Using the labour supply responses of lottery winners to evaluate tax and transfer policies

David Cesarini, Erik Lindqvist, Matthew Notowidigdo, Robert Östling

24 January 2016



Recently, citizens and politicians in Switzerland began considering a universal basic income programme, which is currently scheduled for a voter referendum in late 2016.  The programme attracted widespread media attention; the Washington Post described the proposal as ‘universal and unconditional’ with every citizen receiving the guaranteed income no matter what, with “no work requirements, no means-testing, and no restrictions on how the money is used”.

In many countries, cash welfare programmes are designed instead as conditional transfer programmes and phased out as income increases. As is taught in many introductory labour economics and public economics classes (e.g. Chapter 2 in Gruber 2011), conditional transfer programmes generate both income and substitution effects due to higher ‘effective’ marginal tax rates for low-income workers. As a result, a common criticism is that conditional transfer programmes discourage work.

By contrast, the universal and unconditional aspect of the Swiss policy does not change effective marginal tax rates or work incentives. However, the programme could still reduce employment and average hours worked through the income effect.1 Most existing empirical evidence points towards leisure being a normal good, so that increases in (unearned) income reduce labour supply (Keane 2011).

Empirical evidence on income effects in labour supply

A large empirical literature has provided estimates of income effects using a variety of different empirical strategies, but disagreement over the magnitude remains. Although some agreement exists that large, permanent changes in real wages induce relatively modest differences in labour supply, Kimball and Shapiro (2008) write that “there is much less agreement about whether the income and substitution effects are both large or both small”. As a result, it is difficult to precisely forecast the labour market consequences of basic income programmes like the one discussed above. 

A key empirical challenge in estimating income effects in labour supply is isolating variation in unearned income or wealth that is unrelated to other determinants of labour supply. One way to address this challenge is to use lotteries, which randomly assign wealth. This allows researchers to study the effect of unearned income on labour supply using the well-understood framework of a randomised controlled trial. In many lotteries, participants purchase different numbers of tickets, which means that the participants do not all have the same chance of winning. However, by conditioning on the number of tickets, one can provide credible estimates of the effect of lottery wealth on labour supply.

The use of lotteries to study labour supply is pursued in a classic paper by Imbens et al. (2001), who study a small sample of 496 lottery players in Massachusetts by linking survey data on the lottery players to administrative data containing information on annual labour earnings. They find modest reductions in labour earnings suggesting every dollar of universal basic income would reduce labour earnings by roughly $0.11.

New evidence from Swedish lottery winners

In recent work, we build on and extend the work by Imbens et al. (2001) using a very large, newly collected sample of lottery players in Sweden, drawing from a sample of several million lottery players who appear fairly representative of the national population. In our main analysis, we follow the lottery players for 5-10 years after winning a lottery prize. Figure 1 shows the annual earnings reduction to a lump-sum lottery prize in our main sample. Overall, we find broadly similar results to Imbens et al. (2001).

Figure 1. Effect of wealth on individual gross labour earnings

Notes: This figure reports estimates obtained from equation (2) estimated in the pooled lottery sample with gross labor earnings as the dependent variable. A coefficient of 1.00 corresponds to an increase in annual labor earnings of 1 SEK for each 100 SEK won. Each year corresponds to a separate regression and the dashed lines show 95% confidence intervals.

We also provide several additional results that may prove useful for policy.

  • First, we estimate the effect of winning the lottery on both pre-tax and after-tax earnings. 

Most of the existing empirical literature has not emphasised this distinction, even though both after-tax and pre-tax earnings responses are relevant. For example, most models of individual labour supply make predictions regarding how after-tax earnings respond to unearned income. By contrast, pre-tax earnings responses are useful for understanding how widespread increases in unearned income affect aggregate economic activity. This distinction is especially important in countries with high tax rates, since taxes create a significant wedge between pre-tax and after-tax earnings. In Sweden, we find that the lottery-induced reduction in taxes and social security contributions combined is larger in magnitude than the estimated reduction in after-tax earnings, highlighting the fiscal costs of the labour supply reductions. On average, each $100 won reduces annual after-tax earnings by about $0.60 while taxes and social security contributions fall by $0.80, implying a total annual productivity loss of $1.40.

  • Second, we are able to measure earnings responses of both the lottery winners themselves as well as their spouses. 

We find that spouses also reduce their labour earnings, although by less than the winner. As a result, the overall household labour earnings reduction is larger than the individual response of the winner, suggesting that focusing on just winners understates the aggregate effects of unearned income shocks.2

  • Lastly, we compare the dynamic response to a lump-sum lottery prize with the dynamic response to ‘instalment prizes’, which pay out a constant amount every month for a pre-determined (and randomly assigned) number of years.

This comparison is useful because any differences between these two types of prizes would suggest important departures from ‘textbook’ economic models and could also indicate the importance of liquidity constraints or myopia. In the Swedish data, however, we find no evidence of significant differences between the responses, which suggests a limited role for liquidity constraints in determining the magnitude of income effects in labour supply.

  • Our preferred estimates suggest that every dollar won in a lottery reduces lifetime after-tax labour earnings of winners by $0.10-$0.20.

The reduction in lifetime earnings is largest for younger winners. The reduction in pre-tax earnings and social security contributions (which is a broader measure that more accurately captures the decline in economic activity) is more than twice as large.  Additionally, we find that the overall earnings reduction comes from both intensive margin and extensive margin changes, meaning that winning a lottery causes both of a reduction in work hours as well as a reduction in the probability of being employed. 

