A. Contemporaneous Correlation Between Sending and Receiving Firms’ Productivities
Every regression specification so far has assumed that productivity of the send-ing firm in year t − 1 (the year before the move) is linked with productivity of the receiving firm in year t + 1, the year after the move. Indeed, because spillover effects take time, a correlation between sending and receiving firms’ productivities instantaneous to hiring workers in year t will not be consistent with the spillovers hypothesis, implying instead that our gap measure captures other factors codeter-mining the sending and receiving firms’ performance. To control for this possibility, we augment equation (4) with sending firms’ productivity in year t + 1. Firm and worker characteristics in year t + 1 are included as well.
The estimates from the thus augmented specification, shown in column 1 of Table 12, imply that recruiting 10 percent of total workforce from 10 percent more productive firms is associated with an 0.056 percent instantaneous increase in pro-ductivity of the receiving firm, reflecting the weak positive link between sending and receiving firms’ productivity reported in the introduction. This contemporane-ous correlation is weak relative to the estimated gap’s effects on productivity in years t + 1 to t + 5, and is not statistically significant. Adding it does not materi-ally affect our earlier estimates. The insignificance of sending firms’ productivity in t + 1 implies that the contemporaneous link between sending and receiving firms’ productivities can be explained away by controlling for similarities in observed firm and worker characteristics, which we routinely do. Hence, common factors affecting sending and receiving firms’ productivities cannot explain our main result.
B. Productivity Shocks in Receiving Firms
The gap’s effect is identified on the assumption that it is uncorrelated with the error term _ε j, t+1 in equation (4). Because this assumption clearly fails when the error term is serially correlated, in which case the gap will pick up the receiving firm’s past productivity shocks, we have added lags of the dependent variable whenever possible to eliminate this correlation. However, even in the absence of serial correla-tion in the error term, one can think of plausible situacorrela-tions in which our identifica-tion assumpidentifica-tion may be violated. For instance, a one-off shock to receiving firm’s productivity in year t − 1 may affect its hiring behavior in year t, when the new hires come, by improving its ability to attract workers from more productive firms.
The positive correlation between the productivity shock in t − 1 and the gap will induce an upward bias to the estimate of the gap’s effect.
To eliminate this correlation, we apply the estimation procedure developed in Olley and Pakes (1996) which relies on the theoretical result that a profit-maxi-mizing firm will increase capital investment at the time of experiencing a positive productivity shock. Assuming firm j ’s current capital stock Kjt is equal to the sum of capital from the previous period and capital investments, the profit-maximizing
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choice of investment, Ijt , is described as a function f ( ⋅ ) of the current capital stock and the unobserved productivity shock ω jt as follows:
I jt = f ( K jt , ω jt).
Assuming f ( ⋅ ) is monotonic in both capital and productivity shock, it can be inverted to express ω jt as a function of observable investments and capital (all in logs):
ω jt = g( kjt , ijt).
As in Olley and Pakes (1996), we approximate the unknown function g with a third-degree polynomial series of capital and investments and include this approximation
Table 12—Receiving Firm’s Productivity and the Gap with Controls for Productivity Shocks and Firm Fixed Effects
(1) (2) (3) (4) (5)
Panel A
Productivity gap (β) 0.149*** 0.126*** 0.122*** 0.071*** 0.113
(0.043) (0.040) (0.038) (0.027) (0.103) Mean future productivity of sending firms 0.056
(0.043)
X, Y1, and Y2 for period (t + 1) Yes No No No No
Control for TFP shocks with investments No Yes Yes No No
Firm-level fixed effects No No No Yes Yes
R2 0.497 0.490 0.507
N 48,867 59,655 58,339 59,655 89,907
Panel B
Positive productivity gap (βP) 0.328*** 0.278*** 0.254*** 0.185*** 0.321**
(0.090) (0.090) (0.091) (0.064) (0.164)
Negative productivity gap (βN) 0.032 0.002 0.023 −0.002 0.019
(0.072) (0.078) (0.075) (0.057) (0.094)
Mean future productivity of more productive 0.010
sending firms (0.073)
Mean future productivity of less productive 0.095
sending firms (0.068)
X, Y1, and Y2 for period (t + 1) Yes No No No No
Control for TFP shocks with investments No Yes Yes No No
Firm-level fixed effects No No No Yes Yes
R2 0.498 0.490 0.507
N 48,867 59,655 58,339 59,655 89,907
Notes: All specifications include industry-year fixed effects, average size of the sending firm, characteristics of receiving firm (X), and firm-average characteristics of new and incumbent workers (Y1 and Y2) as additional con-trols. Robust standard errors in parentheses are clustered at the firm level. The time period covered is 1995–2007.
