Moving the Goalposts: Addressing Limited Overlap in Estimation of Average Treatment Effects by Changing the Estimand *Estimation of average treatment effects under unconfoundedness or exogenous treatment assignment is often hampered by lack of overlap in the covariate distributions. This lack of overlap can lead to imprecise estimates and can make commonly used estimators sensitive to the choice of specification. In such cases researchers have often used informal methods for trimming the sample. In this paper we develop a systematic approach to addressing such lack of overlap. We characterize optimal subsamples for which the average treatment effect can be estimated most precisely, as well as optimally weighted average treatment effects. Under some conditions the optimal selection rules depend solely on the propensity score. For a wide range of distributions a good approximation to the optimal rule is provided by the simple selection rule to drop all units with estimated propensity scores outside the range [0.1, 0.9].

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may AbstractWe show how to price the time series and cross section of zero coupon bonds via ordinary least squares regressions. Our approach allows computationally fast estimation of term structure models with a large number of pricing factors. Even though we do not impose cross-equation restrictions in the estimation, we show that our return regressions generate a term structure of interest rates with small pricing errors compared to commonly reported specifications, both in and out-of-sample.

A large part of the recent literature on program evaluation has focused on estimation of the average effect of the treatment under assumptions of unconfoundedness or ignorability following the seminal work by Rubin (1974) and Rosenbaum and Rubin (1983). In many cases however, researchers are interested in the effects of programs beyond estimates of the overall average or the average for the subpopulation of treated individuals. It may be of substantive interest to investigate whether there is any subpopulation for which a program or treatment has a nonzero average effect, or whether there is heterogeneity in the effect of the treatment. The hypothesis that the average effect of the treatment is zero for all subpopulations is also important for researchers interested in assessing assumptions concerning the selection mechanism. In this paper we develop two nonparametric tests. The first test is for the null hypothesis that the treatment has a zero average effect for any subpopulation defined by covariates. The second test is for the null hypothesis that the average effect conditional on the covariates is identical for all subpopulations, in other words, that there is no heterogeneity in average treatment effects by covariates. Sacrificing some generality by focusing on these two specific null hypotheses we derive tests that are straightforward to implement.

Estimation of average treatment effects under unconfoundedness or exogenous treatment assignment is often hampered by lack of overlap in the covariate distributions. This lack of overlap can lead to imprecise estimates and can make commonly used estimators sensitive to the choice of specification. In such cases researchers have often used informal methods for trimming the sample. In this paper we develop a systematic approach to addressing such lack of overlap. We characterize optimal subsamples for which the average treatment effect can be estimated most precisely, as well as optimally weighted average treatment effects. Under some conditions the optimal selection rules depend solely on the propensity score. For a wide range of distributions a good approximation to the optimal rule is provided by the simple selection rule to drop all units with estimated propensity scores outside the range [0.1,0.9].

We present an affine term structure model for the joint pricing of real and nominal bond yields that explicitly accommodates liquidity risk premia. We estimate the model using a new, computationally efficient procedure that is based on return regressions. The model allows us to address a number of salient questions about the transmission of monetary policy. We show that variations in U.S. nominal term premia are primarily driven by variations in real term premia rather than inflation and liquidity risk premia. Nonetheless, adjusting breakevens for inflation and liquidity risk substantially improves forecasts of inflation. Our estimates imply that the Federal Reserve's large-scale asset purchases lowered Treasury yields primarily by reducing real term premia. Real term premia also account for the positive response of long-term real forward rates to surprise changes in the federal funds target. Applying our model to U.K. data, we find that the inflation risk premium dropped sharply when the Bank of England formally adopted an inflation target.

A large part of the recent literature on program evaluation has focused on estimation of the average effect of the treatment under assumptions of unconfoundedness or ignorability following the seminal work by Rubin (1974) and Rosenbaum and Rubin (1983). In many cases however, researchers are interested in the effects of programs beyond estimates of the overall average or the average for the subpopulation of treated individuals. It may be of substantive interest to investigate whether there is any subpopulation for which a program or treatment has a nonzero average effect, or whether there is heterogeneity in the effect of the treatment. The hypothesis that the average effect of the treatment is zero for all subpopulations is also important for researchers interested in assessing assumptions concerning the selection mechanism. In this paper we develop two nonparametric tests. The first test is for the null hypothesis that the treatment has a zero average effect for any subpopulation defined by covariates. The second test is for the null hypothesis that the average effect conditional on the covariates is identical for all subpopulations, in other words, that there is no heterogeneity in average treatment effects by covariates. Sacrificing some generality by focusing on these two specific null hypotheses we derive tests that are straightforward to implement.

We use the term structure of disagreement of professional forecasters to document a novel set of facts: (1) forecasters disagree at all horizons, including the long run; (2) the term structure of disagreement differs markedly across variables: it is downward sloping for real output growth, relatively flat for inflation, and upward sloping for the federal funds rate; (3) disagreement is time-varying at all horizons, including the long run. These new facts present a challenge to benchmark models of expectation formation based on informational frictions. We show that these models require two additional ingredients to match the entire term structure of disagreement: First, agents must disentangle low-frequency shifts in the fundamentals of the economy from short-term fluctuations. Second, agents must take into account the dynamic interactions between variables when forming forecasts. While models enriched with these features capture the observed term structure of disagreement irrespective of the source of the informational friction, they fall short at explaining the time variance of disagreement at medium-and long-term horizons. We also use the term structure of disagreement to analyze the monetary policy rule perceived by professional forecasters and show that it features a high degree of interest-rate smoothing and time variation in the intercept.

We estimate the elasticity of intertemporal substitution (EIS)-the elasticity of expected consumption growth with respect to variation in the real interest rate-using subjective expectations from the newly released FRBNY Survey of Consumer Expectations (SCE). This dataset is unique, since it includes consumers' expectations of both consumption growth and inflation, with the latter providing subjective variation in ex ante real interest rates. As a result, we can estimate a subjective version of the consumption Euler equation, without having to take a stand on the process of expectation formation. Our main finding is that this subjective EIS is precisely and robustly estimated to be around 0.8 in the general population, consistent with typical macroeconomic calibrations of the Euler equation. However, we find some evidence that the EIS rises to slightly above one for high-income individuals, consistent with the assumptions in asset pricing models featuring long-run risks or rare disasters.