Life-Cycle Earnings and Returns to Education: A Study of Norwegian Females

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Life-Cycle Earnings and Returns to Education:

A Study of Norwegian Females

Kristine Sundberg

Master of Philosophy in Economics Department of Economics

University of Oslo

Submitted May 11, 2018

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Life-Cycle Earnings and Returns to Education: A Study of Norwegian Females http://www.duo.uio.no/

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Abstract

This thesis examines life-cycle and long-term returns to schooling for Norwegian females. The results are compared to estimated returns to schooling for Norwegian males. The literature addressing returns to schooling is extensive. However, the majority of existing empirical evidence relates to males. By providing evidence on life-cycle and long-term returns to schooling for Norwegian females, this thesis seeks to extend the existing literature. To address the identification problem due to endogeneity of schooling, three instrumental variables (IV) for schooling are applied in an IV approach. The instruments utilize changes in the length of compulsory schooling and diﬀerences in individuals’ access to high schools and colleges or universities in Norway. By exploiting these instruments, a picture of the causal relationship between years of schooling and earnings over the life-cycle and in the long-term is provided for Norwegian females. Main results from applying the IV approach reveal that additional schooling has increased earnings over the life-cycle and in the long-term and that females have experienced lower returns to schooling, as well as less growth in their earnings over the life-cycle, compared to males.

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Preface

I would like to thank my supervisor, Manudeep Bhuller, for invaluable guidance and support during the process of writing this thesis. His supervision has been crucial for this work and I appreciate the time he has devoted to this project. I would like to thank him for introducing me to the interesting field of educational economics and to empirical work. Additionally, I would like to thank him for always being available in terms of guidance, useful comments and feedback, and for always being positive and motivating. Moreover, I would like to thank Statistics Norway for providing me with access to Norwegian register data, as well as a study space. The Norwegian register data has been essential in terms of writing this thesis and the study space at Statistics Norway has made the process both pleasant and inspiring. Lastly, I would like to thank fellow students at Statistics Norway for great company during the process. I would also like to thank Anders for proof reading and for practical help in terms of typesetting and document preparation. Any remaining inaccuracies or errors are my own.

Oslo, May 2018 Kristine Sundberg

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List of Tables

4.1 Descriptive Statistics . . . 27

6.1 First-Stage Estimates . . . 36

6.2 Long-Term Returns to Schooling . . . 40

6.3 Life-Cycle Returns to Schooling . . . 42

6.4 Robustness Checks: Long-Term Returns to Schooling . . . 47

7.1 Robustness Checks: First-Stage Estimates for Females . . . 58

7.2 Robustness Checks: First-Stage Estimates for Males . . . 59

List of Figures

2.1 Exposure to Compulsory School Reform and Availability of High School and College/University . . . 6

2.2 Trends in Education and Earnings . . . 9

6.1 Returns to Schooling: Age-Specific Estimations . . . 44

7.1 Residential and Labor Market Regions . . . 57

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1. Introduction

The amount of empirical work confirming a positive causal association between additional schooling and earnings is large, see, e.g., Heckman et al. (2006) and Card (1999). However, methods and identification strategies applied in such research differ. Assuming schooling is endogenously determined by observable and unobservable factors, analyses of average earnings for different levels of schooling with, e.g., Mincer’s earnings function as an underlying framework, rise a number of issues. Because unobservable factors, such as ability and preferences, may affect individuals’ schooling decisions and earnings outcomes, a key empirical challenge is to account for endogeneity of schooling.

The majority of empirical evidence addressing years of schooling and the associated returns relates to males, see, e.g., Bhuller et al. (2017) and Nybom (2017). Because of the lower labor market participation rates among females in early periods and the lower variation in males’

labor force participation rates over the life-cycle, longitudinal register data on earnings have typically been more detailed for males. Additionally, proxies for unobserved ability, such as results from ability test scores conducted by the military, have been available for males only. In literature, such proxies for unobserved ability have been applied as an identification strategy to account for endogeneity of schooling, see, e.g., Bhuller et al. (2017) and Nordin (2008). In order to apply such identification strategies and to ensure information as complete possible, the majority of empirical evidence on returns to schooling relates to males.

This thesis seeks to extend the existing literature by providing evidence on returns to schooling for Norwegian females. Following Bhuller et al. (2017), returns to schooling are estimated in both life-cycle earnings and long-term earnings. Life-cycle returns are estimated for the age intervals 20-25, 26-30, 31-35 and 36-40, whereas long-term returns are estimated for the age interval 20-40. Estimated returns to schooling are provided for both females and males.

The analysis uses rich longitudinal data containing earnings records for the Norwegian 1947- 1976 birth cohorts over the 1967-2014 period. The construction of the data is advantageous

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in the way that it allows to control for eﬀects that are fixed to specific cohorts and municipalities, i.e., the lowest level of local administration in Norway, as well as addressing selection problems in measuring educational returns.

To address problems of selection bias, such as endogeneity of educational choices, an instrumental variables approach (IV) with three instruments is applied. The number of years of schooling acquired by individuals is instrumented on: i) exposure to a compulsory schooling reform that increased compulsory schooling in Norway by 2 years, ii) access to a high school in the childhood municipality at age 16, and iii) access to a college or a university in the childhood region at age 16, where childhood municipality and region corresponds to the municipality and region of birth. By applying the IV approach, any exogenous variation in years of schooling acquired by individuals is exploited, yielding consistent, yet not unbiased, estimates of returns to schooling over the life-cycle and in the long-term for Norwegian females.

The thesis unfolds as follows. Section 2 provides the institutional background and a brief literature review. This section discusses important institutional reforms aﬀecting the Nor- wegian schooling system, in addition to trends in years of schooling and earnings for the 1947-1976 birth cohorts. A brief literature review on the topic is provided at the end of Section 2. Section 3 describes the underlying theoretical framework. Section 4 describes the data and its construction. Section 5 presents the empirical specification of the analysis and a discussion of how endogeneity of schooling is taken into account. Results are presented in Section 6, including results from the first-stage analysis, OLS estimates and 2SLS estimates of returns to schooling for both females and males. Section 7 provides a discussion of the results and draws concluding remarks.

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2. Background

2.1 Institutional Background

Changes in the Norwegian Education System

Today, compulsory schooling in Norway comprises of 10 years. Children are enrolled in primary schools at age 6, and complete secondary school at age 16. High school typically lasts for 3 years. In high school, students choose either a vocational or an academic field of study.

The vocational field of study include occupation-oriented training, whereas the academic field of study qualifies for higher education, such as attainment in colleges or universities.