In column 2, a third order polynomial of investments and capital is included to control for firm level productivity shocks in period t. Column 3 includes a third order polynomial of capital and investments to control for productivity shock at time periods t and (t + 1). The system-GMM estimator in column 5 includes three lags of the dependent variable, the lag length of 4 and 5 for the equation in differences and the lag length of 3 for the equation in levels.
The p-value of the test statistic for autocorrelation in residuals is always greater than 0.1; the p-value for the overi-dentificaion test is always less than 0.05.
*** Significant at the 1 percent level.
** Significant at the 5 percent level.
* Significant at the 10 percent level.
in equation (4) to control for ω jt−1 . The estimation results presented in column 2 of Table 12 do not suggest that past productivity shocks affect the choice of firms from which the new hires come, since the estimates for the gap are similar to those obtained earlier from specifications without extra controls for unobserved produc-tivity shocks. That said, these extra controls do help explain the variation in pro-ductivity among firms, since most of the terms in the polynomial approximation for function g( ⋅ ) (not shown) are statistically significant.
Continuing with the issue of productivity shocks in receiving firms, even when past and contemporaneous shocks have been controlled away, the gap may still be correlated with productivity shocks happening in the future if job movers can anticipate future productivity developments and choose to apply to firms where pro-ductivity prospects are brightest. These firms will then have more applicants than vacancies, and if they prefer to hire workers from more productive firms there will be a positive correlation between the productivity shock in year t + 1, _ε j, t+1 , and the gap, leading to an overestimate of its effect. Once again we use the insight from Olley and Pakes (1996) to control for this future productivity shock by a polynomial function of capital stock and investments in years t and t + 1.
The results of this exercise, shown in column 3, are very similar to our previously reported findings, although we hasten to add that our controls for future productivity shocks may be weak. In the absence of more elaborate tools to rule out this “antici-pated shocks” explanation behind our results, we do acknowledge that our findings fall just short of a straight knowledge spillovers story. There may be a number of factors escaping our control that contribute to the preference for workers from more productive firms. If spillovers are one of these factors, our results should be taken as evidence for their presence. However, the importance of spillovers in influencing hiring preferences is unknown.
C. Unobserved Firm-Level Heterogeneity
Continuing on the issue of identifiability of productivity spillovers separately from other unobserved influences, suppose now that firms do not hire workers randomly but target sending firms with particular characteristics. For instance, some domestic firms may prefer to hire workers from multinationals in pursuit of productivity gains from their knowledge. If the (long-term) stable preferences in hiring reflect certain management practices, their presence may result in a correlation between the sending and receiving firms productivities over time which is not due to the productivity gap as such. Although, by construction, the gap cancels common influences to the receiving and sending firms’ productivities, as an extra control for their long-term productivity determinants, we add the receiving firms’ fixed effects as a robustness check.
Including the receiving firm fixed effects leads to a considerable reduction in the gap’s coefficients (column 4 of Table 12). The fixed effects estimate for the positive productivity gap, 0.185, implies a productivity gain of 0.23 percent for an average firm, which is a third less than the 0.35 percent implied by the baseline specification (Section II). However, we caution against relying too much on these estimates because of the fixed effects estimator’s known downward bias to the coefficients on the lags of the dependent variable. Because the gap is by construction negatively correlated
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with the receiving firm’s productivity in year t − 1, a downward bias to the coefficient on A j, rt−1 will result in a downward bias to the coefficient on the gap as well. To try to correct for this bias, we apply the system GMM estimator proposed by Blundell and Bond (1998). This estimator works by exploiting the moment conditions involving the error term and lags of the dependent variable acting as instruments.
The moment conditions we exploit are as follows:
(11) E[ z j, t−s Δ ε jt ] = 0 and E[ x j, t Δ ε jt ] = 0 for s = 4, 5 (12) E[Δ z j, t−s ε jt ] = 0 and E[Δ x j, t ε jt ] = 0 for s = 3,
where z j, t = ( A j, rt ), x j, t =
(
˜ _gap j, t−1 , X j, t, Y _ j, 1t , Y _ j, 2t)
, and Δ x j, t = x j, t − x j, t−1 . The first set of moment conditions (11), as in Arellano and Bond (1991), is obtained from first-differencing equation (4), which removes firm fixed effects and makes past lags of pro-ductivity orthogonal to the first-differenced error term Δ ε jt . The second set of moment conditions (12) comes from the original equation (4) where lagged differences of the dependent variable are used as instruments for the lagged productivity levels. Blundell and Bond (1998) demonstrate that exploiting the additional moment conditions in (4) can lead to a dramatic improvement in estimation efficiency, especially when the autoregression process for productivity shows high persistence as we demonstrate in subsection IIIC. The moment conditions were chosen so as to eliminate residual auto-correlation (which would invalidate them). The presence of residual autoauto-correlation under a given set of moment conditions can be tested, and in this specification, three lags of the dependent variable were enough to eliminate it.The system GMM estimates in column 5 of Table 12 are similar to the previ-ously reported OLS results, indicating that recruiting workers from more produc-tive firms is associated with future productivity growth. The implied productivity gain for a firm hiring at the mean gap is 0.4 percent the year after the hiring, very close to the previously reported estimates. However, the system GMM specifica-tion is not without problems of its own. Apart from the requirement of no autocor-relation in the error term, which it satisfies, another condition for its consistency is that the instruments employed in the moment conditions must all be exogenous. We were unable to find a configuration of the moment conditions that would comply with this requirement at an acceptable level of the overidentification test statistic, implying that some of the instruments that we employ in the moment conditions may be correlated with the error term. In fact, several previous studies (Griliches and Mairesse 1995; Levinsohn and Petrin 2003) also encountered technical prob-lems implementing system GMM. We therefore stick to OLS regression results as our preferred specification.
