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Testing for Weak Instruments in Linear IV Regression
Abstract
Weak instruments can produce biased IV estimators and hypothesis tests with large size distortions. But what, precisely, are weak instruments, and how does one detect them in practice? This paper proposes quantitative definitions of weak instruments based on the maximum IV estimator bias, or the maximum Wald test size distortion, when there are multiple endogenous regressors. We tabulate critical values that enable using the first-stage F-statistic (or, when there are multiple endogenous regressors, the Cragg-Donald (1993) statistic) to test whether given instruments are weak. A technical contribution is to justify sequential asymptotic approximations for IV statistics with many weak instruments.
... We formally test the strength of our MFHS instrument using the general rule of thumb as per Staiger and Stock (1997) and Stock and Yogo (2005). Specifically, we test whether the F-statistics from the first stage regressions of the endogenous variable (vertical indicator) for the focal and rival firms are greater than ten. ...
... The weakness of the MFHS IV has also been noted by Boehm and Sonntag (2023). Weak instrumental variables can pose a challenge in estimation because they can lead to biased estimates of causal relationships (Stock and Yogo 2005). To address the weak IV issue, we adopt the MLIV procedure outlined in Singh et al. (2020) and construct a stronger instrumental variable. ...
Vertical integration, a strategic approach where firms control multiple stages of production and distribution, offers potential operational efficiencies and market power. While the operations management literature emphasizes its benefits for supply chain coordination, reduced transaction costs, and risk mitigation from informational asymmetries, certain antitrust studies concern how vertical mergers may enable dominant firms to limit competition by creating entry barriers and causing input or market foreclosure. There is some evidence of the potential supply chain benefits of vertical integration across a few industries. However, empirical evidence on its anti-competitive effects remains scarce. This paper contributes to closing this gap by examining vertical integration's impact on firms' market power, as measured by their price-marginal cost markups. Our research investigates pre-and post-integration markups to determine whether firms gain anti-competitive market power after integration, diverging from competitive market pricing. Since firms' marginal costs are usually not observed in data, we estimate markups using production function estimations, following recent advances in empirical industrial organization. We compile a novel dataset on vertical integration cases using the FactSet Revere and the SDC platinum databases. Specifically, we identify 213 vertical mergers between firms with existing buyer-supplier relationships from 2003 to 2022. Methodologically, we employ a staggered difference-indifference approach in conjunction with instrumental variables (constructed using mutual fund stock outflow events) that cause an exogenous variation in firms' decisions to integrate vertically. Our analysis reveals that vertical integration increased acquiring firms' markups by 13% and their rivals' markups by 12%, on average. We also report a steady increase in post-integration markups since 2003, which suggests growing market power and industry concentration in the last two decades and implies a need for stricter antitrust enforcement. Interestingly, we find that the increase in firms' market power does not come from improved operational or cost efficiencies but rather from higher than competitive prices. Our paper offers causal evidence of vertical integration's anti-competitive and welfare-reducing outcomes. The insights from our paper contribute to the ongoing operations and antitrust discussions and are relevant for high-profile vertical merger cases.
... The results can be found in Column (1) of Table 3. The Kleibergen-Paap rk Wald F statistic exceeds 16.38, which is the critical value at the 10% significance level [40], suggesting that there is no issue with weak instruments. The coefficient of Treat × Post is significant, which is consistent with the baseline results. ...
... The results can be found in Column (1) of Table 3. The Kleibergen-Paap rk Wald F statistic exceeds 16.38, which is the critical value at the 10% significance level [40], suggesting that there is no issue with weak instruments. The coefficient of Treat × Post is significant, which is consistent with the baseline results. of the policy, we put the dependent variable ESG one period ahead and then conducted the baseline regression using Model (1). ...
As ESG (environmental, social, and corporate governance) is consistent with the spirit of sustainable development, it is useful to elevate ESG performance to realize the sustainable development of enterprise and society. Using the data of Chinese A-share listed firms in the period of 2011 to 2019, this paper takes the National Big Data Comprehensive Pilot Zone policy as a quasi-natural experiment and uses the difference-in-differences method to assess the effect of digital economy development on ESG performance. This paper reveals the following: (1) the digital economy can facilitate ESG performance; (2) digitalization of the economy helps enterprises to propel digital transformation, which in turn lifts ESG performance; (3) digital economy development has a deeper impact on private enterprises, especially for those in China’s capital cities; and (4) digital economy development moderates the inhibiting effect of ESG performance on corporate financial constraints. The findings of this paper indicate that digitalization of the economy can help to achieve sustainable development.
... We consider the lagged value of IVs to generate exogenous variation in variables IQI, 'Government effectiveness' and 'Rule of law' (INST). The validity and power of the instruments is tested through the following validation tests: the Angrist-Pischke test of excluded instruments, the under identification and the weak identification tests, with cutoffs provided by Stock and Yogo [87], the weak-instrument-robust inference tests and the Hansen J statistic for overidentification of all instruments. ...
... The strength of the instruments is verified through the F statistic of the Kleibergen-Paap weak identification test. Based on the critical values of Stock and Yogo [87], 29 the F statistic relative to Column (13) with a value of 8.22 is between the critical values of 15% and 20% (closer to 15% value), while the F statistic relative to Column (14) with a value of 8.59 is over the critical values of 10%. We can conclude that the relevance of our IVs is good in Column (13) and very good in Column (14). ...
This paper investigates the role of institutional quality in explaining cross-regional variation in population health status in Italy. We first introduce a composite Regional Health Status Indicator summarizing life expectancy, mortality and morbidity data. Then, we study the empirical relationship between this indicator and a set of socioeconomic, health system and institutional controls at the Italian regional level over the period of 2011–2019. We find that institutional quality is a driver of population health. Furthermore, well-functioning local institutions and regions compliant with national standards in terms of public healthcare services (Essential Levels of Care) make socioeconomic context no longer relevant for population health, potentially reducing inequalities.
... confirm that our instrument satisfies relevance and exogeneity requirements. In addition, the Kleibergen-Paap rk Wald F statistic is the weak identification test that is compared with the critical values of Stock and Yogo (2005), showing that our instrument is strong. Finally, the GMM distance test statistic of endogeneity indicates the adequate treatment of both LLPs and NCOs as endogenous. ...
... The GMM distance test statistic of endogeneity has the null hypothesis that endogenous regressors can be treated as exogenous. The Kleibergen-Paap rk Wald F statistic is the weak identification test which rejects the null hypothesis that the instrument is weak based on Stock and Yogo (2005) critical values. Robust standard errors clustered at the bank level in parentheses. ...
