We consider statistical inference for regression when data are grouped into clus- ters, with regression model errors independent across clusters but correlated within clusters. Examples include data on individuals with clustering on village or region or other category such as industry, and state-year dierences-in-dierences studies with clustering on state. In such settings default standard errors can greatly overstate es- timator precision. Instead, if the number of clusters is large, statistical inference after OLS should be based on cluster-robust standard errors. We outline the basic method as well as many complications that can arise in practice. These include cluster-specic �xed eects, few clusters, multi-way clustering, and estimators other than OLS.

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A Practitioner’s Guide to Cluster-Robust Inference

In this article we propose a variance estimator for the OLS estimator as well as for nonlinear estimators such as logit, probit, and GMM. This variance estimator enables cluster-robust inference when there is two-way or multiway clustering that is nonnested. The variance estimator extends the standard cluster-robust variance estimator or sandwich estimator for one-way clustering (e.g., Liang and Zeger 1986; Arellano 1987) and relies on similar relatively weak distributional assumptions. Our method is easily implemented in statistical packages, such as Stata and SAS, that already offer cluster-robust standard errors when there is one-way clustering. The method is demonstrated by a Monte Carlo analysis for a two-way random effects model; a Monte Carlo analysis of a placebo law that extends the state–year effects example of Bertrand, Duflo, and Mullainathan (2004) to two dimensions; and by application to studies in the empirical literature where two-way clustering is present.

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Robust Inference with Multi-way Clustering

A long-standing question in social science is to what extent differences in management cause differences in firm performance. To investigate this, the authors ran a management field experiment on large Indian textile firms, providing free consulting on modern management practices to a randomly chosen set of treatment plants and compared their performance to the control plants. They find that adopting these management practices had three main effects. First, it raised average productivity by 11 percent through improved quality and efficiency and reduced inventory. Second, it increased decentralization of decision making, as better information flow enabled owners to delegate more decisions to middle managers. Third, it increased the use of computers, necessitated by the data collection and analysis involved in modern management. Since these practices were profitable this raises the question of why firms had not adopted these before. Their results suggest that informational barriers were a primary factor in explaining this lack of adoption. Modern management is a technology that diffuses slowly between firms, with many Indian firms initially unaware of its existence or impact. Since competition was limited by constraints on firm entry and growth, badly managed firms were not rapidly driven from the market.

/pdf/does-management-matter-evidence-from-india-njalqn82hr.pdf

Does Management Matter? Evidence from India

Large Panels with Common Factors and Spatial Correlation

We analyze the introduction of highly subsidized, universally accessible child care in Quebec, addressing the impact on child care utilization, maternal labor supply, and family well‐being. We find strong evidence of a shift into new child care use, although some crowding out of existing arrangements is evident. Maternal labor supply increases significantly. Finally, the evidence suggests that children are worse off by measures ranging from aggression to motor and social skills to illness. We also uncover evidence that the new child care program led to more hostile, less consistent parenting, worse parental health, and lower‐quality parental relationships.

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Universal Childcare, Maternal Labor Supply, and Family Well-Being

https://economics.uwo.ca/people/conley_docs/conley_papers/inferencewithdependentdata.pdf

Inference with dependent data using cluster covariance estimators

Grouped effects estimators in fixed effects models

In this paper, we consider estimation of nonlinear panel data models that include individual specific fixed effects. Estimation of these models is complicated by the incidental parameters problem; that is, noise in the estimation of the fixed effects when the time dimension is short generally results in inconsistent estimates of the common parameters due to the nonlinearity of the problem. We present a penalty for the objective function that reduces the bias in the resulting point estimates. The penalty function involves only cross-products of scores and the hessian matrix and so is simple to construct in practice. The form of the penalty also provides interesting intuition into how the bias reduction is working. We present simulation results that suggest that the penalized optimization approach may substantially reduce the bias in nonlinear fixed effects models.

