Hardship Financing, Productivity Loss, and the Economic Cost of Illness and Injury in Cambodia

Keywords: social health protection, poverty, financial risk protection, Universal Health Coverage, hardship financing Limit: 8, 000 Current: 7, 575

Financial risk protection is a core dimension of Universal Health Coverage. Hardship financing, defined as borrowing and selling land or assets to pay for healthcare, is a measure of last recourse. To inform efforts to improve Cambodia's social health protection system we analyze 2019-2020 Cambodia Socio-economic Survey data to assess hardship financing, illness and injury related productivity loss, and estimate related economic impacts. We apply two-stage Instrumental Variable multiple regression to address endogeneity relating to net income. More than 98,500 households or 2.7% of the total population resorted to hardship financing over the past year. Factors significantly increasing risk are having an Equity card, higher out-ofpocket healthcare expenditures, illness or injury related productivity loss, and spending of savings. The economic burden from annual lost productivity from illness or injury amounts to US$ 459.9 million or 1.7% of GDP. The estimated household economic cost related to hardship financing is US$ 250.8 million or 0.9% of GDP. Such losses can be mitigated with policy measures such as linking a catastrophic health coverage mechanism to the Health Equity Funds, capping interest rates on health-related loans, and using loan guarantees to incentivize microfinance institutions and banks to refinance health-related, high-interest loans from money lenders.

Introduction 1.1 Background

Universal Health Coverage aims to ensure access to needed, quality health services without exposure to financial hardship. Substantial out-of-pocket medical expenditures (OOPE) can increase household economic vulnerability and lead to or exasperate poverty, particularly when ill-health leads to a loss of income [START_REF] Mcintyre | What are the economic consequences for households of illness and of paying for health care in low-and middle-income country contexts?[END_REF][START_REF] Mitra | Can households cope with health shocks in Vietnam?[END_REF]. Health shocks can cause households to turn to hardship financing, defined as borrowing and selling assets to pay for healthcare, as a last resort [START_REF] Alam | Economic impacts of health shocks on households in low and middle income countries: a review of the literature[END_REF][START_REF] Deloach | The role of savings and credit in coping with idiosyncratic household shocks[END_REF][START_REF] Kruk | Borrowing and selling to pay for health care in low-and middle-income countries[END_REF]. This can undermine livelihoods and lead to a vicious circle of long-term impoverishment, health poverty, vulnerability, over-indebtedness, negative economic impacts, and low social cohesion [START_REF] Clarke | Defining and measuring health poverty[END_REF][START_REF] Gutiérrez-Nieto | A multivariate study of over-indebtedness' causes and consequences[END_REF][START_REF] Mcintyre | What are the economic consequences for households of illness and of paying for health care in low-and middle-income country contexts?[END_REF][START_REF] Whitehead | Equity and health sector reforms: can low-income countries escape the medical poverty trap[END_REF]. In addition, household debt is an important determinant of health outcomes [START_REF] Clayton | Does debt affect health? Cross country evidence on the debt-health nexus[END_REF]. There is also strong evidence of the positive effect of health on productivity, economic development, and poverty reduction [START_REF] Husain | Contribution of health to economic development: A survey and overview[END_REF][START_REF] Narayan | Investigating the relationship between health and economic growth: Empirical evidence from a panel of 5 Asian countries[END_REF]Nurse et al., 2014;[START_REF] Well | Accounting for the effect of health on economic growth[END_REF]. Arora found that changes in measures of long-term health increased the pace of national economic growth by 30-40% [START_REF] Arora | Health, human productivity, and long-term economic growth[END_REF]. There are several indicators to measure the extent of excessive out-of-pocket health expenditures (OOPE) (see Table 1). However, metrics of economic productivity loss related to illness and injury are scarce, particularly for low-and middle-income countries (LMIC). Simple and direct economic measures are needed to facilitate the regular monitoring and reporting on the devastating burden of excessive OOPE to policy makers. This is essential to ensure a continuous focus on the mitigation of hardship financing as well as to rationalize new investments in health care [START_REF] Alam | Economic impacts of health shocks on households in low and middle income countries: a review of the literature[END_REF][START_REF] Kruk | High-quality health systems in the Sustainable Development Goals era: time for a revolution[END_REF]. Borrowing and selling assets, particularly land, to pay for healthcare [START_REF] Kruk | Borrowing and selling to pay for health care in low-and middle-income countries[END_REF] Distress Financing Borrowing with interest to pay for healthcare [START_REF] Ir | Exploring the determinants of distress health financing in Cambodia[END_REF]) Capacity-to-pay Total household consumption net of subsistence requirements, adjusted for equivalent household size (World Health Organization, 2003) Catastrophic Expenditure Out-of-pocket health expenditures exceeding a pre-specified percentage of consumption or income; common thresholds found in the literature are 10%, 25%, and 40% (Wagstaff, 2019) Debt burden Ratio of debt service to income or consumption expenditure (Murphy, 1998) Over-indebtedness Ratio of debt service to household income, exceeding a prespecified threshold (Liv, 2013) [START_REF] Bylander | Over-indebtedness and microcredit in Cambodia: Moving beyond borrower-centric frames[END_REF] Impoverishment Extent to which people are made poor, or more poor, by spending on health (Wagstaff, 2003)

Cambodian Context

Cambodia is a lower-middle income country with a population of about 16.5 million and Gross Domestic Product (GDP) per capita at US$ 1,643 in 2019. Current health expenditure as a proportion of GDP is 6%; OOPE constitutes 57.5% of total health expenditure (World Bank, 2019). High OOPE is associated with catastrophic health expenditure which can impoverish households or deepen existing poverty [START_REF] Jithitikulchai | Health equity funds as the pathway to universal coverage in Cambodia: care seeking and financial risk protection[END_REF][START_REF] Mcintyre | What are the economic consequences for households of illness and of paying for health care in low-and middle-income country contexts?[END_REF]).

