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FUNCTIONAL INSTRUMENTAL VARIABLE REGRESSION WITH AN APPLICATION TO ESTIMATING THE IMPACT OF IMMIGRATION ON NATIVE WAGES

Published online by Cambridge University Press:  07 November 2024

Dakyung Seong Open the ORCID record for Dakyung Seong [Opens in a new window]  and
Won-Ki Seo Open the ORCID record for Won-Ki Seo [Opens in a new window]
Dakyung Seong*
Affiliation:
University of Sydney
Won-Ki Seo
Affiliation:
University of Sydney
*
Address correspondence to Dakyung Seong, School of Economics, University of Sydney, Camperdown, NSW, Australia, e-mail: [email protected].
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Abstract

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Functional linear regression has gained popularity as a statistical tool for studying the relationship between function-valued variables. However, in practice, it is hard to expect that the explanatory variables of interest are strictly exogenous, due to, for example, the presence of omitted variables and measurement error. This issue of endogeneity remains insufficiently explored, in spite of its empirical importance. To fill this gap, this article proposes new consistent FPCA-based instrumental variable estimators and develops their asymptotic properties in detail. Simulation experiments under a wide range of settings show that the proposed estimators perform considerably well. We apply our methodology to estimate the impact of immigration on native labor market outcomes in the US.

Type
ARTICLES
Information
Econometric Theory , First View , pp. 1 - 36
Copyright
© The Author(s), 2024. Published by Cambridge University Press

Footnotes

The authors express deep appreciation to the editor, the co-editor, and the three anonymous referees for their invaluable and insightful suggestions. We are also thankful to Morten Ø. Nielsen and seminar participants at the University of Sydney, University of Queensland, and SETA 2022 for their helpful comments. Data and R code to replicate the empirical results in Table 3 are available on the authors’ websites.

