Regression Kink Design Research Articles

The Effect of Disability Insurance Payments on Beneficiaries' Earnings

A crucial issue is whether social insurance affects work decisions through income or substitution effects. We examine this in the context of US Social Security Disability Insurance (DI), exploiting discon tinuous changes in the benefit formula with a regression kink design to estimate the income effect of payments on earnings and employment. Using administrative data on all new DI beneficiaries from 2001 to 2007, our preferred estimate is that an increase in DI payments of $1 causes an average decrease in beneficiaries' earnings of $0.20 and that annual employment rates decrease by 1.3 percentage points per $1,000 of DI payments. These findings suggest that the income effect accounts for a majority of DI-induced reductions in earnings. (JEL E24, H55, J14, J22, J31)

The Effects of the Early Retirement Age on Retirement Decisions

We present quasi-experimental evidence on the effects of increasing the Early Retirement Age (ERA) on older workers' retirement decisions. The analysis is based on social security reforms in Austria in 2000 and 2004, and administrative data allows us to distinguish between pension claims and job exits. Using a Regression Kink Design, we estimate that, within a birth cohort, a 1.0 year increase in the ERA leads to a 0.4 year increase in the average job exiting age and a 0.5 year increase in the average pension claiming age. When the ERA increases, many older workers remain in their jobs longer.

The Effects of UI Benefits on Unemployment and Subsequent Outcomes: Evidence from a Kinked Benefit Rule

This paper analyzes the effects of unemployment insurance (UI) benefits on unemployment exits and subsequent labor market outcomes. We exploit a piecewise linear relationship between the previous wage and UI benefits in Finland to identify the causal effects of the benefit level by using a regression kink design. According to our findings, higher benefits lengthen nonemployment spells and decrease time spent in part-time unemployment, and thus result in more full-time unemployment. Also the re-employment probability and post-unemployment wage are negatively affected. The results for the duration of the first post-unemployment job are not conclusive, but in total both employment and earnings in the two years following the beginning of the unemployment spell decrease with higher benefits.

Cross-base tax elasticity of capital gains

ABSTRACTThis paper studies the cross-base tax elasticity of capital gains realizations to labour income taxes when capital gains are taxed at a separate proportional tax rate. Using a longitudinal panel of over 265 000 individuals in Sweden, this paper shows in a regression kink design that labour income taxes affect capital gains realizations in two ways. An increase in the marginal labour income tax rate increases the likelihood of realizing capital gains and the amount of realized capital gains. One implication of this result is that labour income taxes have a lock-out effect but that the magnitude of this effect is smaller than the lock-in effect of the actual capital gains tax.

The Effect of Negative Equity on Mortgage Default: Evidence from HAMP PRA

The Home Affordable Modification Program’s Principal Reduction Alternative (HAMP PRA) is a government-sponsored program to reduce the principal balances and monthly mortgage payments of borrowers with negative equity (mortgage balances in excess of their home value, or “under water”) who are in danger of default. We use administrative data to examine the impact of principal forgiveness — a permanent mortgage balance reduction — on borrowers’ subsequent mortgage default. The program’s rules imply a kink in the relationship between principal forgiveness and a borrower’s initial equity level ceteris paribus. Our identification strategy exploits the quasi-experimental variation in principal forgiveness generated by this kink using a regression kink design (RKD), which compares the relationship between initial equity and default on either side of the kink. The quarterly hazard — the proportion of loans that become more than 90 days delinquent and consequently exit the program — in our sample is 3.1 percent; we estimate that it would have been 3.8 percent absent principal forgiveness, which averaged 28 percent of the initial mortgage balance.

Unemployment Insurance and the Duration of Employment: Evidence from a Regression Kink Design

Can unemployment insurance (UI) affect the behavior of employed workers and the duration of their employment spells? I apply a regression kink design to address this question using data from the Brazilian labor market. Exploiting the UI schedule, I find that a 1% higher potential benefit level increases job duration by around 0.35%. This result is driven by the fact that a higher potential benefit level reduces the probability of job quits, which are not covered by UI. I develop a simple model showing that the positive effect on employment duration implies that the optimal benefit is higher than otherwise and delivers a simple welfare formula based on sufficient statistics. A simple calibration exercise shows that this elasticity affects welfare with a similar magnitude as the well-known elasticity of unemployment duration to the benefit level.

