Bartolucci, Francesco and Grilli, Leonardo and Pieroni, Luca
(2012):
*Estimating dynamic causal effects with unobserved confounders: a latent class version of the inverse probability weighted estimator.*

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## Abstract

We consider estimation of the causal effect of a sequential binary treatment (typically corresponding to a policy or a subsidy in the economic context) on a final outcome, when the treatment assignment at a given occasion depends on the sequence of previous assignments as well as on time-varying confounders. In this case, a popular modeling strategy is represented by Marginal Structural Models; within this approach, the causal effect of the treatment is estimated by the Inverse Probability Weighting (IPW) estimator, which is consistent provided that all the confounders are observed (sequential ignorability). To alleviate this serious limitation, we propose a new estimator, called Latent Class Inverse Probability Weighting (LC-IPW), which is based on two steps: first, a finite mixture model is fitted in order to compute latent-class-specific weights; then, these weights are used to fit the Marginal Structural Model of interest. A simulation study shows that the LC-IPW estimator outperforms the IPW estimator for all the considered configurations, even in cases of no unobserved confounding. The proposed approach is applied to the estimation of the causal effect of wage subsidies on employment, using a dataset of Finnish firms observed for eight years. The LC-IPW estimate confirms the existence of a positive effect, but its magnitude is nearly halved with respect to the IPW estimate, pointing out the substantial role of unobserved confounding in this setting.

Item Type: | MPRA Paper |
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Original Title: | Estimating dynamic causal effects with unobserved confounders: a latent class version of the inverse probability weighted estimator |

Language: | English |

Keywords: | Causal inference, Longitudinal design, Mixture model, Potential outcomes, Sequential treatment |

Subjects: | C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C52 - Model Evaluation, Validation, and Selection H - Public Economics > H2 - Taxation, Subsidies, and Revenue > H25 - Business Taxes and Subsidies C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C33 - Panel Data Models ; Spatio-temporal Models |

Item ID: | 43430 |

Depositing User: | Luca Pieroni |

Date Deposited: | 26 Dec 2012 14:55 |

Last Modified: | 27 Sep 2019 16:28 |

References: | Achy-Brou, A. C., Frangakis, C. E., and Griswold, M.(2010). Estimating treatment effects of longitudinal designs using regression models on propensity scores. Biometrics, 66. Bartolucci, F., Farcomeni, A., and Pennoni, F. (2010). An overview of latent Markov models for longitudinal categorical data. Technical report available at http://arxiv.org/abs/1003.2804. Biernacki, C., Celeux, G., and Govaert, G. (1999). An improvement of the NEC criterion for assessing the number of clusters in a mixture model. Non-Linear Analysis, 20:267-272. Celeux, G. and Soromenho, G. (1996). An entropy criterion for assessing the number of clusters in a mixture model. Journal of Classication, 13(2):195-212. Cole, S. R. and Hernan, M. A. (2008). Inverse probability weights for marginal structural models. American Journal of Epidemiology, 168(6):656-664. Dahlberg, M. and Forslund, A. (2005). Direct displacement eeffcts of labour market programmes. Scandinavian Journal of Economics, 107(3):475-494. Efron, B. and Tibshirani, R. (1994). An Introduction to the Bootstrap. Chapman & Hall/CRC, London. Gill, R. and Robins, J. (2001). Causal inference for complex longitudinal data: the continuous case. Annals of Statistics, 29:1785-1811. Gruun, B. and Leisch, F. (2008). Flexmix version 2: Finite mixtures with concomitant variables and varying and constant parameters. Journal of Statistical Software, 28:1-35. Hamalainen, K. and Ollikainen, V. (2004). Differential effects of active labour market programmes in the early stages of young people's unemployment. Research Reports 115, Government Institute for Economic Research Finland (VATT). Hujer, R., Caliendo, M., and Radic, D. (2002). Estimating the effects of wage subsidies on the labour demand in West-Germany using the IAB establishment panel. Technical report. Kangasharju, A. (2007). Do wage subsidies increase employment in subsidized firms? Economica, 74(293):51-67. Lechner, M. (2009). Sequential causal models for the evaluation of labor market programs. Journal of Business & Economic Statistics, 27:71-83. Lechner, M. and Miquel, R. (2010). Identication of the effects of dynamic treatments by sequential conditional independence assumptions. Empirical Economics, 39:111-137. Lefebvre, G., Delaney, J. A. C., and Platt, R. W. (2008). Impact of mis-specication of the treatment model on estimates from a marginal structural model. Statistics in Medicine, 27:3629-3642. Lefebvre, G. and Gustafson, P. (2010). Impact of outcome model miss-pecification on regression and doubly-robust inverse probability weighting to estimate causal effect. The International Journal of Biostatistics, 6(2):1-24. McLachlan, G. J. and Peel, D. (2000). Finite Mixture Models. Wiley, New York. Robins, J. (1999). Marginal structural models versus structural nested models as tools for causal inference. In Halloran E., B. D., editor, Epidemiology: The Environment and Clinical Trials, pages 95-134. Springer, New York. Robins, J. M., Hernan, M. A., and Brumback, B. (2000). Marginal structural models and causal inference. Epidemiology, 11:550-560. Rosenbaum, P. R. (1987). Model-based direct adjustment. Journal of the American Statistical Association, 82:387-394. Rotnitzky, A., Li, L., and Li, X. (2010). A note on overadjustment in inverse probability weighted estimation. Biometrika, 97:997-1001. Rubin, D. (1974). Estimating causal effects of treatments in randomized and nonrandomized studies. Journal of Educational Psychology, 66. Rubin, D. B. (2005). Causal inference using potential outcomes: design, modeling, decisions. Journal of the American Statistical Association, 100:322-331. Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics, 6:461-464. van der Wal, W. and Geskus, R. (2011). ipw: An r package for inverse probability weighting. Journal of Statistical Software, 43:1-23. |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/43430 |