... We first looked at the diagnostic test of weak instruments. For instruments to be valid, they must have a low correlation with the endogenous explanatory variable (Stock & Yogo, 2002). The Stock and Yogo (2002) test is statistically significant (with a large magnitude and small p-value), rejecting the null hypothesis that the instrument is weak; thus, we can proceed with the knowledge that this is a strong instrument. ...
... For instruments to be valid, they must have a low correlation with the endogenous explanatory variable (Stock & Yogo, 2002). The Stock and Yogo (2002) test is statistically significant (with a large magnitude and small p-value), rejecting the null hypothesis that the instrument is weak; thus, we can proceed with the knowledge that this is a strong instrument. Next, we looked at the results of the Wu-Hausman diagnostic test for endogeneity. ...
Social ties play a prominent role in individuals’ political decision-making. They influence partisan defections, political participation, voting decisions, and political information acquisition. Much of the literature focuses on personal social networks or geographically close networks. Yet one’s social network might also include acquaintances or other connections in more distant places that are maintained via online networks. In this study, we exploit Facebook’s Social Connectedness Index, which reflects social connections across the United States, and we investigate the role of social connectedness in political decision-making among individuals who are located across distant geographical regions. Our results suggest that social connectedness between counties has a homogenizing effect on voting for the same presidential candidate, either Democratic or Republican. On the other hand, social connectedness is likely to have a differentiating effect on voting for an independent or a third-party candidate. Moreover, this effect is moderated by the socioeconomic characteristics of the counties, such as education, race, population density, household income, industry, and gender composition.
... and cognitive diversity (F-value = 10.08) meeting the exogeneity criteria (Sargan's J-statistic = 0.07; p-value = 0.80) (Bascle, 2008;Stock and Yogo, 2005) and ran a two-stage least squares (2SLS) regression predicting political behaviour. The second-stage model confirms that while the interaction effect between cohesion and cognitive diversity and the direct effect of cognitive diversity are significant, the direct effects of cohesion are not. ...
... We repeated this analysis for political behaviour and board involvement in predicting acquisition performance. While the results from the second-stage model confirm our results, our instruments 3 for political behaviour (F-value = 3.84) and board involvement (F-value = 2.98) turned out to be 'weak', despite meeting the exogeneity criteria (Sargan's J-statistic = 1.36; p-value = 0.24; Bascle, 2008;Stock and Yogo, 2005). The Wu-Hausman (1.62; p-value = 0.20) and Durbin-Wu-Hausman (4.04; p-value = 0.13) test results again indicate that our regressors are exogenous, and our results are not biased (Davidson and Mackinnon, 1993). ...
The pre-deal phase of an acquisition is complex, with high stakes, and high uncertainty. Consequently, acquisition decision making can be seen as an inherently political process. While political behavior is a central concept in organizational theory, and despite its inevitability during acquisition decision making due to the contested nature of the pre-deal phase, there is a shortage of theory and evidence concerning the antecedents, consequences, and moderators of political behavior. To address these theoretical shortcomings, we develop and test a theoretical model of political behavior focusing on the TMT’s psychological context. We argue that while political behavior risks undermining acquisition performance, the degree of board involvement during the pre-deal phase can enable some TMTs to attenuate the damaging effects of political behavior. Further, we theorize two key antecedents variously fueling and constraining political behavior. We contend that while TMT cohesion reduces political behavior, cognitive diversity increases political behavior while suppressing the potential for TMT cohesion to prevent political behavior. We test our theoretical model using a field-based sample of 109 UK acquisitions, combining multiple informants with objective secondary data.
... The first step involved ensuring that our instruments fulfilled the relevance criterion-i.e., they were strongly related to the suspected endogenous variables instrumented by them. In addition to the high first-stage F-statistics above the thresholds identified by Stock and Yogo (2002) (see Appendix 3), we offer theoretical arguments for instrument relevance in Appendix 4. Moreover, a rejection of Kleinbergen-Paap statistics (p < .001) ...
Bricolage is a critical strategy used by entrepreneurs to generate resources for new ventures in response to environmental threats that result in resource constraints. However, inconsistent findings exist. Whereas the predominant view in the bricolage literature suggests that resource-constrained or threatening environments motivate new ventures to bricolage to survive and thrive, some empirical evidence shows that some firms choose not to bricolage in such environments. This paper addresses the inconsistent findings by integrating regulatory fit theory with the bricolage literature, arguing that the effect of environmental threat on bricolage depends on entrepreneurs’ dispositional regulatory focus. Data from a time-lagged survey of 396 Taiwanese entrepreneurs support our hypotheses. Our findings suggest that promotion (prevention) focus disposition is positively (negatively) related to bricolage. More importantly, both promotion and prevention foci weaken the effect of environmental threat on bricolage, serving as boundary conditions for this relationship. Finally, our additional analysis reveals gender differences in bricolage and the contingent effect of promotion focus disposition, enabling us to contribute to regulatory fit theory.
... Rights reserved. and Yogo [43] test for weak instruments. The Craag-Donald [19] test statistics (438.14) ...
We examine how bank charter values affect banks' risk-taking strategies in area of operational risk. We investigate whether higher bank charter values influence banks' management incentives in more closely monitoring and managing operational risk (i.e., disciplinary effect of bank charter values), while controlling for other types of bank risk and bank characteristics. Using supervisory data for a sample of large US banks from 2000 to 2017, we construct a measure of bank operational risk exposure. We find that bank charter values are associated with operational risk exposure for several individual event types, specifically Internal and External Fraud, and Employment Practices and Workplace Safety, but not on aggregate, and any such association weakens after the 2008 financial crisis. We benchmark our main results by constructing alternative measures of operational risk exposures, leveraging approaches outlined in Basel II and Basel III bank capital standards. The results point at the sensitivity to the measures of operational risk using different time attributes of loss events and accounting data, as well as data granularity.
... can only affect the dependent variable through the endogenous regressor. In estimating 2SLS, Staiger and Stock (1997) and Stock and Yogo (2005) proposed a rule of thumb for the first stage regression. According to the latter, at the first stage in a single endogenous regressor, the proposed instrumental variable for the endogenous regressor (in addition to all other exogenous regressors) should have a joint F statistic greater than 10 (F > 10). ...