Since the 1960s, a series of educational policy reforms have affected the structure of the educational system in Norway. An important reform is a compulsory schooling reform that increased mandatory years of schooling from 7 to 9 years. The compulsory schooling reform created a new unified type of middle school,ungdomsskole, for grades 8-9, in addition to the already existing primary school for grades 1-7. Prior to the reform, two separate schools were available after completing 7 years of compulsory schooling and individuals could choose to continue with either f ramhaldsskole or realskole. F ramhaldsskole offered vocational and practical training that was not standardized across municipalities in Norway. Realskolewas more academic-oriented and qualified for high school attainment. Prior to the reform, this type of school was not provided at the municipality level and the associated travel costs of attaining academic-oriented schools were large for many individuals. In 1969, f ramhaldsskole and realskolewere officially closed down and become a part of the new institution providing 9 years of compulsory schooling. The new institution offered schooling that was standardized across municipalities and qualified for high school attainment (Brinch and Galloway, 2012).

The compulsory schooling reform was legislated by the Norwegian Parliament in 1959, yet came into force for the first time in 1960 and was gradually implemented throughout the

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country. The implementation was completed in 1972. At this point, all municipalities in Norway were affected. No individual born before 1947 was subject to the compulsory schooling reform, while every individual born after 1958 were affected (Aakvik et al., 2010). The new type of middle school was administrated by the municipalities and the implementation of the reform required each municipality to provide 2 additional years of standardized schooling (Brinch and Galloway, 2012). In addition to induce individuals that were affected to increase their schooling levels, the implementation of the compulsory schooling reform improved individuals’ access to middle schools in general, as well as the professional school quality through the standardization of the curriculum (Aakvik et al., 2010). In order to implement the reform, each municipality had to present a reform plan to be approved by a national committee. Consequently, the timing of the reform was not completely randomized (Brinch and Galloway, 2012).

During the same period of time, the structure of educational institutions oﬀering higher levels of schooling was subject to substantial changes. Until 1974, high school was defined as eithergymnasoryrkesskole. Gymnasqualified for higher educational attainment in universities or colleges, whereas yrkesskole was career-oriented and oﬀered occupational training.

By the 1974 reform, gymnas and yrkesskole was merged into one educational institution.

As prior to the reform, one academic field of study and one vocational field of study was oﬀered by the new high school. Additionally, the 1974 reform entitled all individuals, by law, to attain 3 years of high school.

Simultaneously, due to factors, such as an increasing population, changes in the population’s social and cultural expectations, increased demand for highly educated workers and growing employment options, the demand for university degrees increased, leading to a ca- pacity problem at the universities (Nyborg, 2007). The need for planning higher educational development by the authorities arose and the Norwegian Parliament decided to establish regional colleges through the implementation of a college expansion reform (Carneiro et al., 2014). The first expansion in higher education took place in 1963, following regional college expansions during the 1970s, as proposed by the Ottosen Commission. Not only did access

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to higher education in Norway improve as a result of the college expansion, but the original educational system was subject to substantial changes. The goal of the college expansion was to reduce the high demand for university degrees and induce more individuals to choose shorter degrees that were more occupation-oriented, such as nursing or teaching (Sandvand, 1976). Consequently, the many small professional schools that existed prior to the college expansion was merged with the new regional colleges that were established. As an example, traditional training of nurses and teachers, that prior to the college expansion could be entered without completing a high school degree, was now defined as higher education (Nyborg, 2007).

Figure 2.1 plots the population shares of the 1947-1976 birth cohorts that were subject to the compulsory schooling reform, had access to a high school in the childhood municipality at age 16, and had access to a college or a university in the childhood region at age 16. Assuming that the population has consisted of approximately 50% females and 50% males, the plots are very similar, yet provided for both genders. The plots illustrate how the compulsory schooling reform gradually aﬀected the whole population and confirm an increasing trend in school availability.

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Figure 2.1: Exposure to Compulsory School Reform and Availability of High School and College/University

(a) Females (b) Males

Trends in Educational Attainment and Earnings across Females and Males As discussed above, both school attainment and school availability has increased substantially in Norway since the 1960s. These increases may be explained by several factors, such as changes in the Norwegian industry that increased employment options and the demand for highly skilled workers, changes in the population’s social and cultural expectations towards education and employment in general, and structural changes that aﬀected the educational system in Norway in terms of quality, length and availability (Nyborg, 2007; Hægeland et al., 1999). Evidence from the United States suggest that the most important labor force change took place during the 1970-1990 period, as females’ labor force participation increased due to changes in their length of education and chosen field of study (Becker, 1994). During this period, females started to move away from traditional fields, such as teaching, nursing, and doing household work, and entered fields such as accounting, law and engineering. Females started to take less time oﬀfrom their jobs and the value to females of market skills increased.

Such trends in females’ attainment levels are confirmed in Scandinavian countries (Becker, 1994).

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The increase in the overall schooling level in Norway was particularly large during the 1970- 1990 period (Nyborg, 2007). An increasing trend in school attendance is still persistent.

According to Statistics Norway (SSB, 2018), the share of the Norwegian population that had completed a college degree or a university degree of 4 years or less increased from 10.2%

in 1985 to 33% in 2016. The increase in school attendance has been particularly large for females, and since the late 1980s, a larger share of the female population has been enrolled at universities and colleges compared to males. Surveying recruitment changes in Norwegian education from the 1960s to 1990, Lindbekk (1998) confirms increasing attainment levels for both females and males, as well as reduced attainment diﬀerences across genders and the population in general. In addition to the increasing labor force participation rate among females, reduced diﬀerences in educational attainment may reflect how higher education has become more available to the population since the 1960s and how factors, such as geographical conditions, gender and social background, may have become less important in terms of attainment outcomes (Lindbekk, 1998).

Enrollment ratios among females and males have varied with field of study and with the length of the degree completed. A general trend has been that a larger female share has completed shorter degrees, such as bachelor’s degrees that are oriented towards specific occupations, e.g., nursing and teaching, whereas a larger male share has completed master’s degrees and PhDs (SSB, 2018). In line with the particularly large increase in school attendance for females since the 1960s, Lindbekk (1998) confirms a large increase in attainment levels for average educational levels and a more moderate increase for higher levels. As suggested by Statistics Norway, the increase in the share of females beginning, or completing, master’s degrees or PhDs has exceeded the increase in the male share. If this trend is persistent, the female share acquiring master’s degrees or PhDs may increase above the male share (SSB, 2018).

