# Estimating Causal Effects When the Treatment Affects All Subjects Simultaneously: An Application

## Abstract

**:**

## 1. Introduction

## 2. Data

## 3. Model

#### 3.1. Prior Distributions and Elicitation

#### 3.2. Inference

## 4. Estimation

## 5. Identification and Validity

**Assumption**

**1.**

**Assumption**

**2.**

## 6. Main Results

#### Robustness Checks

## 7. Discussion

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Athey, S. The Impact of Machine Learning on Economics. NBER Working Paper. 2018. Available online: http://www.nber.org/chapters/c14009.pdf (accessed on 5 May 2021).
- Sendhil, M.; Spiess, J. Machine Learning: An Applied Econometric Approach. J. Econ. Perspect.
**2017**, 31, 87–106. [Google Scholar] - Einav, L.; Levin, J.D. The Data Revolution and Economic Analysis; NBER Working Paper; National Bureau of Economic Research: Cambridge, MA, USA, 2013; p. 19035. [Google Scholar]
- Einav, L.; Levin, J.D. Economics in the Age of Big Data. Science
**2014**, 346, 1243089. [Google Scholar] - Varian, H.R. Big Data: New Tricks for Econometrics. J. Econ. Perspect.
**2014**, 28, 3–28. [Google Scholar] - Kleinberg, J.; Ludwig, J.; Mullainathan, S.; Obermeyer, Z. Prediction Policy Problems. Am. Econ. Rev. Pap. Proc.
**2015**, 105, 491–495. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Chalfin, A.; Danieli, O.; Hillis, A.; Jelveh, Z.; Luca, M.; Ludwig, J.; Mullainathan, S. Productivity and Selection of Human Capital with Machine Learning. Am. Econ. Rev. Pap. Proc.
**2016**, 106, 124–127. [Google Scholar] - Athey, S.; Imbens, G. The State of Applied Econometrics—Causality and Policy Evaluation. 2016. Available online: https://arxiv.org/pdf/1607.00699.pdf (accessed on 5 May 2021).
- Varian, H.R. Causal Inference in Economics and Marketing. PNAS
**2016**, 113, 7310–7315. [Google Scholar] - Hegerl, G.; Zwiers, F. Use of models in detection and attribution of climate change. WIREs Clim. Chang.
**2011**, 2, 570–591. [Google Scholar] - Castle, J.L.; Hendry, D.F. Climate Econometrics: An Overview. Found. Trends Econom.
**2020**, 10, 145–322. [Google Scholar] [CrossRef] - Egan, P.J.; Mullin, M. Climate Change: US Public Opinion. Annu. Rev. Political Sci.
**2017**, 20, 209–227. [Google Scholar] - Brodersen, K.H.; Galluser, F.; Koehler, J.; Remy, N.; Scott, S.L. Inferring Causal Impact Using Bayesian Structural Time-Series Models. Annu. Appl. Stat.
**2015**, 9, 247–274. [Google Scholar] - Athey, S.; Imbens, G. Machine Leaning Methods in Economics and Econometrics. Am. Econ. Rev. Pap. Proc.
**2015**, 105, 476–480. [Google Scholar] - Stern, D.I.; Kaufmann, R.K. Anthropogenic and natural causes of climate change. Clim. Chang.
**2014**, 122, 257–269. [Google Scholar] - Ritchie, H.; Roser, M. CO2 and other Greenhouse Gas Emissions. 2019. Available online: https://ourworldindata.org/co2-and-other-greenhouse-gas-emissions (accessed on 5 May 2021).
- Stern, D.I. An atmosphere—Ocean multicointegration model of global climate change. Comput. Stat. Data Anal.
**2006**, 51, 1330–1346. [Google Scholar] - CausalImpact 1.2.1, Brodersen et al., Annals of Applied Statistics. 2015. Available online: http://google.github.io/CausalImpact/ (accessed on 5 May 2021).
- Abadie, A.; Diamond, A.; Hainmueller, J. Synthetic control methods for comparative case studies: Estimating the effect of California’s tobacco control program. J. Am. Stat. Assoc.
**2010**, 105, 493–505. [Google Scholar] - Toda, H.Y.; Yamamoto, T. Statistical inference in vector autoregressions with possibly integrated processes. J. Econom.
**1995**, 66, 225–250. [Google Scholar] - Hendry, D.F.; Pretis, F. Anthropogenic influences on atmospheric CO
_{2}. In Handbook of Energy and Climate Change; Edward Elgar Publishing: Cheltenham, UK, 2013; Chapter 2; pp. 287–326. [Google Scholar]

**Figure 1.**Yearly records of atmospheric concentration of CO${}_{2}$ (bold) and temperature anomalies.

**Figure 3.**Yearly records of anthropogenic radiative forcing for carbon dioxide (RFCO2), methane (RFCH4), dinitrogen oxide (RFN20), CFC11 (RFCFC11), CFC12 (RFCFC12), sulfur emissions (RFSOX), and black and organic carbon (RFBC).

Average | |
---|---|

Actual | 0.15 |

Prediction (s.d.) | −0.045 (0.073) |

95% CI | [−0.18, 0.1] |

Absolute effect (s.d.) | 0.2 (0.073) |

95% CI | [0.053, 0.34] |

Posterior tail-area probability p: 0.007 | |

Posterior probability of a causal effect: 99.3% |

**Table 2.**Inclusion probability, estimated average coefficient and standard deviation of each control variable included in the model.

Inclusion Probability | Average Coefficient (sd) | |
---|---|---|

Ocean Heat Content | 0.049 | 0.001 (0.022) |

RFBC | 0.221 | −0.113 (0.273) |

RFSOX | 0.704 | 0.579 (0.465) |

RFGHG | 0.961 | 0.940 (0.399) |

RFSOLAR | 0.976 | 0.425 (0.123) |

RFVOL | 0.378 | 0.072 (0.101) |

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Binelli, C.
Estimating Causal Effects When the Treatment Affects All Subjects Simultaneously: An Application. *Big Data Cogn. Comput.* **2021**, *5*, 22.
https://doi.org/10.3390/bdcc5020022

**AMA Style**

Binelli C.
Estimating Causal Effects When the Treatment Affects All Subjects Simultaneously: An Application. *Big Data and Cognitive Computing*. 2021; 5(2):22.
https://doi.org/10.3390/bdcc5020022

**Chicago/Turabian Style**

Binelli, Chiara.
2021. "Estimating Causal Effects When the Treatment Affects All Subjects Simultaneously: An Application" *Big Data and Cognitive Computing* 5, no. 2: 22.
https://doi.org/10.3390/bdcc5020022