This study examines the simultaneity of the conditions necessary and sufficient for adopting cost-elimination policies, commonly known as fee-free educational policies, at the upper-secondary level, and the social benefits of these policies in Sub-Saharan Africa (SSA). Some conclusions are reached subject to a review of the theoretical and empirical literature related to these subjects. 1) That there is no consensus about the socio-political factors that drive the adoption of expansionary social policies such as fee-free education; 2) that despite the related challenges and criticisms, the adoption of cost-elimination policies has a significant positive effect on access to education at the basic level in SSA; and, 3) that Western sociology and economics literature identifies educational policies that increase access to education as having a positive externality in terms of crime reduction. However, the understanding of the educationcrime nexus in SSA and the role of educational policies is virtually non-existent. Again, the effects of fee-free policies on upper-secondary school enrolment have received very little attention across the region. Another critical area yet to be understood is the mechanisms that drive the adoption of fee-free policy changes. Based on these gaps, the study aimed to explore, understand, and explain the necessary and sufficient conditions that drive the adoption of fee-free policies in SSA through a case study design that uses qualitative comparative analysis to achieve the first research objective. Subsequently, the study examined the effect of fee-free policies on upper-secondary school enrolment rates. Last, the study investigated the impact of the macro-level rate of school enrolment on crime rates. The main components of the empirical analysis of the last two research objectives consist of panel data analysis of SSA countries from 2003 to 2018. Overall, the results of the three articles that comprise the article-based dissertation make the following theoretical contribution: the manifestations of fee-free policies on the agenda and their subsequent formulation and adoption are strongly embedded in political parties’ striving for political power through competitive electoral politics. The results challenge some core explanations of social policy provision, such as the partisan theory of policy outcomes and the economy. Notwithstanding this, fee-free policies have the utility of positively impacting social variables. These include the intended effect of increasing the rate of school enrolment to improve human capital development, and the unintended effect of reducing the property-related crime rate in 15 society. Therefore, the study suggests that for achieving the desired fee-free policy outcome and its impact, these policies should be encouraged within broader national social-policy-development planning.
... From the regression results, the degree of FD is significantly positively correlated with industrial SO 2 emissions and PM 2.5 concentration. In addition, the F values of the weak instrumental variable test are all significantly larger than the critical value of 16.38 set by Stock and Yogo (2005), indicating no weak instrumental variable problem. Although the values of the regression coefficients have changed slightly, the signs and significance levels are the same as the previous ones, which further supports the conclusion of the main regression. ...
Environmental protection is a basic public service that the government must guarantee and is closely related to public health. An important driver of environmental pollution in China is the local government’s pursuit of a rapid economic development while ignoring environmental protection under the Chinese-style fiscal decentralization system. On the basis of the principal–agent theory between the central and local governments, this study analyzes the environmental deterioration caused by the distortion of local government behavior under fiscal decentralization. In addition, using China’s prefecture-level city data from 2014 to 2018, this study empirically estimates the impact of fiscal decentralization on environmental pollution. SO2 emissions and PM2.5 concentrations are used to measure the degree of environmental pollution. Results show that Chinese-style fiscal decentralization exacerbates environmental pollution and that the impact of fiscal decentralization on environmental pollution differs in regions with varying levels of economic development and cultural penetration. Moreover, fiscal decentralization does not significantly impact environmental pollution in eastern China and in those areas influenced by Confucian culture yet aggravates the environmental pollution in central and western China and in those areas that are not affected by Confucian culture. These results offer important policy implications. Clearly dividing the power and financial power between the central and local governments, establishing an environmental governance system compatible with economic incentives, and building an environmental public finance system can alleviate the impact of Chinese-style fiscal decentralization on environmental pollution.
... The first-stage F-values were 501.25. According to Stock and Yogo (2005), the critical value of the F-value is 16.38 under the assumption that the bias level is less than 10%, which further demonstrates the explanatory power of regional average Internet usage for whether individuals use the internet, and there is no weak instrument problem. The second stage results from Table 5 report that the regressions using instrumental variable are generally consistent with the baseline estimates: a 17.6% increase in the probability of donation for residents who use the internet in the IV-probit regression; and a 18.1% increase in the probability of donation for residents who use the internet in the IV-2sls regression. ...
With the development of digital economy, especially the Mobile payment, the lifestyles such as the private donation, is undergoing accelerated changes in the last decades. Based on the China Family Panel Studies 2018 data, this paper systematically investigated the donation models, empowered by digital technology, have realized economy system refinement and intelligent development. Compared with residents who do not use the Internet, residents who use the Internet are about 10% more likely to donate, and the amount of donations will increase by about 56%. After considering the potential endogeneity problem, results still hold with Propensity Score Matching (PSM) and Instrumental Variable. The mechanism analysis shows that the searching cost and information asymmetry play an important role. The research of this paper has enlightening that the widespread use of digital technologies can effectively change the private donation behavior and penetrate energy consumption via dramatically decreasing searching cost.
... A minimum condition for the validity of the instrument is that it must be sufficiently correlated with the endogenous variable (Verbeek, 2008). Following the suggestion of Stock and Yogo (2005), a minimum test for assessing the instrument's strength involves having an F-statistic greater than 10. All F-statistics in our IV results surpass 10, indicating that our instruments are strongly correlated with the endogenous variable. ...
Obesity (overweight) is a widespread concern not only in high-income nations but also in low-income countries across sub-Saharan Africa (SSA). Although many studies attribute this trend to economic development triggering a shift in nutrition patterns within SSA, they tend overlook a critical factor: the level at which these determinants are measured. Assessing them nationally while drawing comparisons with individual-level obesity data introduces a statistical challenge known as the ecological fallacy. To address this, we utilize local-level night light data as a proxy for local economic development. Analyzing demographic and health surveys from 44 SSA countries spanning the period 1992-2019, we find that local development is associated with a 0.002% increase in the body mass index of women. In addition, we find that night light intensity is associated with 0.2%-0.3% increases in probabilities of a woman being overweight and obese. Our results remain robust when
... This suggests that the enforcement of social security collection among non-SOEs was the primary driver for the majority of the increase in overall SSR. All models passed the underidentification test and weak identification test with high values of LM statistics and F statistics (Stock and Yogo 2005). What about years other than 2005? ...
Despite the lack of electoral accountability, China has built an expanding welfare system that is set to include most citizens. Why does China defy the conventional prediction of an exclusive authoritarian welfare state? This paper looks at the critical time when China first established its social security system in the 1990s and argues that the state adopts a “threat-driven strategy” where the redistribution effort varies with the expected collective action of economic losers. Analyzing an original granular county-level dataset of China’s laid-off workers and social security taxation, the paper finds that a group of newly emerged economic losers, precipitated by state policy, drives the local states’ efforts to redistribute. In particular, the number of laid-off state-owned enterprise workers explains 46% of the variations in social security collection among non-state-owned enterprises. Instrumental variable estimation, with legacy state-owned enterprises established in historical contingencies as the instrument for laid-off workers, shows consistent results. Further analysis on mechanisms demonstrates that layoffs lead to an increase in SOE protests, which in turn foster greater redistribution.