Heterogeneous Effects of Fiscal Equalization Grants on Local Expenditures: Evidence from Two Formula-Based Variations

This paper investigates the effects of fiscal equalization grants on total expenditure and disaggregated expenditures by exploiting two different formula-based exogenous variations in grants. Examining the institutional settings of the Japanese fiscal equalization scheme and estimating local average grant effects with a regression kink design and an instrumental variable approach, I demonstrate that there exist heterogeneous grant effects for two groups of municipalities with different fiscal conditions. That is, estimated grant effects on total expenditure are approximately one-to-one for municipalities around the threshold of grant eligibility, but much more than one-to-one for municipalities that are heavily dependent on fiscal equalization grants. In addition, grant effects on disaggregated expenditures are dispersed across different expenditure items in the former type of municipality but concentrated on construction expenditures in the latter type. I then discuss that the observed grant effect heterogeneity is a consequence of the institutional settings of the Japanese fiscal equalization scheme.

The Effect of Unemployment Benefits on the Duration of Unemployment Insurance Receipt: New Evidence from a Regression Kink Design in Missouri, 2003–2013

We provide new evidence on the effect of the unemployment insurance (UI) weekly benefit amount on unemployment insurance spells based on administrative data from the state of Missouri covering the period 2003-2013. Identification comes from a regression kink design that exploits the quasi-experimental variation around the kink in the UI benefit schedule. We find that UI durations are more responsive to benefit levels during the recession and its aftermath, with an elasticity between 0.65 and 0.9 as compared to about 0.35 pre-recession.

Price Sensitivity of Demand for Prescription Drugs: Exploiting a Regression Kink Design

SummaryWe investigate price sensitivity of demand for prescription drugs, using drug purchase records for the entire Danish population. We identify price responsiveness by exploiting variation in prices caused by kinked reimbursement schemes and implement a regression kink design. The results suggest some price responsiveness with corresponding price elasticities ranging from −0.2 to −0.7. Individuals with chronic disease and especially individuals above the age of 65 respond less to the price of drugs. Copyright © 2015 John Wiley & Sons, Ltd.

Inference on Causal Effects in a Generalized Regression Kink Design

We consider nonparametric identification and estimation in a nonseparable model where a continuous regressor of interest is a known, deterministic, but kinked function of an observed assignment variable. This arises in many institutional settings where a policy variable (such as weekly unemployment benefits) is determined by an observed but potentially endogenous assignment variable (like previous earnings). We provide new results on identification and estimation for these settings, and apply our results to obtain estimates of the elasticity of joblessness with respect to UI benefit rates. We characterize a broad class of models in which a sharp Regression Kink Design (RKD, or RK Design) identifies a readily interpretable treatment-on-the-treated parameter (Florens et al. (2008)). We also introduce a regression kink design generalization that allows for omitted variables in the assignment rule, noncompliance, and certain types of measurement errors in the observed values of the assignment variable and the policy variable. Our identifying assumptions give rise to testable restrictions on the distributions of the assignment variable and predetermined covariates around the kink point, similar to the restrictions delivered by Lee (2008) for the regression discontinuity design. We then use a fuzzy RKD approach to study the effect of unemployment insurance benefits on the duration of joblessness in Austria, where the benefit schedule has kinks at the minimum and maximum benefit level. Our preferred estimates suggest that changes in UI benefit generosity exert a relatively large effect on the duration of joblessness of both low-wage and high-wage UI recipients in Austria.

