David Roodman

How to do Xtabond2: An Introduction to Difference and System GMM in Stata

The Arellano-Bond (1991) and Arellano-Bover (1995)/Blundell-Bond (1998) linear generalized method of moments (GMM) estimators are increasingly popular. Both are general estimators designed for situations with “small T, large N” panels, meaning few time periods and many individuals; with independent variables that are not strictly exogenous, meaning correlated with past and possibly current realizations of the error; with fixed effects; and with heteroskedasticity and autocorrelation within individuals. This pedagogic paper first introduces linear GMM. Then it shows how limited time span and the potential for fixed effects and endogenous regressors drive the design of the estimators of interest, offering Stata-based examples along the way. Next it shows how to apply these estimators with xtabond2. It also explains how to perform the Arellano-Bond test for autocorrelation in a panel after other Stata commands, using abar. The Center for Global Development is an independent think tank that works to reduce global poverty and inequality through rigorous research and active engagement with the policy community. Use and dissemination of this Working Paper is encouraged, however reproduced copies may not be used for commercial purposes. Further usage is permitted under the terms of the Creative Commons License. The views expressed in this paper are those of the author and should not be attributed to the directors or funders of the Center for Global Development.

A Note on the Theme of Too Many Instruments

The difference and system generalized method of moments (GMM) estimators are growing in popularity. As implemented in popular software, the estimators easily generate instruments that are numerous and, in system GMM, potentially suspect. A large instrument collection overfits endogenous variables even as it weakens the Hansen test of the instruments’ joint validity. This paper reviews the evidence on the effects of instrument proliferation, and describes and simulates simple ways to control it. It illustrates the dangers by replicating Forbes [American Economic Review (2000) Vol. 90, pp. 869–887] on income inequality and Levine et al. [Journal of Monetary Economics] (2000) Vol. 46, pp. 31–77] on financial sector development. Results in both papers appear driven by previously undetected endogeneity.

Aid, Policies, and Growth: Comment

In an extraordinarily influential paper, Craig Burnside and David Dollar (2000, p. 847) find that “... aid has a positive impact on growth in developing countries with good fiscal, monetary, and trade policies but has little effect in the presence of poor policies.” This finding has enormous policy implications. The Burnside and Dollar (2000, henceforth BD) result provides a role and strategy for foreign aid. If aid stimulates growth only in countries with good policies, this suggests that (1) aid can promote economic growth, and (2) it is crucial that foreign aid be distributed selectively to countries that have adopted sound policies. International aid agencies, public policy makers, and the press quickly recognized the importance of the BD findings. This paper reassesses the links between aid, policy, and growth using more data. The BD data end in 1993. We reconstruct the BD database from original sources and thus (1) add additional countries and observations to the BD data set because new information has become available since they conducted their analyses, and (2) extend the data through 1997. Thus, using the BD methodology, we reexamine whether aid influences growth in the presence of good policies. Given our focus on retesting BD, we do not summarize the vast pre-BD literature on aid and growth. We just note that there was a long and inconclusive literature that was hampered by limited data availability, debates about the mechanisms through which aid would affect growth, and disagreements over econometric specification (see Gustav F. Papanek, 1972; Robert Cassen, 1986; Paul Mosley et al., 1987; Peter Boone, 1994, 1996; and Henrik Hansen and Finn Tarp’s 2000 review). Since BD found that aid boosts growth in good policy environments, there have been a number of other papers reacting to their results, including Paul Collier and Jan Dehn (2001), CarlJohan Dalgaard and Hansen (2001), Patrick Guillaumont and Lisa Chauvet (2001), Hansen and Tarp (2001), Robert Lensink and Howard White (2001), and Collier and Dollar (2002). These papers conduct useful variations and extensions (some of which had already figured in the pre-BD literature), such as introducing additional control variables, using nonlinear specifications, etc. Some of these papers confirm the message that aid only works in a good policy environment, while others drive out the aid policy interaction term with other variables. This literature has the usual limitations of choosing a specification without clear guidance from theory, which often means there are more plausible specifications than there are data points in the sample. We differentiate our paper from these others by NOT deviating from the BD specification. Thus, we do not test the robustness of the results to an unlimited number of variations, but instead maintain the BD methodology. This paper conducts a very simple robustness check by adding new data that were unavailable to BD. Thus, we expand the sample used over their time period and extend the data from 1993 to 1997. * Easterly: Department of Economics, New York University, 269 Mercer Street, New York, NY 10003, Center for Global Development, and National Bureau of Economic Research (e-mail: william.easterly@nyu.edu); Levine: Department of Finance, Carlson School of Management, University of Minnesota, 321 19th Avenue South, Minneapolis, MN 55455, and National Bureau of Economic Research (e-mail: rlevine@csom.umn.edu); Roodman: Center for Global Development, 1776 Massachusetts Avenue NW, Washington, DC 20036 (e-mail: droodman@cgdev.org). We are grateful to Craig Burnside for supplying data and assisting in the reconstruction of previous results, without holding him responsible in any way for the work in this paper. Thanks also to Francis Ng and Prarthna Dayal for generous assistance with updating the Sachs-Warner openness variable, and to three anonymous referees, Craig Burnside, and Henrik Hansen for helpful comments. 1 See, for instance, the World Bank (1994, 2001, 2002), the U.K. Department for International Development (2000), President George W. Bush’s speech (March 16, 2002), the announcement by the White House on creating the Millennium Challenge Corporation (White House, 2002), as well as a Washington Post editorial (February 9, 2002), a Financial Times column by Alan Beattie (March 11, 2002), and The Economist (March 16, 2002).

