---
title: "Instrumental variables (two-stage least squares)"
description: "Instrumental variables (two-stage least squares) was mentioned in 115 papers in the last 30 days (2026-09-27 to 2026-10-26), ranking #5 of the 104 equations and models mentioned."
url: https://scholar4ai.com/equations/instrumental-variables-two-stage-least-squares
markdown_url: https://scholar4ai.com/equations/instrumental-variables-two-stage-least-squares.md
license: CC BY-NC 4.0 (https://creativecommons.org/licenses/by-nc/4.0/)
data_url: https://scholar4ai.com/data/rankings.json
updated: 2026-10-26T12:13:05+09:00
window: 2026-09-27 to 2026-10-26
source: OpenAlex (CC0)
---

# Instrumental variables (two-stage least squares)

$$
\hat\beta_{\mathrm{2SLS}} = (X^\top P_Z X)^{-1} X^\top P_Z\, y,\quad P_Z = Z (Z^\top Z)^{-1} Z^\top
$$

Uses instruments Z that move the regressors but not the error term to estimate causal effects.

- area: Causal inference
- 12 papers in the last 7 days
- Names searched for: two-stage least squares, instrumental variable, 2SLS, IV regression, IV estimation, IV estimator, IV approach

Back to the ranking: https://scholar4ai.com/rankings/equations.md

## Key findings

- Instrumental variables (two-stage least squares) was mentioned in 115 papers in the last 30 days (2026-09-27 to 2026-10-26), ranking #5 of the 104 equations and models mentioned.
- By journal category: Economics (50), Finance (38), Management (18), Accounting (6), Operations Research (2) and AI (1).
- Most of them appeared in International Review of Economics & Finance (23), The Annals of Regional Science (5) and Economic Analysis and Policy (5).
- Often mentioned together with Ordinary least squares (OLS) (37), Propensity score matching (23) and Two-way fixed-effects panel regression (21).
- Datasets named in the same papers: CSMAR (15), World Development Indicators (World Bank) (10) and Economic Policy Uncertainty index (8).

*Papers mentioning Instrumental variables (two-stage least squares), newest first. Newest 50 of 115 papers; all of them are in /data/papers.json.*