Along with increasing school attainment and labor force participation, both females and males have experienced substantial growth in their earnings levels since the 1960s. How- ever, average earnings levels experienced by females have tended to be lower than average

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earnings levels experienced by males. Due to the particularly large increases in the female rates of labor force participation and educational attainment, the increase in females’ average earnings levels has been higher than the increase in males’ average earnings levels since the 1970s. Consequently, a reduction in earnings diﬀerences has taken place (Kunze, 2017). In 2017, Norwegian females earned an average of 86.7% of the average Norwegian male earnings, indicating that gender diﬀerences in earnings still persisted (SSB, 2018). Trends in educational attainment and earnings levels for the female and male 1947-1976 birth cohorts are illustrated in Figure 2.2 below.

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Figure 2.2: Trends in Education and Earnings

(a) Schooling Attainment by Cohort: Females (b) Schooling Attainment by Cohort: Males

(c) Average Earnings by Cohort: Females (d) Average Earnings by Cohort: Males

(e) Average Earnings by Schooling: Females (f) Average Earnings by Schooling: Males

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On the left y-axis, graphs a) and b) in Figure 2.2 plot the average number of years of schooling for the 1947-1976 birth cohorts of Norwegian females and males, respectively. On the right y-axis, the graphs plot shares that have acquired higher education, both bachelor’s degrees and master’s degrees or PhDs, of each cohort. A bachelor’s degree is defined as having completed 14-16 years of schooling, whereas a master’s degree or a PhD is defined as 17-21 years of schooling. The plots reveal that females born in 1950 completed an average of around 11.3 years of schooling, whereas males born in the same year completed around 11.7 years of schooling. However, for the 1975 birth cohort, females completed an average of 13.6 years of schooling, whereas males completed around 12.8 years. In line with the literature discussed above, a sharper increase in the average number of years of schooling completed by females compared to males is confirmed. Additionally, the plots reveal that the average number of years of schooling completed by females has exceeded years of schooling completed by males on average for cohorts born after 1960.

In terms of higher education, the plots reveal that the shares of the female and male 1950 birth cohort that completed a bachelor’s degree were approximately of the same size, with around 18% of all females and around 19% of all males completing 14-16 years of schooling.

As a contrast, for the 1975 birth cohort, around 42% of the female population completed 14- 16 years of schooling, whereas only 29% of the male population completed the corresponding level of schooling. The plots confirm a more rapid growth in the share of females completing a bachelor’s degree compared to males and that the share of females completing 14-16 years of schooling has exceeded the male share for cohorts born after 1955-1956, as suggested by SSB (2018). In terms of completing a master’s degree or a PhD, the male share appears to be relatively stable across cohorts. For females, a small increase in the share that completed 17-21 years of schooling is revealed. In particular, increasing master’s degree or PhD attainment is revealed for the female 1970-1976 birth cohorts. For the youngest cohorts, i.e., individuals born in 1973-1976, the plots suggest that the female share that completed a master’s degree or a PhD has exceeded the male share. This result contradicts the result of SSB (2018) and should be interpreted with caution, as a females in this category may have completed everything between 17 and 21 years of schooling.

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Graphs c) and d) in Figure 2.2 plot average annualized earnings over the age interval 20-40 in 2015 Norwegian Kroners (NOK) for the 1947-1976 birth cohorts of females and males, respectively. The plots suggest that average yearly earnings for the 1947 birth cohort were around 100,000 NOK for females and 225,000 NOK for males over the age interval 20-40.

For the 1975 birth cohort, average yearly earnings were around 250,000 NOK for females and 350,000 NOK for males. The plots confirm an increase in average yearly earnings for both genders, as well as a steeper increase in earnngs for females. However, average yearly earnings experienced by females are lower compared to males for all birth cohorts. Graphs e) and f) plot years of schooling against average annualized earnings over the age interval 20-40 in 2015 NOK for females and males, respectively. The patterns suggest a strong positive association between completed level of schooling and average yearly earnings for both genders. However, average earnings experienced by females have been lower for all levels of schooling compared to males.

2.2 Literature Review

The literature addressing returns to schooling is extensive. A goal of estimating returns to schooling has been to determine whether there is underinvestment or overinvestment in schooling, which is still of high relevance. Earnings of more educated people are in most cases found to be above the average of the population and the research literature confirming a positive relationship between additional schooling and earnings is large, see, e.g., Harmon and Walker (1995) and Card (1993). Since 1950, a sizeable increase in the marginal rate of return to attaining and completing additional schooling has been documented. Becker (1964) demonstrates how high school and college education in the United States have raised individuals’ earnings and conclude that positive returns to schooling are valid, even after netting out direct and indirect costs associated with acquiring additional schooling and adjusting for family backgrounds and abilities of more educated workers. Since this period of time, evidence of positive returns to schooling has become available in over one hundred countries, with diﬀerent cultures and economic systems, at diﬀerent points in time (Becker, 1994). Such

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evidence is consistent with the changes in the demand favoring highly skilled workers seen across countries since the 1960s (Heckman et al., 2006).

Since the time of Becker (1964), economists have estimated returns to schooling by applying alternative methods and strategies. The improvements in data availability has been advantageous in terms of improving estimated returns to schooling. Work based on multi- variate regression analyses controlling for schooling and age, using data for the UK, typically suggest returns to an additional year of schooling of 7% to 9%. Nordic countries experience lower averages, while the international measure of returns to an additional year of schooling is estimated to be around 6% (Harmon and Oosterbeek, 2000). A problem of particular importance stressed in literature is that returns to schooling vary across individuals, and that individuals self-select into schooling on the basis of of realized returns to schooling, see, e.g., Carneiro et al. (2011). Hence, to address selection problems, such as endogeneity of educational choices and sample selectivity due to labor force participation, an instrumental variable approach is often applied, see, e.g., Angrist and Krueger (1991) and Card (1993).

The literature addressing returns to schooling in Norway is large. Hægeland et al. (1999) estimate earnings equations for the years 1980 and 1990 and find that returns to schooling have been remarkably stable, even when comparing returns to schooling across sectors of the economy. To account for self-selection into schooling, they apply an instrumental variable approach, where separate education earnings profiles are estimated for diﬀerent cohorts. Their results suggest that the increasing level of school attainment in cohorts does not seem to have had a negative eﬀect on returns to schooling experienced by younger cohorts, i.e., additional schooling has been profitable across cohorts. Using population panel data containing records for every Norwegian male over the 1967-2014 period, Bhuller et al. (2017) find that additional schooling gives higher lifetime earnings, as well as a steeper age-earnings profile over the life-cycle. After accounting for income taxes and earnings-related pensions, their preferred estimate imply an internal rate of return of around 11%, suggesting that additional schooling has been profitable.