Estimating Fully Observed Recursive Mixed-Process Models with Cmp

At the heart of many econometric models are a linear function and a normal error. Examples include the classical small-sample linear regression model and the probit, ordered probit, multinomial probit, tobit, interval regression, and truncated-distribution regression models. Because the normal distribution has a natural multidimensional generalization, such models can be combined into mul- tiequation systems in which the errors share a multivariate normal distribution. The literature has historically focused on multistage procedures for fitting mixed models, which are more efficient computationally, if less so statistically, than maxi- mum likelihood. Direct maximum likelihood estimation has been made more prac- tical by faster computers and simulated likelihood methods for estimating higher- dimensional cumulative normal distributions. Such simulated likelihood methods include the Geweke–Hajivassiliou–Keane algorithm (Geweke, 1989, Econometrica 57: 1317–1339; Hajivassiliou and McFadden, 1998, Econometrica 66: 863–896; Keane, 1994, Econometrica 62: 95–116). Maximum likelihood also facilitates a generalization to switching, selection, and other models in which the number and types of equations vary by observation. The Stata command cmp fits seemingly un- related regressions models of this broad family. Its estimator is also consistent for recursive systems in which all endogenous variables appear on the right-hand sides as observed. If all the equations are structural, then estimation is full-information maximum likelihood. If only the final stage or stages are structural, then estima- tion is limited-information maximum likelihood. cmp can mimic a score of built-in and user-written Stata commands. It is also appropriate for a panoply of models that previously were hard to estimate. Heteroskedasticity, however, can render cmp inconsistent. This article explains the theory and implementation of cmp and of a related Mata function, ghk2(), that implements the Geweke–Hajivassiliou–Keane algorithm. Copyright 2011 by StataCorp LP.

The Impact of Microcredit on the Poor in Bangladesh: Revisiting the Evidence

Abstract We replicate and reanalyse the most influential study of microcredit impacts (M. M. Pitt & S. R. Khandker’s, ‘The impact of group-based credit on poor households in Bangladesh: Does the gender of participants matter?’, published in the Journal of Political Economy, 106, 1998). That study was celebrated for showing that microcredit reduces poverty, a much hoped for possibility (though one not confirmed by recent randomised controlled trials). We show that the original results on poverty reduction disappear after dropping outliers, or when using a robust linear estimator. Using a new program for estimation of mixed process maximum likelihood models, we show how assumptions critical for the original analysis, such as error normality, are contradicted by the data. We conclude that questions about impact cannot be answered in these data.

An Index of Donor Performance

The Commitment to Development Index of the Center for Global Development rates 21 rich countries on the “development-friendliness” of their policies. It is revised and updated annually. In the 2004 edition, the component on foreign assistance combines quantitative and qualitative measures of official aid, and of fiscal policies that support private charitable giving. The quantitative measure uses a net transfers concept, as distinct from the net flows concept in the net Official Development Assistance measure of the Development Assistance Committee, which does not net out interest received. The qualitative factors are three: a penalty for tying aid; a discounting system that favors aid to poorer, better-governed recipients; and a penalty for “project proliferation.” The selectivity weighting approach avoids some conceptual problems inherent in the Dollar and Levin (2004) elasticity-based method. The proliferation penalty derives from a calibrated model of aid transaction cost developed in Roodman (forthcoming). The charitable giving measure is based on an estimate of the share of observed private giving to developing countries that is attributable to a) lower overall taxes (income effect) and b) specific tax incentives for giving (price effect). Despite the adjustments, overall results are dominated by differences in quantity of official aid given. This is because while there is a seven-fold range in net concessional transfers/GDP among the score countries, variation in overall aid quality across donors appears far lower, and private giving is generally small. Denmark, the Netherlands, Norway, and Sweden score highest while the largest donors in absolute terms, the United States and Japan, score in the bottom third. Standings by the 2004 methodology have been relatively stable since 1995.