Cambodia's overall policy of financial sector self-regulation 2 , similar to other LMICs, has enabled the microfinance industry to pursue an aggressive market expansion [START_REF] Afonso | Doing Good by Doing Well? Microfinance, Self-Regulation and Borrowers' Over-indebtedness in the Dominican Republic[END_REF][START_REF] Bateman | The next domino to fall? The Rise and Fall of Global Microcredit: Development, debt and disillusion[END_REF][START_REF] Green | Regulating Over-indebtedness: Local State Power in Cambodia's Microfinance Market[END_REF]. Cambodia is considered a microfinance-saturated country with high levels of household debt raising concerns about over-indebtedness [START_REF] Bylander | Over-indebtedness and microcredit in Cambodia: Moving beyond borrower-centric frames[END_REF]. In response, the government instituted an 18% cap on annual microfinance interest rates in 2017. However, to maintain profits Microfinance Institutions (MFIs) increased loan fees and loan sizes while imposing harsher penalties for late repayment [START_REF] Bylander | Over-indebtedness and microcredit in Cambodia: Moving beyond borrower-centric frames[END_REF][START_REF] Green | Regulating Over-indebtedness: Local State Power in Cambodia's Microfinance Market[END_REF]. The Microfinance Information Exchange (MIX) Market reports a substantial increase in micro-credit borrowing in Cambodia over the past decade 3 . Total outstanding loans increased from US$ 1.17 billion among 1.25 million borrowers in 2010 to over US$10 billion among 2.22 million borrowers in 2018 (see Figure 2). A recent Microfinance Index of Market Outreach and Saturation (MIMOSA) report estimates Cambodia's credit penetration rate between 21.8 and 34.9 borrowers per 100 adults, yielding the highest saturation in the MIMOSA framework. The household debt burden is further compounded by the large and continuing growth in loan sizes (MIMOSA, 2020). In 2017, the International Monetary Fund (IMF) raised concerns about rapid credit growth in Cambodia and noted it to be the main domestic risk [START_REF] Bylander | Over-indebtedness and microcredit in Cambodia: Moving beyond borrower-centric frames[END_REF].

2 Cambodia does have regulations governing transparency and loan disclosure standards (including the 2017 Prakas on

Resolution of Consumer Complaints).

3 Data includes ACLEDA bank. The issue of rapidly increasing indebtedness is compounded by the high cost of borrowing, particularly among the poor who have less collateral, and therefore limited access to loans from formal commercial banks or micro-finance institutions. Poor people often turn to informal loan providers. The use of unregulated money lenders who charge high interest rates is well documented [START_REF] Ir | Toward a typology of health-related informal credit: an exploration of borrowing practices for paying for health care by the poor in Cambodia[END_REF][START_REF] Kenjiro | Why illness causes more serious economic damage than crop failure in rural Cambodia[END_REF] with outstanding debt to be between 2.5-15% per month. This can lead to a vicious debt cycle of impoverishment and insolvency as productive assets including land are sold or confiscated to settle the debt [START_REF] Bateman | Land titling improves access to microcredit in Cambodia: be careful what you wish for[END_REF][START_REF] Damme | Out-of-pocket health expenditure and debt in poor households: evidence from Cambodia[END_REF][START_REF] Kenjiro | Why illness causes more serious economic damage than crop failure in rural Cambodia[END_REF]. Over-indebtedness can even force families to abandon their residence [START_REF] Green | Regulating Over-indebtedness: Local State Power in Cambodia's Microfinance Market[END_REF]. The Cambodian Children's Fund reports that over 80% of families who relocate to the Steung Meanchey garbage dump site carry significant debt with interest rates between 10-20% per month; nearly two-thirds of the indebted families borrowed for medical treatment.

The 2014 Cambodia Demographic and Health Survey found that 20% of people reporting to be ill or injured in the past 30 days resorted to hardship financing: relying either on loans (12.4%) or on selling assets (7.6%)

to pay for transport and healthcare (National Institute of Statistics/Cambodia, Directorate General for Health/Cambodia, & ICF International, 2015). However, there is evidence that catastrophic health expenditure (i.e. OOPE exceeding 40% of capacity-to-pay) has significantly decreased from 11% of households identified as poor in 2014 to 7% in 2017 [START_REF] Jithitikulchai | Health equity funds as the pathway to universal coverage in Cambodia: care seeking and financial risk protection[END_REF].

Social Health Protection

The Cambodian government's highest-level strategy and policy documents envisage the strengthening of social health protection with the reduction of poverty, vulnerability, and inequality as explicit policy goals Cambodia's largest social health protection scheme, the Health Equity Fund (HEF), aims to provide financial risk protection to the poorest by enabling access to free public health care with the issuance of an Equity card (covering about 16% of the population). This scheme is complemented by the National Social Security Fund (NSSF) which provides social health insurance to registered private sector workers, civil servants, and some selected populations [START_REF] Kolesar | Expanding social health protection in Cambodia: An assessment of the current coverage potential and gaps, and social equity considerations[END_REF]. By the end of 2020, these schemes collectively covered approximately 30% of the population [START_REF] Kolesar | Decision time: Cost estimations and policy implications to advance Universal Health Coverage in Cambodia[END_REF]. These schemes serve as the foundational elements for Cambodia to achieve financial risk protection and Universal Health Coverage.

However, there is evidence showing that Health Equity Fund members still borrow to pay for healthcare.