| Date | Title | Journal | Authors | Affiliations |
|---|---|---|---|---|
| 2026-10-24 | [Fiscal information and stated willingness to pay taxes: evidence from a survey experiment](https://doi.org/10.1007/s10797-026-10007-3) | [International Tax and Public Finance](https://scholar4ai.com/journals/international-tax-and-public-finance.md) | José María Durán-Cabré, Alejandro Esteller Moré, Riccardo Secomandi | Barcelona School of Economics; Universitat de Barcelona; University of Ferrara |
| 2026-10-23 | [Job insecurity and health: evidence from older European workers](https://doi.org/10.1007/s00181-026-02992-5) | [Empirical Economics](https://scholar4ai.com/journals/empirical-economics.md) | Eduard Suari‐Andreu, Tim Schwartz, Max van Lent et al. | Leiden University; Network for Studies on Pensions, Aging and Retirement; SEO Amsterdam Economics; … |
| 2026-10-23 | [An identification-and dimensionality-robust test for instrumental variables models](https://doi.org/10.1016/j.jeconom.2026.106348) | [Journal of Econometrics](https://scholar4ai.com/journals/journal-of-econometrics.md) | Manu Navjeevan | Texas A&M University |
| 2026-10-23 | [Competition, Digitalization, and Innovation: Empirical Evidence from Developing and Emerging Economies](https://doi.org/10.1007/s10842-026-00487-8) | [Journal of Industry Competition and Trade](https://scholar4ai.com/journals/journal-of-industry-competition-and-trade.md) | Riham Ahmed Ezzat | Cairo University |
| 2026-10-23 | [Social inclusiveness and COVID-19 outcomes: evidence from local districts and provinces in South Korea](https://doi.org/10.1007/s00168-026-01589-1) | [The Annals of Regional Science](https://scholar4ai.com/journals/the-annals-of-regional-science.md) | Kee Hoon Chung, Dong Chul Shim, DaEun Kim et al. | Kyung Hee University; Korea University; Korea University; … |
| 2026-10-23 | [Managerial slack, information environment and stock price crash risk: Evidence from China](https://doi.org/10.1016/j.iref.2026.106011) | [International Review of Economics & Finance](https://scholar4ai.com/journals/international-review-of-economics-finance.md) | Chuyue Wu, Yuyang Ling, Yikai Han | Central University of Finance and Economics |
| 2026-10-22 | [Business networks and the persistence of entrepreneurship: evidence from China](https://doi.org/10.1007/s11187-026-01292-7) | [Small Business Economics](https://scholar4ai.com/journals/small-business-economics.md) | Han Wang, Neil Lee | University of Southampton; London School of Economics and Political Science |
| 2026-10-21 | [“Made in heaven, matched by parents”: Can arranged marriage restrict labour market autonomy and participation of women?](https://doi.org/10.1016/j.worlddev.2026.107589) | [World Development](https://scholar4ai.com/journals/world-development.md) | Sugata Bag, Anirban Kar | University of Delhi; Centre for Development Economics |
| 2026-10-21 | [When bargaining power matters: foreign direct investment and bilateral GDP disparities](https://doi.org/10.1007/s00181-026-02990-7) | [Empirical Economics](https://scholar4ai.com/journals/empirical-economics.md) | Xing Xu, Emin Gahramanov, Qinglai Meng et al. | Shanghai Institute of Technology; American University of Sharjah; Oregon State University; … |
| 2026-10-21 | [Buffering institutional erosion: organizational ties and SME exports under populism](https://doi.org/10.1057/s41267-026-00911-5) | [Journal of International Business Studies](https://scholar4ai.com/journals/journal-of-international-business-studies.md) | Xiaolong Shui, Luyang Chen, Michael; id_orcid 0000-0002-4701-6283 Witt | University of Bristol; Bristol Robotics Laboratory; University of Westminster; … |
| 2026-10-21 | [The economic geography of Churches: housing market effects in Stockholm](https://doi.org/10.1007/s10824-026-09609-w) | [Journal of Cultural Economics](https://scholar4ai.com/journals/journal-of-cultural-economics.md) | Mats Wilhelmsson | KTH Royal Institute of Technology |
| 2026-10-20 | [Adopting AI, inviting risk? An empirical analysis of corporate cybersecurity consequences in IT firms](https://doi.org/10.1007/s12525-026-00939-3) | [Electronic Markets](https://scholar4ai.com/journals/electronic-markets.md) | Wei Xiao, Shan Xu, Jin Li et al. | City University of Hong Kong; Xi'an Jiaotong University; Pusan National University |