References

REFERENCES

Autor, D. H., & Dorn, D. (2013). The growth of low-skill service jobs and the polarization of the US labor market. American Economic Review , 103(5), 1553–1597.CrossRefGoogle Scholar
Babii, A. (2022). High-dimensional mixed-frequency IV regression. Journal of Business & Economic Statistics , 40, 1470–1483.CrossRefGoogle Scholar
Bekker, P. A. (1994). Alternative approximations to the distributions of instrumental variable estimators. Econometrica , 62(3), 657–681.CrossRefGoogle Scholar
Benatia, D., Carrasco, M., & Florens, J.-P. (2017). Functional linear regression with functional response. Journal of Econometrics , 201(2), 269–291.CrossRefGoogle Scholar
Borjas, G. J. (1987). Self-selection and the earnings of immigrants. American Economic Review , 77(4), 531–553.Google Scholar
Borjas, G. J., Grogger, J., & Hanson, G. H. (2011). Substitution between immigrants, natives, and skill groups. Working Paper 17461, National Bureau of Economic Research.CrossRefGoogle Scholar
Bosq, D. (2000). Linear processes in function spaces . Springer.CrossRefGoogle Scholar
Card, D. (2009). Immigration and inequality. American Economic Review , 99(2), 1–21.CrossRefGoogle Scholar
Carrasco, M. (2012). A regularization approach to the many instruments problem. Journal of Econometrics , 170(2), 383–398.Google Scholar
Carrasco, M., Florens, J.-P., & Renault, E. (2007). Linear inverse problems in structural econometrics estimation based on spectral decomposition and regularization. Handbook of Econometrics , 6, 5633–5751.CrossRefGoogle Scholar
Chao, J. C., & Swanson, N. R. (2005). Consistent estimation with a large number of weak instruments. Econometrica , 73(5), 1673–1692.CrossRefGoogle Scholar
Chen, C., Guo, S., & Qiao, X. (2022). Functional linear regression: Dependence and error contamination. Journal of Business & Economic Statistics , 40(1), 444–457.CrossRefGoogle Scholar
Conway, J. B. (2007). A course in functional analysis . Springer.CrossRefGoogle Scholar
Crambes, C., & Mas, A. (2013). Asymptotics of prediction in functional linear regression with functional outputs. Bernoulli , 19(5B), 2627–2651.CrossRefGoogle Scholar
Delicado, P. (2011). Dimensionality reduction when data are density functions. Computational Statistics & Data Analysis , 55(1), 401–420.CrossRefGoogle Scholar
Dustmann, C., Frattini, T., & Preston, I. P. (2013). The effect of immigration along the distribution of wages. The Review of Economic Studies , 80(1), 145–173.CrossRefGoogle Scholar
Egozcue, J. J., Díaz-Barrero, J. L., & Pawlowsky-Glahn, V. (2006). Hilbert space of probability density functions based on Aitchison geometry. Acta Mathematica Sinica , 22(4), 1175–1182.CrossRefGoogle Scholar
Flood, S., King, M., Rodgers, R., Ruggles, S., & Warren, J. R. (2020). Integrated public use microdata series, current population survey: Version 8.0 [dataset]. Minneapolis, MN: IPUMS. https://doi.org/10.18128/D030.V8.0.Google Scholar
Florens, J.-P., & Van Bellegem, S. (2015). Instrumental variable estimation in functional linear models. Journal of Econometrics , 186(2), 465–476.CrossRefGoogle Scholar
Glitz, A. (2012). The labor market impact of immigration: A quasi-experiment exploiting immigrant location rules in Germany. Journal of Labor Economics , 30(1), 175–213.CrossRefGoogle Scholar
Hall, P., & Horowitz, J. L. (2007). Methodology and convergence rates for functional linear regression. Annals of Statistics , 35(1), 70–91.CrossRefGoogle Scholar
Hausman, J. A. (1983). Specification and estimation of simultaneous equation models. Handbook of Econometrics , 1, 391–448.CrossRefGoogle Scholar
Horváth, L., & Kokoszka, P. (2012). Inference for functional data with applications . Springer.CrossRefGoogle Scholar
Hron, K., Menafoglio, A., Templ, M., Hrůzová, K., & Filzmoser, P. (2016). Simplicial principal component analysis for density functions in Bayes spaces. Computational Statistics & Data Analysis , 94, 330–350.CrossRefGoogle Scholar
Hu, B., & Park, J. Y. (2016). Econometric analysis of functional dynamics in the presence of persistence . Indiana University.Google Scholar
Imaizumi, M., & Kato, K. (2018). PCA-based estimation for functional linear regression with functional responses. Journal of Multivariate Analysis , 163, 15–36.CrossRefGoogle Scholar
Jaimez, R. G., & Bonnet, M. J. V. (1987). On the Karhunen-Loeve expansion for transformed processes. Trabajos de Estadistica , 2, 81–90.CrossRefGoogle Scholar
Kokoszka, P., Miao, H., Petersen, A., & Shang, H. L. (2019). Forecasting of density functions with an application to cross-sectional and intraday returns. International Journal of Forecasting , 35(4), 1304–1317.CrossRefGoogle Scholar
Llull, J. (2018). Immigration, wages, and education: A labour market equilibrium structural model. The Review of Economic Studies , 85(3), 1852–1896.CrossRefGoogle Scholar
Loader, C. R. (1996). Local likelihood density estimation. Annals of Statistics , 24(4), 1602–1618.CrossRefGoogle Scholar
Mas, A. (2007). Weak convergence in the functional autoregressive model. Journal of Multivariate Analysis , 98(6), 1231–1261.CrossRefGoogle Scholar
Newey, W. K., & Windmeijer, F. (2009). Generalized method of moments with many weak moment conditions. Econometrica , 77(3), 687–719.Google Scholar
Nielsen, M. Ø., Seo, W.-K., & Seong, D. (2023). Inference on the dimension of the nonstationary subspace in functional time series. Econometric Theory , 39(3), 443–480.CrossRefGoogle Scholar
Ottaviano, G. I. P., & Peri, G. (2012). Rethinking the effect of immigration on wages. Journal of the European Economic Association , 10(1), 152–197.CrossRefGoogle Scholar
Park, J. Y., & Qian, J. (2012). Functional regression of continuous state distributions. Journal of Econometrics , 167(2), 397–412.CrossRefGoogle Scholar
Peri, G., & Sparber, C. (2009). Task specialization, immigration, and wages. American Economic Journal: Applied Economics , 1(3), 135–169.Google Scholar
Petersen, A., & Müller, H.-G. (2016). Functional data analysis for density functions by transformation to a Hilbert space. Annals of Statistics , 44(1), 183–218.CrossRefGoogle Scholar
Ramsay, J. O., & Silverman, B. W. (2005). Functional data analysis . Springer.CrossRefGoogle Scholar
Seo, W.-K. (2024). Functional principal component analysis for cointegrated functional time series. Journal of Time Series Analysis , 45(2), 320–330.CrossRefGoogle Scholar
Seo, W.-K., & Beare, B. K. (2019). Cointegrated linear processes in Bayes Hilbert space. Statistics & Probability Letters , 147, 90–95.CrossRefGoogle Scholar
Shang, H. L. (2014). A survey of functional principal component analysis. AStA Advances in Statistical Analysis , 98(2), 121–142.Google Scholar
Sharpe, J., & Bollinger, C. R. (2020). Who competes with whom? Using occupation characteristics to estimate the impact of immigration on native wages. Labour Economics , 66, 101902.CrossRefGoogle Scholar
Silverman, B. W. (1998). Density estimation for statistics and data analysis . Routledge.Google Scholar
Staudenmayer, J., & Buonaccorsi, J. P. (2005). Measurement error in linear autoregressive models. Journal of the American Statistical Association , 100(471), 841–852.CrossRefGoogle Scholar
Sun, X., Du, P., Wang, X., & Ma, P. (2018). Optimal penalized function-on-function regression under a reproducing kernel Hilbert space framework. Journal of the American Statistical Association , 113(524), 1601–1611.CrossRefGoogle Scholar
Walker, A. M. (1960). Some consequences of superimposed error in time series analysis. Biometrika , 47(1/2), 33–43.CrossRefGoogle Scholar
Yao, F., Müller, H.-G., & Wang, J.-L. (2005). Functional linear regression analysis for longitudinal data. Annals of Statistics , 33(6), 2873–2903.CrossRefGoogle Scholar
Zhang, C., Kokoszka, P., & Petersen, A. (2021). Wasserstein autoregressive models for density time series. Journal of Time Series Analysis , 43(1), 30–52.CrossRefGoogle Scholar
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