Jacobs et al. found that 83% of payment-exempted patients resorted to borrowing, on average, 3.4 times the total direct costs of the illness episode; by comparison 48% of paying patients borrowed, at a rate of 0.74 (i.e.

less than) the total direct costs [START_REF] Jacobs | Do exemptions from user fees mean free access to health services? A case study from a rural Cambodian hospital[END_REF]. In a separate study, 82% of paymentexempted patients borrowed 6.6 times the total direct costs relating to the illness. It is hypothesized that the excessive borrowing (in relation to direct costs) by patients entitled to free care is due to opportunity costs related to the illness [START_REF] Ir | Toward a typology of health-related informal credit: an exploration of borrowing practices for paying for health care by the poor in Cambodia[END_REF]. Another study found that the Health Equity Fund did not reduce the likelihood of incurring health-related debt, but did reduce the amount of that debt [START_REF] Flores | Financial protection of patients through compensation of providers: the impact of Health Equity Funds in Cambodia[END_REF].

Productivity and Economic Impact

Increased productivity can contribute to the prevention and reduction of vulnerability, poverty and inequality, ultimately leading to increased human capacity and economic growth [START_REF] Nspc | Social Protection System Monitoring and Evaluation Mechanism Manual[END_REF]. Improving labor productivity is fundamental for Cambodia to remain competitive, particularly given rising competition from other low-wage garment exporting countries (World Bank Group, 2017). Estimating the economic cost of illness and injury requires the quantification of productivity loss as well as the appropriate assignment of a monetary value to that loss. The former can be estimated by recording the number of days a person stopped doing their usual activities. There are three primary methods for estimating the latter: (1) salary conversion;

(2) introspective methods; and, (3) estimating the cost of countermeasures related to absenteeism (i.e.

absence from work) and presenteeism (i.e. reduced productivity while at work) [START_REF] Mattke | A review of methods to measure healthrelated productivity loss[END_REF]. A fourth "human capital approach", similar to salary conversion, uses prevailing wage rates. These methods typically take the employer perspective, assigning a lower value to conditions that are more frequent among low wage earners or those not in the workplace, do not account for lost future earnings, and underestimate the true cost of illness and injury [START_REF] Finkelstein | Cost-of-illness analyses for policy making: a cautionary tale of use and misuse[END_REF].

Furthermore, most cost-of-illness studies are done in high-income countries and focus on a specific condition or illness [START_REF] Mitchell | Measuring health-related productivity loss[END_REF]. As such, these methods are problematic for contexts with high informal sector populations such as in most low-and middle-income countries (LMIC). The dearth of studies on the economic costs of illness in LMIC exemplifies the need for a more generalized approach that can be conducted routinely and measures the productivity loss and economic impact associated with illness and injury, particularly in countries with high levels of informal workers. To inform efforts to improve Cambodia's social health protection system, this study identifies risk factors associated with hardship financing and assesses the impact of hardship financing on household consumption expenditure. In addition, we estimate the annual economic productivity loss and economic burden of hardship burden as well as provide policy recommendations to mitigate the situation.

Methods

Data

This study analyzes the nationally representative household data from the 2019-2020 Cambodia Socioeconomic Survey completed by the National Institute of Statistics, Ministry of Planning. The dataset contains information on demographic characteristics, housing, education, labor force, household income, consumption, liabilities, and healthcare for 10,075 households, including 5,614 households with at least one member having reported an illness or injury in the past 30 days. Both land and asset selling for health are included when reporting hardship financing in the past 30 days as this was recorded for households indicating an illness or injury. However, report of hardship financing for health in the past year excludes non-land asset selling as it was not included as a survey response option.

Statistical methods

First, this study describes the characteristics of unproductive household debt, defined as debt taken for purposes that are not directly associated with revenue generation. We calculate descriptive statistics for the period of the debt, time to full repayment, source of the loan, primary purpose of the loan, total amount borrowed, current outstanding debt, monthly interest rate, and estimate the total outstanding healthcare debt.

Second, we use two-stage Instrumental Variable (IV) Probit regression to identify factors that explain the risk of hardship financing at the household level. Independent variables used in the model are: (1) Equity card (binary); (2) log OOPE (continuous); (3) total non-productive days in the household due to illness or injury in the past 30 days (discrete); (4) savings used to finance healthcare (binary); and, (5) log net income (continuous. Net income is an endogenous variable as report of household income in a survey is well-known to contain measurement error related to under-reporting. In addition, income is likely correlated with unobserved factors that are also directly correlated with the dependent variable hardship financing, most notably mortality. Finally, there is also potential for reverse causality as hardship financing may affect net income, particularly related to debt and interest repayment. To address endogeneity net income is instrumented by head of household age and total adult years of education in the household; this restricts the effect of net income on the error term [START_REF] Angrist | Mostly harmless econometrics: An empiricist's companion[END_REF][START_REF] Kennedy | A guide to econometrics[END_REF]. These instruments are expected to impact on hardship financing only through their effect on net income. Equation 1 expresses the final hardship financing risk model.

Hardship_Financing i =B 0 + B 1 Equity_card i + B 2 ln_OOPE i + B 3 Total_non_productive_days i + B 4 Savings_spent i + B 5 ln_net_income [IVs: Age_household_head, Adult_years_edu] i + ε (1)
The analysis tested other factors that could explain hardship financing including Covid-19 period4 , household size, educational level of head of household, age of head of household, age of head of household squared, sex of head of household, provider type (i.e. public, private, non-medical, and overseas), hospitalization (i.e. yes or no), number of inpatient days, chronic disease, number of people over sixty years of age in the household (discrete), disabled people in the household (binary), and total working age adults (i.e. 15-59 years) in the household. Other variables tested for model fit were any member of the household reporting to have an NSSF social health insurance card (i.e. yes or no), Phnom Penh residence (i.e. yes or no), and any current loan with an MFI or bank (i.e. yes or no). Descriptive statistics for all variables of interest are presented in Table 2. These variables were excluded from the final hardship financing model as they did not improve the fit as evaluated using the log ratio test [START_REF] Deb | Health Econometrics Using Stata[END_REF]. To limit the influence of outliers, net income and consumption expenditure data were winsorized to transform values below the 1 st percentile to the 1 st percentile and values above the 99 th percentile to the 99 th percentile [START_REF] Ghosh | Outliers: An Evaluation of Methodologies[END_REF]. Analyses were adjusted for sample design; Stata 17 was used for data management and analysis [START_REF] Statacorp | Stata Statistical Software: Release 17[END_REF].

