ESTUDIOS DE CARACTERIZACIÓN DE RSU

log likelihood -7882.0 -7885.0 -7909.3 no. obs. 16,235 16,235 16,235 F 5.03 5.20 6.05 (r,n-k) (4,16212) (4,16218) (4,16224) prob>F 0.0005 0.0003 0.000 708.78 702.87 654.14 d.f. (22) (16) (10) prob>%^ 0.000 0.000 0.000

The dependent variable is 1 if the firm adjusts and 0 otherwise: T he regressors are: lagged values, in levels, o f employment (number o f em ployees), L, real sales, Q, the real wage-bill, WB, investment in machinery (in real terms), INV, profitability (in real terms), P, and firm size, S measured as the reciprocal o f employment, 1/L.

with the degrees o f freedom in parentheses, is a test o f the joint significance o f all regressors except the constant.

3.6. Estim ation o f the Euler equation (step 2)

Step 2. W e estimate (48), over the sample o f firms which do adjust. In order to take into account the possible selection bias introduced by eliminating the companies characterized by zero adjustment from the sample, w e include in the Euler equation the inverse Mills’ ratio, calculated in the first stage o f this estimation procedure, both as a regressor and as an instrument. W e may rewrite the selectivity corrected Euler equation (48) in levels explicitly as

+ + $ 2 4 - 1 + + « a + ( 3 2 )

fixed effects

In order to estimate (52) only on companies which adjust w e adopt the following method o f selecting the employment variable: we keep or drop according to whether it is different from or equal to If the observation corresponds to the lower branch o f (39) and is therefore uninformative in relation to the parameter vector t|r. It is arguable that w e should exclude additionally observations for which I^+i=I^. However, the correct sample selection would, in that case, require that observations where be discarded. N ote, however, that the Euler equation (35) does not exclude this equality and also that, because o f the realization error, the selection condition I^f^E^I^+i, may be quite different from the condition I^T^I^+i.

The selection method adopted creates gaps in the dataset corresponding to the equalities between 1^ and L^.^We then estimate the Euler equation in levels using all the remaining observations. In the differenced equation w e consider at least two consecutive adjustment periods. In fact, in order to eliminate the fixed effects fj w e need to take differences and this requires that we use only observations

A complication in considering limited dependent variables in panel data is given by the presence o f the fixed effect as conditioning variable and by the fact that w e only observe sample moments conditional on selection. In particular, in a dynamic context, we would have

where y-,* is observable subject to endogenous selection:

If selectivity interacts with the fixed effect then the selection model is unidentified in the absence of additional prior restrictions on the distribution o f the latent variable. We do not deal with this problem here. For a com plete account see Labeaga (1992) and Arellano, Bover and Labeaga (1993).

corresponding to successive changes i.e. different from i and 1^., different from Lt.2- This selection o f the observations creates many gaps within the tim e-series

corresponding to each firm. These gaps must also be taken into account when constructing the instruments.

W e need to modify the definition o f the GMM estimator to take into account selection. Write S; (i= l,...,N ) as the diagonal selection matrix (sj) where s j = l if observation t is included for firm i and s j = 0 if this observation is omitted. Write

>2P _{K o'}

o'

o'

o'

o' o'

Then the GM M estimator (33), modified for selection becom es

Z/r

Z,

0

z=

•

4

₀

(S3)

(54)

where the matrix of regressor variables X is expanded to include the inverse Mills’ ratio.

W e have written a program in Gauss to implement the GM M estimator (54) for our problem. The estimates we report adopt a slightly more general procedure than that implemented in the Arellano and Bond program D PD . D P D im poses a common intercept on the implied reduced form regression for the instruments for each year in the sample, despite the fact that the number o f instruments in these regressions increases through the sample. We drop this restriction which is

unnecessary in view o f the large number of observations at our disposal. In fact, however, the effect on the estimated coefficient values is minor. The program is reported in Appendix 3.5.

W e include as instruments the inverse Mills’ ratio at tim e t, calculated according to the timing o f the instruments, lagged values o f em ploym ent, output, the wage-bill, investment, profitability and size. All instruments are dated according to the specifications shown in Figure 36 in Section 3.2. W e use the wage-bill and employment separately as instruments, rather than the lagged per-capita wage, because the wage-bill variable is less affected by possible m easurem ent errors problems affecting employment, as discussed above. We follow the sam e approach for productivity, using lagged values o f output and employment. T he selection term, Ait is included both as regressor and as instrument calculated according to the timing o f the instruments as explained in Section 3.5. The timing o f the inverse Mills’ ratio is consistent with that in the decision rule adopted in the selection of the observations in the sample in line with the Euler equation. For the equation in levels w e use the inverse Mills’ ratio in levels with the same timing is the same as the dependent variable. In the case of the differenced equation, the selection we operate takes into account two consecutive periods. We then take the inverse Mills’ ratio in first differences (A,-Aw).

To see this return to Section 3.4. where we discussed the selection process. For clarity, rewrite equation (39)

= + i f = l (55)

' 1 V . if