Research independence: drivers and impact on PhD students’ careers

Figures & data

Figure 1. Independence values of students X and Y. Note: The left-side radar plot reports the similarity values calculated between professor A’s five articles published between 2004 (t−3) and 2008 (t+1) and student X’s thesis defended in 2007 (t). Articles are ordered clockwise by publication date and are labeled with an id with the following format “p.publication year.article two-digit identifier”. The arrows indicate the value of student X’s Independence (0.152) from her supervisor, which is calculated as 1-max(sim). The right-side radar plot reports the similarity values calculated between professor A’s articles published between 2002 (t−3) and 2006 (t+1) and student Y’s thesis defended in 2005 (t). Articles are ordered clockwise by publication date. The arrows indicate the value of student Y’s Independence (0.058) from her supervisor, which is calculated as 1-max(sim).

Figure 2. Standardized Independence score distribution. Note: The two figures report the Kernel density estimation of the Independence distribution by defense cohort (left panel) and thesis discipline (right panel). Values of Independence reported in the panels are standardized and range from −2 standard deviations to 6 standard deviations.

Table 1. Descriptive statistics for the variable Independence.

	Independence [Standardized]
	Mean	SD	Min	Max	Obs.
Entire sample	0.00	1	−2	5.94	42,630
By defense cohort
2004< = Defense year< = 2007	0.18	1.1	−2	5.93	11,097
2008< = Defense year< = 2010	0.00	1	−2	5.93	13,468
2011< = Defense year< = 2013	−0.12	1	−2	5.94	18,065
By discipline
Engineering	0.03	0.9	−2	5.75	10,797
Mathematics	0.06	1.1	−1.9	5.85	5,878
Medicine-biology-chemistry	−0.07	1	−2	5.93	18,489
Physics	0.09	1	−1.9	5.94	7,466

Table 2. Descriptive statistics for dependent and independent variables.

	Entire sample (42,630)		Conditional on starting an academic career (20,735)
	Mean	SD	Mean	SD
Dependent variables
Academic career	0.49	0.5
Number of publications			5.68	6.72
Average citations per article			3.26	4.74
Number of distinct coauthors			26.97	43.16
Foreign affiliation			0.46	0.5
US affiliation			0.11	0.31
Student’s characteristics
At least one pub. during the PhD period	0.64	0.48	0.85	0.36
At least one pub. coauthored with the supervisor during the PhD period	0.56	0.5	0.76	0.43
Female Stud.	0.39	0.49	0.39	0.49
Age	27.59	9.56	27.18	8.81
French	0.7	0.46	0.74	0.44
Missing age	0.09	0.29	0.08	0.28
Missing Nationality	0.12	0.32	0.11	0.31
Supervisor’s characteristics
Average yearly citations received by the sup articles	8.06	3.32	8.23	3.14
Number of distinct coauthors during the PhD period	50.94	72.37	57.38	76.2
Number of sup publications during the PhD period	15.24	15.15	16.73	15.97
Female Sup.	0.23	0.42	0.25	0.43
Thesis characteristics
Having a co-supervisor	0.39	0.49	0.39	0.49
Engineering	0.25	0.43	0.19	0.39
Mathematics	0.14	0.34	0.11	0.31
Medicine-biology-chemistry	0.43	0.5	0.53	0.5
Physics	0.18	0.38	0.18	0.38

Note: Due to space constraints, the table does not include the statistics for the 10 Defense year dummies and the 10 University dummies. Statistics are available upon request.

Table 3. Regression explaining Independence.

	(1)
	OLS
	Independence [Standardized]
Student’s characteristics
At least one pub. during the PhD period	0.37***
	(0.018)
At least one pub. co-authored with the supervisor during the PhD period	−0.85***
	(0.018)
Female supervisor – Female student	−0.15***
	(0.016)
Male supervisor – Female student	−0.060***
	(0.011)
Female supervisor – Male student	−0.018
	(0.015)
Male supervisor – Male student	Ref.
Age	−0.0044***
	(0.0012)
French	0.036***
	(0.013)
Missing age	−0.17***
	(0.039)
Missing Nationality	0.0069
	(0.018)
Supervisor’s characteristics
Number of publications during the PhD period	−0.0012***
	(0.00045)
Average yearly citations received per article	−0.019***
	(0.0016)
Number of distinct co-authors during the PhD period	−0.00096***
	(0.000097)
Thesis characteristics
Having a co-supervisor	0.047***
	(0.0098)
Mathematics	−0.065***
	(0.015)
Medicine-biology-chemistry	0.13***
	(0.013)
Physics	0.18***
	(0.015)
Engineering	Ref.
Defense year dummies	Yes
University dummies	Yes
Constant	0.77***
	(0.052)
Observations	42,630
R-squared	0.115