Third, testing all variables described above, we fit a multivariate two-stage least squares instrumental variable (2SLS IV) regression model to assess the impact of hardship financing on household non-medical consumption expenditure, food consumption expenditure, and non-food/non-healthcare consumption expenditure. All consumption expenditure data was transformed to a one-month period. There is risk of bias when assessing the impacts of health shocks on household economic outcomes [START_REF] Alam | Economic impacts of health shocks on households in low and middle income countries: a review of the literature[END_REF]. This is particularly problematic as it is important to control for income which is highly correlated with consumption expenditure. In addition to the endogeneity issues noted above, there are additional unobserved factors that are likely correlated with both income and consumption expenditure such as savings, negative personal circumstances, food prices, food preferences, social networks, and thriftiness [START_REF] Braucher | Theories of overindebtedness: Interaction of structure and culture[END_REF][START_REF] Gathergood | Self-control, financial literacy and consumer over-indebtedness[END_REF][START_REF] Kempson | Over-indebtedness in Britain: Department of Trade and Industry London[END_REF]. Finally, household income is likely to shift as part of a functional relationship between other variables within the model, specifically the primary variable of interest: hardship financing. For example, a loan or sale of land can be expected to (temporarily) increase household income which could lead to an increase in consumption expenditure.

To address this endogeneity, we employ 2SLS IV regression. This restricts the correlation of household income with the error term, thus limiting the effect to operate only through modeled household net income and the other independent variables. The instrumental variables used for this equation are: (1) the age of the head of household (discrete); and (2) NSSF card (binary, indicating formal, registered employment of at least one member of the household. These instruments are expected to impact on the consumption expenditure only through their effect on net income. The model controls for other explanatory factors as shown in Equation 2.

Consumption_Expenditure i =B 0 + B 1 Hardship_Financing i + B 2 HHsize i + B 3 Female_head i + B 4 PhnomPenh_residence i + B 5 MFI_Bank_loan i + B 6 Covid-19 i + B 7 Equity_card i + B 8 Working_age_HHmembers i + B 9 Working_age_HHmembers 2 i + B 10 ln_net_income i [IV: Age_household_head, NSSF_card] + ε (2)
Diagnostic test statistics for both IV regression models relating to endogeneity, under identification, over identification, and weak identification are presented in Appendix 1. We calculate the economic impact of lost productively due to illness or injury using equation 3.

(3)

First, we estimate the value for one (1) workday by dividing 2019 GDP by the total number of workdays.

The latter is calculated by multiplying the 2019 working age population by the number of working days in 2019 net the estimated total non-productive days due to illness or injury. The value for one (1) day of work is then multiplied by the estimated total non-productive days due to illness: this represents the lost GDP.

Finally, the proportion of GDP lost is calculated by dividing the estimated GDP lost by the sum of GDP and GDP lost.

The annual economic burden related to hardship financing is estimated by summing the total health-related loan principal and interest with health-related land sale income over the past year. We consider land sale primarily for health purposes as an expense similar to spending savings. This is because sale of land is a loss of a productive asset, and the proceeds of the sale are reported for non-productive purposes (i.e. paying for health related issues). This approach is further rationalized in the discussion section.

Finally, we estimate the total hardship burden and the potential interest savings among health-loan borrowers for three annual interest rate cap scenarios (18%, 12%, and 8%). First, the total interest is calculated by multiplying the principle, monthly interest rate, total repayment period in months. Second, we adjust the monthly interest rate for all health-loans over each interest rate scenario to the cap and calculate the modeled interest. The difference between the total interest and modeled interest represents the potential interest rate savings. Moneylenders charge 2.5-3.4% higher monthly interest rates compared with Microfinance Institutions, and 2.7-3.6% higher compared with banks (Figure 1). Figure 2 shows the total principal and interest burden for health-related loans taken in the past year.

Results

Overall

Moneylenders account for 3.6% of these loans (not shown). However, the total related debt (principal and interest) accounts for 6.6% or US$ 13.9 million; over half of that debt (US$ 7.4 million) is due to interest (see Figure 2). Banks are estimated to provide 39.4% of health-related loans (not shown), however only

account

Selling Land

Among the 3.4% [CI: 3.0-3.9%] of households that report selling land in the past year, the primary reasons for doing so is for family health issues (39.3%) and paying debt (19.9%). Households also report selling land to buy a motor bike or cell phone (14.1%), invest in business (8.7%), agricultural purposes (3.1%), rituals such as weddings and funerals (3.4%), and other purposes (11.3%) (see Figure 3).

Determinants of Hardship Financing

There are several factors which explain hardship financing for health in Cambodia (see Table 3). After controlling for other covariates in the model, characteristics that significantly predict resort to hardship financing for health are having an Equity card (p<0.05), increased OOPE (p<0.001), non-productive days associated with the illness or injury (p<0.01), and spending of savings on the illness or injury (p<0.05). An increase in net income is associated with a decreased likelihood of hardship financing (<0.001).

Economic Impact of Hardship Financing on the Household

The impact of hardship financing (over the past year) on household consumption expenditure was assessed using multivariate 2SLS IV regression. Table 4 presents the results from the structural equation (column 1), the first stage regression (column 2), and the second-stage results for total non-medical consumption expenditure (column 3), non-food, non-medical consumption expenditure (column 4), and food consumption expenditure (column 5). The following narrative focuses on the results presented in columns 3-5.

