The Instrumental Variables Method in Practice

Estimating the private return to schooling and the value of human capital externalities by OLS may not always be appropriate. This is because of the strong possibility of correlation between the disturbance u and the schooling variable. As discussed above, this correlation may produce a biased estimator. Because of such bias, it therefore becomes advisable to apply IV methods. When adopting the IV approach, it is important to determine the right instrument for the model. Finding a suitable instrument is not easy. However, social and natural experiments can be useful and many such instruments have been used (see Harmon and Walker, 1995; Duflo, 2001; Plug, 2001; Liu, 2007; Leigh and Ryan, 2008). Alternatively, parental background variables are often chosen (see Brunello and Miniaci, 1999; Callan and Harmon, 1999; Uusitalo, 1999; Trostel et al., 2002; Lemke and Rischall, 2003). But to be useful these instruments must satisfy the IV criteria of being correlated with the schooling variable and correctly excluded from the earnings equation. The following are examples of the variables used as instruments in empirical study: family background (Brunello and Miniaci, 1999; Callan and Harmon, 1999; Uusitalo, 1999; Trostel et al., 2002; Lemke and Rischall, 2003), sibling’s report of the other sibling’s education (Ashenfelter and Krueger, 1994; Bronars and Oettinger, 2006; Miller et al., 1995 and 2006), the month of birth (Plug, 2001; Leigh and Ryan, 2008), government policy in education (Duflo, 2001), and changes in the minimum school leaving ages (compulsory education law) (Harmon and Walker, 1995; Liu, 2007; Leigh and Ryan, 2008).

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Tables 4.1 and 4.2 provide a summary of selected studies on, respectively, the return to education and human capital externalities utilising IV as the methodological approach.

Given the importance of the IV approach to research in this area, additional comment on seven studies (the first four studies are on the private return to schooling and the final three studies cover the human capital externalities) are presented below. The first and the second of these studies, Angrist and Krueger (1991), and Harmon and Walker (1995), utilise institutional features of the education system as instruments in the model. Following this we cover studies that adopt family background information as instrument variables, namely Ashenfelter and Zimmerman (1997), and Lemke and Rischall (2003). The three studies involving the use of the IV method when

quantifying human capital externalities are by Acemoglu and Angrist (2000), Moretti

(2004), and Liu (2006).

Angrist and Krueger (1991) use an individual’s quarter of birth interacted with year of birth or state of birth as an instrument for their schooling variable. In general, the IV estimates of the return to schooling from this study are slightly higher than the corresponding OLS estimates. However, the differences between the OLS and the IV estimates are typically statistically insignificant. This study, therefore, can be argued to show that there is little endogeneity bias in the conventional OLS estimate of the return to schooling.

Harmon and Walker (1995) use a pair of dummy variables that capture changes in the minimum school leaving age in Britain - from 14 to 15 in 1947 and from 15 to 16 in 1973 - as instruments for their schooling variable. The IV estimate (15.25 percent) was reasonably precisely estimated, and was considerably higher than the OLS estimate (6.13 percent). Hence, in contrast to Angrist and Krueger (1991), this study suggests that the possible endogeneity of the schooling variable should be taken seriously.

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Table 4.1: Summary of Selected Empirical Studies on the Return to Education Using IV as the Methodological Approach

No. Author (s) Instrument (s) Control (s) Note (s)

1 Angrist and Krueger (1991) Quarter of birth interacted with year of

birth.

Quadratic in age, race, marital status, and urban residence.

To correct bias in the return to schooling due to omitted ability variable, the authors create a natural experiment where quarter of birth is used as an instrument for education.

2 Harmon and Walker (1995) Indicator for changes in the minimum

school leaving age in 1974 and 1973.

Quadratic in age, year, and region. To address the endogeneity of schooling, this study exploits the

experimental nature of two changes in the minimum school leaving age to provide instruments for education.

3 Miller et al. (1995) The co-twin’s report on educational

attainment.

Gender, marital status, interaction between gender and marital status, race, and quadratic in age.

To deal with an ability bias problem, this study use one twin’s responses on the difference in schooling for the pair in a within- twin earnings function. The key idea behind this strategy is that some of the unobserved differences that bias a cross-sectional comparison of education and earnings are reduced or eliminated within families. To address measurement error problems, the co- twin’s report on other twin’s responses is used as instrument.

4 Ashenfelter and Zimmerman (1997) - Brothers’ education.

- Father’s education.

Age. The omitted variable and measurement error problems were

tackled using one brother’s (father or son) schooling as an instrumental variable for his sibling’s (son or father) schooling.

5 Lemke and Rischall (2003) - Quarter of birth.

- College proximity.

- Parental education (father’s and mother’s education).

