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Wage risk, and government and spousal insurance

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Wage risk, and government and spousal insurance


The optimal size and structure of government benefit programs crucially depend on households’ income risk and their ability to self-insure against it. In particular, the welfare gains from government insurance programs such as income support, unemployment benefits, and working tax credits are increasing in non-insurable income risk. 

Another important consideration is that, in most countries, the benefit system is closely linked to household structure. In the US, for instance, eligibility for the Earned Income Tax Credit (EITC) depends on the number of children, and in the UK entitlement to many benefits such as Income Support or the new Universal Credit, depends on marital status and the number of children. Motivated by these considerations, Blundell et al. (2016) estimate a model of labour supply and savings for women in the UK and find that expanding tax credits for workers can be more welfare improving than other, equally costly, policy interventions, such as lowering taxes.

Thus, to properly evaluate benefit reforms, it is important to both accurately measure the income risk faced by households and to account for households’ demographic structure. Recent research (Arellano et al. 2017, Guvenen et al. 2015) has documented that earnings dynamics in the US and Norway differ substantially from what is typically assumed in models used for the evaluation of welfare policies. More specifically, they find that income risk, and in particular shock persistence, differs by age and position in the income distribution. For instance, younger workers face more volatile and less persistent earnings than older workers, and the same applies to lower-income workers compared to higher-income ones. In De Nardi et al. (2020a), we show that accounting for these heterogeneous dynamics is important when measuring the welfare costs of earnings risk. 

In a second paper (De Nardi et al. 2020b), we show that these rich dynamics are also present in UK earnings and wages. We do so by using administrative data from the UK Social Security (New Earnings Survey Panel Database, NESPD) and survey data from the UK British Household Panel Survey (BHPS). Some of these features, such as the lower persistence for younger and lower-income workers (Figure 1), have important implications for household insurance which are not captured by the typical linear model of labour income in which the persistence and variance of shocks are the same for everyone, irrespective of age and current income. 

Figure 1 Persistence of male earnings (left) and female wages (right) by age and position in the earnings (wage) distribution

Wage risk, and government and spousal insurance 1

To better evaluate welfare policies, we estimate two wage processes using BHPS data. Both feature a permanent and transitory shock, but the first one is a traditional, linear model of age-independent wage dynamics with normal shocks and constant persistence. In contrast, the second one is the much more flexible non-linear (NL) process proposed in Arellano et al. (2017) which does not impose constant persistence and age-independence.

By construction the first one, the traditional or canonical model of wage dynamics, cannot capture all of the rich dynamics that we observe in the data. As a result, we find that it implies biased estimates of economically important moments, such as the average persistence and variance of shocks over one’s life cycle. Notably, we find that in the UK, the canonical process overestimates the average persistence of earnings for male earners and underestimates it for female earners (Figure 2). 

Figure 2 Persistence of men’s earnings (left) and women’s wages (right), flexible non-linear (NL) process (with confidence bands) vs canonical process

Wage risk, and government and spousal insurance 2

These biases are significant and can thus affect policy evaluation. We investigate this possibility by building a rich life-cycle model of households, with includes couples and singles, children, and a female labour supply decision. We then use our model to study the optimal benefit system under both wage processes. 

We take as a reference the UK benefit system before the 2016 reform and summarise it by a combination of income support (an income floor independent of working status) and in-work benefits (that only accrue to workers). These benefit amounts depend on the number of children in the household and are tapered away at constant rates as household income increases. We then compute, under each wage process, the optimal benefit system within the linear class that we consider, where the optimal welfare system maximizes ex-ante social welfare under the veil of ignorance.

We find that wage dynamics substantially affect policy evaluation. Under the rich non-linear process, the optimal benefit system is very close to the baseline system in place in the UK before 2016. In contrast, under the canonical system one would incorrectly conclude that income support should be significantly lower while in-work benefits should be much higher (Figure 3, where income-support benefits are represented as dots). 

The difference between the systems arises because of the differences in the estimated persistence across the two wage processes. To analyse these discrepancies, we focus on the case of single women, who are major recipients of government benefits and whose labour supply is more likely to adjust due to changes in the welfare system. By counterfactually underestimating the persistence of women’s wages, the canonical process underestimates the insurance value of income support. When low labour income realisations are incorrectly measured as relatively short-lived, it is not very costly to induce single women with bad wage realizations to work. Further, the government even benefits because it gets additional resources from their labour taxes. 

However, under the more realistic non-linear process, women’s wages are more persistent and such a reform has a very negative impact on the welfare of the persistently low-income women who have high costs of participating in the labour market (high costs which might be due, for instance, to health issues), and who would be pushed into low-paid work by the reform. Thus, it is more beneficial to offer more insurance in the form of income support when they are out of work, even if this lowers their labour market participation.

Figure 3 Implied total level of benefits, by income levels, marital status, and number of children

Wage risk, and government and spousal insurance 3

Note: For singles, circles represent benefits for households where everyone is out of work, while lines represent benefits for households in which at least one member works. Earnings and benefits are expressed as the share of average male earnings

In 2016, the UK introduced a comprehensive reform of its benefit system that unified a set of different programs into a single benefit called Universal Credit. This reform introduced a single tapering rate for all benefits of 63p per pound of post-tax income, but also generalized two features that were only present in a subset of benefits. First, it introduced an initial earnings disregard for families with children, implying that the first £2,304 of labour market income are not taken into account for benefit purposes.

We use our model to evaluate the welfare implications of this benefit reform under the rich non-linear wage process, and find that it was, on average, welfare improving.1 This improvement is due to the introduction of the earnings disregard, which particularly benefits lower-income families with children. This finding thus suggests that flexible benefit functions including elements such as disregards are important for welfare.

Importantly however, the average welfare improvement under Universal Credit masks very heterogeneous effects: Because singles without children do not benefit from the earnings disregard, they lose welfare under this reform. 

Hence, our work finds that realistically modelling wages dynamics and household structure is crucial for informed policy evaluation. To the extent that traditional linear wage models miss important features of the data, their implications substantially alter the evaluation of a given policy reform and do so heterogeneously in the population, thus leaving some vulnerable groups much worse off.


Arellano, M, R Blundell and S Bonhomme (2017), “Earnings and consumption dynamics: A non-linear panel data framework”, Econometrica 85(3): 693–734.

Blundell, R, M Costa Dias, C Meghir and J Shaw (2016), “Female labor supply, human capital, and welfare reform”, Econometrica 84(5): 1705– 1753. 

De Nardi, M, G Fella and G Paz-Pardo (2020a), “Nonlinear household earnings dynamics, self-insurance, and welfare”, Journal of the European Economic Association 18(2): 890-926.

De Nardi, M, G Fella and G Paz-Pardo (2020b), “Wage Risk and Government and Spousal Insurance,” NBER Working Paper 28294.

Guvenen, F, F Karahan, S Ozkan and J Song (2015), “What do data on millions of U.S. workers reveal about life-cycle earnings risk?”, NBER Working Paper 20913.


1 It should be pointed out that, for tractability, we do not model the substantial delays in access to benefits that characterise Universal Credit and which are likely to have a substantial negative impact on the welfare of liquidity-constrained households with low labour income.

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