D. Human Capital Revisited
Recall the human capital interpretation of our results that we have considered before. Namely, because more productive workers are more likely to be found in above-average firms, the gap may absorb the effect of unobservable skills of the new workers as well as spillovers. So far we have two pieces of evidence against
the human capital explanation of our results: the gap’s effect hardly changing after controlling for human capital, and the gap’s effect being different for the positive and negative gaps. In this subsection we devise yet another test for the human capital versus the spillovers story which is robust to the possibility that workers’ skills may not be fully reflected in the salary. This possibility may arise, for instance, when more productive firms screen high-quality workers better.
We look at the effects of the positive gap defined for moving workers with differ-ent length of tenure at their sending firms. Suppose that tenure at the sending firm along with education and skill level (recall subsection IIIB) facilitates spillovers by improving a worker’s ability to accumulate knowledge. Then the coefficient on the gap should increase with tenure. If, however, the gap’s coefficient does not change with tenure, two possibilities arise: (i) tenure does not facilitate spillovers, or (ii) the gap’s coefficient measures not spillovers but the effect of unobserved and uncom-pensated skills of new workers coming from more productive firms.
Since we do not have information on workers’ employment outside our sample period, the constructed measure of tenure will be censored for early years. For this reason, we focus on the time period between 2001 and 2007, which will enable us to derive a reasonably uncensored tenure variable for the first six years. With this mea-sure, we construct average positive productivity gaps for six groups of new workers who have tenure in the sending firm varying from 1 to 6-plus years, the last group including all observations with censored tenure.
Results presented in Table 13 show a tendency for the gap’s coefficient, and its significance, to increase with new workers’ tenure at their sending firms, which is consistent with the spillovers hypothesis. However, because the gap’s coefficients by tenure are estimated rather imprecisely, the restriction that they are equal cannot be rejected. Therefore, on the basis of this evidence alone we cannot decisively reject the alternative, “uncompensated skills,” explanation. Nor can we accept this alternative explanation, since the underlying assumption that longer-tenured workers are better able to accumulate knowledge may be wrong. In any case, the significant difference between the coefficients on the positive and negative gaps remains the only strong evidence in favor of the spillovers versus the human capital story behind our results.
E. Alternative Measures of Productivity
Until now we have measured productivity as value added per worker. Although this measure is widely used, it disregards differences in capital intensity. In this subsection we use several alternative measures of economic performance, defined relative to a multifactor production technology, which take into account the inten-sity of factors of production other than labor. With firm level output Q, production technology F, and the vector of input factors X, we can define the total factor pro-ductivity (TFP) of firm j at time t, Ajt, as its output net of input factor contributions:
(13) ajt = qjt − f ( xjt),
where z = ln Z. Using different parametrizations of the production function and esti-mates of its coefficients, we construct several measures of TFP. To remove common
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influences on productivity, we demean ajt by industry-year averages defined at the 4-digit level of the NACE classification.
As a first parametrization of F( ⋅ ) we take the Cobb-Douglas production func-tion with capital (k), labor (l ), and materials and energy (m) inputs as the factors of production, calculating
(14) ait = qit − α k kit − α l lit − α m mit .
We apply a selection of empirical methodologies to estimate the parameters of Cobb-Douglas production technology, α k , α l , α m . Our starting point is the ordinary least squares (OLS) estimator of the production function, which we apply separately for each three-digit industry group in our sample, to allow for differences in input elastici-ties within the sample. The regression results with TFP estimated with OLS are reported in column 1 of Table 14. The results with this alternative measure of productivity are consistent with our benchmark results for value added per worker. The coefficient on the productivity gap and its positive part are positive and statistically significant, while the coefficient for new workers coming from less productive firms is insignificant. In addition to the OLS estimates of TFP, we employ a two-step semiparametric estimator by Olley and Pakes (1996) to control for input factor endogeneity to unobserved past productivity shocks. The TFP measure based on Olley and Pakes-estimated produc-tion funcproduc-tion is highly correlated with that based on OLS. Consequently, the changes in the estimates of our interest (column 2) are fairly small.9
9 Alternative estimates of Cobb-Douglas production function, such as Levinsohn and Petrin (2003) and Wooldridge (2009), yield productivity measures which are very similar to OLS and Olley-Pakes estimates.