Hardship financing is associated with an overall 8.6% decrease in total non-medical consumption expenditure (p<0.001), and a decrease of 10.8% in food expenditure (p<0.001) after controlling for other significant covariates, including net income. In addition, non-medical consumption expenditure increases by 5.5% with each additional household member. Female headed household's non-medical expenditure is 13.4% (p<0.001) less compared to male headed households. Non-medical expenditure is 26.0% (p<0.001) higher for households in Phnom Penh compared to the rest of the country, this is mostly attributable to higher food expenditure (33.1%, p<0.001). Households reporting any type of micro-finance or bank loan have higher non-medical expenditure (23.5%, p<0.001), with non-medical, non-food expenditure 53.3% higher (p<0.001) and food expenditure 4.0% higher (p<0.01). Non-medical spending was 6.3% (p<0.01) during the COVID-19 period; this is driven by a 9.2% decrease in food expenditure (p<0.001).

Households with an

Productivity Loss and Economic Cost

As discussed above, productivity loss is a significant determinant of hardship financing. Among households reporting any illness or injury in the past 30 days, the mean number of lost productive days (i.e. when the individual stopped doing usual activities) is 1.54 [CI: 1.40-1.70]. Among households reporting nonproductive days in the past 30 days, the mean number of days lost is 11. ].

Using Formula 3, we estimate the GDP contribution of one person-day at US$ 12.01. This yields an estimated total annual lost productivity due to illness or injury of US$ 459.9 million with uncertainty limits (UL) of US$ 395.1 -US$ 524.6 million. This represents an annual loss of GDP of 1.7% [UL 1.4-1.9%] in 2019.

Table 5 presents population-level estimates and corresponding 95% confidence intervals relating to the household economic cost of health-related hardship financing. Over the past 12 months the principal on health loans amounts to US$ 129 million; these loans carry a total interest burden of US$ 82.1 million. Total lost wealth due to land sale in the past 12 months amounts to US$ 39.7 million. Thus, the total annual household economic cost due to hardship financing is estimated at US$ 250.8 million [CI: million] and equates to 0.9% of GDP [CI: 0.6-1.3%] in 2019. Finally, we estimate the potential reduced economic burden of health debt using three refinancing scenarios:

capping monthly interest on all health debt at 1.5%, 1.3%, and 1%; calculating this over the loan period would reduce the total interest burden by US$ 4.8 million, 10.1 million, and 21.2 million, respectively.

Discussion

Limitations

The Cambodia Socio-economic Survey was not designed specifically to investigate hardship financing.

Thus, the analysis was limited in several aspects. Specifically, this prohibited a more comprehensive examination of the characteristics of health shocks and hardship financing. For example, the hardship financing regression model (1) was limited to report of hardship financing within the past month as health care-seeking indicators were limited to that period. This is because hardship financing over the past year cannot be plausibly explained by health and related care-seeking in the past 30 days. Thus, we were unable to link the amount of the financial burden due to sale of assets and debt related to health issues directly with the illness or injury episode as the former was reported for the past 12 months.

In addition, there are many risks for bias when analyzing health shocks. Two-way causality or endogeneity between economic outcomes and health events and unobserved characteristics of the household may increase illness susceptibility and economic severity can lead to bias [START_REF] Alam | Economic impacts of health shocks on households in low and middle income countries: a review of the literature[END_REF]. Reduced consumption expenditure, particularly food consumption expenditure, has the potential to increase vulnerability to adverse health events over time. To address this constraint, we limited the effect of bias relating to net income by using instrumental variables. In relation to the consumption expenditure equation ( 2), it is important to note that food consumption expenditure data is based on one-week recall, and the primary explanatory variable of interest, hardship financing, is reported over the past year. This reduces the plausibility of reverse causality. As noted above, reverse causality is a potential issue as a health shock could be caused by or result in a chronic health condition. However, we tested two chronic disease variables (i.e. report of illness in the past 30 days coming and going for the past year; and, report of illness classified as chronic such as high blood pressure or diabetes). These variables were excluded from the final model as neither was found to be significant. Furthermore, borrowing or asset selling could cause a temporary increase in consumption expenditure. This could be expected to reduce the likelihood of finding statistically significant negative impacts on consumption expenditure, which suggests that the estimates presented in this study may be conservative.

The survey asked how many days an ill or injured individual in the household stopped doing usual activities.

Although the calculation of productivity loss could be restricted to adults of working age, we believe it is important to count all reported days lost in the household. First, it is reasonable to assume that children and older persons who stop doing their usual activities require an adult member of the household to also stop doing their usual activities to provide care. Second, the survey does not capture presenteeism, or a level of reduced productivity due to illness or injury. Therefore, we consider that limiting productivity loss to the reported activity stoppage yields a conservative estimate.

Further to the description in the methods section, the annual economic cost of hardship financing is estimated by summing the total health-related loan principal and interest with health-related land sale income over the past year. This method assumes that the land sale value is of the same magnitude of the direct and in-direct health-related costs. Although it can be argued that this may not be the case, we believe that it can be considered a good or even conservative proxy for several reasons. First, in Cambodia land can be subdivided into relatively small units which provides the seller the possibility to only sell what is considered necessary vis-à-vis the primary purpose. Second, selling land under distress such as in a health crisis would likely give the purchaser negotiating leverage, thus minimizing any incentive for the seller to "over sell".

Third, the method does not account for future loss of income related to the sale. Fourth, it does not incorporate sale of non-land assets. Lastly, it does not capture households with no opportunity to borrow or land to sell rendering it impossible to seek care following a health shock [START_REF] Onarheim | Selling my sheep to pay for medicines-household priorities and coping strategies in a setting without universal health coverage[END_REF]. Moreover, we believe it is important to estimate the economic/monetary cost for hardship financing as it is easier to communicate to policy makers. Finally, the estimate can be made using regularly available survey data, so it is easy to replicate and therefore monitor over time.

Interpretation

Hardship financing is a measure of last resort for households facing health shocks. The measure explicitly captures inability to pay as well as indirect and opportunity costs [START_REF] Kruk | Borrowing and selling to pay for health care in low-and middle-income countries[END_REF]. Direct costs can be relatively minor compared to the large indirect cost burden from illness [START_REF] Pavel | Cost of illness for outpatients attending public and private hospitals in Bangladesh[END_REF].