A Penalty Function Approach to Bias Reduction in Non-linear Panel Models with Fixed Effects

I. INTRODUCTION Governments are charged with the responsibility of crafting national budgets. Over time budgets tend to move between balance, surplus, and deficit. These fluctuations result from the fact that all too often a government makes financial decisions in one year that have implications for spending commitments and revenue streams a number of years down the road. Thus, responsible government budgeting involves examining the budget position over time, that is, engaging in intertemporal budgeting. Economists generally utilize two criteria to assess the intertemporal budget's sustainablity: does the government run persistent deficits? If so, what is the resulting level of debt? Are these two criteria sufficient to make predictions regarding budget sustainability? Recent work by Bohn (1995, 1998) and Ball et al. (1998) suggests that budgets are far too complicated to be evaluated with respect to deficits and debt alone. These authors have shown that persistent deficits and accumulation of debt does not necessarily imply that the debt is unmanageable and, hence, fiscal processes unsustainable. The implication of their work is that the standard approach to testing whether government adheres to its intertemporal budget constraint, cointegration analysis, does not provide sufficient criteria for determining whether the fiscal process is truly sustainable. Consequently, in this article we develop a more encompassing set of criteria under more realistic assumptions for determining whether a country exhibits a sustainable budgeting process. Our criteria for sustainability are based the multicointegration approach first presented by Granger and Lee (1989, 1990) and further developed in Engsted, Gonzalo and Haldrup (1997) and Haldrup (1998). The budgeting practices of 15 industrialized countries (Belgium, Canada, Denmark, Finland, France, Great Britain, Greece, Italy, the Netherlands, Norway, Portugal, Spain, Sweden, Switzerland and the United States) are evaluated in terms of the criteria. Our sample spans the modern era, 1960-98. We extend the intertemporal budgeting literature by employing the multicointegration framework to develop the appropriate policy responses to deficits and debt accumulation and to test for their presence. The methodology assesses both the stock and flow relationships that should characterize sustainable fiscal processes when the data are nonstationary. Cointegration between the spending-revenue flow relationship is the first component of our criteria. Cointegration between the flow of revenue (spending) and the stock of debt is the second. Jointly these conditions characterize multicointegration between government spending and revenue. In the multicointegration case, the system is characterized by a complex stock-flow equilibrium relationship that is not uncommon in intertemporal models of economic behavior. Such a relationship is typically associated with issues of optimal control where the levels and rates of change of the variables making up the system are determinants of the policy response. Multicointegration can ensure that a country's budgeting strategy is sustainable in "bad" states of nature, that is, when the rate of economic growth falls short of the real interest rate on sovereign debt. (1) Bohn (1995) and Ball et al. (1998) point out that existing theoretical models that underpin traditional sustainability tests are too simple. Specifically, Bohn (1995) shows that the sustainability of imbalances in a stochastic setting involves satisfying an intertemporal budget constraint and a transversality condition that differs from that implicit in simple (deterministic) models. The transversality condition requires that the limit of the debt discounted at a rate that is a function of the probability distribution of future debt and the marginal rate of substitution between present and future consumption be zero. This correct discounting is critical in economies where the rate of growth has been higher than the real interest rate. …

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Multicointegration and sustainability of fiscal practices

In Leachman et al. (2005) we use the multicointegration approach to test for sustainable fiscal budgeting processes in a stochastic setting in 15 industrialized countries. In this paper, we extend the analysis in order to rank these same countries as well as an additional three, according to the degree to which their budget processes are sustainable. Rankings are related to theories regarding the political economy of budget deficits. Evidence clearly indicates that fiscal performance is better where fiscal budgeting institutions are strong. Additionally, we find that in conjunction with fiscal strength, greater degrees of federalism positively affect intertemporal budget management.

Alan Bester

Papers

Inference with dependent data using cluster covariance estimators

Grouped effects estimators in fixed effects models

A Penalty Function Approach to Bias Reduction in Non-linear Panel Models with Fixed Effects

Multicointegration and sustainability of fiscal practices

The political economy of budget deficits