Linh T. Tô

Data transformations often facilitate regression analysis, yet many commonly used transformations make hypothesis testing misleading because the results depend on the measurement units of the data. This paper aims to address this issue by characterizing the set of transformations where measurement units do not affect conclusions in linear regressions. The equivalence theorem establishes that desirable properties—scale-equivariant coefficient estimates, scale-invariant t-statistics, and scale-invariant semi-elasticities—arise if and only if the transformation is a logarithmic or a power function. Power transformations thus offer a natural extension of logarithmic transformations that both preserves the essential feature of obtaining unit-independent estimates for unitless quantities of interest and can handle zero or negative values. On the other hand, popular alternatives that approximate the shape of the logarithmic function at large values, such as adding a small positive constant before applying a logarithmic transformation or the inverse hyperbolic sine transformation, result in similar inferences as in an untransformed linear regression when expressing outcomes in large measurement units and imply arbitrarily large effect sizes or arbitrarily large confidence intervals when expressing outcomes in small measurement units. We demonstrate using data from a randomized experiment that such transformations reverse the sign or significance of treatment effect estimates for up to 15 out of 49 outcomes variables when measurement units are changed to natural alternatives (e.g., from US dollars to local currency).

@article{thakralto2023when,
  title={When Are Estimates Independent of Measurement Units},
  author={Thakral, Neil and T{\^o}, Linh T},
  journal={Mimeo},
  year={2023}
}

In this study, we examine how the same hiring opportunity leads to different labor market outcomes for male and female full-time workers. By utilizing matched employer-employee data from Germany, our empirical approach leverages 30,000 unforeseen worker deaths spanning from 1980 to 2016 which enables us to explore how firms react to exogenous vacancies. We find that when a position becomes vacant, female replacements have starting wages that are on average 20 log points lower compared to their male counterparts. Even after considering the pre-hire wage of replacement workers at their previous firm, half of this gap persists. The gender disparity in opportunities cannot be attributed to redistribution of wages paid among other coworkers. Over time, the gap tends to widen on average, and it remains stable for those who remain employed full-time in the subsequent five years after being hired.

@article{illing2023hiring,
  title={Hiring and the Dynamics of the Gender Gap},
  author={Illing, Hannah and Schwank, Hanna and T{\^o}, Linh T},
  journal={Mimeo},
  year={2023}
}

This paper develops a framework for estimation of the effect of a policy or treatment in settings with variation in treatment timing. We propose a simple and intuitive two-stage estimator that is robust to treatment-effect heterogeneity. In the first stage, we identify group and period effects using the sample of untreated observations. In the second stage, we estimate average treatment effects by comparing treated and untreated outcomes after removing these group and period effects. The procedure can be extended to environments with individual fixed effects and inference can be conducted from within a conventional asymptotic framework. We establish the theoretical properties of the two-stage approach and highlight its advantages over existing proposals. Simulations of randomly generated placebo laws in state-level wage data demon- strate that our method outperforms alternative approaches for estimation and inference.

@article{gardner2023two,
  title={Two-Stage Differences in Differences},
  author={Gardner, John and Thakral, Neil and T{\^o}, Linh T and Yap, Luther},
  journal={Mimeo},
  year={2023}
}

This paper studies the distribution of workplace flexibility in the labor market and its sources. We collect information on which workers have workplace flexibility along three dimensions, flexible location, flexible scheduling of hours, and flexible total number of hours worked. Low-wage workers can choose to work part-time more flexibly but have a significant disadvantage when it comes to flexible location and scheduling. We overcome challenges in measuring individual-level willingness-to-pay (WTP) by using an adaptive discrete choice experiment, finding WTP for all three dimensions of workplace flexibility to be relatively flat across the wage distribution. Differences in preferences thus cannot account for the facts, suggesting that workers may face unequal compensating prices to obtain the same workplace amenity. We microfound this relationship with a model in which workplace flexibility interacts with production processes that utilize labor inputs at different skill levels. Using a structural model of compensating differentials, we quantify that unequal amenity prices explain 7.2% of wage inequality and 8% of total utility inequality. The results highlight that the unequal distribution of workplace flexibility contributes to the widening of wage inequality even in the presence of compensating differentials.