... The value of the corresponding statistic is 103.67 (p-values = 0.0000), which reinforces the results of the Anderson (1951) test.Although relevant, the instruments may still be weak, which would lead to poor estimation. An F version of theCragg-Donald (1993) Wald test can be utilized to examine this issueand Stock and Yogo (2005) provide the relevant critical values for this test. The Cragg-Donald F-statistic is 188.39, which is higher than any of the. ...
In this article, we empirically examine the relation between democracy level and stock index returns in a sample of 74 countries. Compared with democracies, autocratic states are characterized by lower returns despite exhibiting higher return volatility. Even though this higher volatility can be mostly attributed to diversifiable country‐specific risk, the capital asset pricing model cannot explain the return differential. Instead, it is the level of investor protection that can fully account for the phenomenon described here. Autocratic leaders may be reluctant to promulgate regulations shielding investors, and the resultant expropriation depresses the returns realized by outsiders.
We estimate the short-run effect of air pollution on mental illness. Using the China Family Panel Studies covering 12,615 urban residents during 2014-2015, we find a significantly positive effect of air pollution-instrumented by thermal inversions—on mental illness measured by the Kessler Psychological Distress Scale. Specifically, a 1 SD (18.04 mu-g/m3) increase in PM2.5 concentrations over a month increases the probability of having a score value associated with severe mental illness by 7.58 percentage points, or 0.37 SD. We find suggestive evidence that indirect channels—like reduced exercise and physical health—play a role in the effect.
Research offers conflicting predictions about the impact of credit conditions on mental health. We first assess how bank regulatory reforms that improved credit conditions, for example, by enhancing the efficiency of credit allocation and lowering lending rates, impacted mental health. We discover that among low-income individuals, these regulatory reforms reduced mental depression, boosted labor market outcomes, eased access to mortgage debt, and reduced the ranks of the “unbanked.” We also find that mergers of large regional banks that led to branch closures and tighter credit constraints in affected counties harmed the mental health of lower-income individuals in treated counties.
This paper was accepted by Kay Giesecke, finance.
Funding: C. Lin and M. Tai acknowledge financial support from the National Natural Science Foundation of China [Grant 72192841] and the Research Grants Council of the Hong Kong Special Administration Region, China [Project T35/710/20R].
Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.00194 .
The purpose of this paper is to examine the effect of contextual (community) level social trust on women’s empowerment. The specific knowledge gap explored in this study is that the previous studies theorized that community trust has a positive impact on women’s empowerment. Thus, an increase in trust in the community will empower women. However, such an assumption has been never empirically tested and confirmed. Against this backdrop, the present paper develops a theoretical argument on why the increase in community trust should lead to a higher level of women empowerment. Then, a cross-country survey was used as a data source to test the effect of community trust on women’s empowerment. A traditional single-stage OLS and instrumental variable regressions are estimated to test the effect of community trust on women’s empowerment and quantify the magnitude of such impact. The key finding of this paper is that community trust indeed significantly strengthens the empowerment of women by increasing women’s ownership of assets and improving the decision-making authority of women in the family. Importantly, our findings are robust for the separate rural and urban samples, as well as the samples of younger and older women. Equally, our findings are robust for an alternative set of instruments. The main implication of these findings is that policymakers, social administrators, and government authorities who are working on promoting gender equality should give priority to promoting community-based interventions that nurture and maintain women’s trust.
This study investigates the existence of a calorie gap (CG) within gender, caste, and religion groups utilising an entitlement framework. We employed National Sample Survey data on consumer expenditure spanning from 2004–05 to 2011–12 and applied the Oaxaca-Blinder decomposition technique for our analysis. The results of the Oaxaca decomposition indicate that entitlement failure plays a significant role in expanding the CG amongst gender and caste groups in both rural and urban areas, while its impact is only seen within religious groups in urban areas. The failure of exchange entitlement intensifies the CG amongst caste and religious groups in rural areas. Moreover, our quantile-specific Oaxaca decomposition findings reveal that the contributions of entitlement and exchange entitlement gaps to the overall CG fluctuate across quantiles. We propose that increased social awareness and public exposure aimed at reducing caste and religion-based discrimination, alongside programmes and policies designed to enhance the resource base of female-headed households, minority castes, and religious minorities, may aid in the reduction of the CG.
We explore whether digital inclusion, a public policy designed to provide high-speed internet infrastructure for historically digitally excluded populations, is associated with the social and ethical challenge of financial inclusion. Using evidence from a sizable P2P lender in the U.S., we document that digital inclusion is positively associated with P2P lending penetration and that this relation is more pronounced in counties with limited commercial bank loan penetration and higher minority populations. Our new evidence from cross-sectional tests suggests that digital inclusion plays a key role in financial inclusion, particularly in regions with more vulnerable and/or underserved populations. In consequence tests, we document that high-risk borrowing is less likely to be denied in counties with higher digital inclusion and that digital inclusion is positively associated with P2P lending efficiency in the form of more repeated borrowing, decreased funding time, and improved funding fulfillment. In addition, we show that the availability of alternative information, a plausible channel through which digital inclusion is related to financial inclusion, is positively associated with efficiency in P2P lending. Our findings indicate that digital inclusion can empower financial service providers and other stakeholders to collaboratively fulfill their ethical and social responsibilities to meet the financial needs of historically marginalized groups.
This article examines the responsiveness of new housing supply to prices and costs, using the case of Ireland at quarterly frequency from the 1970s, as well as a county‐level panel from the 1990s. Across four error‐correction specifications, and supported by an instrumental variables approach, we find the estimated elasticity of new housing supply to prices of +0.9 in the baseline, while that of costs is larger in magnitude (−1.9). We present evidence that responsiveness to prices rose after the 1980s, then fell in the 2000s, before rising again and also that elasticities vary at the county level.
We analyze how bank sentiment affects bank liquidity hoarding, distinguishing unexplained beliefs of bank managers from fundamental‐based beliefs. We build a bank management sentiment measure from textual analysis of 10‐Ks and utilize a comprehensive bank liquidity hoarding measure. We find that negative bank sentiment increases liquidity hoarding not warranted by a bank's fundamental conditions or external circumstances. Further analysis confirms that our findings reflect bank volition rather than being driven solely by borrowers or depositors. We address endogeneity concerns using exogenous weather conditions as instruments. Overall, our findings suggest that bank sentiment can influence how much liquidity banks provide to the economy and financial system.
