“Migration and sovereign default risk” a comment

1. Overview

Alessandria et al. (2020) (ABD henceforth) study the interconnection between migration and sovereign default in the Euro Area. Empirically, the authors use data from Spain, Ireland, Portugal, and Greece before, during, and after the Great Recession. ABD document that the decline in economic activity experienced by those countries in 2008 coincided with an increase in the sovereign debt spreads and a reversal in the flow of capital and workers. More pointedly, the paper reports a strong negative correlation between sovereign spreads and net migration (the difference between immigration and emigration flows). For example, net migration in Portugal contracted from 0.1% in 2008 to about -0.4% in 2012. During the same period, Portugal’s government bond spreads jumped by 10 percentage points.

The same empirical message emerges from a panel regression exercise using 23 European countries. For the period 2008 - 2016, ABD find that net migration displays a positive correlation with economic activity but a negative correlation with sovereign spreads and unemployment. Importantly, the authors show that these correlations are robust to several controls.

Motivated by these empirical findings, ABD propose a sovereign default model featuring: 1) a production function that uses labor and capital; and, crucially, 2) the factors of production can freely move in and out of the small open economy. These features have been considered separately in the literature. For example, Gordon and Guerron-Quintana (2018) introduce labor and capital in an otherwise standard default model. They report that higher capital leads to a decline in sovereign spreads. Regarding labor mobility, Mandelman and Zlate (2012) report that immigration to the U.S. from Mexico is positively correlated with future wage gains. Furthermore, Gordon and Guerron-Quintana (2019) study the impact of migration on the borrowing decisions of cities in the United States.

ABD’s model is calibrated to match salient moments in Spanish data such as the volatility of GDP, the average and volatility of spreads, and, importantly, the average and volatility of the net migration rate in Spain. The model does reasonably well matching other moments. However, it must be noticed that ABD’s benchmark model induces excess smoothness in consumption when compared to the data.2

The main takeaways from the model can be summarized as follows. First, the migration channel explains about 60% of the observed spreads. Furthermore, the trade balance and investment become less volatile when the model has no migration. Second, from a worker’s point of view, it is always better to have the option to migrate. Third, following an adverse productivity shock, GDP per capita drops by an additional percentage point in the model featuring migration. Fourth, even ten years after the shock, the economy has not recovered, which is consistent with the Spanish experience surrounding the debt crisis in the 2010s. In the model, the long lasting recession results from the slow adjustment of population and physical capital. As stressed in Gordon and Guerron-Quintana (2017) and Gordon and Guerron-Quintana (2018), capital plays a critical role in generating prolonged slumps and asymmetric (negatively skewed) business cycles in emerging economies.

The rest of the discussion proceeds as follows. Section 2 uses a simple model to highlight the role of migration in sovereign borrowing decisions. In Section 3, I argue that there is an even more worrisome problem lurking sovereign entities: unfunded pension liabilities. The final section provides some remarks.

2. Understanding migration and borrowing

To grasp the impact of migration on borrowing decisions, suppose an economy comprised of a unit measure of islands and a unit measure of households.3 Consider an arbitrary island. In the first (second) period, the island has a per person deterministic endowment of y ₁ (y ₂). The local government issues $-b_2$ debt per person (b ₂ > 0 means assets) at price $\overline{q}$. Hence, total debt issuance is $-b_2{n}_1,$ where n ₁ is the initial measure of households on the island. At the beginning of the second period, households draw an idiosyncratic utility cost of moving ϕ ∼ F(ϕ) and then decide whether to migrate. If they migrate, they pay ϕ and obtain expected utility J, which is an equilibrium object.

Households value consumption according to $u\left(c_1\right)+\beta u\left(c_2\right),$ where c ₁ (c ₂) is consumption in the first (second) period. Household utility in the second period is u(c ₂) if they stay and $J-\varphi$ if they move, so migration decisions follow a cutoff rule in ϕ with indifference at $J-u\left(c_2\right)$. Consequently, the outflow rate is $o_2=F(J-u\left(c_2\right))$. The inflow rate is given by $i_2=\overline{i}\mathbf{I}\left(u\left(c_2\right)\right),$ where I is a differentiable, increasing function and $\overline{i}$ is an equilibrium object that ensures aggregate inflows equal aggregate outflows. (As a result, inflows can depend on the distribution of utility across islands, but that information must be summarized in $\overline{i}$.) The population law of motion is $n_2=(1+i_2-o_2)n_1$. Furthermore, let’s assume that the migration decision is noisy in the sense that F(0) > 0, so that some people will move even if $u\left(c_2\right)=J$.