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In literature addressing Norwegian returns to schooling an identification strategy, with the compulsory schooling reform that was implemented during the 1960s as an instrument, has been applied to account for endogeneity of schooling. Following such an IV strategy, Aakvik et al. (2010) confirm that the compulsory schooling reform increased the general level of schooling beyond the additional 2 years of compulsory schooling, and that the reform gen- erated higher returns to schooling in terms of earnings. Results presented by Bhuller et al.

(2011) indicate that application of the IV strategy produces higher returns to schooling, suggesting that the returns vary across individuals and that the instrument changed the schooling choice of a subgroup with relatively high returns to schooling. They suggest that the subgroup induced to increase their schooling level because of the reform experienced an increase in earnings levels, as well as a more rapid growth in their earnings levels over the life-cycle. Black et al. (2005) confirm a positive eﬀect of the compulsory schooling reform on school attainment, above the compulsory 2 years, and a positive and significant eﬀect of the compulsory schooling reform on earnings levels.

Results presented by Carneiro et al. (2014) suggest that the Norwegian municipalities that were exposed to the college expansion reform that increased the availability of colleges in the municipalities affected, comprised of a more educated labor force. In these municipalities, the share of high and middle-skilled workers was 6% higher, on average, compared to control municipalities that were not affected by the college expansion reform. In addition, the log-earnings for high-skilled workers increased in treated municipalities, relative to estimated log-earnings in the control municipalities. When exploiting the changes in years of schooling following the compulsory schooling reform, Aakvik et al. (2010) find that returns to schooling are strongly nonlinear. Their results suggest that returns to upper secondary school, shorter degrees at regional colleges, as well as longer degrees, such as master’s programs at universities, were high in terms of earnings. They confirm substantial differences between the average treatment effect on the treated, i.e., returns to schooling for those affected by the compulsory schooling reform, for bachelor’s and master’s degrees at universities. The average treatment effect was particularly high for medium-length educations, i.e., degrees of up to 2 years in colleges or universities.

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3. Theoretical Framework

3.1 The Schooling Decision

Education and training are considered as the most important investments in human capital.

In classical human capital theory, additional schooling raises earnings and individual labor productivity by providing knowledge, skills and valuable tools. Consequently, individual investments in human capital are arguably crucial in terms of economic growth (Montenegro and Patrinos, 2014). In the classical theory, individuals face a market opportunity locus yielding the level of earnings associated with diﬀerent schooling choices. Individuals reach the optimal schooling decision by balancing benefits from additional schooling, which are reaped over the life-cycle, against associated physical and psychic costs, which are born ear- lier on (Card, 2001).

The human capital approach is a central concept in analyzing individual demand for education. The human capital approach was originally motivated by Gary Becker and Jacob Mincer. The model derived by Mincer (1974) is typically used as a benchmark in empirical analyses addressing returns to schooling. Human capital theory generally builds on the extensive work performed by Becker (1964), where years of schooling is chosen by individuals in order to maximize the expected present value of future income streams.

Following Becker (1975), this section derives important relations between earnings, investment costs and rates of returns. Let Y be an activity providing a person that enters the activity at a particular age, referred to as age zero, a real net earnings stream of Y0 during the first period, Y1 during the next period, and so on. In the last period, the net earnings stream is given by Yn. The activity, Y, may be any kind of investment in human capital, such as additional schooling, on-the-job training, information, health and morale. Net earnings are given by gross earnings during any given period, minus any costs associated to the investment in human capital during the same period.

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The present value of the net earnings stream in activity Y is given by:

V(Y)= Xn

j=0

Yj

(1 +i)^j+1 (3.1)

Where iis the market discount rate, assumed to be equal in all periods for simplicity. IfX is another activity, such as entering into the labor force with little or no investment in human capital, providing a net earnings stream ofX0,X1, ...,Xn, with a present value ofV(X), the gain, d, from choosing Y overX is given by:

d=V(Y) V(X)= Xn

j=0

Y_j X_j

(1 +i)^j+1 (3.2)

The cost of investing in human capital is given by net earnings foregone by making the investment, rather than choosing an activity that requires no investment. Assuming that activity Y requires investment in the initial period only, and that X does not require any investment, the cost of choosing Y rather than X is given by the diﬀerence between their net earnings in the initial period. The total return from making the investment is given by the present value of the diﬀerences between net earnings in later periods. By rearranging Equation (3.2), the relationship between costs and returns from investing in human capital is explicitly given by:

d= Xn

j=1

kj

(1 +i)^j C=R C (3.3)

WhereRmeasures total return,C =X₀ Y₀ and measures the cost of making the investment, and kj =Yj Xj, for j = 1,2, ..., n. The relationship between costs and returns can be be derived by defining the internal rate of return, r, which is a rate of discounting that equates the present values of the two earnings streams, i.e., the rate equates the present value of returns to the present value of costs. The internal rate of return, r, is implicitly defined by:

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C= Xn

1

kj

(1 +r)^j (3.4)

By rearranging Equation (3.4), the condition for individuals’ optimal human capital investment decision is given by:

Xn

j=0

Y_j (1 +r)^j+1

Xn

0

X_j

(1 +r)^j+1 =d= 0 (3.5)

At the optimal human capital investment decision, the present values of the potential investment choices equate. Becker (1975) proves how costs and rates of returns may be estimated by using information on net earnings. This is fortunate, as returns to human capital investment are typically not separated from other earnings, the associated costs are only sometimes and incompletely separated, and returns from other investments, such as on-the-job training and information, are not readily available.

The framework outlined above may be restricted to consider the choice of investment in additional schooling only. Following Mincer (1974) and Becker (1964), Harmon and Oosterbeek (2000) presents a theoretical framework assessing the optimal schooling decision. Investment periods of education are usually measured in years of schooling. Individuals choose the number of years of schooling that maximizes the expected present value of their future income stream up to a date of retirement, net of the costs associated to the investment in additional schooling. Following Harmon and Oosterbeek (2000), the optimum is characterized at the point where the present value of an additional year of schooling equals the cost associated with acquiring that additional year. If ws is the future wage associated with investing in one additional year of schooling, the equilibrium is given by:

T sX

t=1

ws ws 1

(1 +rs)^t =ws 1+cs (3.6)

Where s is schooling, T is a date of retirement, cs is net costs associated with s years of

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schooling andrsis the internal rate of return to syears of schooling. An individual’s optimal investment decision implies investment in an additional year of schooling if rs> i, wherei is the market interest rate. If T is large, rearranging Equation (3.6) yields:

ws ws 1

rs

=ws 1+cs (3.7)

Ifcsis suﬃciently small, which is a reasonable assumption in the Norwegian case as monetary schooling fees are low, Equation (3.7) may be expressed as:

rs ⇡ w_s w_s ₁

ws 1 ⇡log(ws) log(ws 1) (3.8)

Equation (3.8) illustrates how the return from investing in an additional year of schooling, s, is approximately given as the diﬀerence in the log-wages between choosing s over s 1.

