National Bureau of Economic Research

This paper describes a simple method of calculating a heteroskedasticity and autocorrelation consistent covariance matrix that is positive semi-definite by construction. It also establishes consistency of the estimated covariance matrix under fairly general conditions.

Most papers that employ Differences-in-Differences estimation (DD) use many years of data and focus on serially correlated outcomes but ignore that the resulting standard errors are inconsistent. To illustrate the severity of this issue, we randomly generate placebo laws in state-level data on female wages from the Current Population Survey. For each law, we use OLS to compute the DD estimate of its “effect” as well as the standard error of this estimate. These conventional DD standard errors severely understate the standard deviation of the estimators: we find an “effect” significant at the 5 percent level for up to 45 percent of the placebo interventions. We use Monte Carlo simulations to investi-gate how well existing methods help solve this problem. Econometric corrections that place a specific parametric form on the time-series process do not perform well. Bootstrap (taking into account the autocorrelation of the data) works well when the number of states is large enough. Two corrections based on asymptotic approximation of the variance-covariance matrix work well for moderate numbers of states and one correction that collapses the time series information into a “pre”-and “post”-period and explicitly takes into account the effective sample size works well even for small numbers of states.

Output per worker varies enormously across countries. Why? On an accounting basis our analysis shows that differences in physical capital and educational attainment can only partially explain the variation in output per worker—we find a large amount of variation in the level of the Solow residual across countries. At a deeper level, we document that the differences in capital accumulation, productivity, and therefore output per worker are driven by differences in institutions and government policies, which we call social infrastructure. We treat social infrastructure as endogenous, determined historically by location and other factors captured in part by language.

This paper develops a model based on Schumpeter's process of creative destruction. It departs from existing models of endogenous growth in emphasizing obsolescence of old technologies induced by the accumulation of knowledge and the resulting process or industrial innovations. This has both positive and normative implications for growth. In positive terms, the prospect of a high level of research in the future can deter research today by threatening the fruits of that research with rapid obsolescence. In normative terms, obsolescence creates a negative externality from innovations, and hence a tendency for laissez-faire economies to generate too many innovations, i.e too much growth. This business-stealing effect is partly compensated by the fact that innovations tend to be too small under laissez-faire. The model possesses a unique balanced growth equilibrium in which the log of GNP follows a random walk with drift. The size of the drift is the average growth rate of the economy and it is endogenous to the model ; in particular it depends on the size and likelihood of innovations resulting from research and also on the degree of market power available to an innovator.

This paper develops asymptotic distribution theory for instrumental variable regression when the partial correlation between the instruments and a single included endogenous variable is weak, here modeled as local to zero. Asymptotic representations are provided for various instrumental variable statistics, including the two-stage least squares (TSLS) and limited information maximum- likelihood (LIML) estimators and their t-statistics. The asymptotic distributions are found to provide good approximations to sampling distributions with just 20 observations per instrument. Even in large samples, TSLS can be badly biased, but LIML is, in many cases, approximately median unbiased. The theory suggests concrete quantitative guidelines for applied work. These guidelines help to interpret Angrist and Krueger's (1991) estimates of the returns to education: whereas TSLS estimates with many instruments approach the OLS estimate of 6%, the more reliable LIML and TSLS estimates with fewer instruments fall between 8% and 10%, with a typical confidence interval of (6%, 14%).

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No. This paper investigates the relationship between financing constraints and investment-cash flow sensitivities by analyzing the firms identified by Fazzari, Hubbard, and Petersen as having unusually high investment-cash flow sensitivities. We find that firms that appear less financially constrained exhibit significantly greater sensitivities than firms that appear more financially constrained. We find this pattern for the entire sample period, subperiods, and individual years. These results (and simple theoretical arguments) suggest that higher sensitivities cannot be interpreted as evidence that firms are more financially constrained. These findings call into question the interpretation of most previous research that uses this methodology.