Note: The table includes one regression model estimated on a sample of 42,630 students. Nationality and Age information is missing for 12% and 9% of the students, respectively. In our econometric estimates, we control for missing information including two dummy variables Missing Nationality and Missing age. Column 1 reports the variable coefficients estimated with the Ordinary Least Square (OLS) method. Standard errors are reported in parentheses. Significance levels are indicated as follows: *** p < .01, ** p < .05, * p < .1.

Figure 3. Predicted probability of starting an academic career vs. Independence, including the Independence squared term in the regression. Note: The figure represents the predicted probability of starting an academic career for an average student. We define an average student as a student having all the control variables included in the econometric model reported in Column 3 of Table 4 at their average value.

Table 4. Regression estimating the relationship between independence and the probability of starting an academic career.

	(1)	(2)	(3)
	Logit (Marginal effects)	Logit (Marginal effects)	Logit (coefficients)
	Academic career	Academic career	Academic career
Independence [Standardized]	0.010***		0.097***
	(0.0023)		(0.015)
Independence^2			−0.031***
			(0.0061)
Independence Q2		0.033***
		(0.0061)
Independence Q3		0.036***
		(0.0062)
Independence Q4		0.039***
		(0.0064)
Student’s characteristics
At least one pub. during the PhD period	0.31***	0.31***	1.55***
	(0.0076)	(0.0076)	(0.041)
At least one pub. co-authored with the supervisor during the PhD period	0.066***	0.068***	0.34***
	(0.0079)	(0.0078)	(0.040)
Age	−0.010***	−0.010***	−0.053***
	(0.00063)	(0.00063)	(0.0032)
French	0.023***	0.022***	0.11***
	(0.0060)	(0.0060)	(0.030)
Missing age	−0.33***	−0.33***	−1.65***
	(0.020)	(0.020)	(0.10)
Missing nationality	0.0071	0.0068	0.034
	(0.0084)	(0.0084)	(0.043)
Female supervisor – Female student	−0.021***	−0.021***	−0.11***
	(0.0075)	(0.0075)	(0.038)
Male supervisor – Female student	−0.035***	−0.035***	−0.18***
	(0.0052)	(0.0052)	(0.027)
Female supervisor – Male student	0.024***	0.024***	0.12***
	(0.0070)	(0.0070)	(0.035)
Male supervisor – Male student	Ref.	Ref.	Ref.
Supervisor’s characteristics
Number of publications during the PhD period	−0.000016	−0.00011	−0.00053
	(0.00021)	(0.00021)	(0.0011)
Average yearly citations received per article	0.0029***	0.0031***	0.016***
	(0.00076)	(0.00076)	(0.0039)
Number of distinct co-authors during the PhD period	0.00018***	0.00019***	0.00096***
	(0.000046)	(0.000046)	(0.00024)
Thesis characteristics
Having a co-supervisor	0.020***	0.020***	0.10***
	(0.0046)	(0.0046)	(0.023)
Mathematics	0.058***	0.059***	0.30***
	(0.0074)	(0.0074)	(0.038)
Medicine-biology-chemistry	0.13***	0.13***	0.67***
	(0.0059)	(0.0059)	(0.031)
Physics	0.080***	0.080***	0.41***
	(0.0068)	(0.0068)	(0.035)
Engineering	Ref.	Ref.	Ref.
Defense year dummies	Yes	Yes	Yes
University dummies	Yes	Yes	Yes
Constant			−0.20
			(0.13)
Observations	42,630	42,630	42,630
R-squared / Pseudo R-squared	0.162	0.162	0.162

Note: The table includes 3 regression models estimated on a sample of 42,630 students. Nationality and Age information is missing for 12% and 9% of the students, respectively. In our econometric estimates, we control for missing information including two dummy variables Missing Nationality and Missing age. Columns 1, 2, and 3 report the marginal effects of a Logit model estimated with the maximum likelihood method. Standard errors are reported in parentheses. Significance levels are indicated as follows: *** p < .01, ** p < .05, * p < .1.

Table 5. Regression estimating the relationship between Independence and academic career outcomes.

