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Using recent results in the measurement error literature, we show that the official U.S. unemployment rate substantially underestimates the true level of unemployment, due to misclassification errors in the labor force status in the Current Population Survey. During the period from January 1996 to August 2011, the corrected monthly unemployment rates are between 1 and 4.4 percentage points (2.1 percentage points on average) higher than the official rates, and are more sensitive to changes in business cycles. The labor force participation rates, however, are not affected by this correction.

Virtually all methods aimed at correcting for covariate measurement error in regressions rely on some form of additional information (e.g., validation data, known error distributions, repeated measurements or instruments). In contrast, we establish that the fully nonparametric classical errors-in-variables model is identifiable from data on the regressor and the dependent variable alone, unless the model takes a very specific parametric form. This parametric family includes (but is not limited to) the linear specification with normally distributed variables as a well-known special case. This result relies on standard primitive regularity conditions taking the form of smoothness constraints and nonvanishing characteristic functions assumptions. Our approach can handle both monotone and nonmonotone specifications, provided the latter oscillate a finite number of times. Given that the very specific unidentified parametric functional form is arguably the exception rather than the rule, this identification result should have a wide applicability. It leads to a new perspective on handling measurement error in nonlinear and nonparametric models, opening the way to a novel and practical approach to correct for measurement error in data sets where it was previously considered impossible (due to the lack of additional information regarding the measurement error). We suggest an estimator based on non/semi-parametric maximum likelihood, derive its asymptotic properties and illustrate the effectiveness of the method with a simulation study and an application to the relationship between firm investment behavior and market value, the latter being notoriously mismeasured.

Using recent results in the measurement error literature, we show that the official U.S. unemployment rates substantially underestimate the true levels of unemployment, due to misclassification errors in labor force status in Current Population Surveys. Our closed-form identification of the misclassification probabilities relies on the key assumptions that the misreporting behaviors only depend on the true values and that the true labor force status dynamics satisfy a Markov-type property. During the period of 1996 to 2009, the corrected monthly unemployment rates are 1 to 4.6 percentage points (25% to 45%) higher than the official rates, and are more sensitive to changes in business cycles. Labor force participation rates, however, are not affected by this correction. We also provide results for various subgroups of the U.S. population defined by gender, race and age.

Consider an observed binary regressor D and an unobserved binary variable D*, both of which affect some other variable Y . This paper considers nonparametric identification and estimation of the effect of D on Y , conditioning on D* = 0. For example, suppose Y is a person's wage, the unobserved D* indicates if the person has been to college, and the observed D indicates whether the individual claims to have been to college. This paper then identifies and estimates the difference in average wages between those who falsely claim college experience versus those who tell the truth about not having college.We estimate this average returns to lying to be about 7% to 20%. Nonparametric identification without observing D* is obtained either by observing a variable V that is roughly analogous to an instrument for ordinary measurement error, or by imposing restrictions on model error moments.