library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(wooldridge)
data("jtrain")
?jtrainlm1 <- lm(hrsemp ~ grant + employ, data = jtrain)
summary(lm1)##
## Call:
## lm(formula = hrsemp ~ grant + employ, data = jtrain)
##
## Residuals:
## Min 1Q Median 3Q Max
## -41.512 -11.769 -6.894 3.219 137.339
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 13.56561 1.53159 8.857 < 2e-16 ***
## grant 33.71094 3.17701 10.611 < 2e-16 ***
## employ -0.06028 0.01527 -3.948 9.37e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 22.44 on 387 degrees of freedom
## (81 observations deleted due to missingness)
## Multiple R-squared: 0.2421, Adjusted R-squared: 0.2382
## F-statistic: 61.8 on 2 and 387 DF, p-value: < 2.2e-16lm2 <- lm(lhrsemp ~ grant + employ, data = jtrain)
summary(lm2)##
## Call:
## lm(formula = lhrsemp ~ grant + employ, data = jtrain)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.383 -1.346 -0.162 1.028 3.575
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.4786187 0.0914151 16.175 < 2e-16 ***
## grant 2.1065903 0.1896246 11.109 < 2e-16 ***
## employ -0.0024020 0.0009114 -2.635 0.00874 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.339 on 387 degrees of freedom
## (81 observations deleted due to missingness)
## Multiple R-squared: 0.2475, Adjusted R-squared: 0.2436
## F-statistic: 63.66 on 2 and 387 DF, p-value: < 2.2e-16lhrsemp = 1.48 + 2.11grant - 0.00240employ. (3 s.f) The coefficient is 2.11 and is statistically significant at the 5% level of significance as its p-value is < 2e-16. This would mean that receiving a grant would be associated with a 211% increase in job training time per employee, ceterus paribus.
Time invariant: Firm’s culture towards employee development. Corporate culture is generally stable over time and that firm’s culture towards employee development can and will significantly influence both its propensity to apply for job training grants and number of hours it decides to provide per employee. Firms that prioritze an employee’s development are likely to seek more grant opportunities and offer better training programmes that increase the number of hours of job training per employee. Firm-invariant: National Unemployment Rate. The unemployment rate varies across time but not across different firms at any given point in time. The unemployment rate will affect government policies on job training grants and firm’s training behaviors. For example, high employment rates will lead governments to make grants more accessible to firms to stimulate employment. Fully-flexible: Firm’s earnings. The annual earnings or profits for a company will fluctuate across different firms. This will influence how willing the company is fund employee training and likelihood of seeking grants. For example, when the firm has high profits, it would likely invest in more training programmed that increase the training hours per employee, while simultaneous lowering the need for grants.
lm3 <- lm(hrsemp ~ grant + employ + factor(year) + factor(fcode), data = jtrain)
summary(lm3)##
## Call:
## lm(formula = hrsemp ~ grant + employ + factor(year) + factor(fcode),
## data = jtrain)
##
## Residuals:
## Min 1Q Median 3Q Max
## -48.604 -3.865 0.307 3.952 92.419
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 14.28557 10.14426 1.408 0.160297