| 2026-10-19 | [Firm-level effects of AI attention on wages and productivity: A global comparative study](https://doi.org/10.1016/j.techfore.2026.124913) | [Technological Forecasting and Social Change](https://scholar4ai.com/journals/technological-forecasting-and-social-change.md) | Swapnanil SenGupta | Goethe University Frankfurt; Halle Institute for Economic Research |
| 2026-10-19 | [A reciprocal perspective on internationalization and ESG in EMNEs: The role of digitalization](https://doi.org/10.1016/j.ibusrev.2026.102668) | [International Business Review](https://scholar4ai.com/journals/international-business-review.md) | Chao Zhang, Ioannis Petrakis, Zonghan He et al. |  |
| 2026-10-17 | [The transparency dividend: Effects of corporate environmental management information disclosure on green-tech FDIs in emerging-market cities](https://doi.org/10.1016/j.intman.2026.101433) | [Journal of International Management](https://scholar4ai.com/journals/journal-of-international-management.md) | Zhuoran Liu, Yameng Zhang, Honglan Yu et al. | Xi’an Jiaotong-Liverpool University; University of Sheffield |
| 2026-10-17 | [The shapes of knowledge spillovers: the AC-KS model](https://doi.org/10.1007/s11187-026-01286-5) | [Small Business Economics](https://scholar4ai.com/journals/small-business-economics.md) | Gustavo A. Barboza, Alessandro Braga, Aubin Duchier | Loyola University New Orleans |
| 2026-10-17 | [Does advertising expand the market for hospital services? Evidence from Medicare](https://doi.org/10.1016/j.jhealeco.2026.103191) | [Journal of Health Economics](https://scholar4ai.com/journals/journal-of-health-economics.md) | Abby E. Alpert, Atul Gupta, Michael R. Richards et al. | Cornell University; John Brown University |
| 2026-10-17 | [Heavy inheritance: Genetic pathways from excess weight to biological aging and health in old age](https://doi.org/10.1016/j.ehb.2026.101659) | [Economics & Human Biology](https://scholar4ai.com/journals/economics-human-biology.md) | Vera Sagalova, Holger Strulik B | University of Göttingen |
| 2026-10-17 | [The role of immigrant caregivers in improving the welfare of elders and reducing public health costs](https://doi.org/10.1007/s00148-026-01216-5) | [Journal of Population Economics](https://scholar4ai.com/journals/journal-of-population-economics.md) | Lisa Capretti, Joanna Aleksandra Kopinska, Rama Dasi Mariani et al. | University of Rome Tor Vergata; Sapienza University of Rome; Roma Tre University |
| 2026-10-17 | [Electrifying the factory and beyond: The impact of digital proximity on energy transition](https://doi.org/10.1016/j.eneco.2026.109651) | [Energy Economics](https://scholar4ai.com/journals/energy-economics.md) | Yijia Song, Qinyi Huang, Jiaqi Chen et al. | Southwestern University of Finance and Economics; Sichuan University |
| 2026-10-16 | [The unstable boundary: conditional classification of non-performing loan determinants and its implications for banking regulation](https://doi.org/10.1057/s41261-026-00365-7) | [Journal of Banking Regulation](https://scholar4ai.com/journals/journal-of-banking-regulation.md) | Michael Giannoulakis | University of Greenwich |
| 2026-10-16 | [Agricultural Transformation and the Vulnerability to the Resource Curse in Developing Countries](https://doi.org/10.1057/s41294-026-00292-6) | [Comparative Economic Studies](https://scholar4ai.com/journals/comparative-economic-studies.md) | Sèna Kimm Gnangnon | World Bank |
| 2026-10-15 | [Geographic proximity of investors and firms' ESG performance: Evidence on local retail and institutional investors](https://doi.org/10.1016/j.adiac.2026.100906) | [Advances in Accounting](https://scholar4ai.com/journals/advances-in-accounting.md) | Chengfeng Du, Huiqi Gan, Khondkar Karim | University of Massachusetts Lowell |
| 2026-10-15 | [Gas flaring, agricultural productivity and labor reallocation: Evidence from Nigeria](https://doi.org/10.1016/j.jdeveco.2026.103947) | [Journal of Development Economics](https://scholar4ai.com/journals/journal-of-development-economics.md) | Arinze Nwokolo | Pan-Atlantic University |
| 2026-10-15 | [Understanding the determinants and consequences of share-pledging: a systematic literature review and future research agenda](https://doi.org/10.1007/s11301-026-00643-8) | [Management Review Quarterly](https://scholar4ai.com/journals/management-review-quarterly.md) | Rohith Radhakrishnan, E Geetha, Agnes S. Joseph | Manipal Academy of Higher Education; Narsee Monjee Institute of Management Studies |