Inference on Causal Effects in a Generalized Regression Kink Design

We consider nonparametric identification and estimation in a nonseparable model where a continuous regressor of interest is a known, deterministic, but kinked function of an observed assignment variable. This arises in many institutional settings where a policy variable (such as weekly unemployment benefits) is determined by an observed but potentially endogenous assignment variable (like previous earnings). We provide new results on identification and estimation for these settings, and apply our results to obtain estimates of the elasticity of joblessness with respect to UI benefit rates. We characterize a broad class of models in which a sharp Regression Kink Design (RKD, or RK Design) identifies a readily interpretable treatment-on-the-treated parameter (Florens et al. (2008)). We also introduce a regression kink design generalization that allows for omitted variables in the assignment rule, noncompliance, and certain types of measurement errors in the observed values of the assignment variable and the policy variable. Our identifying assumptions give rise to testable restrictions on the distributions of the assignment variable and predetermined covariates around the kink point, similar to the restrictions delivered by Lee (2008) for the regression discontinuity design. We then use a fuzzy RKD approach to study the effect of unemployment insurance benefits on the duration of joblessness in Austria, where the benefit schedule has kinks at the minimum and maximum benefit level. Our preferred estimates suggest that changes in UI benefit generosity exert a relatively large effect on the duration of joblessness of both low-wage and high-wage UI recipients in Austria.

Inference on Causal Effects in a Generalized Regression Kink Design

We consider nonparametric identification and estimation in a nonseparable model where a continuous regressor of interest is a known, deterministic, but kinked function of an observed assignment variable. We characterize a broad class of models in which a sharp “Regression Kink Design” (RKD or RK Design) identifies a readily interpretable treatment-on-the-treated parameter (Florens, Heckman, Meghir, and Vytlacil (2008)). We also introduce a “fuzzy regression kink design” generalization that allows for omitted variables in the assignment rule, noncompliance, and certain types of measurement errors in the observed values of the assignment variable and the policy variable. Our identifying assumptions give rise to testable restrictions on the distributions of the assignment variable and predetermined covariates around the kink point, similar to the restrictions delivered by Lee (2008) for the regression discontinuity design. Using a kink in the unemployment benefit formula, we apply a fuzzy RKD to empirically estimate the effect of benefit rates on unemployment durations in Austria.

The causal effect of coalition governments on fiscal policies: evidence from a Regression Kink Design

Proportional election systems are widespread across countries and often lead to coalition governments. This creates interest in how the form of government (single-party or coalition governments) causally influences fiscal policies. It is difficult to estimate this causal effect empirically because the form of government is not randomly assigned to political units. I overcome this problem by using a Regression Kink Design which exploits that there is a slope change in the treatment probability at the 50% vote share of the strongest party. This method is applied to a large panel data set of German local governments. I find that contrary to the theoretical prediction, coalition governments significantly decrease expenditures.

Cross-Base Tax Elasticity of Capital Gains

This paper studies the cross-base tax elasticity of capital gains realizations to labor income taxes when capital gains are taxed at a separate proportional tax rate. Using a longitudinal panel of over 265,000 individuals in Sweden, this paper shows in a regression kink design that labor income taxes affect capital gains at the extensive and intensive margins. An increase in the marginal labor income tax rate increases the likelihood of realizing capital gains and the amount of realized capital gains. One implication of this result is that the excess burden of labor income taxation is affected by cross-base tax elasticities.

A Kink that Makes You Sick: The Incentive Effect of Sick Pay on Absence

This paper examines the effect of the replacement rule of the Finnish sickness insurance system on the duration of sickness absence. A pre-determined, piecewise linear policy rule in which the replacement rate is determined by past earnings allows identification of the effect using a regression kink design. We find a substantial and robust behavioral response. The statistically significant point estimate of the elasticity of the duration of sickness absence with respect to the replacement rate is on the order of 1.4.

Stimulating Local Public Employment: Do General Grants Work?