In this study, we examine the impact of a new mobile-based, dockless bike-sharing service on public transportation usage. This new bike-sharing model removes the constraint of having fixed stations and gives users full flexibility on where to pick up and return bikes. This innovative feature of dockless bike sharing potentially disrupts the current norms of how people commute. The dockless shared bikes offer easy connections between destinations and public transportation stations. They can potentially promote public transportation, by improving its flexibility and outreach. To examine this impact, we collaborate with one of the largest dockless bike-sharing companies in China and collect unique daily-station-level panel data of shared-bike rides and subway traffic. Our findings indicate that a 1% increase in shared-bike rides leads to an increase of 0.35% in subway traffic. Further analyses show that this positive effect is stronger when people need to travel a longer distance to reach subway stations. These results suggest one potential underlying mechanism for the positive relationship we observe, that is, dockless shared bikes alleviate the “last-mile problem” for public transportation, making it a more appealing mode of transportation, compared with alternatives. Overall, we find that dockless shared bikes, in contrast to ridesharing or traditional bike sharing, act as a complement, rather than a substitute, for public transportation. Dockless shared bikes present a greener way of commuting, with significant environmental and societal impacts.
E-commerce platforms are playing an increasingly important role in influencing manufacturers’ supply chain and product decisions. An emerging supply chain innovation, known as the platform-based consumer-to-manufacturer (PC2M) model, has been initiated by several large e-commerce platforms based on established digital links between consumers and manufacturers. These links enable consumer inputs into manufacturers’ operations, indirectly by capturing consumer preferences from platform-accumulated big data and directly by enabling consumer interaction with manufacturers through the e-commerce platform. Although manufacturers are increasingly integrating PC2M into new product development (NPD), there is little research on operations innovations in connection with the PC2M model and its impact on manufacturers’ new product success. To fill this research gap, we investigate the PC2M model of JD.com, a leading e-commerce platform in China that launched the PC2M model in 2018. We first identify two uses of PC2M by manufacturers to facilitate product development—platform-enabled big data analytics (PBA) and platform-enabled simulated product trials (PST)—and explore how PC2M enables operations innovations in NPD. Next, drawing on the knowledge-based view, we develop research hypotheses and empirically examine whether PC2M adoption improves new product performance using a large-scale, transactional dataset from JD.com. Through a series of carefully executed analyses, our study consistently finds that use of either PBA or PST in manufacturers’ NPD processes improves new product performance. We also explore how these effects vary across product types and markets with varying new product introduction rates. The findings offer important managerial insights for improving new product success in today's data-rich environment.
Using a unique dataset on the performance of soccer players in China (retrieved from 632 matches involving 24 teams during the 2014 to 2016 seasons), we investigate the effect of air pollution on different performance indicators that rely on different mixtures of the physical and cognitive inputs of players. To ensure a causal interpretation, we implement an instrumental variable (IV) approach using thermal inversion as the instrument for air pollution. We found that players’ performance indicators, especially those more related to cognitive factors, are more strongly influenced by air pollution. One standard deviation (SD) increase in the Air Quality Index (AQI) leads to 2.5% decrease in the number of players’ passes and 5.1% increase in the number of fouls. However, for performance indicators that are more related to players’ physical condition, e.g., running distances, no such significant impact is identified. Overall, these findings suggest that the negative impact of short-term air pollution exposure on outdoor worker performance is mainly cognitive, which we believe could lead to important policy implications, not only for competitive sports but also across a much broader spectrum of business sectors.
This paper presents an empirical analysis of the social contract (SC) in MENA based on a simple model synthesizing three main characteristics of a SC linking governments and citizens: Participation, Protection, and Provision. Using this 3‐P framework, we focus on the role of provision and protection in determining citizen participation, a question that drew much attention following the recent economic and social developments in MENA. We compare our characterization of the SC in MENA and Organisation for Economic Co‐operation and Development (OECD) countries and find robust empirical evidence that, in MENA, the benefits provided to citizens through improved delivery of basic services have come at the cost of impaired participation. We also find that digital transformation, a potential channel through which the SC may improve, has an inversely U ‐shaped effect suggesting that institutional changes are called for in MENA countries before their SC is comparable to that of OECD countries.
Background
Stunting is associated with adverse outcomes in adulthood. This article specifically aims to analyse the relationship between childhood stunting and education as well as cognitive outcomes for adults in Indonesia.
Methods
Pooled data from wave one (1) and two (2) of the Indonesia Family Life Survey (IFLS) in 1993 and 1997 identified a sub-sample of 4,379 children aged 0–5 by their height-for-age (HAZ) to be compared for their differences in educational outcomes and cognitive abilities in 2014. HAZ was used to proxy relative height to determine stunting status based on 2006 WHO child’s growth standards. Education and cognitive abilities outcomes include years of schooling, age of school entry, grade repetition, and scores for cognitive and math tests. The study employs estimation models of pooled regressions and instrumental variable (IV) to address problems of endogeneity and bias from omitted variables.
Results
Stunting and relatively small stature had significant associations with cognitive development, and they worked as intermediaries to cognitive developmental barriers as manifested in reduced educational outcomes. A lack of one SD in HAZ was associated with 0.6 years shortened length of the school, 3% higher chances of dropouts from secondary school, and 0.10–0.23 SD lowered cognitive and numerical scores. Similarly, stunting is associated with decrease cognitive test scores by 0.56–0.8 SD compared to non-stunting, two years less schooling, and 0.4 years of delayed entry to school. As for cognitive abilities, stunting is associated with lower cognitive and numerical abilities by 0.38–0.82 z -scores.
Conclusion
Growth retardation during childhood in Indonesia was associated with lower cognitive abilities, particularly during school age, and this correlation faded as individuals grew up. Subsequently, growth retardation is significantly linked to lower educational outcomes. Impaired growth has implications for reduced lifetime earnings potential mediated by diminished cognitive capacity and lower educational attainment. The finding suggests that development in Indonesia during recent decades has not provided an adequate environment to enable children to achieve their potential educational outcomes.
Saving is a main source of financing capital and R&D investment, which can facilitate economic growth and development. Saving also acts as a buffer against uncertainty and external shocks, which can smooth growth volatility and promote economic growth. Thus understanding the determination of saving is vital for policymaking. This paper evaluates the saving consequence of population aging in China, a fast growing economy that has been experiencing rapid population aging with high saving rates. However, whether and how population aging affects saving remains controversial. Instead of verifying whether population aging increases or decreases saving, this paper takes a step further to examine potential nonlinearity in the nexus, which allows one to address the reason for inconclusiveness. Using China's provincial data over the period 1989–2019, it indeed finds significant existence of nonlinearity. Household saving follows an inverted‐U process with population aging. The effect holds for regions with moderate saving rates. For regions with the least and highest saving rates, household saving follows a U‐shaped process. Similar results are found for total saving.
