We establish five facts about prices in the U.S. economy: 1) The median implied duration of consumer prices when sales are excluded at the product level is between 8 and 11 months. The median implied duration of finished goods producer prices is 8.7 months. 2) One-third of regular price changes are price decreases. 3) The frequency of price increases responds strongly to inflation while the frequency of price decreases and the size of price increases and price decreases do not. 4) The frequency of price change is highly seasonal: It is highest in the 1st quarter and lowest in the 4th quarter. 5) The hazard function of price changes for individual consumer and producer goods is downward sloping for the first few months and then flat (except for a large spike at 12 months in consumer services and all producer prices). These facts are based on CPI microdata and a new comprehensive data set of microdata on producer prices that we construct from raw production files underlying the PPI. We show that the 1st, 2nd and 3rd facts are consistent with a benchmark menu-cost model, while the 4th and 5th facts are not.

In this paper we propose a new variance estimator for OLS 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 multi-way 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 et al. (2004) to two dimensions; and by application to two studies in the empirical public/labor literature where two-way clustering is present.

Microeconometrics researchers have increasingly realized the essential need to account for any within-group dependence in estimating standard errors of regression parameter estimates. The typical preferred solution is to calculate cluster-robust or sandwich standard errors that permit quite general heteroskedasticity and within-cluster error correlation, but presume that the number of clusters is large. In applications with few (5-30) clusters, standard asymptotic tests can overreject considerably. We investigate more accurate inference using cluster bootstrap-t procedures that provide asymptotic refinement. These procedures are evaluated using Monte Carlos, including the much-cited differences-in-differences example of Bertrand, Mullainathan and Duflo (2004). In situations where standard methods lead to rejection rates in excess of ten percent (or more) for tests of nominal size 0.05, our methods can reduce this to five percent. In principle a pairs cluster bootstrap should work well, but in practice a wild cluster bootstrap performs better.

Abstract. We discuss instrumental variables (IV) estimation in the broader context of the generalized method of moments (GMM), and describe an extended IV estimation routine that provides GMM estimates as well as additional diagnostic tests. Stand–alone test procedures for heteroskedasticity, overidentification, and endogeneity in the IV context are also described.

and two anonymous referees for helpful comments and suggestions. Cornwell and Mustard gratefully acknowledge

This paper presents a novel way to conduct inference using dependent data in time series, spatial, and panel data applications. Our method involves constructing t and Wald statistics utilizing a cluster covariance matrix estimator (CCE). We then use an approximation that takes the number of clusters/groups as fixed and the number of observations per group to be large and calculate limiting distributions of the t and Wald statistics. This approximation is analogous to ‘fixed-b’ asymptotics of Kiefer and Vogelsang (2002, 2005) (KV) for heteroskedasticity and autocorrelation consistent inference, but in our case yields standard t and F distributions where the number of groups essentially plays the role of sample size. We provide simulation evidence that demonstrates our procedure outperforms conventional inference procedures and performs well comparably to KV.

This introduction to the plm package is a slightly modified version of Croissant and Millo (2008), published in the Journal of Statistical Software. Panel data econometrics is obviously one of the main fields in the profession, but most of the models used are difficult to estimate with R. plm is a package for R which intends to make the estimation of linear panel models straightforward. plm provides functions to estimate a wide variety of models and to make (robust) inference. Keywords:˜panel data, covariance matrix estimators, generalized method of moments, R. 1.

a large number of datasets from a large number of countries which are based on household-level surveys, statistically representative of the populations of those countries, and which include data on non-durable expenditures. These data on expenditures can be used to measure economic welfare—indeed, this kind of measurement is a chief raison d’etre of this collection of survey data. Though the micro-data from these surveys are not generally available, the Bank provides data on aggregate expenditures by decile for many of these countries. Further, for many countries data from more than one year is available, so that it’s possible to construct an unbalanced panel of data on the level and distribution of expenditures for a number of countries over the last several decades. We also have data on country-level measures of agricultural income, as well as other aggregate income. The question: how do changes in the sectoral composition of income affect the distribution of expenditures across households within a country? 1. Models The question of how changes in the sectoral composition of income affect the distribution of expenditures is an important one for all many of policy issues. Given this importance, it’s surprising how little reliable guidance there seems to be in either the theoretical or empirical literature. Here we briefly and selectively review a few models and bits of evidence the subject. We will assume two sectors throughout—an agricultural and non-agricultural sector, both for simplicity, and because Date: All code and data used to generate this paper are available at

Relying on volunteer labor, open source projects like the Apache web server create commercial quality software. Why developers contribute freely without direct remuneration has been widely debated. We offer empirical evidence that such participation can be explained by existing theories in labor economics. Analyzing panel data covering a four-year period, we find that increases in human capital, measured as project contribution, do not lead to increased wages. In contrast, credentials earned through a merit-based ranking system are associated with significantly increased wages. Our results suggest that status within an open source meritocracy operates as a credible signal of productive capacity. * We thank the open source programmers who have contributed to this study. We also thank the participants of the

We develop a general approach to robust inference about a scalar parameter when the data is potentially heterogeneous and correlated in a largely unknown way. The key ingredient is the following result of Bakirov and Székely (2005) concerning the small sample properties of the standard t−test: For a significance level of 5 % or lower, the t−test remains conservative for underlying observations that are independent and Gaussian with heterogenous variances. One might thus conduct robust large sample inference as follows: partition the data into q ≥ 2 groups, estimate the model for each group and conduct a standard t−test with the resulting q parameter estimators. This results in valid and in some sense efficient inference when the groups are chosen in a way that ensures the parameter estimators to be asymptotically independent, unbiased and Gaussian of possibly different variances. We provide examples of how to apply this approach to time series, panel, clustered and spatially correlated data.