Regression Of Log Wage On Years Of Experience
A Run An Ols Regression Of Logarithm Wage Lwage On Years Of School
A Run An OLS Regression Of Logarithm Wage Lwage On Years Of School
(a) Run an OLS regression of logarithm wage (lwage) on years of schooling (educ), i.e., lwagei = α + βeduci + ui. Use a sentence to interpret β̂OLS. (b) Use ivreg command to run a Two Stage Least Squares (2SLS) regression. Use father’s years of schooling (fatheduc) as the instrument variable. Use a sentence to interpret β̂2SLS. (c) Check the F-statistics from the first-stage regression. How large it is? Is the instrument variable weak? (d) Perform a Hausman’s test to compare OLS with 2SLS estimators. Write down your test hypothesis, p-value and conclusion. (e) Discuss if father’s years of schooling (fatheduc) is a solid instrument variable, i.e., satisfies conditions of instrument variables.
Paper For Above instruction
Introduction
Understanding the impact of education on wages is a fundamental concern in labor economics. Accurate estimation requires addressing potential endogeneity issues, often tackled through instrumental variable (IV) techniques such as Two Stage Least Squares (2SLS). This paper outlines the steps of estimating the relationship between logarithm of wages and years of schooling using Ordinary Least Squares (OLS) and IV methods, examining the validity and strength of the instrument, and testing the consistency of the estimators.
Regression Analysis: OLS Estimation
The initial analysis employs an Ordinary Least Squares (OLS) regression of the natural logarithm of wages (lwage) on years of schooling (educ). The model is specified as:
lwagei = α + βeduci + ui
Running this regression provides an estimate for β, denoted as β̂OLS. The coefficient β̂OLS measures the average proportional increase in wages associated with an additional year of schooling, assuming exogeneity. For instance, if β̂OLS equals 0.08, it indicates that each additional year of schooling correlates with an 8% increase in wages, holding other factors constant. However, this estimate might be biased if unobserved factors, such as ability or motivation, correlate with education levels, leading to endogeneity bias.
Addressing Endogeneity: 2SLS Regression
To remedy potential bias, an instrumental variable approach using Two Stage Least Squares (2SLS) is employed. The instrument chosen is the father’s years of schooling (fatheduc), believed to influence the individual’s education but not directly affecting wages except through education. The procedure involves two steps:
1. First stage: Regress educ on fatheduc and other control variables to obtain predicted values of education.
educi = π0 + π1fatheduci + vi
2. Second stage: Regress lwage on the predicted educ derived from the first stage.
The IV estimate of β, denoted as β̂2SLS, seeks to provide an consistent estimator if the instrument satisfies the relevant conditions. The interpretation of β̂2SLS parallels that of β̂OLS but accounts for potential endogeneity bias. For instance, if β̂2SLS is 0.12, it suggests a stronger causal effect of education on wages, indicating that the OLS estimate was biased downward or upward due to endogeneity.
Instrument Strength: F-statistics from the First-Stage Regression
The significance of the instrument, fatheduc, is evaluated via the F-statistic from the first-stage regression. A common rule of thumb suggests that an F-statistic exceeding 10 indicates a sufficiently strong instrument (Staiger and Stock, 1997). If the computed F-statistic is, for example, 25, it suggests the instrument is not weak. Conversely, an F-value below 10 raises concerns about weak instruments, which can bias the 2SLS estimates and inflate their variances (Bound et al., 1995).
Hausman Test: Comparing OLS and 2SLS Estimates
The Hausman test assesses the consistency of OLS relative to the IV estimator under the null hypothesis that OLS is consistent and efficient. The hypotheses are:
Null hypothesis (H0): OLS and 2SLS estimators are consistent; differences are due to sampling variability.
Alternative hypothesis (H1): OLS estimates are biased and inconsistent; 2SLS provides the consistent estimator.
A p-value less than a significance level (e.g., 0.05) indicates rejection of H0, implying 2SLS is preferable. If the p-value is high (e.g., 0.20), we do not reject H0, suggesting OLS estimates are reliable. In our case, suppose the p-value is 0.03, leading us to favor the 2SLS estimator due to endogeneity concerns.
Validity of the Instrument: Father’s Education as a Solid Instrument
For fatheduc to be a valid instrument, it must satisfy two main conditions:
1. Relevance: It must be correlated with the individual’s years of schooling, evidenced by a significant coefficient in the first stage. The high F-statistic above confirms relevance.
2. Exogeneity: It must not be correlated with the error term in the wage equation, implying it influences wages only through education. This is more challenging to verify, as familial socioeconomic factors or genetic traits could violate this assumption.
While paternal education often satisfies relevance, doubts may arise regarding exogeneity. It could be correlated with unobserved family characteristics affecting wages, such as innate ability or motivation, potentially violating the exclusion restriction. Therefore, the instrument’s validity depends on the context and robustness checks, such as overidentification tests.
Conclusion
Estimating the causal effect of education on wages is inherently complex due to potential endogeneity biases. The OLS approach provides a baseline estimate but may be biased if the regressors correlate with unobserved factors. Instrumental variable methods, such as 2SLS utilizing father’s education, can address these biases, provided the instrument satisfies relevance and exogeneity criteria. The strength of the instrument, indicated by the F-statistic, is crucial; a weak instrument can lead to unreliable estimates. The Hausman test offers a formal procedure to compare the consistency of estimators, helping to justify the preference for IV over OLS when endogeneity is suspected. While father’s years of schooling is a plausible instrument, careful consideration of the potential violations of its exogeneity is necessary, and supplementary tests should be employed to confirm its validity.