3.2 The Mincer Equation

Mincer’s work was originally motivated by providing evidence of quantitative explanatory power of the human capital model. In his specifications, Mincer (1958, 1974) emphasizes the point that investment in additional schooling reduces the time individuals spend in the working force if retirement is fixed to a certain age, and that such an investment postpones the time in which individuals receive their earnings. Such time costs, in addition to monetary outlays, make up the total cost of the investment. Additional schooling is not undertaken unless it will raise the level of the expected future income stream. At the time the investment in additional schooling is undertaken, the present value of real earnings streams, with and without investment in additional schooling, equate. They are equal only at a positive discount rate, which may be defined as the internal rate of return on the investment.

The empirical approximation of the human capital theoretical framework is typically rep- resented by the Mincerian human capital earnings function. This function is widely applied

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as log-specifications. The log-specification may be given on the following functional form of the earnings function:

lnyi =↵+ Xi+rsi+ xi+ x²_i +ui (3.9)

The specification above is motivated by the frameworks presented by Mincer (1958, 1974), whereyi is an earnings measure for any individuali,si is years of schooling,xiis a measure of experience, typically given by age or the age at which schooling is left. Xi incorporates other variables that are assumed to aﬀect earnings. ui is a mean zero residual incorporating unobserved factors that may explain earnings, with E(u|si, xi) = 0. Experience,xi, is included both as a linear and a quadratic term to take the concavity of earnings profiles into account, as Mincer (1974) documented a concave shape of earnings profiles where workers acquiring more years of schooling experience a more rapid growth in their earnings. Under certain assumptions, in Equation (3.9) may be interpreted as the rate of return to schooling. The rate of return is assumed to be equal for all levels of schooling. Although the specifications presented by Mincer (1958, 1974) are algebraically similar, the economic content of the two frameworks diﬀer. Based on the work of Heckman et al. (2006), the main points of both frameworks are presented in the following.

The original Mincer model is presented by Mincer (1958). The model is built upon the principle of compensating differences to explain why persons with different levels of schooling receive different earnings over their lifetime. The model assumes identical abilities and opportunities among individuals, perfect credit markets and a perfectly certain environment.

Occupations differ in the amount of schooling that is required. Individuals incur no direct costs of schooling, although earnings are foregone while in school. Because individuals are identical, a compensating wage differential to work in occupations that require more years of schooling is required. By equating the present value of earnings streams, net of the associated schooling costs for different levels of schooling, the compensating differential is determined.

The present value of earnings associated with the level of schooling, s, is given by:

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V(s) = Y(s) Z T

s

e ^rtdt= Y(s)

r (e ^rs e^rT) (3.10)

Where Y(s) is constant annual earnings over the lifetime for an individual that has invested in s years of schooling. The length of the individuals’ working life is given by T. Here, r is an externally determined interest rate. Equilibrium across heterogeneous schooling levels requires indiﬀerence between schooling choices, where allocations are driven by demand conditions. By equating the earnings streams across schooling levels and taking the natural logarithm, annual earnings of an individual with s years of schooling may be expressed by the following specification:

lnY(s) = lnY(0) +rs+ ln 1 e ^rT

1 e ^{r(T s)} (3.11)

The model implies that people with higher levels of schooling receive higher earnings. The final term in Equation (3.11) adjusts for finite life and disappears as T gets large. When T is large, the percentage increase in lifetime earnings that is associated with an additional year of schooling must be equal to the interest rate, r. Because the internal rate of return to schooling equates lifetime earnings streams for different choices of schooling levels, it must also be equal to the interest rate, r. Hence, in Equation (3.9) can be interpreted as the internal rate of return. When = r, the market for schooling reaches an equilibrium. The Mincer (1958) model does not take uncertainty about future earnings, non-pecuniary costs and benefits of schooling and experience into account. The intercept and slope coefficients are assumed to be identical across individuals and individuals are assumed to base their schooling decisions on average earnings levels within the schooling and experience categories. More recent literature stresses how returns to schooling varies across individuals. Consequently, the Mincer coefficient may not provide a consistent picture of the rate of return to schooling.

The framework presented by Mincer (1974) is more frequently applied today. The model may be referred to as Mincer’s accounting identity model. It is less tied to the underlying

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between actual earnings, potential earnings and human capital investment in both schooling and experience. Mincer (1974) treats the rate of return as a parameter so that a change in an individual’s investment does not aﬀect the marginal and average rate of return from the additional investment. Investment costs are treated as time costs. Underlying assumptions are years of schooling being exogenously given, no earnings while in school, zero net investments in additional human capital during the working life, a stationary environment so that cross- sectional earnings profiles can be used as guides on individuals’ life-cycle earnings, a constant flow of individual earnings throughout their working life, and zero depreciation. In addition, schooling and experience are included as separated terms so that earnings profiles cannot diverge with experience across diﬀerent schooling levels. The model assumes heterogeneous individuals. To reflect heterogeneity in returns, is allowed to vary across the population.

Potential earnings at time t,Pt, are given by:

Pt=Pt 1(1 +kt 1 t 1)⌘

t 1

Y

j=0

(1 + jkj)P0 (3.12)

Where the costs of investment in schooling, Ct, are expressed as a fraction, kt of potential earnings, so that Ct = ktPt. t is the average return to investments in schooling at age t.

