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Open Access Publications from the University of California

Recent Work

The department was founded in 1964 and has 35 permanent members. We are a relatively young group, all committed to a rigorous analytical approach to both teaching and research. As a consequence, we have a congenial and cooperative atmosphere in which department members take an unusually active interest in their colleagues' research. There are no social or administrative distinctions between junior and senior faculty, except on promotion decisions. Eight faculty members are Fellows of the Econometric Society, three are on the Econometric Society Council, and three are Fellows of the American Academy of Arts and Sciences. Five are NBER Research Associates, and twelve have NSF grants.

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Cover page of A Simple and Trustworthy Asymptotic t Test in Difference-in-Differences Regressions

A Simple and Trustworthy Asymptotic t Test in Difference-in-Differences Regressions


We propose an asymptotically valid t test that uses Student's t distribution as the reference distribution in a difference-in-differences regression. For the asymptotic variance estimation, we adopt the clustering-by-time approach to accommodate cross-sectional dependence. This approach often assumes the clusters to be independent across time, but we allow them to be temporally dependent. The proposed t test is based on a special heteroscedasticity and autocorrelation robust (HAR) variance estimator. We target the type I and type II errors and develop a testing-oriented method to select the underlying smoothing parameter. By capturing the estimation uncertainty of the HAR variance estimator, the t test has more accurate size than the corresponding normal test and is just as powerful as the latter. Compared to the nonstandard test developed in the literature, the standard t test is just as accurate but much more convenient to use. Model-based and empirical-data-based Monte Carlo simulations show that the t test works quite well in finite samples.

Cover page of Asymptotic F Tests under Possibly Weak Identification

Asymptotic F Tests under Possibly Weak Identification


This paper develops asymptotic F tests robust to weak identification and temporal dependence. The test statistics are modified versions of the S statistic of Stock and Wright (2000) and the K statistic of Kleibergen (2005), both of which are based on the continuous updating generalized method of moments. In the former case, the modification involves only a multiplicative degree-of-freedom adjustment. In the latter case, the modification involves an additional multiplicative adjustment that uses a J statistic for testing overidentification. By adopting fixed-smoothing asymptotics, we show that both the modified S statistic and the modified K statistic are asymptotically F-distributed. The asymptotic F theory accounts for the estimation errors in the underlying heteroskedasticity and autocorrelation robust variance estimators, which the asymptotic chi-squared theory ignores. Monte Carlo simulations show that the F approximations are much more accurate than the corresponding chi-squared approximations in finite samples.

Cover page of Heteroscedasticity and Autocorrelation Robust F and t Tests in Stata

Heteroscedasticity and Autocorrelation Robust F and t Tests in Stata


In this article, we consider time series OLS and IV regressions and introduce a new pair of commands, har and hart, which implement a more accu- rate class of heteroscedasticity and autocorrelation robust (HAR) F and t tests. These tests represent part of the recent progress on HAR inference. The F and t tests are based on the convenient F and t approximations and are more accurate than the conventional chi-squared and normal approximations.  The underlying smoothing parameters are selected to target the type I and type II errors, the two fundamental objects in every hypothesis testing problem. The estimation com- mand har and the post-estimation test command hart allow for both kernel HAR variance estimators and orthonormal series HAR variance estimators. In addition, we introduce another pair of new commands, gmmhar and  gmmhart which imple- ment the recently developed F and t tests in a two-step GMM framework. For this command we opt for the orthonormal series HAR variance estimator based on the Fourier bases,  as it allows us to develop convenient F and t approxima- tions as in the first-step GMM framework.  Finally, we present several examples to demonstrate the use of these commands.

Cover page of Testing for Moderate Explosiveness in the Presence of Drift

Testing for Moderate Explosiveness in the Presence of Drift


This paper considers a moderately explosive autoregressive(1) process with drift where the autoregressive root approaches unity from the right at a certain rate. We first develop a test for the null of moderate explosiveness under independent and identically distributed errors. We show that the t statistic is asymptotically standard normal regardless of whether the errors are Gaussian. This result is in sharp contrast with the existing literature wherein nonstandard limiting distributions are obtained under different model assumptions. When the errors are weakly dependent, we show that the t statistic based on a heteroskedasticity and autocorrelation robust standard error follows Student's t distribution in large samples. Monte Carlo simulations show that our tests have satisfactory size and power performance in finite samples. Applying the asymptotic t test to ten major stock indexes in the pre-2008 financial exuberance period, we find that most indexes are only mildly explosive or not explosive at all, which implies that the bout of the irrational rise was not as serious as previously thought.

Cover page of Human Capital and Structural Change

Human Capital and Structural Change


What explains labor reallocation out of agriculture? We propose an accounting framework that leverages observable variation across birth cohorts to study the role of human capital accumulation. We model a dynamic overlapping generations economy where heterogeneous individuals choose whether to stay in or move out of agriculture, subject to mobility frictions. The model shows analytically that labor reallocation within- and across-cohorts pins down the relative role of human capital vs. sectoral prices/productivities in labor reallocation. We apply the framework to micro data from 52 countries. We document novel empirical patterns on labor reallocation by cohort and use them, through the lens of our model, to discipline the size of mobility frictions and show two results: (i) human capital explains one third of labor reallocation, on average; but (ii) it has a minor role in explaining why some countries have faster reallocation than others. Furthermore, we use years of schooling as a direct measure of human capital to validate our main approach and we exploit a large-scale school construction program in Indonesia as a natural experiment to study the effects of an exogenous increase in human capital. We show that the program led to labor reallocation out of agriculture.

Cover page of Simple, Robust, and Accurate F and t Tests in Cointegrated Systems

Simple, Robust, and Accurate F and t Tests in Cointegrated Systems


This paper proposes new, simple, and more accurate statistical tests in a cointegrated system that allows for endogenous regressors and serially dependent errors. The approach involves first transforming the time series using orthonormal basis functions in L²[0,1], which has energy concentrated at low frequencies, and then running an augmented regression based on the transformed data and constructing the test statistics in the usual way. The approach is essentially the same as the trend instrumental variable approach of Phillips (2014), but we hold the number of orthonormal basis functions fixed in order to develop the standard F and t asymptotic theory. The tests are extremely simple to implement, as they can be carried out in exactly the same way as if the transformed regression is a classical linear normal regression. In particular, critical values are from the standard F or t distribution. The proposed F and t tests are robust in that they are asymptotically valid regardless of whether the number of basis functions is held fixed or allowed to grow with the sample size. The F and t tests have more accurate size in finite samples than existing tests such as the asymptotic chi-squared and normal tests based on the fully modified OLS estimator of Phillips and Hansen (1990) and can be made as powerful as the latter test.