## grant 34.39102 2.41695 14.229 < 2e-16 ***
## employ -0.08119 0.05171 -1.570 0.117632
## factor(year)1988 -0.78872 1.88628 -0.418 0.676207
## factor(year)1989 4.97762 1.90377 2.615 0.009473 **
## factor(fcode)410440 -3.29311 12.79194 -0.257 0.797053
## factor(fcode)410495 19.24098 12.58121 1.529 0.127439
## factor(fcode)410500 -1.90978 11.66653 -0.164 0.870101
## factor(fcode)410509 -17.63945 17.25476 -1.022 0.307626
## factor(fcode)410513 -7.74328 12.73403 -0.608 0.543686
## factor(fcode)410517 -14.00401 12.62880 -1.109 0.268537
## factor(fcode)410518 -10.45248 12.05088 -0.867 0.386572
## factor(fcode)410521 6.54594 12.73403 0.514 0.607669
## factor(fcode)410523 12.26933 11.71278 1.048 0.295869
## factor(fcode)410529 -11.78582 12.14018 -0.971 0.332577
## factor(fcode)410531 0.83575 12.27613 0.068 0.945777
## factor(fcode)410533 7.29105 12.77008 0.571 0.568546
## factor(fcode)410535 -14.87000 12.85854 -1.156 0.248605
## factor(fcode)410536 -12.87804 12.71975 -1.012 0.312300
## factor(fcode)410538 10.60802 16.73271 0.634 0.526678
## factor(fcode)410540 -11.48722 12.07983 -0.951 0.342549
## factor(fcode)410544 -12.07899 12.40692 -0.974 0.331208
## factor(fcode)410546 -1.16542 11.66245 -0.100 0.920480
## factor(fcode)410547 -13.20164 12.58795 -1.049 0.295301
## factor(fcode)410556 -8.62771 16.41823 -0.525 0.599702
## factor(fcode)410560 -13.78751 12.57449 -1.096 0.273925
## factor(fcode)410561 -12.74319 12.92666 -0.986 0.325177
## factor(fcode)410562 -10.82824 12.69847 -0.853 0.394627
## factor(fcode)410563 -7.81794 11.78136 -0.664 0.507564
## factor(fcode)410564 0.22511 11.72589 0.019 0.984698
## factor(fcode)410565 -1.41798 11.59008 -0.122 0.902724
## factor(fcode)410566 -10.58184 12.76283 -0.829 0.407828
## factor(fcode)410567 -6.61394 12.16627 -0.544 0.587179
## factor(fcode)410569 -13.67926 12.54781 -1.090 0.276683
## factor(fcode)410571 6.55870 12.69847 0.516 0.605963
## factor(fcode)410577 -7.46357 11.72322 -0.637 0.524934
## factor(fcode)410586 32.68013 11.58302 2.821 0.005164 **
## factor(fcode)410591 -11.88518 12.41311 -0.957 0.339251
## factor(fcode)410593 -15.27594 12.97290 -1.178 0.240101
## factor(fcode)410596 -2.49113 12.75560 -0.195 0.845319
## factor(fcode)410603 19.33303 14.02195 1.379 0.169193
## factor(fcode)410604 -6.21007 11.58291 -0.536 0.592336
## factor(fcode)410606 2.70432 11.59071 0.233 0.815705
## factor(fcode)410609 -12.89446 12.36420 -1.043 0.298004
## factor(fcode)410612 1.59527 11.90246 0.134 0.893487
## factor(fcode)410626 -9.97840 12.47613 -0.800 0.424583
## factor(fcode)410635 -4.17935 11.65271 -0.359 0.720151
## factor(fcode)410639 -2.64167 11.62877 -0.227 0.820479
## factor(fcode)410640 26.15859 12.80661 2.043 0.042138 *
## factor(fcode)410665 -11.70554 14.09445 -0.831 0.407041
## factor(fcode)410680 10.79538 12.15577 0.888 0.375344
## factor(fcode)410686 -14.21531 12.94200 -1.098 0.273089
## factor(fcode)418006 -8.07600 12.01482 -0.672 0.502094
## factor(fcode)418008 -20.94622 12.90103 -1.624 0.105715
## factor(fcode)418011 -17.99731 12.15300 -1.481 0.139889
## factor(fcode)418013 -18.90927 12.71207 -1.488 0.138137
## factor(fcode)418014 72.58272 12.85629 5.646 4.44e-08 ***
## factor(fcode)418021 -23.58014 12.86370 -1.833 0.067976 .
## factor(fcode)418024 -8.39975 11.92684 -0.704 0.481915
## factor(fcode)418035 -18.54954 12.49128 -1.485 0.138799
## factor(fcode)418036 14.65283 22.99540 0.637 0.524571
## factor(fcode)418045 39.53593 12.74839 3.101 0.002147 **
## factor(fcode)418046 -16.18847 12.69807 -1.275 0.203532
## factor(fcode)418052 -8.32509 13.00804 -0.640 0.522759
## factor(fcode)418054 -21.63189 12.00600 -1.802 0.072784 .