	(1)	(2)	(3)	(4)	(5)
	Conditional on starting an academic career
	OLS	OLS	OLS	Logit (Marginal effects)	Logit (Marginal effects)
	Number of publications	Average citations per article	Number of distinct co-authors	Foreign affiliation	US affiliation
Independence [Standardized]	0.13***	−0.26***	0.22	−0.013***	−0.013***
	(0.050)	(0.036)	(0.31)	(0.0038)	(0.0026)
Student’s characteristics
At least one pub. during the PhD period	2.13***	0.30**	9.52***	0.085***	0.044***
	(0.19)	(0.13)	(1.15)	(0.014)	(0.010)
At least one pub. co-authored with the supervisor during the PhD period	−0.23	−0.062	−1.01	0.011	0.0032
	(0.17)	(0.12)	(1.02)	(0.013)	(0.0083)
Female supervisor – Female student	−1.58***	−0.34***	−4.97***	−0.10***	−0.034***
	(0.15)	(0.11)	(0.94)	(0.012)	(0.0075)
Male supervisor – Female student	−1.69***	−0.30***	−5.76***	−0.089***	−0.020***
	(0.11)	(0.078)	(0.67)	(0.0082)	(0.0052)
Female supervisor – Male student	0.085	0.13	1.67*	−0.0097	0.0032
	(0.14)	(0.100)	(0.86)	(0.010)	(0.0064)
Male supervisor – Male student	Ref.	Ref.	Ref.	Ref.	Ref.
Age	0.045***	−0.070***	0.86***	−0.0034***	−0.0060***
	(0.015)	(0.011)	(0.090)	(0.0011)	(0.00086)
French	−0.35***	−0.088	2.48***	−0.18***	0.017**
	(0.13)	(0.095)	(0.81)	(0.0098)	(0.0070)
Missing age	1.10**	−1.93***	24.7***	−0.10***	−0.19***
	(0.47)	(0.33)	(2.85)	(0.036)	(0.027)
Missing nationality	−0.41**	0.090	−0.42	−0.11***	0.013
	(0.18)	(0.13)	(1.13)	(0.014)	(0.0095)
Supervisor’s characteristics
Number of publications during the PhD period	0.033***	−0.011***	−0.42***	0.00062*	−0.000039
	(0.0042)	(0.0030)	(0.026)	(0.00032)	(0.00018)
Average yearly citations received per article	0.061***	0.26***	0.54***	0.0076***	0.0039***
	(0.017)	(0.012)	(0.10)	(0.0013)	(0.00071)
Number of distinct co-authors during the PhD period	0.011***	0.0041***	0.24***	0.000100	0.00013***
	(0.00092)	(0.00066)	(0.0056)	(0.000070)	(0.000036)
Thesis characteristics
Having a co-supervisor	0.15	−0.15**	−0.055	0.031***	−0.016***
	(0.096)	(0.069)	(0.59)	(0.0072)	(0.0047)
Mathematics	−0.18	−0.25**	−2.36**	0.067***	0.023**
	(0.17)	(0.12)	(1.06)	(0.013)	(0.010)
Medicine-biology-chemistry	0.24*	0.98***	6.46***	0.082***	0.055***
	(0.13)	(0.095)	(0.81)	(0.010)	(0.0074)
Physics	1.53***	0.49***	10.1***	0.14***	0.060***
	(0.15)	(0.11)	(0.93)	(0.011)	(0.0080)
Engineering	Ref.	Ref.	Ref.	Ref.	Ref.
Defense year dummies	Yes	Yes	Yes	Yes	Yes
University dummies	Yes	Yes	Yes	Yes	Yes
Constant	2.20***	3.03***	−21.0***
	(0.60)	(0.43)	(3.69)
Observations	20,735	20,735	20,735	20,735	20,735
R-squared / Pseudo R-squared	0.082	0.059	0.170	0.04	0.04

Note: The table includes 5 regression models estimated on a sample of 20,735 students who pursue an academic career. Nationality and Age information is missing for 12% and 9% of the students, respectively. In our econometric estimates, we control for missing information including two dummy variables Missing Nationality and Missing age. Columns 1, 2, and 3 report the variable coefficients estimated with the Ordinary Least Square (OLS) method. Columns 4 and 5 report the marginal effects of a Logit model estimated with the maximum likelihood method. Standard errors are reported in parentheses. Significance levels are indicated as follows: *** p < .01, ** p < .05, * p < .1.