Advances in information technology (IT) may affect the organizational design of production. Exploiting the rapid diffusion of the internet in the United States, we assess the sensitivity of production chain organization to this innovation in IT access and use. Extending theories of the firm that recognize the importance of downstream transfers (selling as opposed to sourcing) and plural governance in organizational design, we predict IT-driven shifts in downstream vertical integration. In a detailed panel of Census Bureau data for over 5,600 manufacturing plants, we observe the extent of a production unit’s downstream transactions within the firm alongside concurrent sales to external customers—a mix we refer to as plural selling. Our main finding is that the use of the internet for external coordination precipitated a significant decline in downstream vertical integration across the manufacturing sector. Instrumental variables estimation points to a causal relationship but also heterogeneous treatment effects. Key drivers of plural organization, such as complementarities and constraints across differently governed transactions, help explain such heterogeneity, as does concurrent use of internal production management IT. Our study is the first study to leverage a plural governance framework and large-scale microdata to understand how U.S. production chain organization shifted in response to this rapid and far-reaching technological change.
This paper was accepted by David Simchi-Levi, information systems.
Funding: This research was performed at the Atlanta, Boston, and Cornell (supported by the Cornell Center for the Social Sciences) Federal Statistical Research Data Centers [Project 1069 (CBDRB-FY22-279)]. Support for the Research Data Centers network from the National Science Foundation [Grant ITR-0427889] is gratefully acknowledged, as is support from the Social Sciences and Humanities Research Council of Canada.
Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2019.01586 .
Purpose – We analyzed the effects of different combinations of organic soil amendments (OSAs) and chemical fertilizers on agrifood production, focussing on banana yields in China, the second-largest producer of bananas globally.
Design/methodology/approach – We computed these combinations by dividing the expenditures on OSAs by those on chemical fertilizers and called them OSA-CF ratios. First, we classified farmers based on quintiles of expenditures on chemical fertilizers. Then, we studied the association between OSA-CF ratios and banana yields for each quintile. We also considered an alternate specification in which farmers were grouped along the OSA-CF ratio continuum. The first group comprised farmers not using OSAs. Their OSA-CF ratio was zero. Farmers applying low, medium, and high OSA-CF ratios constituted groups two, three, and four; the groups were delineated based on the OSA-CF ratio tertiles, and the associations between tertiles of OSA-CF ratios and banana yields for each quintile were analyzed. The data used in this study were collected by surveying 616 households in three major banana-producing provinces (Guangdong, Hainan, and Yunnan) of China. Standard linear regressions and the twostage predictor substitution method were employed to complete the analysis.
Findings – There were variations in the effects of OSA-CF ratios on banana yields obtained by farmers in different quintiles. For the first and second quintiles, low, medium, and high OSACF ratios improved banana yields relative to not using OSAs. For farmers in the first quintile using only chemical fertilizers, applying a low OSA-CF ratio was associated with an improvement of 792 kg/mu in banana yields. For their counterparts in the second quintile, the same transition was associated with a gain of 534 kg/mu. For the fifth quintile, comprising farmers spending 320 yuan/mu or more on chemical fertilizers, applying a high OSA-CF ratio instead of using only chemical fertilizers was associated with a 401 kg/mu decline in banana yields. Even so, for this group, no differences were observed between the yields of farmers not applying OSAs and those using low and medium OSA-CF ratios.
Originality – Farmers apply OSAs such as organic fertilizers and farmyard manure to adjust and remedy soil nutrition to improve farm productivity. However, little is known about how combining OSAs with chemical fertilizers affects banana yields. This study provided the first attempt to explore the associations between OSA-CF ratios and banana yields using cross-sectional data on farming households.
Practical implications – Banana farmers in southern China, using only chemical fertilizers, can improve yields by combining them with OSAs if their chemical fertilizer expenditures are less than 66.67 yuan/mu. Those using only chemical fertilizers and spending between 68 yuan/mu and 300 yuan/mu on them can maintain yields by applying OSAs in conjunction with chemical fertilizers. However, yields may decline for farmers using only chemical fertilizers and spending 320 yuan/mu or more on them if they incorporate OSAs such that the OSA-CF ratio reaches 0.78 or higher. Overall, combining OSAs with chemical fertilizers can improve yields while attenuating the adverse effects of chemical fertilizers on the environment. Policymakers should inform farmers of these benefits and accelerate the transition to sustainable agriculture through educational and awareness programs.
In this article, we examine the relation between independent directors with past military service and merger activity. We find that firms with a greater proportion of independent directors with military experience complete fewer mergers, and the deals are of smaller value. Our results are robust to instrumental variable estimation. The reduction in merger and acquisition activity is concentrated in firms with weak CEOs, suggesting independent directors with military service do not improve firm agency problems.
If a firm afflicted by a disaster chooses to donate to disaster relief, how will this decision affect the firm's market value? From a self-protection perspective, diverting resources to support the public may jeopardize a firm's continuity and thereby reduce its value. Yet from a reputation-building perspective, supporting the public in need may enhance corporate reputation and thus increase firm value. In this study, we contrasted the two perspectives to develop a conceptual framework consisting of various competing hypotheses. We tested these hypotheses using data on Chinese firms’ donations to disaster relief during the first coronavirus disease 2019 outbreak. Our analysis shows that firms’ donations generally led to an increase in firm value. This was especially true for firms that were smaller or less profitable, firms that donated goods in addition to cash, and firms that donated before an increasing number of industry peers had done so. These results support the reputation-building perspective, suggesting that even when firms are afflicted by disaster exposure, their donations are still recognized as a value-adding investment. In contrast, donating a larger amount of cash and donating on an earlier day after the onset of the outbreak resulted in a lower firm value. These results align with the self-protection perspective, pointing to the need to consider resource preservation.