Table 13—Receiving Firm’s Productivity and the Gap by Length of Tenure at Sending Firm Positive productivity gap for workers with 1 year of experience at sending firm 0.196
(0.175) Positive productivity gap for workers with 2 years of experience at sending firm 0.263
(0.183) Positive productivity gap for workers with 3 years of experience at sending firm 0.288**
(0.134) Positive productivity gap for workers with 4 years of experience at sending firm 0.263**
(0.131) Positive productivity gap for workers with 5 years of experience at sending firm 0.410***
(0.151) Positive productivity gap for workers with 6+ years of experience at sending firm 0.333***
(0.106)
R2 0.497
N 44,496
Notes: All specifications include industry-year fixed effects, average size of sending firm, characteristics of receiv-ing firm (X), and firm-average characteristics of new and incumbent workers (Y1 and Y2) as additional controls.
Robust standard errors in parentheses are clustered at the firm level. The time period covered is 2001–2007.
*** Significant at the 1 percent level.
** Significant at the 5 percent level.
* Significant at the 10 percent level.
Next, we use a more general parameterization of production technology F( ⋅ ) with a full set of input interactions and order terms, known as the translog produc-tion funcproduc-tion. The translog specificaproduc-tion offers a number of advantages over Cobb-Douglas function, most notable of which is the ability to better control for the effect of firm size on output by allowing for nonlinear effects of factor inputs on out-put. Estimation results for equation (4) with productivity measure derived from the translog production function are presented in column 3 of Table 14. Although the coefficient on the overall productivity gap becomes insignificant, the estimate on the positive productivity gap is even larger than in columns 1 and 2.
All specifications in Table 14 feature a positive and significant coefficient on the positive gap. The coefficients in specifications with TFP-based productivity measures (columns 1, 2, and 3) are about half of those in the benchmark speci-fication. Although their magnitudes cannot be directly compared, we can gauge the effects of one standard deviation’s change in the gap relative to the depen-dent variable’s standard deviation. For instance, recalling the descriptive statistics in Table 3, a standard deviation’s (0.056) increase in the positive gap is linked to 0.056 × 0.28 / 0.65 = 0.024 standard deviation’s increase in log value added per worker. Analogously, a one standard deviation’s (0.029) increase in Olley and Pakes’s measure of the positive gap corresponds to 0.025 × 0.166 / 0.23 = 0.021 standard deviations of TFP. Hence, relative to their sample variation, the effects of these two measures of productivity gap are fairly similar.
Table 14—Results for Alternative Measures of Firm Performance Productivity measure
OLS OP Translog Profit Profit Profit
(1) (2) (3) (4) (5) (6)
Panel A
Productivity gap (β ) 0.076*** 0.102*** 0.035 0.018 0.034 0.038
(0.033) (0.036) (0.031) (0.014) (0.099) (0.040)
R2 0.321 0.301 0.332 0.543 0.540 0.527
N 59,362 59,362 59,362 83,477 41,265 40,382
Panel B
Positive productivity gap (βP) 0.101*** 0.166*** 0.186*** 0.310*** 0.312** 0.207***
(0.039) (0.078) (0.068) (0.078) (0.151) (0.050)
Negative productivity gap (βN) 0.024 0.042 −0.055 −0.101*** −0.130 −0.118
(0.036) (0.047) (0.070) (0.033) (0.0830) (0.112)
R2 0.322 0.302 0.332 0.544 0.542 0.528
N 59,362 59,362 59,362 83,477 41,265 40,382
Notes: All specifications include industry-year fixed effects, average size of sending firm, characteristics of receiv-ing firm (X), firm-average characteristics of new and incumbent workers (Y1 and Y2) as additional controls. Robust standard errors in parentheses are clustered at the firm level. The time period covered is 1995–2007. In column 1, productivity is constructed from Cobb-Douglas production function estimated by OLS. In column 2, productivity is constructed from Cobb-Douglas production function estimated by Olley-Pakes method. In column 3, productivity is constructed from the translog production function estimated by OLS. In column 4, productivity gap is constructed using value added per worker (benchmark measure), and in column 5, it is constructed using Solow residuals from the translog production function.
*** Significant at the 1 percent level.
** Significant at the 5 percent level.
* Significant at the 10 percent level.
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Finally, in the last three columns of Table 14 we report regression results for the
Finally, in the last three columns of Table 14 we report regression results for the