| 2026-10-15 | [Investment additionality and job creation: evidence from reforms to regional development funding in Germany](https://doi.org/10.1007/s00168-026-01570-y) | [The Annals of Regional Science](https://scholar4ai.com/journals/the-annals-of-regional-science.md) | Björn Alecke, Timo Mitze | University of Koblenz and Landau; Universität Koblenz |
| 2026-10-15 | [Asymmetric trading costs and ancient Greek cities](https://doi.org/10.1007/s00199-026-01751-y) | [Economic Theory](https://scholar4ai.com/journals/economic-theory.md) | Yuxian Chen, Yannis M. Ioannides, Ferdinand Rauch | Brown University; Tufts University; University of St.Gallen; … |
| 2026-10-15 | [Unfunded mandates, institutional quality, and social progress: an analysis for OECD countries](https://doi.org/10.1007/s00168-026-01581-9) | [The Annals of Regional Science](https://scholar4ai.com/journals/the-annals-of-regional-science.md) | Miriam Hortas‐Rico, David Martínez-Algora | Universidad Autónoma de Madrid |
| 2026-10-14 | [From tests to treatments: How is increased diagnostic testing related to inpatient and outpatient cancer care?](https://doi.org/10.1016/j.ehb.2026.101657) | [Economics & Human Biology](https://scholar4ai.com/journals/economics-human-biology.md) | Ni Gao, Panos Kasteridis, Peter Mathew Sivey et al. | University of York; Renmin University of China |
| 2026-10-13 | [Digital Finance and Trade in the Green Transition: Evidence from Emerging Asian Economies](https://doi.org/10.1007/s10690-026-09644-9) | [Asia-Pacific Financial Markets](https://scholar4ai.com/journals/asia-pacific-financial-markets.md) | Asma Rehman Ullah, Shahzeb Khurshid, Alishba Rahman Ullah et al. | Rawalpindi Medical University; Pir Mehr Ali Shah Arid Agriculture University; University of Duhok; … |
| 2026-10-13 | [Digital financial inclusion and SME performance: a structural equation modeling analysis of FinTech adoption impact in emerging markets](https://doi.org/10.1186/s43093-026-01024-z) | [Future Business Journal](https://scholar4ai.com/journals/future-business-journal.md) | Rodrigo Bochner |  |
| 2026-10-13 | [The real effects of long-term stock price informativeness: evidence from green innovation in China](https://doi.org/10.1016/j.jaccpubpol.2026.107481) | [Journal of Accounting and Public Policy](https://scholar4ai.com/journals/journal-of-accounting-and-public-policy.md) | Ying Fang, Xiangyu Wang, Duoduo Yu | Xiamen University; Xiamen University of Technology |
| 2026-10-13 | [Training and productivity in micro-firms](https://doi.org/10.1016/j.respol.2026.105637) | [Research Policy](https://scholar4ai.com/journals/research-policy.md) | Marco Rispoli, Federico Tamagni | Prometeia (Italy); Scuola Superiore Sant'Anna |
| 2026-10-12 | [In the shadow of the CEO: How CFO co-option distorts capital allocation](https://doi.org/10.1016/j.jcae.2026.100603) | [Journal of Contemporary Accounting & Economics](https://scholar4ai.com/journals/journal-of-contemporary-accounting-economics.md) | Minjie Yu, Lin Li, Mengjia Yang et al. | Huzhou Normal University |
| 2026-10-12 | [Artificial intelligence in credit markets: Algorithmic lending, financial inclusion, and regulatory arbitrage](https://doi.org/10.1016/j.iref.2026.105937) | [International Review of Economics & Finance](https://scholar4ai.com/journals/international-review-of-economics-finance.md) | Podong Song, Shutong Wu, Janson Partab | Kunming University; Yunnan University of Finance And Economics; Shanghai University of Finance and Economics; … |
| 2026-10-10 | [Innovation bridging sustainability: the role of digital finance, institutional policy stringency, and climate physical risks for advancing energy transformation](https://doi.org/10.1186/s40854-026-00972-3) | [Financial Innovation](https://scholar4ai.com/journals/financial-innovation.md) | Huma Iftikhar, Luo Guang, Ningyu Qian | Huazhong University of Science and Technology |
| 2026-10-10 | [Does social media deployment by local governments raise voters’ offline engagement – Evidence from the German state of Hesse](https://doi.org/10.1016/j.qref.2026.102247) | [The Quarterly Review of Economics and Finance](https://scholar4ai.com/journals/the-quarterly-review-of-economics-and-finance.md) | Abeer Ibtisam Aziz, Ivo Bischoff | University of Kassel |