Lessons for economists and policymakers

We conclude by discussing some broad lessons for tax and transfer programmes.  Returning to textbook labour economics and public economics, many policies generate both income and substitution effects. The lottery estimates described above directly inform income effects. Under the assumption that the income and substitution effects are similar in magnitude, income effects can also indirectly inform the magnitude of substitution effects. The similarity of income and substitution effects implies that the long-run labour supply elasticity is small in magnitude, which in turn suggests that permanent changes in tax rates are unlikely to have large long-run effects on aggregate employment and average hours worked.3

A more subtle lesson from the lottery estimates is that labour supply effects from transitory changes in wages and taxes are also unlikely to be large. Standard analysis of labour supply responses to transitory changes in wages and taxes focuses on the Frisch elasticity, which in standard models is related to the income effect, the substitution effect, and the intertemporal elasticity of substitution (IES).4 Unfortunately, there no consensus on the appropriate value of intertemporal elasticity of substitution in the literature. For example, Hall (1988) argues for a low value, whereas Gruber (2006) provides empirical evidence suggesting a higher value of the elasticity of substitution. However, none of the values in this wide range — when combined with the estimated income effects from Swedish lottery data — can produce large implied Frisch elasticities. This may provide useful guidance to macroeconomists regarding the role of labour supply shifts in understanding business cycle fluctuations, which often use the Frisch elasticity when calibrating macroeconomic models.

Lastly, the lottery estimates described in this column complement several recent papers that emphasise non-negligible income effects in labour supply for prime-age adults in developed countries. Picchio et al. (2015) estimate income effects using the Dutch State Lottery; Autor et al. (2015) estimate large income effects from disability compensated for US veterans; Gelber et al. (2015) estimate income effects from US Social Security Disability Insurance programme. Although the magnitudes vary across these papers, taken together the results provide fairly clear evidence to policymakers that unconditional cash transfer programmes in developed countries will likely reduce aggregate labour supply by a meaningful amount.5 Although the ‘textbook’ treatment of income effects in labour supply emphasises that unearned income does not distort the labour-leisure choice, we emphasise that this does not mean that income effects can or should be ignored by policymakers. Our estimates of the income effect can be used to quantify the labour supply effect and thereby to better understand the fiscal consequences of the introduction of universal basic income programmes. 


Autor, D H, M Duggan, K Greenberg, and D S Lyle (2015), “The Impact of Disability Benefits on Labour Supply: Evidence from the VA’s Disability Compensation Program”, Working Paper.

Browning, M (2005), “A working paper from April 1985: Which demand elasticities do we know and which do we need to know for policy analysis?”, Research in Economics 59(4), 293–320.

Cesarini, D, E Lindqvist, M Notowidigdo, and R Östling(2015), “The Effect of Wealth on Individual and Household Labour Supply: Evidence from Swedish Lotteries”, NBER Working Paper No. 21762.

Gelber, A, T Moore, and A Strand (2015). “The Effect of Disability Insurance Payments on Beneficiaries’ Earnings: Is the Income Effect Large?”.

Gruber, J (2006), “A Tax-Based  Estimate  of  the  Elasticity  of  Intertemporal  Substitution”, NBER Working Paper No. 11945.

Gruber, J (2013), Public Finance and Public Policy, 4th Edition, New York: Worth Publishers.

Hall, R E (1988), “Intertemporal Substitution in Consumption”, Journal of Political Economy, 96(2), 339-357.

Imbens, G W, Rubin, D B and Sacerdote, B I (2001), “Estimating the Effect of Unearned Income on Labour Earnings, Savings, and Consumption: Evidence from a Survey of Lottery Players”, American Economic Review 91(4), 778–794.

Keane, M (2011), “Labour Supply and Taxes: A Survey”, Journal of Economic Literature 49(4), 961–1075.

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Pencavel, J(1986), “Labour Supply of Men: A Survey”, in O Ashenfelter and R Layard., eds, Handbook of Labour Economics, Vol. 1, North-Holland, pp. 3–102.

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1 Following Pencavel (1986), the income effect in labour supply is also called the marginal propensity to earn out of unearned income.

2 Although not the focus of this column, the findings for spouses also helps determine appropriate models of household labour supply. The fact that winners consistently reduce labour earnings more than their spouses is consistent with some — but not all — of the standard household labour supply models in the literature, as described in more detail in Cesarini et al. (2015).

3 This captures the view of many labour economists according to a recent interview with David Card, who says “the long-run labour supply elasticity is pretty small, and probably negative.”

4 The relationship between the income effect and Frisch elasticity is given by Ziliak and Kniesner (1999) and Browning (2005), and we use this relationship in Cesarini et al. (2015) to calculate plausible magnitudes of Frisch elasticity implied by our estimates

5 Additionally, it is conceivable that universal income transfers can have additional ‘social multiplier’ effects, for example due to changes of work-related norms, which are not incorporated in our estimates of the income effect.



Topics:  Labour markets Taxation

Tags:  lotteries winning, labour supply, income effect, substitution effect, taxation

Assistant Professor of Economics, New York University; Co-director, Social Science Genetic Association Consortium

Assistant Professor, Stockholm School of Economics; Affiliated Researcher, Research Institute of Industrial Economics (IFN)

Associate Professor of Economics, Northwestern University; Fellow, Institute for Policy Research

Assistant Professor of Economics at the Institute for International Economics Studies (IIES), Stockholm University