Parental income, Armed Forces Qualification Test12 ,

parental education, age, race, living in the South in 1995, and living in Metropolitan Statistical Area in 1995.

Three types of instruments, namely parental education, quarter of birth, and college proximity, were utilised to cope with endogeneity of schooling problem.

6 Aslam et al. (2010) - The distance in metres to nearest

primary school when the individual was of school-going age.

- Square of the distance in metres to nearest primary school when the individual was of school-going age. - Father’s completed education in years. - Mother’s completed education in years. - The score on the Raven test.13

Gender and dummy variable for short-literacy test. This study addresses the endogeneity of schooling and cognitive

skills using two approaches: IV and household fixed-effects. The vector of instruments used to control for the endogeneity of schooling attainment and of cognitive skills includes: parental education (father’s and mother’s completed years of schooling), distance to primary school in metres (when individual was of primary school-going age) and its square, and the individual’s Raven test score.

Source: Author’s compilation.

12

The AFQT is a measure of skill for people under 18.

13

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Another important set of variables to identify the causal effect of schooling in the IV approach comes from family background information, such as father’s education and mother’s education. This information can be included in the estimating equation as a direct control for unobserved ability, or used as an instrument for completed education. Ashenfelter and Zimmerman (1997), Lemke and Rischall (2003), and Aslam et al. (2010) are examples of researchers who employ family background as an instrumental variable.

Ashenfelter and Zimmerman (1997) employ father’s schooling as an instrument in one set of models, and brother’s schooling in another. The use of brother’s schooling as an instrument leads to IV estimates that are 1.5-7.4 percent above the corresponding OLS estimates. When father’s schooling is used as an instrument the IV estimates are 5.2-6.2 percent higher than the OLS estimates. This study therefore shows the importance of considering endogeneity bias via the IV method, and draws attention to family background factors being useful instruments.

Lemke and Rischall (2003) exploit both institutional features of the education system (quarter of birth and college proximity) and family background information (parental education as instruments). When using parental education to instrument the schooling variable and neither parental income nor the Armed Forces Qualification Test (AFQT) are included in the wage equation, the return to education is 13.4 percent, which exceeds the comparable OLS estimate of 9.4 percent. When the AFQT and parental income are introduced into the wage equation, instrumenting with parental education actually leads to lower IV estimates than those obtained using OLS. Nevertheless, the authors argue that parental education is a valid and useful instrument. Different from previous results, when adopting quarter of birth as an instrument for schooling, the Basmann test rejects the validity of all of the quarter of birth instruments. When utilising college proximity as an instrument for the schooling variable, the Basmann test fails to reject the validity of the college proximity instruments, and therefore the IV estimates of the return to schooling were imprecise. The estimated effects of parental income and the AFQT on wages were also statistically insignificant. In sum, when adopting the institutional features of the education system as instruments, the weak correlation between the instruments and years of schooling generates imprecise estimates of the return to schooling. Hence,

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these findings suggest a preference for parental education over institutional factors as instruments for the schooling variable in the wage equation.

Thus, studies that use an IV approach in the analysis of the private return to schooling generally report an advantage to the method. Moreover, the family background information often used as instruments appears to have offered a statistically sound basis for this type of estimation. The following passages will review variables used to instrument the aggregate human capital that is essential to the empirical assessment of human capital externalities.

Acemoglu and Angrist (2000) measure the aggregate human capital by the average level of schooling in the state. To allow for the possibility that education levels may be endogenous they instrument for the average level of schooling in each state using dummies for compulsory schooling laws in the US and the differences in child labour laws across states. In comparison, when the private rate of return was considered, the instruments for the individual’s level of schooling were quarter of birth dummy variables. Acemoglu and Angrist (2000) show that inconsistent estimates of the private return to education will lead to inconsistent estimates of the externality, because individual and aggregate schooling are correlated. Under the IV approach, the estimates revealed that a year increase in the average level of schooling led to only a 1-3 percent increase in wages, and this was not significantly different from zero. In contrast, the OLS estimates suggested that externalities were much more important, with the impact of an extra year of average schooling being around 7 percent. This finding can be explained in part by the fact that these two instruments - compulsory attendance laws and child labour laws - mainly affect the left-hand side of the educational distribution, mostly in middle school or high school, and could be weakly correlated with the regional fraction of college graduates (Morreti, 2006; Canton, 2009). This study therefore shows that it is necessary to find the instruments that affect the entire education distribution.

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Table 4.2: Summary of Selected Empirical Studies on Human Capital Externalities Using IV as the Methodological Approach

No. Author (s) Instrument (s) Control (s) Note (s)

1 Acemoglu and Angrist (2000)

- Quarter of birth dummy variables. - Percentage of child labour. - Percentage of compulsory attendance.