## factor(fcode)418065 4.94811 15.01775 0.329 0.742064
## factor(fcode)418066 -11.39225 13.65088 -0.835 0.404769
## factor(fcode)418076 -1.26325 11.92684 -0.106 0.915733
## factor(fcode)418083 -3.93126 13.02953 -0.302 0.763116
## factor(fcode)418084 13.87903 13.50471 1.028 0.305072
## factor(fcode)418091 -6.59816 11.96050 -0.552 0.581670
## factor(fcode)418097 -16.63625 11.61133 -1.433 0.153171
## factor(fcode)418098 -8.68742 12.73321 -0.682 0.495701
## factor(fcode)418107 10.13352 12.63606 0.802 0.423339
## factor(fcode)418109 77.80775 12.90103 6.031 5.80e-09 ***
## factor(fcode)418118 -15.42989 12.78322 -1.207 0.228552
## factor(fcode)418124 -18.87936 12.69110 -1.488 0.138110
## factor(fcode)418125 -0.75144 11.61164 -0.065 0.948453
## factor(fcode)418126 -3.95304 12.11298 -0.326 0.744434
## factor(fcode)418140 5.14486 12.69807 0.405 0.685699
## factor(fcode)418147 -5.63242 12.23669 -0.460 0.645707
## factor(fcode)418163 -8.12913 11.88859 -0.684 0.494747
## factor(fcode)418168 11.58017 12.91901 0.896 0.370916
## factor(fcode)418177 -4.06979 11.61048 -0.351 0.726237
## factor(fcode)418213 -12.96102 13.70878 -0.945 0.345336
## factor(fcode)418220 -12.25118 12.62926 -0.970 0.332949
## factor(fcode)418225 -22.16141 12.69110 -1.746 0.081997 .
## factor(fcode)418229 -15.11356 12.92666 -1.169 0.243441
## factor(fcode)418237 -22.38548 12.52979 -1.787 0.075212 .
## factor(fcode)418239 -2.83073 11.81071 -0.240 0.810778
## factor(fcode)418243 -14.57232 12.77735 -1.140 0.255173
## factor(fcode)418245 -13.11095 12.41311 -1.056 0.291884
## factor(fcode)419198 11.90553 12.84889 0.927 0.355035
## factor(fcode)419201 -11.50523 12.71263 -0.905 0.366321
## factor(fcode)419242 -7.63265 12.07914 -0.632 0.528036
## factor(fcode)419268 -15.99176 13.00804 -1.229 0.220083
## factor(fcode)419272 6.80971 12.32722 0.552 0.581157
## factor(fcode)419275 16.27349 12.74030 1.277 0.202668
## factor(fcode)419289 -2.00893 12.82683 -0.157 0.875671
## factor(fcode)419297 14.98716 11.84924 1.265 0.207109
## factor(fcode)419298 -9.01946 11.87036 -0.760 0.448069
## factor(fcode)419302 4.37560 16.15393 0.271 0.786715
## factor(fcode)419303 0.19768 12.95409 0.015 0.987837
## factor(fcode)419305 -23.73961 13.03144 -1.822 0.069688 .
## factor(fcode)419307 10.01960 14.15369 0.708 0.479655
## factor(fcode)419309 3.58514 12.93883 0.277 0.781944
## factor(fcode)419319 36.58669 11.85656 3.086 0.002258 **
## factor(fcode)419328 -20.95350 12.55587 -1.669 0.096400 .
## factor(fcode)419335 -7.43617 11.99993 -0.620 0.536028
## factor(fcode)419339 -11.89315 12.15577 -0.978 0.328821
## factor(fcode)419343 -4.97514 11.92028 -0.417 0.676767
## factor(fcode)419344 -18.53251 17.43864 -1.063 0.288927
## factor(fcode)419351 -17.72972 12.84152 -1.381 0.168613
## factor(fcode)419357 59.93358 11.92684 5.025 9.57e-07 ***
## factor(fcode)419376 -11.08161 12.38620 -0.895 0.371818
## factor(fcode)419378 44.12874 12.56904 3.511 0.000529 ***
## factor(fcode)419379 -7.48988 12.57783 -0.595 0.552058
## factor(fcode)419380 -8.28919 12.10458 -0.685 0.494103
## factor(fcode)419381 -8.04900 12.86370 -0.626 0.532071
## factor(fcode)419384 -8.31770 11.90360 -0.699 0.485352
## factor(fcode)419388 -17.47353 12.38020 -1.411 0.159362
## factor(fcode)419400 57.34797 12.91139 4.442 1.34e-05 ***
## factor(fcode)419401 3.27106 11.81749 0.277 0.782163
## factor(fcode)419409 11.08450 11.84583 0.936 0.350312
## factor(fcode)419410 33.63342 12.60901 2.667 0.008141 **
## factor(fcode)419420 0.76599 12.79768 0.060 0.952320
## factor(fcode)419433 -8.48454 12.70506 -0.668 0.504870
## factor(fcode)419434 -5.50178 11.71278 -0.470 0.638960
## factor(fcode)419449 