| 2026-10-10 | [AI governance policies, legal regulation, and corporate economic value co-creation](https://doi.org/10.1016/j.eap.2026.10.005) | [Economic Analysis and Policy](https://scholar4ai.com/journals/economic-analysis-and-policy.md) | Wenjing Lyu, Ke Tang, 崔雨 | China University of Political Science and Law; University of Birmingham; Capital University of Economics and Business |
| 2026-10-10 | [Digital-real economy integration and the value of China's energy enterprises](https://doi.org/10.1016/j.irfa.2026.105456) | [International Review of Financial Analysis](https://scholar4ai.com/journals/international-review-of-financial-analysis.md) | Yunze Wang, Baohua Gao | Peoples' Friendship University of Russia; Ocean University of China; Chinese Academy of International Trade and Economic Cooperation |
| 2026-10-10 | [The unseen pain of the Vietnam War: long-term effects of Agent Orange on labor market outcomes](https://doi.org/10.1007/s00148-026-01217-4) | [Journal of Population Economics](https://scholar4ai.com/journals/journal-of-population-economics.md) | Luu Duc Toan Huynh, Po Yin Wong | Queen Mary University of London |
| 2026-10-09 | [Political elites and access to economic opportunities in China’s rural market transition](https://doi.org/10.1016/j.worlddev.2026.107590) | [World Development](https://scholar4ai.com/journals/world-development.md) | Lin Xie, Mengting Liang, Q.F. Hou J.M. Han C.Y. Li et al. | South China Agricultural University; Louisiana State University Agricultural Center; Zhejiang University |
| 2026-10-09 | [Product market competition and target difficulty: The role of innovation](https://doi.org/10.1016/j.iref.2026.105958) | [International Review of Economics & Finance](https://scholar4ai.com/journals/international-review-of-economics-finance.md) | Seul Gi Oh |  |
| 2026-10-09 | [The impact of regional economic growth pressure on CSR disclosure: Evidence from China](https://doi.org/10.1016/j.iref.2026.105959) | [International Review of Economics & Finance](https://scholar4ai.com/journals/international-review-of-economics-finance.md) | Huahong Yan, Mingxuan Zhu, Jing Liu et al. | Capital University of Economics and Business; Shanxi University of Finance and Economics |
| 2026-10-09 | [The impact of pension fund market entry reform on household risk asset allocation: A financial analysis based on lifecycle theory](https://doi.org/10.1016/j.iref.2026.105964) | [International Review of Economics & Finance](https://scholar4ai.com/journals/international-review-of-economics-finance.md) | Guang Guo, Ying Liu, Wenhao Ling | Henan University |
| 2026-10-09 | [How digital intelligence drives corporate green innovation: Evidence from China](https://doi.org/10.1016/j.strueco.2026.10.004) | [Structural Change and Economic Dynamics](https://scholar4ai.com/journals/structural-change-and-economic-dynamics.md) | Tong Feng, Xiaomin Wang, Tianxin Wang et al. | Tianjin University of Finance and Economics; Qingdao Technical College |
| 2026-10-08 | [Entrepreneurship development, corruption perception, and sustainable development outcomes in emerging economies: the moderating role of digital financial inclusion](https://doi.org/10.1186/s43093-026-01019-w) | [Future Business Journal](https://scholar4ai.com/journals/future-business-journal.md) | Seun Adebowale Adebanjo |  |
| 2026-10-08 | [Drought-index insurance, advisory services and farm productivity in Ghana](https://doi.org/10.1016/j.foodpol.2026.103207) | [Food Policy](https://scholar4ai.com/journals/food-policy.md) | Angela Boakye Afriyie, Awudu Abdulai | Christian-Albrechts-Universität zu Kiel |
| 2026-10-08 | [The impact of marketization on urban economic resilience: evidence from China](https://doi.org/10.1007/s00168-026-01572-w) | [The Annals of Regional Science](https://scholar4ai.com/journals/the-annals-of-regional-science.md) | Ping Su, Bingqian Bu | Chongqing University of Technology |
| 2026-10-08 | [How energy poverty shapes investment in financial assets? Evidence from Chinese households](https://doi.org/10.1016/j.iref.2026.105953) | [International Review of Economics & Finance](https://scholar4ai.com/journals/international-review-of-economics-finance.md) | 白辰文, Yupeng Shi, Qin Si et al. | Central University of Finance and Economics |
| 2026-10-08 | [When women take all: Direct election and female leadership](https://doi.org/10.1016/j.jebo.2026.107791) | [Journal of Economic Behavior & Organization](https://scholar4ai.com/journals/journal-of-economic-behavior-organization.md) | Davide Cipullo | Università Cattolica del Sacro Cuore; Enel (Italy) |