We estimate that over a one-year period 2.7% of households or about 98,505 nationally resort to borrowing or selling land to pay for healthcare.

In addition, households with an Equity card are significantly associated with increased risk of hardship financing, after controlling for other co-variates including net income. As an Equity card entitles all members of the household to free public healthcare financed under the Health Equity Funds, one would hope to find possession of the card to provide financial risk protection. However, our results are consistent with other recent studies. Further to the evidence presented in the introduction, Por et al. found a significantly higher proportion of households holding an Equity card (24.7%) resorted to borrowing with interest to pay for healthcare compared to non-entitled households (12.5%) [START_REF] Ir | Exploring the determinants of distress health financing in Cambodia[END_REF]. Another study found that Equity card households benefit most when health care-related costs are low, however it fails to provide the same degree of financial protection when costs are high or accrue over time, even among beneficiaries seeking care from public facilities [START_REF] Jithitikulchai | Health equity funds as the pathway to universal coverage in Cambodia: care seeking and financial risk protection[END_REF].

There are several possible explanations. First, the Equity card is granted based on a household asset score with community validation, thus Equity card holders should be lower income and more vulnerable to income shocks such as serious health events. However, the model employed IV regression to control for net income which limits its affect to age of the head of household and combined years of adult education of the household. Statistical tests of the model show these to be valid instruments (see Appendix 1). The regression results show net income to be a highly statistically significant (p<0.001) protective factor against hardship financing.

Second, there is evidence showing low public healthcare utilization among Equity card holders. This may be attributable to systematic factors including distance and low awareness of the Equity card entitlement as well as patient avoidance of public facilities due to provider competency and attitude (Nagpal, 2019). In addition, service availability at public facilities may be limited, particularly for non-communicable diseases [START_REF] Jithitikulchai | Health equity funds as the pathway to universal coverage in Cambodia: care seeking and financial risk protection[END_REF]. Patients may need to pay unofficial fees or face substantial indirect financial shocks relating to needed medical care and/or lost productivity. These factors could lead to delayed careseeking until the illness becomes very serious and preference to use private providers due to convenience, quality perceptions, or other reasons [START_REF] Kolesar | Healthcare access among Cambodia's poor: an econometric examination of rural care-seeking and out-of-pocket expenditure[END_REF].

This study found both OOPE and productivity loss to be factors that significantly increase the likelihood of hardship financing. This underscores the importance that the economic cost of illness and injury is not limited to the direct cost of healthcare or OOPE. In traditional economic analyses OOPE is cited as evidence of willingness to pay and viewed as a potential funding source to be pooled through social health insurance mechanisms. However, hardship financing underscores that paying for healthcare does not equate to ability to pay [START_REF] Whitehead | Equity and health sector reforms: can low-income countries escape the medical poverty trap[END_REF].

We did not find households reporting at least one member with an NSSF card significantly associated with hardship financing. The NSSF card currently only provides coverage for the formally employed worker, not the household. Thus, its potential protective affect is diluted.

Spending of savings to pay for healthcare is also significantly associated with hardship financing as this strategy increases economic vulnerability of the household. This is consistent with other evidence that households tend to first use savings when available, then resort to credit and/or selling productive assets [START_REF] Deloach | The role of savings and credit in coping with idiosyncratic household shocks[END_REF].

When assessing the household economic impact of borrowing or selling land to pay for healthcare in the past 12 months results show that hardship financing is statistically associated with a 10.8% decrease in food consumption expenditure, after controlling for other statistically significant factors including net income.

This evidences the longer-term impact of hardship financing on the household's well-being and is consistent with multiple other studies showing health shocks can lead to reduced consumption [START_REF] Alam | Economic impacts of health shocks on households in low and middle income countries: a review of the literature[END_REF][START_REF] Wagstaff | Are health shocks different? Evidence from a multishock survey in Laos[END_REF].

Given the relatively low proportion (2.7%) of the population resorting to hardship financing, the economic impact can easily be overlooked by policy makers. However, this equates to US$ 250.8 million or 0.9% GDP. In addition, the economic burden from the annual lost productivity due to illness or injury is substantial as the total economic loss amounts to US$ 459.9 million or 1.7% of GDP. This is a conservative estimate as it does not explicitly incorporate future lost earnings due to mortality.

It is important to recognize that microfinance plays a role in health financing. In Cambodia most MFIs actively market, encourage and grant loans for non-productive assets and activities [START_REF] Bylander | Over-indebtedness and microcredit in Cambodia: Moving beyond borrower-centric frames[END_REF].

This study found that MFIs account for nearly half (48.1%) of health loans and 69.4% of health debt including US$ 88.7 million in principal and US$ 57.8 million in interest. We also found that households holding any MFI or bank loan to have higher non-medical consumption expenditure, food expenditure, and non-food, non-medical expenditure, after controlling for other factors including net income. Evidence from Indonesia shows that access to microfinance institutions helps smooth consumption against health shocks [START_REF] Gertler | Do microfinance programs help families insure consumption against illness?[END_REF]. Likewise, a study in Bangladesh found that the household sale of livestock to pay for healthcare, presenting a significant long-term cost, can be mitigated with microcredit [START_REF] Islam | Health shocks and consumption smoothing in rural households: Does microcredit have a role to play?[END_REF]. And, a quasi-experimental study from India found that debt was the principle mitigating mechanism when faced with a health-shock which lead to significant increases in indebtedness [START_REF] Mohanan | Causal effects of health shocks on consumption and debt: quasi-experimental evidence from bus accident injuries[END_REF].

Por et al. call for research to "investigate whether extending microcredit to the poor can be used as a means to avert borrowing from informal creditors for health care expenses, and how this might be done" [START_REF] Ir | Toward a typology of health-related informal credit: an exploration of borrowing practices for paying for health care by the poor in Cambodia[END_REF]. Although this is beyond the scope of this study, we present related policy recommendations.