10.95579 12.05565 0.909 0.364344
## factor(fcode)419450 3.31244 12.83617 0.258 0.796576
## factor(fcode)419459 5.76207 11.72589 0.491 0.623575
## factor(fcode)419461 -13.78826 12.54279 -1.099 0.272691
## factor(fcode)419467 78.16565 12.94200 6.040 5.53e-09 ***
## factor(fcode)419472 4.56994 11.62923 0.393 0.694675
## factor(fcode)419473 -13.01751 12.74030 -1.022 0.307879
## factor(fcode)419479 -9.61108 13.77288 -0.698 0.485932
## factor(fcode)419482 -6.38288 12.72688 -0.502 0.616439
## factor(fcode)419483 -4.63523 11.58598 -0.400 0.689443
## factor(fcode)419486 -7.83873 11.70984 -0.669 0.503847
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 14.19 on 251 degrees of freedom
## (81 observations deleted due to missingness)
## Multiple R-squared: 0.8036, Adjusted R-squared: 0.6956
## F-statistic: 7.441 on 138 and 251 DF, p-value: < 2.2e-16jtrain_demean <- jtrain %>%
mutate(hrsemp_demean = with(jtrain, hrsemp - ave(hrsemp, fcode)),
grant_demean = with(jtrain, (grant - ave(grant, fcode))),
employ_demean = with(jtrain, employ - ave(employ, fcode)))
lm_demean <- lm(hrsemp_demean ~ grant_demean + employ_demean, data = jtrain_demean)
summary(lm_demean)##
## Call:
## lm(formula = hrsemp_demean ~ grant_demean + employ_demean, data = jtrain_demean)
##
## Residuals:
## Min 1Q Median 3Q Max
## -50.000 -3.542 -0.057 4.817 96.000
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.118e-16 6.190e-01 0.000 1.000
## grant_demean 3.490e+01 1.929e+00 18.099 <2e-16 ***
## employ_demean -3.774e-02 4.270e-02 -0.884 0.377
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.94 on 369 degrees of freedom
## (99 observations deleted due to missingness)
## Multiple R-squared: 0.4734, Adjusted R-squared: 0.4706
## F-statistic: 165.9 on 2 and 369 DF, p-value: < 2.2e-16Compared to the coefficient of 33.7 in (a), the coefficient increases to 34.9 (3sf), where both are statistically significant at the 5% level of significance as its p-value is < 2e-16. The time-invariant confounders’ effects are removed when we did firm-demeaning. Compared with the coefficient of 34.4 in (d), the coefficient increases slightly 34.9 (3sf), where both are statistically significant at the 5% level of significance as its p-value is < 2e-16. The similarity in the two values can be attributed to the two-way fixed effect removing entity-invariant confounders’ effects as well.
Time invariant: Firm’s culture towards employee development. Model in (d) controls for this confounder as the model contains factor(fcode), which controls for unobserved, time-invariant characteristics of each firm. Model in (e) also controls for this confounder as it uses within-firm demeaning. The firm’s corporate culture is time-invariant, hence it will be subtracted and eliminated from the analysis through demeaning.
Firm-invariant: National Unemployment Rate. Model in (d) does controls for this confounder as the model contains factor(year), which controls for unoserved factors that vary over the years. The model in (e) does not control for this confounder as the model only demeans within-firm variables and does not inlcude time-varying factors shared across all firms.
Fully-flexible: Firm’s earnings. Model in (d) does not control for this as the firms revenue and profit vary across time and firms. Model in (d) only controls for unobserved time-invariant firm characteristics and time-specific factors common to all firms. Model in (e) does not control for this as factor as well. Model 2 removes firm-specific averages through demeaning but does not control for variables that vary both over time and across firms, such as the firm’s earnings.