Formal schooling is defined as the number of years spent in full-time investment, implying kt = 1. Because formal schooling is assumed to take place at the beginning of an individual’s lifetime, the associated rate of return, , is constant across all years of schooling. If the rate of return to post-school investment is constant over all ages and equal to 0, this yields:

lnPt⌘lnP0+sln(1 + s) +

t 1

X

j=s

(ln 1 + 0kj)⇡lnP0+s s+ 0 t 1

X

j=s

kj (3.13)

Mincer (1974) assumes that the rate of post-school investment is linearly declining, given by:

ks+x = (1 _T^x), where x = t s 0 is work experience at age t, and T is assumed to be independent of schooling level. Given these assumptions, the relationship between potential earnings, schooling and experience is given by:

lnPx+s ⇡lnP0+s s+ ( 0+ ⁰

2T )x ⁰

2T x² (3.14)

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Observed earnings are given by potential earnings less investment costs, which gives the relationship for observed earnings as expressed by the Mincer equation:

lnY(s, x)⇡lnPx+s (1 x

T) = [lnP0 ] + ss+ ( 0+ ⁰ 2T + 

T)x ⁰

2T x² (3.15)

The specification above corresponds to Equation (3.9), without the disturbance term. In this specification, s represents the average rate of return across all schooling investments and not the internal rate of return or the marginal rate of return to schooling. The framework does not take uncertainty, the dynamics following the choice of schooling, the sequential revelation of uncertainty, or ability bias, into account. Consequently, forecasting the total variation in earnings that is associated with the choice of schooling at the time the schooling decision is made is not possible.

A random coeﬃcients model of the returns to education has been important in the human capital literature since the work of Becker (1964) and Mincer (1974). By taking uncertainty into account and simplifying Equation (3.15) to regard the choice of schooling, Heckman et al.

(2006) present a convenient random coeﬃcients model for the economic returns to schooling.

The random coeﬃcients model is given by:

lnyi =↵i+ isi (3.16)

Where the rate of return, i, and the intercept, ↵i, varies across individuals, i. Assuming the only cost of schooling is foregone earnings while acquiring additional schooling, perfect markets, and that yi is the annual flow of lifetime earnings, i may be interpreted as a percentage growth rate in earnings with schooling. Assuming ↵i =↵+"↵i and i = +" _i and that the means of "↵i and " _i are zero, rearranging Equation (3.16) yields:

lnyi = ¯↵+ ¯ + ["↵i+" _isi] (3.17) As long as the growth rate, i, is a random variable, its distribution can be studied using diﬀerent methods. The conventional measure is the average growth rate, given observed

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individual-specific characteristics (Heckman et al., 2006).

The Mincer (1974) function is widely used as a framework in empirical analyses assessing the association between schooling and earnings as log-specifications. However, certain assumptions must hold in order to interpret in Equation (3.9) as the average rate of return to schooling. If the assumptions presented above hold, the Mincer regression function may be estimated using data on post-schooling earnings of employed individuals, excluding observations on earnings while in school and dropping observations that have zero earnings. Because the Mincer log-earnings specification may be estimated using data on employed workers, the problem of sample selection bias arises. Sample selection bias is particularly a major concern for female workers, as they are more likely to experience substantial variation in their labor force participation over the life-cycle. Consequently, the use of alternative models and empirical methods may be favorable in terms of providing a consistent picture of the relationship between years of schooling and the associated returns.

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4. Data and Descriptives

4.1 Data Sources

Following Bhuller et al. (2017), the analysis uses longitudinal databases with earnings histories maintained by Statistics Norway for the 1947-1976 birth cohorts. This data contains earnings records, demographic information and socioeconomic data for almost all Norwegian individuals during the 1967-2014 period. To determine childhood municipality of birth and to create interacted instruments for robustness checks, the data has been merged with census data from 1960. Because educational attainment is reported directly from educational establishments to Statistics Norway, the chance of measurement error in years of schooling is small. However, the education register started in 1970 and the census data from 1960 is self-reported, leading to a chance of measurement error (Black et al., 2005).

The dependent variable of interest is long-term earnings. Long-term earnings are defined as average annual earnings over the age interval 20-40. Earnings diﬀerences before age 20 and after age 40 are excluded in the analysis. This sample restriction is made to ensure information as complete as possible. The majority of the individuals in the sample do not experience substantial earnings before age 20, and there is little evidence of large returns to schooling at younger ages. Data on earnings are only available until 2014. Hence, earnings histories for the 1975-1976 birth cohorts at ages 38-40 are missing. However, this is not likely to aﬀect the main results of the analysis in any substantial way.

The regressor of interest is years of schooling acquired by individuals. Few monetary costs are associated with schooling in Norway. However, the costs of acquiring additional schooling may be related to psychic costs, travel costs or costs of moving. The analysis uses two constructed data sets, one for females and one for males. The lower labor market participation rates documented among females during the 20^th century may lead to potential empirical problems, especially in terms of comparing estimated female returns to schooling to the re-

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turns experienced by males. The analysis is ex-post and will provide a picture of the actual returns to schooling that have been experienced by the female and male 1947-1976 birth cohorts in Norway during the 1967-2014 period over the 20-40 age interval. I will further also use information on birth cohort, childhood municipality and childhood labor market region in the analysis.

To provide a picture of the causal relationship between years of schooling, and life-cycle and long-term earnings, three instrumental variables are utilized in a 2SLS framework. The instruments are as follows: i) a dummy variable for exposure to the compulsory schooling reform implemented in Norway during the 1960s, ii) a dummy variable for access to a high school in the childhood municipality at age 16, and iii) a dummy variable for access to a college or a university in the childhood region at age 16, where childhood municipality and region correspond to the municipality and region of birth. I utilize the same source of information on exposure to the compulsory school reform as in Bhuller et al. (2017). The construction of remaining instrumental variables is based on educational data contained in the regional database provided by the Norwegian Centre for Research Data (NSD). NSD’s regional database is a complete system for publishing regional data at all regional levels in Norway¹. The educational data include information on the number of primary schools, secondary schools, high schools, colleges and universities in all municipalities, in addition to the number of students enrolled at the diﬀerent types of schools, fields of study, class sizes, and other relevant educational information.

For the analysis, I use information on the number of schools in diﬀerent municipalities at diﬀerent times to create the instrumental variables that are applied. Specifically, I construct indicators for whether or not a high school was available in the the childhood municipality at age 16, and whether or not a college or a university was available in the the childhood region at age 16. To fix ideas, in terms of access to a high school, the instrumental variable

1Part of the data used in the analysis are obtained from the Norwegian Society of Social Data Services’

(NSD) Municipal Information Database. NSD is not responsible for the analysis of the data or the interpre- tations made here.

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equals one if a high school was present in the the childhood municipality at age 16, and zero otherwise. Data sets containing identifiers for school availability in all municipalities are constructed on the basis of the information provided by NSD. This data set is next merged with the panel data provided by Statistics Norway.