First, the institutional and legal environment can increase or reduce the risks of over-indebtedness [START_REF] Schicks | Over-indebtedness in microfinance-an empirical analysis of related factors on the borrower level[END_REF]. Government has a role to play relating to social services, safety nets, and regulation that could limit credit market saturation and predatory lending [START_REF] Bylander | Over-indebtedness and microcredit in Cambodia: Moving beyond borrower-centric frames[END_REF]. This is particularly relevant for people who are vulnerable due to health shocks which force households to make difficult decisions that can undermine their economic well-being. There are several possible policy levers which can increase financial risk protection, a multi-pronged approach is recommended.

As discussed above, Equity card households are at higher risk of financial hardship. This social health insurance mechanism should provide financing risk protection during serious health shocks which lead beneficiaries to borrow and sell land. A qualitative study is needed to better understand the dynamics of financial risk protection among Equity card households whose members are entitled to free public health care with a few minor exceptions (most notably cancer treatment). The program should develop a catastrophic health coverage mechanism to provide financial risk protection for serious illness and injury.

Health financing savings and loans products require careful design to optimize value and minimize risk [START_REF] Leatherman | Health financing: A new role for microfinance institutions[END_REF]. MFIs and banks could refinance health-related loans with high interest rates and develop a range of low-interest health loan products. Refinancing all health-related loans to the current 18% interest cap would reduce the total interest burden by US$ 4.8 million. Given the seriousness of the issue of health debt, a lower interest cap could be set for health-related loans. For example, refinancing all health loans at an annual 12% cap, equivalent to 1% monthly, has the potential to decrease the total interest burden by US$ 21.2 million; and, decreasing the annual rate to 8% annually (or 0.67% monthly) could decrease the total interest burden by US$41.1 million. High risk borrowers with limited or no collateral using informal lenders can be targeted through the Health Equity Fund and transitioned to lower interest rate health loans from formal lenders by offering loan guarantees.

Cambodia is accumulating experience directly related to these recommendations. The Cambodia Children's Fund has successfully demonstrated the importance and feasibility of transitioning informal, health loans with high interest rates among the absolute poor. The Association of Banks in Cambodia and Cambodia Microfinance Association recently called for its members to follow the National Bank of Cambodia's 2020 directive on credit restructuring. These measures include waiving penalties, easing terms of emergency loans, and cutting interest rates [START_REF] Kunmakara | ABC, CMA set out six debt relief measures, Business. The Phnom Penh Post[END_REF]. And, the Royal Government of Cambodia recently launched a $200 million credit guarantee program for small and medium sized businesses targeting the agriculture, industry and service sectors [START_REF] Kunmakara | 200M credit guarantee scheme launched[END_REF]. In conclusion, Cambodia's social health protection platform can be strengthened with policy measures to enhance financial risk protection and mitigate vulnerability to the devastating economic effects of health shocks.

Figure 1 .1

 1 Figure 1. Simplified flow-chart of key issues relating to the economic consequences of illness 1

Figure 2 .

 2 Figure 2. Loan Growth in Cambodia from 2010-2018

Figure 1 .

 1 Figure 1. Median and mean monthly interest rates by lender type

Table 1 .

 1 Key Financial Risk Protection Metrics and Definitions

	Terminology	Definition	Reference
	Hardship Financing

  . Por et al. describe multiple types of informal credit for health including small, shortterm loans which are typically granted for periods of 10-20 days, generally under US$ 100 with interest amounting to 20% of the loan. Longer-term health loans, commonly without a specified repayment period, can accrue a daily interest rate of 1% or a monthly rate of 5% to 30% which often results in the total interest exceeding the amount borrowed[START_REF] Ir | Toward a typology of health-related informal credit: an exploration of borrowing practices for paying for health care by the poor in Cambodia[END_REF].Van Damme et al. found interest rates among households

Table 2 .

 2 Key variable summary statistics and expected direction in relation to dependent variables by modelTable statistics are not weighted. n.a. = not applicable for collinear, dependent and instrumental variables † denotes dependent variables ‡ denotes instrumented variable § denotes instruments

		Units	Mean Median	Std.	min	max Expected	Expected
					Dev.			Direction	Direction
								Model 1	Model 2
	Hardship Financing Model 1
	Hardship financing (past 12 months) †	binary	.03	0	.17	0	1	n.a	n.a.
	Consumption Expenditure Model 2
	Monthly non-medical expenditure †	US$	388.81 324.38	248.21	75.89	1530.91	n.a.	n.a.
	Monthly non-food, non-medical exp. †	US$	148.81	96.22	160.07	9.86	1013.84	n.a.	n.a.
	Monthly food expenditure †	US$	238.49 213.05	123.26	58.19	719.06	n.a.	n.a.
	Variables of interest
	Monthly net income ‡	US$ 1837.88 597.56 4188.99 -1888.35 28081.40	-	+
	Hardship financing (past 30 days)	percent	.02	0	.14	0	1	n.a.	-
	Equity card	percent	.10	0	.3	0	1	-	-
	NSSF card §	percent	.14	0	.35	0	1	-	n.a.
	Out-of-pocket health expenditures	US$	37.68	3.66	183.07	0 13853.66	+	-
	Non-productive days	days	.86	0	4.32	0	65	+	-
	Savings spent for healthcare	percent	.01	0	.10	0	1	+	-
	Head of household age §	years	48.32	48	13.84	17	96	n.a.	n.a.
	Head of household sex (female)	percent	.20	0	.40	0	1	+	-
	Head of household education	years	8.27	6	12.62	0	88	-	+
	Cumulative total adult education §	years	17.9	14	14.9	0	122	n.a.	+
	Household size	people	4.42	4	1.77	1	17	-	+
	Adults over 60 years	people	.43	0	.69	0	4	+	+
	Disabled household member	percent	.10	0	.29	0	1	+	+
	Adults of working age	people	2.68	2	1.42	0	12	-	+
	Care-seeking at public provider	percent	.22	0	.41	0	1	-	+
	Hospitalization in past 30 days	percent	.06	0	.25	0	1	+	-
	Cumulative in-patient days	days	.28	0	1.71	0	52	+	-
	Report of current illness for >1year	percent	.46	0	.50	0	1	+	-
	Chronic illness type reported	percent	.07	0	.26	0	1	+	-
	Covid-19 period	percent	.38	0	.48	0	1	+	-
	Residing in Phnom Penh	percent	.09	0	.29	0	1	-	+
	Current MFI or bank loan	percent	.31	0	.46	0	1	-	+