Following the 2016 US presidential election, many have expressed concern about the effects of false stories (“fake news”), circulated largely through social media. We discuss the economics of fake news and present new data on its consumption prior to the election. Drawing on web browsing data, archives of fact-checking websites, and results from a new online survey, we find: 1) social media was an important but not dominant source of election news, with 14 percent of Americans calling social media their “most important” source; 2) of the known false news stories that appeared in the three months before the election, those favoring Trump were shared a total of 30 million times on Facebook, while those favoring Clinton were shared 8 million times; 3) the average American adult saw on the order of one or perhaps several fake news stories in the months around the election, with just over half of those who recalled seeing them believing them; and 4) people are much more likely to believe stories that favor their preferred candidate, especially if they have ideologically segregated social media networks.

One strand of endogenous-growth\tmodels assumes constant returns to a broad concept of capital. I extend these models to include tax- financed government services that affect production or utility. Growth and saving rates fall with an increase in utility-type expenditures; the two rates rise initially with productive government expenditures but subsequently decline. With an income tax, the decentralized choices of growth and saving are "too low," but if the production function is Cobb-Douglas, the optimizing government still satisfies a natural condition for productive efficiency. Empirical evidence across countries supports some of the hypotheses about government and growth.

We present a model embodying moderate amounts of nominal rigidities that accounts for the observed inertia in inflation and persistence in output. The key features of our model are those that prevent a sharp rise in marginal costs after an expansionary shock to monetary policy. Of these features, the most important are staggered wage contracts that have an average duration of three quarters and variable capital utilization.

We apply an understanding of what computers do to study how computerization alters job skill demands. We argue that computer capital (1) substitutes for workers in performing cognitive and manual tasks that can be accomplished by following explicit rules; and (2) complements workers in performing nonroutine problem-solving and complex communications tasks. Provided that these tasks are imperfect substitutes, our model implies measurable changes in the composition of job tasks, which we explore using representative data on task input for 1960 to 1998. We find that within industries, occupations, and education groups, computerization is associated with reduced labor input of routine manual and routine cognitive tasks and increased labor input of nonroutine cognitive tasks. Translating task shifts into education demand, the model can explain 60 percent of the estimated relative demand shift favoring college labor during 1970 to 1998. Task changes within nominally identical occupations account for almost half of this impact.

Uncertainty appears to jump up after major shocks like the Cuban Missile crisis, the assassination of JFK, the OPEC I oil-price shock, and the 9/11 terrorist attacks. This paper offers a structural framework to analyze the impact of these uncertainty shocks. I build a model with a time-varying second moment, which is numerically solved and estimated using firm-level data. The parameterized model is then used to simulate a macro uncertainty shock, which produces a rapid drop and rebound in aggregate output and employment. This occurs because higher uncertainty causes firms to temporarily pause their investment and hiring. Productivity growth also falls because this pause in activity freezes reallocation across units. In the medium term the increased volatility from the shock induces an overshoot in output, employment, and productivity. Thus, uncertainty shocks generate short sharp recessions and recoveries. This simulated impact of an uncertainty shock is compared to vector autoregression estimations on actual data, showing a good match in both magnitude and timing. The paper also jointly estimates labor and capital adjustment costs (both convex and nonconvex). Ignoring capital adjustment costs is shown to lead to substantial bias, while ignoring labor adjustment costs does not. Copyright 2009 The Econometric Society.

This study investigates whether marketwide liquidity is a state variable important for asset pricing. We find that expected stock returns are related cross-sectionally to the sensitivities of returns to fluctuations in aggregate liquidity. Our monthly liquidity measure, an average of individual-stock measures estimated with daily data, relies on the principle that order flow induces greater return reversals when liquidity is lower. From 1966 through 1999, the average return on stocks with high sensitivities to liquidity exceeds that for stocks with low sensitivities by 7.5 percent annually, adjusted for exposures to the market return as well as size, value, and momentum factors. Furthermore, a liquidity risk factor accounts for half of the profits to a momentum strategy over the same 34-year period.