This paper examines how principal–principal conflict influences chief executive officer (CEO) compensation in an emerging economy. To reduce the negative influence of blockholder rent appropriation (BRA) on firms, a controlling blockholder (hereafter, the blockholder) with strong power might exploit a CEO, the primary agent of a firm, leading to possible principal–agent (PA) conflict. In this case, such PA conflict can be negatively reflected in the CEO’s compensation contract. Drawing on the social theory of agency, we suggest that the cognitive frameworks and power relations of the blockholder and the CEO influence CEO compensation design. The cognitive framework explains that an optimal compensation design is affected by the social norm of CEO compensation and a CEO’s personal value system in an emerging market. Power relations indicate how blockholders may exercise their power for the optimal stringent CEO compensation design depending on their interdependent relationship with a CEO. Based on the two underlying mechanisms, we examine how BRA influences the compensation of the three types of CEOs who have different cognitive values and power relations with the blockholder, including a blockholder as the CEO, a blockholder-affiliated CEO, and a professional CEO. By analyzing 3,621 listed Chinese firms from 2006 to 2021, we find that BRA negatively affects the compensation of a blockholder CEO and a professional CEO, and has a negligible effect on that of an affiliated CEO. We further find that the negative effect of BRA on compensation is stronger for professional CEOs at state-controlled firms than those at private firms.
This study shows that, unlike the positive role played by other institutional investors documented in the literature, venture capital (VC) in pursuit of short‐term gains through exit strategies reduces the stock price informativeness of portfolio companies, especially when VC is associated with a higher level of the ability (longer‐term VC directors, large VC syndicate), incentive (private VC sponsors), and willingness (less reputable VCs) to manipulate information. Furthermore, internal and external monitoring helps mitigate the negative impact of VC on stock price informativeness. Finally, earnings management and reduced information disclosure mediate the relationship between VC involvement and stock price informativeness.
Site visits allow visitors to physically inspect productive resources and interact with on-site employees and executives face to face. We posit that, by allowing visitors to acquire investment-related information and monitor the management team, site visits offer disciplinary benefits for corporate investments. Using mandatory disclosures of site visits in China, we find that corporate investments become more responsive to growth opportunities as the intensity of site visits increases, consistent with the notion that site visits yield disciplinary benefits. We also find that the positive association between site visits and investment efficiency is more pronounced when visitors can glean more investment-related information and when they have stronger incentives and greater power to monitor managers. This positive association is also stronger among firms with more severe agency problems and higher asset tangibility. The overall evidence supports the notion that site visits serve as a unique venue for institutional investors and financial analysts to acquire valuable information and serve a monitoring function, which generates disciplinary benefits for corporate investments.
This paper was accepted by Suraj Srinivasan, accounting.
Supplemental Material: The data files are available at https://doi.org/10.1287/mnsc.2022.00302 .
We draw attention to two problems associated with the use of instrumental variables (IV), the importance of which for empirical work has not been fully appreciated. First, the use of instruments that explain little of the variation in the endogenous explanatory variables can lead to large inconsistencies in the IV estimates even if only a weak relationship exists between the instruments and the error in the structural equation. Second, in finite samples, IV estimates are biased in the same direction as ordinary least squares (OLS) estimates. The magnitude of the bias of IV estimates approaches that of OLS estimates as the R(2) between the instruments and the endogenous explanatory variable approaches 0. To illustrate these problems, we reexamine the results of a recent paper by Angrist and Krueger, who used large samples from the U.S. Census to estimate wage equations in which quarter of birth is used as an instrument for educational attainment. We find evidence that, despite huge sample sizes, their IV estimates may suffer from finite-sample bias and may be inconsistent as well. These findings suggest that valid instruments may be more difficult to find than previously imagined. They also indicate that the use of large data sets does not necessarily insulate researchers from quantitatively important finite-sample biases. We suggest that the partial R(2) and the F statistic of the identifying instruments in the first-stage estimation are useful indicators of the quality of the IV estimates and should be routinely reported.d
New results on the exact small sample distribution of the instrumental variable estimator are presented by studying an important special case. The exact closed forms for the probability density and cumulative distribution functions are given. There are a number of surprising findings. The small sample distribution is bimodal. with a point of zero probability mass. As the asymptotic variance grows large, the true distribution becomes concentrated around this point of zero mass. The central tendency of the estimator may be closer to the biased least squares estimator than it is to the true parameter value. The first and second moments of the IV estimator are both infinite. In the case in which least squares is biased upwards, and most of the mass of the IV estimator lies to the right of the true parameter, the mean of the IV estimator is infinitely negative. The difference between the true distribution and the normal asymptotic approximation depends on the ratio of the asymptotic variance to a parameter related to the correlation between the regressor and the regression, error. In particular, when the instrument is poorly correlated with the regressor, the asymptotic approximation to the distribution of the instrumental variable estimator will not be very accurate.
This chapter discusses asymptotic properties of some estimators in structural models. Under normality, the k-class estimators are asymptotically efficient and the members with a = 1 are equivalent to the class of bias-adjusted maximum likelihood estimators. The bias-adjusted maximum likelihood estimators constitute an essentially complete class of second-order optimal estimators. Although the k-class estimators are not asymptotically efficient in the absence of normality, they have identical skewness and kurtosis coefficients to order T-1. Under symmetry, the bias-adjusted least variance ratio estimators, although no longer maximum-likelihood based, dominate the other k-class estimators. The effect of skewness and kurtosis of the error distribution on the sampling properties of the alternative estimators is counterintuitive.
In this article we study the small sample properties of the so called general k-class estimators of simultaneous equations. Two members of the family of k-class estimators are found, one of which is unbiased to the degree of our approximation and the other possesses a minimum second moment around the true parameter value, again to the order of our approximation.
Approximate distribution theory derives results from assumptions on the stochastic process generating the data. The quality of the approximation is not better than the quality of the specifications on which it is based. The models used by econometricians are, at best, crude and rather arbitrary. As most of the approximation methods employ information on the first four moments of the data whereas the usual asymptotic theory typically requires information only on the first two moments, some loss in robustness must be expected. However, if a rough idea about the degree of skewness and kurtosis is available, that information can be often exploited to obtain considerably improved approximations to sample statistics. The chapter discusses that sophisticated approximation theory is most appropriate in situations where the econometrician is able to make correct and detailed assumptions about the process being studied. In current practice, applied econometricians occasionally draw incorrect conclusions on the basis of alleged asymptotic properties of their procedures. In recent years, an extraordinary fondness for asymptotic theory has developed among econometricians. Considerable effort is devoted to showing that some new estimator or test is asymptotically normal and efficient. The assertion that a given estimator is approximately normal suggests that the speaker believes that it would be sensible to treat the estimator as though it were really normal. Accurate and convenient approximations for the distributions of econometric estimators and test statistics are of great value.