After all migration has taken place, the government pays back its total obligation, $-b_2{n}_1,$ by taxing the n ₂ households lump sum. Consequently, per person consumption in the second period is $c_2=y_2+b_2{n}_1/n_2$. Proposition 1 in Gordon and Guerron-Quintana (2019) shows that the local government’s Euler equation for borrowing is

$$u^{\prime }\left(c_1\right)\overline{q}=\beta \frac{1-o_2}{1-o_2+i_2}{u}^{\prime }\left(c_2\right)(1-\frac{b_2}{n_2}\frac{\partial n_2}{\partial b_2}).$$ (1)

The Euler equation reflects two competing forces. One is an externality seen in the term $\frac{1-o_2}{1-o_2+i_2}\le 1$. Because the planner does not value the utility of future immigrants and because they bear $\frac{i_2}{1-o_2+i_2}$ of the debt burden (which is their share of the second period population), the marginal cost associated with an additional unit of debt is $1-\frac{i_2}{1-o_2+i_2}$ or $\frac{1-o_2}{1-o_2+i_2}$. Everything else equal, higher in-migration lowers the effective discount factor ($\beta \frac{1-o_2}{1-o_2+i_2}$) and increases borrowing.

The other force, seen in the term $1-\frac{b_2}{n_2}\frac{\partial n_2}{\partial b_2},$ shows that for each migrant attracted to the island through less borrowing, the overall debt burden per person falls. (Conversely, if b ₂ > 0, each additional entrant reduces assets per person, which discourages savings.) Hence, a forward looking government, internalizing the effects of city finances on migration decisions, should exercise more financial discipline all else equal to attract migrants to the island to reduce debt per person.

It is straightforward to show that optimal choices by a benevolent planner who maximizes the utility of individuals in all islands require that marginal rates of substitution must be equated across individuals, i.e., $\beta u^{\prime }\left({\widehat{c}}_{2,i}\right)/u^{\prime }\left({\widehat{c}}_{1,i}\right)=\beta u^{\prime }\left({\widehat{c}}_{2,j}\right)/u^{\prime }\left({\widehat{c}}_{1,j}\right)$ for almost all i, j. It is easy to show these must also equal $\overline{q},$ i.e.,

$$u^{\prime }\left({\widehat{c}}_{1,i}\right)\overline{q}=\beta u^{\prime }\left({\widehat{c}}_{2,i}\right)$$ (2)

for almost all i. In comparing (2) with the local government’s Euler Eq. (1), it is clear that overborrowing will occur if the optimal bond choice b ₂ is close to zero. In that case, the incentive to attract people—reflected in the term $1-\frac{b_2}{n_2}\frac{\partial n_2}{\partial b_2}$—is close to zero, while the externality of new migrants shouldering the burden—reflected in $\frac{1-o_2}{1-o_2+i_2}$—is not. This excessive borrowing may translate into higher spreads. Under these circumstances, an adverse productivity shock in the second period may trigger default, reduce the attractiveness of the island (lower u(c ₂)), and hence, a reversal in population flows.

3. The elephant in the room: unfunded pension liabilities

Sovereign debt is only one of the financial burdens that countries, states, provinces, and cities are facing. This section uses data from cities in the United States to show that unfunded pension liabilities are also a significant financial problem.4

3.1. Some evidence

According to Rauh (2017), the total amount of unfunded liabilities for all government-sponsored programs, cities, and states was $3.8 trillion in 2017. This is about 1/6th of the U.S. GDP in that year. Rauh (2017) also shows that the public pension (retirement) systems in Chicago have the worst unfunded liabilities among the largest pension systems in the country. In contrast, San Francisco’s pensions are among the best funded.

Fig. 1 displays the pension plan’s assets as a percent of liabilities (funded ratio) and the unfunded liabilities for Chicago and San Francisco over the last 17 years. Either measure confirms that the pensions system for San Francisco’s municipal employees is much better funded than that for municipal workers in Chicago. Indeed, San Francisco’s plan had more assets than accrued liabilities before the Great Recession (hence the negative values in the bottom panel in Fig. 1). In contrast, Chicago’s pension plan started the 2000s with an almost balanced system. Since then it has consistently deteriorated with less than 30% of accrued liabilities being funded by 2018 (San Francisco’s funding ratio is 90% for the same year).

Fig. 1.

Case studies – Chicago and San Francisco. Note: Funded ratio corresponds to the pension’s assets as a percent of liabilities. Unfunded liabilities are unfunded actuarial accrued liability ($ billions) on an actuarial value basis. Taken from the cities’ Comprehensive Annual Financial Reports.

Fig. 1 also shows that the pension plans were severely affected during and after the financial crisis of 2008–2009. For example, the San Francisco’s funding ratio dropped by 200 basis points between 2008 and 2012. Chicago’s unfunded liabilities doubled during the same period. A stark contrast between these two cities is that San Francisco has been able to stabilize its pension system whereas Chicago’s pension has continued deteriorating in recent years. But even for San Francisco, it is clear that its pension system is in worse shape than at the turn of this century.

3.2. A stylized model

To highlight the role of pensions in the finances of a sovereign entity (city, state, or country), consider once again an island economy. In each period, two generations coexist in the economy: young and old. For simplicity, assume there is no population growth and that individuals have access to a pay-as-you-go (PAYG) pension system but not to financial markets. The young generation gets an endowment $y_t^y,$ pays a proportional tax ${\tau }_t^y,$ and faces the budget constraint$c_t^y=(1-{\tau }_t^y)y_t^y.$ From the young generation’s perspective, fiscal policy consists on taxes paid today ${\tau }_t^y$ and a promised pension tomorrow $T_{t+1}^o$.