Age, individual education, state average education, state of residence.

- Quarters of birth dummy variables are used to instrument the individual’s schooling.

- To solve the problem of omitted variables bias from correlation between average schooling and other state year effects embodied in the error component the authors construct instruments using compulsory schooling laws effective in individuals’ states of birth at the time they were 14. - Dummies of compulsory attendance laws and child labour laws are used to

instrument individual as well average schooling variables. 2 Moretti (2004) - The city demographic structure (age

structure).

- The presence of a land-grant college in a city.

Sex, race, individual education and experience as well as college share at the level of 2001 Metropolitan Statistical Area.

Age structure used as instrument for first differences model and the presence of a land grant college used as an instrument for cross-sectional estimations.

3 Liu (2007) - Compulsory Education Law. - The share of college graduates in the

city population in 1990.

Gender, city average education in years, city-sector average education in years, the fraction of college-educated workers, the fraction of workers employed in the business sector, the fraction of workers employed in the government sector, the fraction of workers employed in the industry sector, the fraction of workers employed in the commerce sector, the fraction of workers employed in the state sector, the fraction of workers employed in the collective sector, including the town and village enterprises, the fraction of workers employed in the foreign-investment sector, including joint ventures and wholly foreign-owned enterprises.

The problem of omitted variable bias is tackled in the following ways: (i) the author introduces proxy variables for unobserved factors into the earnings regression, (ii) the lagged city average education or lagged dependent variable is employed to account for unobserved city-specific factors, (iii) assuming no structural change in the earnings equation between 1988 and 1995, the author ran city-fixed-effects regressions to purge city-specific and time-invariant unobservable, (iv) this study estimates the external returns to education by implementing city- fixed-effects regressions using cross-sectional data from 1995 to restrict externalities to operate at the city-sector level.

4 Muravyev (2008) - City college share in 1994. - City college share in 1989. - Number of higher education

establishments in a city at the end of the Soviet time.

Index of the cost of living, dummy for the cities whose economies are centred on the oil extraction industry, dummy variable for cities which are administrative centres of the regions, city size (inhabitants), and regional dummies, a dummy variable for the presence of wage arrears in either of the two jobs, work experience, work experience squared, and gender.

- To solve identification problems arising from the endogeneity of average education, the study exploits a natural experiment.

- For robustness checks the authors use four important characteristics of cities: location, status (an administrative centre of a region or not), prevalence of the oil extraction industry in the city economy and city size.

5 García-Fontes and Hidalgo (2009)

Demographic variables. Schooling level, gender, works in agriculture dummy, marital status, share of workers by schooling level, fraction of workers with secondary or college education, total workers, physical capital stock and ICT capital stock, and population proportions for each age group.

- The authors instrument the change in regional schooling levels over the 1981- 1991 period by 1981 demographic structure and the change in regional schooling levels over the 1991-2001 period by 1991 demographic structure. - For robustness analysis, this study employs total regional physical capital and

ICT capital.

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Moretti (2004) examines the spillover effects from a college education among different education groups. This externality was measured by comparing wages for otherwise similar individuals who work in cities with different shares of college graduates in the labour force. The existence of unobservable characteristics of individuals and cities that may raise wages and be correlated with college share was a major issue in this comparison. The unobservable city-specific demand shocks were handled by using two instrumental variables, namely: the (lagged) city demographic

structure and the presence of a land-grant college. In this study, human capital

externalities are identified using variation in the number of college graduates. Different from Acemoglu and Angrist (2000), Moretti (2004) does find significant human capital externalities for US cities. This shows that adopting instruments that affect the upper part of the education distribution is important for identifying external returns to schooling.

Liu (2006) estimates the external returns to education in Chinese cities. Two instruments are used in the IV section of this analysis: the first instrument relates to a compulsory education law (CEL), whereas the second one is a measure of city- specific human capital from a past period. The OLS estimates indicate that a one-year increase in city average education could raise individual earnings from 4.9 percent to 6.7 percent. The 2SLS estimates of the external returns range from 11 percent to 13 percent. This study provides two important conclusions: firstly, the human capital’s contribution through externalities is comparable to its direct contribution. Secondly, private returns as well as external returns to education respond to institutional changes. Hence, this study illustrates the necessity of considering endogeneity bias using an IV-2SLS approach, and the importance of adopting CEL and a measure of city specific human capital as instruments.

4.5 Conclusion

This chapter has outlined the research methodology that will be utilised in the analysis that follows. Two methods of regression analysis have been discussed: OLS and the IV model. The IV results from the studies discussed suggest that it is particularly important to consider family background in any instrumental variables analysis of the return to education. In the next chapter, attention is given to the empirical study of the economic returns to schooling in the context of Indonesia.

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