 the 1snes msth sevos) and then estsmate the mode1 as usua1. fo cveate 1agged savsab1es 4ou need to be cavefu1. One posssbs1st4 ss to flvst shsft the mho1e sectov (e.g., cveate sn MAfGAB the yst—fi as ”4_f=[D,4];”). fhen, 4ou vep1ace msth sevos a11 1snes sn mhsch 4eav = f (so that the 1agged savsab1e fov the flvms’ flvst 4eav ss sevo and not the pvessous flvms’ 1ast obsevsatson). Fsna114 4ou dvop the 1snes msth sevos mhen estsmatsng Øh and g (.).
HINf W: If 4ou mant to covvect fov se1ectson, 4ou need to estsmate the pvobst Pst = Pr zst‡fi = fi|sst, hst befove dvopsng the mssssng savsab1es sn
MAfGAB. It ma4 be eassev to estsmate Pst sn SfAfA, sase the vesu1ts and then mose to MAfGAB.
OBS: Note that the usua1 standavd evvovs sn the second stage ms11 be mvong ssnce the4 need covvectson fov the evvov sn the flvst stage estsmatovs. fhss can be done ana14tsca114 (ussng Pahes and O11e4 (f99†)), ov st can be “bootstvapped™. Don’t movv4 about the covvectsons needed.