Because the structure of the municipalities and the educational system in Norway has been exposed to substantial changes since 1960, these changes have been taken into account to merge the data in a consistent way. Changes in the structure of the municipalities include merger and splits. In order to maintain a consistent classification of municipality across all years, the municipality structure from 2013 is utilized. However, any splits that occurred during the 1960-2013 period were reversed. This means that the municipality structure of the final data set treats municipalities that were divided into two, or more, entities during the period as one entity. In 2013, Norway had 428 municipalities. The municipality structure of the final data set, however, consists of 396 municipalities. This smaller number illustrates how splits of a few municipalities that took place during the 1960-2013 period have been reversed in the data set utilized here.

Structural changes of the Norwegian educational system since 1960 include changes in terms of schooling levels. As discussed in Section 2, the termsgymnasandyrkesskoledefined until 1974 the schooling level that today corresponds to high school. To create a variable indicating school availability in all municipalities during the 1960-2013 period, the data on number of schools in municipalities provided by NSD is exploited. The latest educational structure is used to create consistent school variables indicating the availability of the relevant school type in all municipalities. The number of schools corresponding to the specific schooling level was first aggregated in each municipality. Thereafter, variables indicating school availability of diﬀerent schooling levels were created for each municipality.

In the analysis, the standard errors are clustered at the region level. The division of regions follows the structure presented by Gundersen and Juvkam (2013), where the Norwegian mu-

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nicipalities are classified into 160 residential and labor market regions². This classification uses the centre structure as its starting point, where variables, such as the total number of residents of the urban settlement in municipalities, the number of jobs, number of commuters travelling to the municipality, services available in the municipality, public institutions in the municipality and centrality or distance to centre functions, are taken into account (Gunder- sen and Juvkam, 2013). In order for the region structure to be consistent with the 2013 municipality structure that is coded to be constant in the data set used in the analysis, some regions have been merged together. Consequently, the data set consists of 156 regions and not 160, as proposed by Gundersen and Juvkam (2013).

The Norwegian earnings data is advantageous in the way that it consists of long earnings histories for almost all individuals. However, immigrants are excluded in the data set and individuals with no information on years of schooling are not included in the analysis. Indi- viduals with missing information on childhood municipality are dropped from the sample, as this information is needed in order to apply the instrumental variables. Because exposure to the compulsory schooling reform is used as an instrument, regions with missing information on the timing of the reform implementation are also dropped from the sample. As a result, the IV sample consists of 145 regions, for which information on the timing of the reform is available.

4.2 Descriptive Statistics

Table 4.1 reports summary statistics for the main outcome variables in the resulting data set.

Panel A describes average life-cycle earnings for females, males and both, over age intervals 20-25, 26-30, 31-35 and 36-40. Panel A also describes average long-term earnings over the age interval 20-40. Panel B describes average years of schooling for females, males, and both.

The number of observations with available information on years of schooling completed is reported in Panel B. Table 4.1 illustrates how female average earnings were substantially lower over the life-cycle and in the long-term compared to males, although the average educational

2See Figure 7.1 in the Appendix for an illustration of the division of residential and labor market regions.

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attainment for females is larger than the average attainment for males.

Table 4.1: Descriptive Statistics

Females Males All

(1) (2) (3)

Panel A.Mean Earnings

Mean Earnings, Age 20 - 25 111 058.8 156 357.3 134 305.6

(74 832.4) (88 902.5) (85 409.5)

(120 971.5) (141 540.8) (142 554.7)

Mean Earnings, Age 31 - 35 202,282.8 336 210.0 270 854.9

(147 766.9) (203 075.6) (190 399.4)

(175 778.3) (266 495.1) (237 302.3)

(105 789.4) (140 190.5) (134 618.3)

Panel B. Educational attainment

Years of Schooling 12.35 12.17 12.26

(2.76) (2.65) (2.77)

Number of Observations (Panel B) 828,812 872,936 1,701,748

Note: Descriptive statistics for the Norwegian female and male birth cohorts 1947-1976. Panel A displays sample averages of annual earnings over diﬀerent age intervals, whereas panel B reports average years of schooling. Standard deviations are reported in parentheses. Earnings are reported in Norwegian Kroner (NOK) adjusted to 2015 levels.

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5. Empirical Strategy

5.1 Empirical Specification

The objective of the thesis is to estimate returns to schooling in life-cycle and long-term earnings for females. A key challenge in identifying casual effects of schooling on earnings relates to the endogeneity of educational choices. Individuals that attain more years of schooling may be positively selected on observable factors, such as social background and geographical characteristics, or unobservable factors, such as abilities or preferences. Such observable and unobservable factors may be correlated with labor market outcomes, making the estimated coefficient on schooling in an earnings regression function unable to capture the casual effect of additional schooling on life-cycle and long-term earnings.

To account for the endogeneity of educational choices, an instrumental variables (IV) approach with three instruments is applied. As instruments, indicators for exposure to the compulsory schooling reform that increased compulsory schooling in Norway from 7-9 years, access to a high school in the childhood municipality at age 16 and access to a college or a university in the childhood region at age 16 are applied. Following Bhuller et al. (2017), the empirical model of the analysis may be characterized by the following system:

Ya= as+X

c

cadc+X

m

madm+"a (5.1)

s= aZ1+ aZ2+'aZ3+X

c

✓cadc+X

m

✓madm+ua (5.2)

The system is estimated by the two-stage least squares (2SLS) method, where the first-stage is given by Equation (5.2) and the second-stage is given by Equation (5.1). Z₁ is an indicator variable equal to one if the individual was exposed to the compulsory schooling reform, i.e., acquired 9 years of compulsory schooling, and zero otherwise. Z₂ and Z₃ are indicator

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variables equal to one if the individual had access to a high school in the childhood municipality, and a college or a university in the childhood region, respectively, and zero otherwise.

Subscript a denotes the age at which earnings are measured. Subscriptm denotes childhood municipality and subscript c denotes birth cohort. By including municipality-fixed eﬀects and birth cohort-fixed eﬀects in the analysis, controlling for characteristics that are fixed to specific cohorts and municipalities is possible. Standard errors are robust and clustered at the level of labor market region, which allow for arbitrary correlation of errors within clusters and assume independence across clusters.

The goal of the analysis is to provide a picture of the causal relationship between years of schooling and life-cycle and long-term earnings for Norwegian females. In Section 5.2 below, I will provide the assumptions underlying the IV approach and discuss how this approach allows me to construct consistent estimates of the causal eﬀects of schooling on life-cycle and long-term earnings. Following Bhuller et al. (2017), the analysis uses life-cycle and long-term earnings in levels to circumvent the problem of sample selection bias. If a log-earnings specification was estimated using annual earnings, this would be a serious concern for females, as they have experienced more variation in their labor force participation over their working life than males.