New Data, New Doubts: Revisiting 'Aid, Policies, and Growth'

The Burnside and Dollar (2000) finding that aid raises growth in a good policy environment has had an important influence on policy and academic debates. We conduct a data gathering exercise that updates their data from 1970–93 to 1970–97, as well as filling in missing data for the original period 1970–93. We find that the BD finding is not robust to the use of this additional data.

Aid Project Proliferation and Absorptive Capacity

Much public discussion about foreign aid has focused on whether and how to increase its quantity. But recently aid quality has come to the fore, by which is meant the effectiveness of the aid delivery process. This paper focuses on one process problem, the proliferation of aid projects and the associated administrative burden for recipients. It models aid delivery as a set of production activities (projects) with two inputs, the donor’s aid and a recipient-side resource, and two outputs, namely, development and “throughput,” which proxies for the private benefits for both donor and recipient of implementing projects, from kickbacks to career rewards for disbursing. The donor’s allocation of aid across projects is taken as exogenous while the recipient’s allocation of its resource is modeled and subject to a budget constraint. Unless the recipient cares purely about development, increasing aid can reduce development in some circumstances. Sunk costs, representing the administrative burden for the recipient of donor meetings and reports, are introduced. Using data on the distribution of projects by size and country, simulations of aid increases are run in order to examine how the project distribution evolves, how the recipient’s resource allocation responds, and how this affects development if the recipient is not a pure development optimizer. With Cobb-Douglas production, a threshold is revealed beyond which marginal aid effectiveness drops sharply. It occurs when development maximization calls for the recipient to withdraw from some donor-backed projects—but the recipient does not, for the sake of throughput. Donors can push back this threshold by moving to larger projects if there are scale economies in aid projects.

Through the Looking Glass, and What OLS Found There: On Growth, Foreign Aid, and Reverse Causality

The cross-country literature on foreign aid effectiveness has relied on the use of instruments to distinguish causality from mere correlation. This paper uses simple non-instrumental techniques in the spirit of Granger to demonstrate that the main aid-growth connection is a negative causal relationship from growth to aid—-aid, that is, as a fraction of recipient GDP. Coarsely, when GDP goes up, aid/GDP goes down. The endogeneity of aid, long suspected, is real. Less understood is that adding certain common controls to regressions puts this relationship through the looking glass, flipping both its sign and apparent direction: aid seems to cause growth. Ideally, instrumentation expunges the endogeneity shown here. In practice, estimates of aid’s impact have run into problems. Autocorrelation in the errors is widespread, and can render endogenous lagged variables used as regressors or instruments. The pitfalls of “difference” and “system” include invalidity and proliferation of instruments. Multicollinearity in term pairs of interest, such as aid and aid2 or “project” and “program” aid, can amplify endogeneity bias. The combination of specification problems and widespread fragility (shown in earlier work) leads to pessimism about the ability of cross-country econometrics to demonstrate aid effectiveness. This does not rule an average positive effect, nor does it contradict the fact that aid has saved millions of lives, but it does suggest that the average effect on economic growth is too small to be detected statistically.

Competitive Proliferation of Aid Projects: A Model

The proliferation of aid projects may overburden recipient governments with reporting requirements, donor visits, and other administrative overhead, siphoning off scarce domestic recipient resources, such as tax revenue or the time of skilled government officials, from directly productive use. But greater oversight may also improve the administration of projects, increasing development. I present a model of aid projects that reflects both sides of this coin. It posits a distinction between national-level governance and project-level governance. A donor can raise project-level governance above the baseline national level by requiring oversight activities of the recipient, although the benefits from doing so are less where national-level governance is already high. The model assumes that larger projects demand proportionally less oversight activity from the recipient. Comparative statics analysis suggests that to maximize development, projects should be larger where aid volume is higher, to avoid overburdening recipient administrative capacity; where recipient resources are scarcer, for the same reason; and where national governance is good, since the marginal benefit of oversight is then lower. A multi-donor generalization shows how donors that are imperfectly altruistic, caring most about the success of their own projects, will tend to sink into competitive proliferation, in which each donor subdivides its aid budget into smaller projects to raise the marginal productivity of the recipient’s resources in those projects and attract them away from other donors. The inefficiency arises from the lack of a market among donors for recipient resources. In a Nash equilibrium, competitive proliferation reduces overall development. But the smallest (selfish) donors can gain. This would discourage them from cooperating with other donors to contain competitive proliferation.