@article{drakethakralto2022flexibility,
  title={Wage Differentials and the Price of Workplace Flexibility},
  author={Drake, Marshall, and Thakral, Neil and T{\^o}, Linh T},
  journal={Mimeo},
  year={2022}
}

Cash transfer payments are an increasingly widespread policy tool in developed and developing countries, used for both short-term objectives such as boosting consumer spending and long-term objectives such as poverty alleviation. This paper proposes that the marginal propensity to consume out of a windfall depends on a new state variable, the time horizon over which households anticipate receiving a payment. We test this in three different settings arising from a systematic survey of the literature: a natural experiment provided by the randomized disbursement dates of the 2008 U.S. fiscal stimulus payments, and randomized controlled trials on unconditional cash transfers in Kenya and Malawi. Our data show evidence of excess anticipation-dependence: Consumption consistently responds more strongly to the receipt of additional income after a shorter anticipation duration, in excess of what standard models predict. While households receiving stimulus payments do not increase spending in advance, the additional consumption expenditure in the month after receiving payment drops by about 30 percent for each additional week that a household waits for their payment. Savings data from Kenya and Malawi show comparable effects. We estimate a model that incorporates this novel form of history dependence to discuss implications for the design of fiscal stimulus policies and cash transfer programs. Our evidence and approach reconcile seemingly conflicting results that consumption responds to anticipated payments in some settings but not others.

@article{thakralto2022consumption,
  title={Anticipation and Consumption},
  author={Thakral, Neil and T{\^o}, Linh T},
  journal={Mimeo},
  year={2022}
}

This paper evaluates the hypothesis that, in setting wages, firms respond to costly signals by workers when such costs are informative of their values to the firms. For workers who become mothers, uncertainty about their future values can influence firms’ decisions to distribute career and promotion opportunities. Consequently, workers may forgo paid parental leave even when there is no human capital depreciation associated with taking leave. I build a signaling model with a continuous choice of leave period when such choice is restricted due to the maximum allowed paid leave duration. Using administrative data from Denmark and a parental leave policy extending the maximum allowed duration of parental leave, I show how a leave extension affects wages, hours, and promotion opportunities for workers whose signaling ability changes with the extension. In contrast to human capital theory, an individual can take longer leave but gain in wages when the larger choice set allows more workers to signal their type. The paper provides evidence of the labor market consequences of parental leave-taking due to signaling and the importance of asymmetric information in shaping parental leave choice.

@article{to2018signaling,
  title={The Signaling Role of Parental Leave},
  author={T{\^o}, Linh T},
  journal={Mimeo},
  year={2018},
  keywords={asymmetric information, statistical discrimination, wages, labor supply}
}

We present a model of intertemporal choice based on anticipatory utility and examine the consequences of temptation goods, which decision-makers do not fully value prospectively. We discuss implications of the resulting time-inconsistent preferences for the decision making of the poor and show how the model gives rise to a poverty trap. We use data from randomized experiments on cash transfers in Kenya and Malawi to test one of the distinct empirical predictions of the model, that households with more time to anticipate receiving a lump-sum payment spend less on temptation goods, namely tobacco and alcohol.

@article{thakralto2020temptation,
  title={Anticipation and Temptation},
  author={Thakral, Neil and T{\^o}, Linh T},
  journal={Mimeo},
  year={2020}
}

This paper provides field evidence on how reference points adjust, a degree of freedom in reference-dependence models. Examining this in the context of cabdrivers’ daily labor-supply behavior, we ask how the within-day timing of earnings affects decisions. Drivers work less in response to higher accumulated income, with a strong effect for recent earnings that gradually diminishes for earlier earnings. We estimate a structural model in which drivers work towards a reference point that adjusts to deviations from expected earnings with a lag. This dynamic view of reference dependence reconciles conflicting “neoclassical” and “behavioral” interpretations of evidence on daily labor-supply decisions.

@article{thakralto2022consumption,
  title={Anticipation and Consumption},
  author={Thakral, Neil and T{\^o}, Linh T},
  journal={Mimeo},
  year={2022}
}