# ECO £404 – Assignment £

## 1 Estimatimg Productiom 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.

## 1.1 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.

## 1.2 Øuestiom

fi. Estimate the production function using pooled OLS for both the unbal- anced and for the balanced panel data. What do you find? Are the estimates significant? 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?

3. Assume cst = gcst—fi ‡ Øst, where |g| c fi and Øst is i.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?

4. Return to the original model (fi) and assume the model satisfies the OP assumptions. Estimate the model using investments as a proxy for cst.

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.