We apply the regression kink design to the Swedish grant system and estimate causal effects of intergovernmental grants on local public employment. Our robust conclusion is that grants do not stimulate local public employment. We find no statistically significant effects on total local public employment, and we can exclude even moderate effects. When disaggregating the total effect by sector, we find that personnel in the traditional welfare sectors are unaffected, a conclusion which applies to both publicly and privately employed in these sectors. The only positive and statistically significant effect of grants is that on administrative personnel. (JEL H75, H77, J45)

Assessing the Welfare Effects of Unemployment Benefits Using the Regression Kink Design

I show how, in the tradition of the dynamic labor supply literature, one can identify the moral hazard effects and liquidity effects of unemployment insurance (UI) using variations along the time profile of unemployment benefits. I use this strategy to investigate the anatomy of labor supply responses to UI. I identify the effect of benefit level and potential duration in the regression kink design using kinks in the schedule of benefits in the US. My results suggest that the response of search effort to UI benefits is driven as much by liquidity effects as by moral hazard effects. (JEL D82, J22, J65)

Optimal Patent Term and Cross-Industry Measures of Patent Term Sensitivity

Patents are monopolies granted to inventors in order to promote innovation, but they have a limited term because they also impose social costs. There is little empirical research on what constitutes an optimal patent term, or whether patent term should vary across industry categories.We take a first step in studying these issues by examining cross-industry differences in patent term sensitivity. We take advantage of a change in law --- the passage of the TRIPS agreement in 1994 --- that caused patent term to be measured from the date a patent application was filed rather than the date the patent was granted, thereby reducing patent term by the amount of time an application was pending before the U.S. Patent and Trademark Office. Using a new dataset, we determine what portion of this delay is attributable to applicants for 331,113 issued patents filed in 1994-1996. This shows, for the first time, how patent applicants in different industries sped up their prosecution behavior in response to the change in law, which gives us a measure of industry sensitivity to patent term change.We predict, via a formal model, that patent applicants in industries with higher profits toward the end of patent term are the applicants most likely to speed up patent prosecution after TRIPS. Our results show that pharmaceutical patentees sped up patent prosecution significantly, which accords with prior theory on the primacy of patents in this industry. We find, however, that software patentees also significantly sped up prosecution, which is unexpected given prior theory suggesting patents are less important in spurring software development. Our patent delay measure is highly correlated with patent renewal rates across industries, suggesting our measure assesses the value of patents to applicants in different industries.Additionally, our paper exploits another, separate aspect of the legal change that gave some firms longer patent term extensions vis a vis others. We perform an event study and find that firms receiving longer extensions tended to have higher market returns. We obtain similar results using a new empirical technique known as regression kink design, which addresses potential selection issues.Our results provide support for our formal model, suggesting that patentees in industries most likely to receive higher profits near the end of patent term were the ones most sensitive to the change in patent term rules. More generally, our results suggest we have credibly estimated the value of patents across industries, which can guide further research on optimal patent term and the effect of patents on innovation.

The Causal Effect of Coalition Governments on Fiscal Policies: Evidence from a Regression Kink Design

Proportional election systems are widespread across countries and often lead to coalition governments. This creates interest in how the form of government (single-party or coalition governments) causally influences fiscal policies. It is difficult to estimate this causal effect empirically because the form of government is not randomly assigned to the political units. I overcome this problem by using a Regression Kink Design which exploits that there is a slope change in the treatment probability at the 50%-vote share of the strongest party. This method is applied to a large panel data set of German local governments. I find that contrary to the theoretical prediction, coalition governments significantly decrease expenditures.

Assessing the Welfare Effects of Unemployment Benefits Using the Regression Kink Design

I investigate in this paper partial equilibrium labor supply responses to unemployment insurance (UI) in the US. I use administrative data on the universe of unemployment spells in five states from the late 1970s to 1984, and non-parametrically identify the effect of both benefit level and potential duration in the regression kink (RK) design using kinks in the schedule of UI benefits. I provide many tests for the robustness of the RK design, and demonstrate its validity to overcome the traditional issue of endogeneity in UI benefit variations on US data. I also show how, in the tradition of the dynamic labor supply literature, one can identify the purely distortionary effects of UI using variations along the returns-to-employment profile brought about by exogenous variations in the benefit level as well as in the benefit duration. I then use these estimates to calibrate the welfare effects of an increase in UI benefit level and in UI potential duration.