5.2 Endogeneity of Schooling and Instrumental Variables

Several factors lead to biased OLS estimates of Equation (5.1). Firstly, OLS estimates are likely to suﬀer from ability bias. Ability bias is of particular concern if both individuals’

schooling decisions and earnings outcomes are positively correlated with ability, and ability remains unobserved. In such a case, OLS yields estimates that are upward biased (Hansen and Wahlberg, 2005). On the other hand, individuals with higher abilities may experience higher opportunity costs of schooling. In this case, schooling and ability is negatively correlated and OLS estimates will be downward biased (Griliches, 1977). Another factor leading to biased OLS estimates is measurement errors in terms of educational attainment. Mea- surement errors in years of schooling will produce OLS estimates that are downward biased

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(Griliches, 1977). Lastly, the schooling decision is likely to depend on subjective discount rates. If ability and subjective discount rates are correlated, OLS will again produce estimates that are biased (Hansen and Wahlberg, 2005). Aakvik et al. (2010) discusses how factors, such as ability bias, time preferences and financial constraints are common sources of endogeneity in schooling.

In Norway, educational attainment is well documented and reported to Statistics Norway.

The chance of measurement errors in years of schooling is therefore low, although a chance of misreporting is present. Additionally, schooling fees are very low and the major costs of school attainment relate to travelling and moving, or to individuals’ psychic costs of acquiring additional schooling. The key empirical challenge in achieving consistent estimates of returns to schooling is therefore to account for endogeneity of schooling. Empirical concerns following schooling being endogenously determined are typically approached through the application of an IV model using an exogenous source of variation in schooling outcomes.

The IV literature confirming biased OLS estimates is large. Many studies report IV estimates that are substantially higher than the corresponding OLS estimates, see, e.g., Card (1993), using geographic variation in college proximity to estimate the returns to schooling, or Harmon and Walker (1995), using a compulsory schooling law raising the minimum school- leaving age in the UK as a source of exogenous variation in estimating returns to schooling.

IV estimates being substantially higher than the corresponding OLS estimates may be the case if the instruments that are applied affect the schooling decisions of individuals with relatively high marginal returns to schooling, compared to the average (Hansen and Wahlberg, 2005). Under assumptions discussed below, the IV estimates provide the local average returns to schooling for the individuals that are affected by the instrument. Hence, the IV estimate may not provide a picture of the average marginal return to schooling for the whole population, but rather coincide with the average return to schooling for the sub-group that is affected by the exogenous variation in schooling outcomes (Hansen and Wahlberg, 2005).

The standard IV approach requires two assumptions to be satisfied: i) instrument relevance,

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i.e., Cov(Zi, s|Zj,dc,dm)6= 0 for each i, i6=j, and ii) instrument exogeneity or instrument exclusion, i.e., Cov(Zi,"|dc,dm) = 0, where dm and dc are vectors containing effects that are fixed to each specific municipality and cohort, respectively. The assumption of instrument relevance requires that even after conditioning each instrumental variable and years of schooling on the other instrumental variables, municipality-fixed effects and cohort-fixed effects, each instrument, Zi, must be correlated with the schooling variable. The assumption of instrument exclusion requires that conditional on effects that are fixed to each specific cohort and municipality, the only way in which an instrument, Zi, can affect earnings is through changing the level of schooling. In cases where these assumptions are satisfied, the IV approach provides consistent, yet not unbiased, estimates of the returns to schooling that can be interpreted as the local average treatment effect (LATE).

However, the assumptions above do only apply to a setting with homogeneous returns to schooling. Assuming heterogeneous returns to schooling, an additional assumption is neces- sary in order to interpret the IV estimate as the local average treatment eﬀect. In addition to the standard IV assumptions of i) instrument relevance and ii) instrument exogeneity, in a setting with heterogeneous returns to schooling, the instrument must satisfy the assumption of iii) monotonicity, that for each individual, i, requires a change in the value of the instrument to either leave the treatment unchanged or to change the treatment in the same direction for all individuals. The assumption is violated if, because of a change in the value of the instrument, some individuals respond by getting the treatment while others stop getting it (Fiorini and Stevens, 2014). Either individuals are always-takers, never-takers or compliers, i.e., there are no defiers (Heckman et al., 2006).

In settings with heterogeneous returns to schooling, where the standard IV assumptions, in addition to the assumption of monotonicity, are satisfied, the IV estimate can be interpreted as the local average treatment eﬀect. A common interpretation of such local average treatment eﬀects is that these are estimated returns to schooling for individuals induced to change their level of schooling as a result of a change in the instrument. Such returns to schooling are usually interpreted as estimates of an average return to schooling for the com-

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pliers of the instrument (Heckman et al., 2006).

The compulsory schooling reform implemented in Norway during the 1960s increased the schooling level of those affected. In order for the compulsory schooling reform to satisfy the requirements for a valid instrument, the timing of the reform implementation must be uncorrelated to underlying cohort trends in earnings across municipalities and in other municipality-specific characteristics. Because different municipalities were exposed to the reform at different times, the length of individuals’ compulsory schooling depended on year and municipality of birth, not on any underlying trends in earnings. Because the reform was implemented gradually, the Norwegian schooling system consisted of two systems for over a decade. In municipalities where the reform was implemented, individuals were not dependent on year or municipality of birth (Aakvik et al., 2010). However, because each municipality had to present a reform plan to be approved by a national committee to implement the reform, the timing of the reform was not completely randomized (Brinch and Galloway, 2012).

Nevertheless, previous work has not been able to identify strong correlations between baseline municipality-specific eﬀects and the reform implementation, see, e.g., Bhuller et al. (2017) and Brinch and Galloway (2012). Any correlation between the reform implementation and characteristics specific to municipalities or cohorts is therefore assumed to be of little concern.

Having access to a high school in the childhood municipality and a college or a university in the childhood region at age 16 is likely to induce individuals to acquire additional years of schooling due to, e.g., lower marginal costs of acquiring that additional schooling in terms of travel costs or psychic costs, compared to those that did not have access to the same schools. As the compulsory schooling reform, the additional two instruments are also used conditional on cohort-fixed and municipality-fixed eﬀects. Consequently, a similar assumption regarding the timing of openings, or closings, of high schools and colleges or universities being unrelated to underlying trends in earnings across municipalities must be satisfied. An additional concern relates to the choice of municipality or region of residence being endoge- nous. However, by using access to a high school in the childhood municipality at age 16 and access to a college or a university in the childhood region age 16, i.e., the municipality and

Life-Cycle Earnings and Returns to Education: A Study of Norwegian Females