The old generation receives a transfer (pension) from the government so its consumption is $c_t^o=T_t^o$. There is a local planner that taxes the young, makes transfers to the old, and sells debt to foreigners. It does so to maximize utility $\log \left(c_t^y\right)+\beta \log \left(c_{t+1}^o\right)+\log \left(c_t^o\right),$ subject to the households’ budget constraints and its own budget constraint $q_t{B}_t+{\tau }_t^y{y}_t^y=B_{t-1}+T_t^o.$ Here, q_t is the price of debt issued today B_t.

If the planner chooses to default on foreigners, the small open economy goes to autarky. Under this scenario, the planner’s budget constraint imposes:

$${\tau }_t^y=\frac{T_t^o}{y_t^y}.$$

If we consider that $T_t^o$ is a non-defaultable promise (pension) made to the old when it was young, the planner is forced to tax the current young generation to make up for the lost funds from abroad.

In contrast, if the planner agrees to repaid its outstanding debt, taxes levied on the young are

$${\tau }_t^y=\frac{T_t^o+B_{t-1}-q_t{B}_t}{y_t^y}.$$

From the planner’s point of view, total liabilities today are $T_t^o+B_{t-1}$. This means that past pension promises become a state variable today. Let $V^d(B,y^y,T^o)=\log \left((1-{\tau }_t^y)y_t^y\right)+\beta \log \left(T_{t+1}^o\right|d)+\log \left(T_t^o\right)$ and $V^{nd}(B,y^y,T^o)=\log \left((1-{\tau }_t^y)y_t^y\right)+\beta \log \left(T_{t+1}^o\right|nd)+\log \left(T_t^o\right)$ denote the planner’s utility from default and good standing, respectively. The conditioning |d refers to choices made under default whereas the conditioning |nd corresponds to those choices made when in good standing.

With full commitment to the old generation, it is optimal to default on foreign creditors if

$$\log \left((1-{\tau }_t^y)y_t^y\right|d)+\beta \log \left(T_{t+1}^o\right|d)+\log \left(T_t^o\right)\ge \log \left((1-{\tau }_t^y)y_t^y\right|nd)+\beta \log \left(T_{t+1}^o\right|nd)+\log \left(T_t^o\right).$$

That is,

$$\log \left((1-{\tau }_t^y)\right|d)+\beta \log \left(T_{t+1}^o\right|d)\ge \log \left((1-{\tau }_t^y)\right|nd)+\beta \log \left(T_{t+1}^o\right|nd).$$

If the young generation is promised the same future pension regardless of the state of the economy ($T_{t+1}^o|nd=T_{t+1}^o|d$), then default is optimal when ${\tau }_t^y|d\le {\tau }_t^y|nd$. That is, the planner defaults if repaying debt imposes a high tax bill on the young generation. Note that the equilibrium is indeterminate since promised pensions are not settled. One potential solution is to promise a pension that leaves the young indifferent between the two stages of life. That is $\log \left((1-{\tau }^y)y^y\right)=\beta \log \left(T^o\right)$.5 This requires a pension in the amount

$$T_{t+1}^o={\left[(1-{\tau }_t^y)y_t^y\right]}^{\frac{1}{\beta }}.$$

Under this pension agreement, the condition to default is the same as before: ${\tau }_t^y|d\le {\tau }_t^y|nd$. Since T^o is a state variable, pension promises do affect the price of debt today. Higher T^o will require issuing more debt tomorrow, making harder to repay.

Conjecture: The price of sovereign debt, q_t, is weakly decreasing in promised pensions to the old, T^o. The intuition is straightforward. As T^o increases, the young generation is taxed at higher rates. In exchange, fiscal policy promises a higher pension tomorrow, which will complicate repayment next period. Alternatively, high T^o can be financed with more debt today. Either way the price of debt is lower.

From the simple model discussed here, it is clear that public pension systems considerably complicate the finances of sovereign economies. Furthermore, the conjecture on the price of debt suggests that moving forward underfunded pensions systems will likely increase the probability of default by small open economies.

4. Final remarks

The results in ABD show that migration brings upon financing challenges on countries. However, migration provides an important adjustment channel during adverse times. Namely, it allows people to reallocate from areas of low productivity to those with high productivity. This is easily seen in the immigration and emigration flows experienced by Spain before and after the 2008 crisis. Gordon and Guerron-Quintana (2019) report an extreme scenario in which migration across cities in the United States comes to a halt. Their simulations suggest that in the absence of migration GDP per capita would drop by as much as 30% compared with the case in which people freely move in the country.

Until recently, migration within and across countries (specially within the European Union) was fluid. It remains to be seen how the current Covid-19 medical crisis will affect 1) future migration patterns; and 2) public finances in economically fragile sovereign entities.