Recent advances in establishing the nature and scope of estimators in econometrics have shed more light on the importance of instrumental variables. In this book, the authors argue that such methods may be regarded as a strong organizing principle for a wide variety of estimation and hypothesis testing problems in econometrics and statistics. In support of this claim they present and develop the methodology of instrumental variables in its most general and explanatory form. They show, for instance, that techniques commonly used to handle simultaneity and related problems can be reduced to one of two generic variables of instrumental variables estimators, allowing them to explore further the conditions under which different proposed estimators are efficient.
The exact noncentral distributions of matrix variates and latent roots derived from normal samples involve hypergeometric functions of matrix argument. These functions can be defined as power series, by integral representations, or as solutions of differential equations, and there is no doubt that these mathematical characterizations have been a unifying influence in multivariate noncentral distribution theory, at least from an analytic point of view. From a computational and inference point of view, however, the hypergeometric functions are themselves of very limited value due primarily to the many difficulties involved in evaluating them numerically and consequently in studying the effects of population parameters on the distributions. Asymptotic results for large sample sizes or large population latent roots have so far proved to be much more useful for such problems. The purpose of this paper is to review some of the recent results obtained in these areas.
The correlation between instruments and explanatory variables is a key determinant of the performance of the instrumental variables estimator. The R-squared from regressing the explanatory variable on the instrument vector is a useful measure of relevance in univariate models, but can be misleading when there are multiple endogenous variables. This paper proposes a computationally simple partial R- squared measure of instrument relevance for multivariate models.
Recent research has emphasized the poor finite-sample performance of the instrumental variables estimator when the instruments are weakly correlated with the regressors. The authors show how the canonical correlations between regressors and instruments can provide a measure of instrument relevance in the general multiple-instrument-multiple-regressor case. However, their simulation results indicate that any such relevance measure probably has little practical merit, as its use may actually exacerbate the poor finite-sample properties of the instrumental variables estimator. Copyright 1996 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.
Weak instruments arise when the instruments in linear instrumental variables (IV) regression are weakly correlated with the included endogenous variables. In generalized method of moments (GMM), more generally, weak instruments correspond to weak identification of some or all of the unknown parameters. Weak identification leads to GMM statistics with nonnormal distributions, even in large samples, so that conventional IV or GMM inferences are misleading. Fortunately, various procedures are now available for detecting and handling weak instruments in the linear IV model and, to a lesser degree, in nonlinear GMM.
We develop a new specification test for IV estimators adopting a particular second order approximation of Bekker. The new specification test compares the difference of the forward (conventional) 2SLS estimator of the coefficient of the right-hand side endogenous variable with the reverse 2SLS estimator of the same unknown parameter when the normalization is changed. Under the null hypothesis that conventional first order asymptotics provide a reliable guide to inference, the two estimates should be very similar. Our test sees whether the resulting difference in the two estimates satisfies the results of second order asymptotic theory. Essentially the same idea is applied to develop another new specification test using second-order unbiased estimators of the type first proposed by Nagar. If the forward and reverse Nagar-type estimators are not significantly different we recommend estimation by LIML, which we demonstrate is the optimal linear combination of the Nagar-type estimators (to second order). We also demonstrate the high degree of similarity for "k"-class estimators between the approach of Bekker and the Edgeworth expansion approach of Rothenberg. An empirical example and Monte Carlo evidence demonstrate the operation of the new specification test. Copyright The Econometric Society 2002.
Properties of instrumental variable estimators are sensitive to the choice of valid instruments, even in large cross-section applications. In this paper we address this problem by deriving simple mean-square error criteria that can be minimized to choose the instrument set. We develop these criteria for two-stage least squares (2SLS), limited information maximum likelihood (LIML), and a bias adjusted version of 2SLS (B2SLS). We give a theoretical derivation of the mean-square error and show optimality. In Monte Carlo experiments we find that the instrument choice generally yields an improvement in performance. Also, in the Angrist and Krueger (1991) returns to education application, when the instrument set is chosen in the way we consider, it turns out that both 2SLS and LIML give similar (large) returns to education.
The paper develops and explores tests, based on standard moment specifications, for the identifiability of parameters apparently estimable by instrumental variables. An asymptotic expansion under standard restrictive assumptions on the error distribution suggests a correction to the asymptotic distribution. A small sampling experiment indicates that the tests are of use.
Modifications of the limited information estimator and of the fixed k-class estimator that possess finite moments are presented. It is demonstrated that, through terms of O(T^-^2) where T is the sample size, the fixed k-class estimator is dominated by the modification of the limited information estimator.
What is the weak-instruments (WI) problem and what causes it? Universal agreement does not exist on these questions. We define weak instruments by two features: (i) two-stage least squares (2SLS) analysis is badly biased toward the ordinary least-squares (OLS) estimate, and alternative "unbiased" estimators such as lim- ited-information maximum likelihood (LIML) may not solve the problem; and (ii) the standard (first-order) asymptotic distribution does not give an accurate framework for inference.1 Thus, a researcher may estimate "bad results" and not be aware of the outcome. The cause of WI is often stated to be a low R2 or F statistic of the reduced-form equation, in the most com- monly occurring situation of one right-hand- side endogenous variable. We find the situation is more complex with an additional factor, the correlation between the stochastic disturbances of the structural equation and the reduced form, that needs to be taken into account. We discuss in this paper a specification test (Hahn and Hausman, 2002a) for WI, a caution against us- ing "no moments" estimators such as LIML in the WI situation, and suggestions for different estimators, an approach to inference of Frank Kleibergen (2002) for WI. We end with a cau- tion of how "small biases" can become "large biases" in the WI situation. We begin with the limited-information struc- tural model under the assumptions of Hausman (1983): (1) Y1 Y2 Z1 u Y2 Z11 Z22 V where we assume that Y1 and Y2 are each single jointly endogenous variables. Without loss of generality, we "partial out" the Z1 variables by multiplying through each equation by the complementary projection QZ1 I Z 1(Z 1Z1)1Z 1 I PZ1. We write the result- ing equations as
Weak Instruments: Diagnosis and Cures in Empirical Econometrics,” forthcomingLatent Roots and Matrix Variates: A Review of Some Asymptotic Results
- J Hahn
- J Hausman
Hahn, J. and J. Hausman (2003): “Weak Instruments: Diagnosis and Cures in Empirical Econometrics,” forthcoming, American Economic Review, Papers and Proceedings. r37 Muirhead, R.J. (1978): “Latent Roots and Matrix Variates: A Review of Some Asymptotic Results,” Annals of Statistics, 6, 5-33
The Distribution of the Instrumental Variables Estimator and its tratio when the Instrument is a Poor One
(1990b): "The Distribution of the Instrumental Variables Estimator and its tratio when the Instrument is a Poor One," Journal of Business 63, 5125-5140.