- Ariana

To try and establish whether age is at least temporally predetermined with respect to productivity and wages, we first experiment the statistical significance of the lagged (1990-94) values of aging and the other variables of interest, interacted with the current values of those same variables (the so called “Instrumental Variables” (IV) approach, for the lagged values are employed as instruments).

We do so retaining our cross-sectional framework of analysis, while also appending some pre-determined variables to the list of the explanatory variables to weaken the potential simultaneity link between current explanatory variables (seniority and experience among others) and the dependent variable (productivity).

A problem with the IV approach is that it is very hard to implement for flexible formulation such as the one underlying graphs 1, 2 and 3 (and the related statistical results in Table A3). A flexible formulation implies many coefficients to estimate whose individual effects may be very hard to disentangle. Hence, we implement a feasible IV approach by experimenting among many less flexible (i.e. with a smaller number of included coefficients) alternative statistical models for each industry. We pick the one that, while giving a reasonable good fit of the data, most closely replicates our cross-sectional specification. As a result, however, our IV approach is implemented using slightly different formulations across industries.

The IV results are reported in Table 6. In spite of the decrease in the number of observations (some of the values for the explanatory variables are missing for 1990-94), they tend to reproduce the thrust of the results reported previously.

Namely, in the forest industry, productivity does not depend on education while the relation between seniority and productivity is constant and does not depend on the number of years of seniority. In electronics, education matters a lot for productivity (and the relation does not depend on the outstanding levels of education) while the relation between seniority and productivity is an inverted U, although less precisely measured than above. In industrial machinery and equipment, education is related to productivity with a smaller effect than in electronics and potential experience matters, not seniority. All these features reproduce the overall features present in previous results. A twist of novelty of the IV estimates is that the estimated statistical relation

between experience and productivity does now change its sign into negative for higher levels of experience (pretty much as seniority does in electronics).

Altogether, the results from IV estimation do substantially confirm the pattern of statistical correlations brought to bear in previous sections.

Table 6 – Statistical results from the Instrumental Variable (IV) approach to explain plant productivity

Notes: Dependent variable: logarithm of plant productivity. Other control variables (included instruments) include dummies for plant vintage groups and size groups. Schooling years, potential experience, potential experience squared, seniority and seniority squared are instrumented when they are included in the model. Excluded instruments are regional dummies (6 regions) and lagged (the average in the period 1990-94) schooling years, potential experience, potential experience squared, seniority and seniority squared. Schooling, experience squared and seniority squared were dropped in forest industry, seniority variables were dropped in machinery industry and experience variables were dropped in electronics industry because their estimates were close to zero, they were statistically insignificant and their removal improved statistical properties of the model. High P-values (> 10%) for the over-identification test (Hansen J statistics) indicate that the validity of the instruments cannot be rejected and low P-values (<0.1%) of relevance test (Anderson canonical correspondence Likelihood Ratio statistic) gives indication that the instruments are relevant.

To verify the importance of the possible residual influence of unobserved plant-specific heterogeneity, we also consider the time dimension of our data. We do so appending plant-specific variables constant over time, thereby carrying out the so called “fixed-effects” estimation of the determinants of plant productivity. By including the time variation of our data, we can

significantly extend sample size (which goes up to 1523 observations for the forest industry, 1717 observations for industrial machinery and 496 observations for electronics).

Clearly, however, the additional observations cannot be taken as independently distributed over time, being repeated observations of the same plant. Thus in our statistical analysis, we allow for the error term (the residual unobserved components not captured by the explanatory variable included in our statistical analysis) to be auto-correlated, i.e. to be time-dependent. This serves the purpose of not being misled by the potentially increased gain of precision achieved in capturing the phenomena at hand, thanks to the increased sample size. Accounting for auto-correlation is instead important to correctly appreciate the explanatory power of our model along the time dimension.

When adopting the fixed-effects statistical model, however, one effectively relinquish information contained in the cross-sectional framework and concentrate on the so called “within-plant”

variation in the panel data set. This may be a good thing if the goal is to answer some questions which – by construction - could not be addressed in the cross-sectional framework, the main of which is whether the relation between the age-related variables, education, productivity and wages is a simultaneous one or whether it operates with some delay.

The results in Table 7, 8 and 9 give useful information in this respect. In general, as expected, the estimated statistical model is less precise than the model estimated using the cross-sectional data only. The total time series variability accounted for by the explanatory variables dramatically falls from the approximate 50% of the cross-sectional estimates to less than 10%. As expected, our statistical model does a better job in predicting plant productivity along the cross sectional dimension. The explanatory power of the variables employed to explain the behaviour of productivity in the forest industry is drastically reduced. But the pattern of correlations seen above for the other industries is still somewhat there, once the lagged values of the variables are considered. Potential experience and education, not seniority, matter for productivity in industrial equipment, while seniority and, mostly, education matter for productivity in electronics.

Yet, along the time series dimension, these effects are present only when the delayed values of the explanatory variables are considered instead of the current ones. Education is indeed positively associated to productivity with a delay of about two years (the lagged value of education is almost significantly related to productivity, though with a small coefficient, even for the forest industry).

Table 7 - Statistical analysis based on the variation within plants over time (fixed effect

Notes: Other controls include dummies for fixed year effects. Autocorrelation of the error terms is allowed.

Table 8 – Statistical analysis based on the variation within plants over time (fixed effect models), machinery industry

Notes: Other controls include dummies for fixed year effects. Autocorrelation of the error terms is allowed.

Table 9 – Statistical analysis based on the variation within plants over time (fixed effect models), electronics industry

(1) (2) (3) Schooling years -0.022 -0.030 (0.088) (0.080) Schooling years (t-1) -0.003 (0.089) Schooling years (t-2) 0.188* 0.217*

(0.079) (0.093) Seniority years 0.042 0.050 0.059 (0.072) (0.070) (0.072) [Seniority years]^2 -0.069+ -0.072+ -0.076+

(0.040) (0.039) (0.040)

Observations 496 496 496 R-squared (within) 0.081 0.093 0.094 Autocorrelation 0.335 0.319 0.325

+ p<0.1, * p<0.05, ** p<0.01, *** p<0.001

Notes: Other controls include dummies for fixed year effects. Autocorrelation of the error terms is allowed.

As to the age-related variables, lagged experience is related to productivity in the forest and the machinery industries. The inverted-U-shaped effect of seniority on productivity in electronics is instead no longer there: the only visible partial correlation between seniority and productivity is negative. Altogether, our main argument on the adverse effect of age on productivity is confirmed by such results.