If competitive equilibrium is defined as a situation in which prices are such that all arbitrage profits are eliminated, is it possible that a competitive economy always be in equilibrium? Clearly not, for then those who arbitrage make no (private) return from their (privately) costly activity. Hence the assumptions that all markets, including that for information, are always in equilibrium and always perfectly arbitraged are inconsistent when arbitrage is costly. We propose here a model in which there is an equilibrium degree of disequilibrium: prices reflect the information of informed individuals (arbitrageurs) but only partially, so that those who expend resources to obtain information do receive compensation. How informative the price system is depends on the number of individuals who are informed; but the number of individuals who are informed is itself an endogenous variable in the model. The model is the simplest one in which prices perform a well-articulated role in conveying information from the informed to the uninformed. When informed individuals observe information that the return to a security is going to be high, they bid its price up, and conversely when they observe information that the return is going to be low. Thus the price system makes publicly available the information obtained by informed individuals to the uniformed. In general, however, it does this imperfectly; this is perhaps lucky, for were it to do it perfectly, an equilibrium would not exist. In the introduction, we shall discuss the general methodology and present some con-

In the wake of the Mexican and Asian currency turmoil, the subject of financial crises has come to the forefront of academic and policy discussions. This paper analyzes the links between banking and currency crises. We find that: problems in the banking sector typically precede a currency crisis—the currency crisis deepens the banking crisis, activating a vicious spiral; financial liberalization often precedes banking crises. The anatomy of these episodes suggests that crises occur as the economy enters a recession, following a prolonged boom in economic activity that was fueled by credit, capital inflows, and accompanied by an overvalued currency. (JEL F30, F41)

We propose and evaluate explicit tests of the null hypothesis of no difference in the accuracy of two competing forecasts. In contrast to previously developed tests, a wide variety of accuracy measures can be used (in particular, the loss function need not be quadratic and need not even be symmetric), and forecast errors can be non-Gaussian, nonzero mean, serially correlated, and contemporaneously correlated. Asymptotic and exact finite-sample tests are proposed, evaluated, and illustrated.

This paper analyzes compensation schemes which pay according to an individual's ordinal rank in an organization rather than his output level. When workers are risk neutral, it is shown that wages based upon rank induce the same efficient allocation of resources as an incentive reward scheme based on individual output levels. Under some circumstances, risk-averse workers actually prefer to be paid on the basis of rank. In addition, if workers are heterogeneous inability, low-quality workers attempt to contaminate high-quality firms, resulting in adverse selection. However, if ability is known in advance, a competitive handicapping structure exists which allows all workers to compete efficiently in the same organization.

Efforts to anticipate how climate change will affect future food availability can benefit from understanding the impacts of changes to date. We found that in the cropping regions and growing seasons of most countries, with the important exception of the United States, temperature trends from 1980 to 2008 exceeded one standard deviation of historic year-to-year variability. Models that link yields of the four largest commodity crops to weather indicate that global maize and wheat production declined by 3.8 and 5.5%, respectively, relative to a counterfactual without climate trends. For soybeans and rice, winners and losers largely balanced out. Climate trends were large enough in some countries to offset a significant portion of the increases in average yields that arose from technology, carbon dioxide fertilization, and other factors.

This critique argues that the preponderance of theoretical reasoning and empirical evidence suggests a positive, first-order relationship between financial development and economic growth. The body of work would push even most skeptics toward the belief that the development of financial markets and institutions is a critical and inextricable part of the growth process and away from the view that the financial system is an inconsequential sideshow, responding passively to economic growth. Many gaps remain, however, and the paper highlights areas in acute need of additional research.

We investigate conditions sufficient for identification of average treatment effects using instrumental variables. First we show that the existence of valid instruments is not sufficient to identify any meaningful average treatment effect. We then establish that the combination of an instrument and a condition on the relation between the instrument and the participation status is sufficient for identification of a local average treatment effect for those who can be induced to change their participation status by changing the value of the instrument. Finally we derive the probability limit of the standard IV estimator under these conditions. It is seen to be a weighted average of local average treatment effects.