  , 2.7% [95%CI: 2.4-3.1%] of households, estimated to represent 98,505 households nationally, report hardship financing to pay for healthcare in the past 12 months: 1.3% [CI: 1.0-1.5%] report distress financing

	for health (i.e. borrowing money with interest); 1.3% [CI: 1.1-1.6%] report selling land; and, 0.05% [CI:
	0.02-0.11%] report both borrowing and selling land.
	Borrowing
	Over one-third (36.5%) [CI: 35.1-38.0%] of households report having at least one loan of any type. Nearly
	70% [CI: 68.3-70.9%] of households with loans are over-indebted with their debt payment exceeding 50% of
	their total consumption expenditure. About 28.3% [CI: 26.8-29.9%] of all households hold unproductive
	loans. Thus, unproductive loans account for over two-thirds (68.7%) [CI: 66.5 -70.8%] of all loans. The
	primary uses of unproductive loans are for household consumption (37.5%), purchase or improvement of the
	dwelling (25.6%), purchase of consumable durables (21.4%), service existing debts (8.1%), illness, injury or
	accident (5.5%), and (1.9%) for rituals such as weddings and funerals.

The median period of unproductive debt is 36 months with the median period to full repayment 23 months.

In relation to health loans, the median debt period is 27 months; the median period to full repayment is 17 months. The median loan size for health is US$ 975.60 with a median monthly repayment amount of US$ 50.73 inclusive of principle and interest. At the population level, we estimate 50,122 households hold a total amount of outstanding health debt in the amount of US$ 88.2 million [CI: US$ 51.9-124.0 million].

Table 3 .

 3 Hardship Financing Predictive Factors

	(1)	(2)	(3)

Table 4 .

 4 Estimated Effects of Hardship Financing (over the past 12 months) on Household Consumption Expenditure (over the past 30 days), controlling for other key factors

	Equity card reported 21.8% lower non-medical expenditure (p<0.001), 35.7% lower
	non-food, non-medical expenditure, and 15.9% (p<0.001) lower food expenditure compared to households
	without an Equity card. Household labor supply is an important determinant of expenditure as non-medical
	expenditure increases by 15.9% (p<0.001) for every working-age adult in the household. However, the
	association is non-linear as the quadratic term (i.e. working-age household members squared) indicates that
	the effect of increased labor supply eventually decreases non-medical consumption expenditure (p<0.001)
	likely attributable to economies of scale within the household. Finally, a 1% increase in net household
	income (instrumented by age of head of household and NSSF card) increases non-medical expenditure by
	18.3% (p<0.001), non-food, non-medical expenditure increasing by 30.8% (p<0.001) and food expenditure
	by 10.5% (p<0.001).

Table 5 .

 5 Economic cost from illness and injury among households: health-related loans, interest, and sale of land for health purposes in US$

Hardship Burden Category Point Estimate Std. Err. [95% CI]

	Health loan principal	129,000,000	22,700,000	83,800,000	174,000,000
	Health loan interest	82,100,000	14,700,000	52,900,000	111,000,000
	Health loan burden	211,100,000	22,900,000	136,700,000	285,000,000
	Land sale income for health	39,700,000	10,900,000	18,100,000	61,400,000
	Total hardship burden	250,800,000		154,800,000	346,400,000
	Proportion of GDP	0.9%		0.6%	1.3%

The impact of COVID-19 is assessed by disaggregating the data into two time periods: before defined as the pre-COVID period (6,276 household interviews) and on or after February 15, 2020 defined as the COVID period (3,799 household interviews).


Guillaume Michel

Christophe Gissinger

Cooling by baroclinic acoustic streaming

) and the approximation (15-16) are plotted in Fig 5 .

In the absence of natural convection, efficient heat transfers rely on externally forced flows. Generating such flows with acoustic waves rather than mechanical fans would enable remote locations to be cooled using virtually infinite lifetime transducers. This outlook is reinforced by the recent discovery that standing acoustic waves drive streaming flows of much higher velocities if the background medium is inhomogeneous. This regime of streaming is investigated experimentally in a cavity filled with stably-stratified air in which horizontal sound waves are found to significantly enhance heat transfers. The additional heat flux scales as the square of the input acoustic power for low amplitude waves and increases with the air stratification. These two features qualitatively match theoretical predictions, although corrections possibly ascribed to gravity are observed.

Introduction.-The generation of streaming flows by acoustic waves in homogeneous fluids requires a dissipation mechanism [START_REF] Lighthill | Acoustic Streaming[END_REF]. Close to solid boundaries, viscosity generates oscillating boundary layers that can locally force a mean flow: this so-called Rayleigh streaming is used in microfluidics to improve the efficiency of catalytic solid phases [START_REF] Bengtsson | Ultrasonic Agitation in Microchannels[END_REF] or to mix chemicals [START_REF] Yaralioglu | Ultrasonic mixing in microfluidic channels using integrated transducers[END_REF]. In the bulk, the attenuation of acoustic beams forces jets, a phenomenon referred to as quartz wind. As reviewed in Ref. [START_REF] Legay | Enhancement of Heat Transfer by Ultrasound: Review and Recent Advances[END_REF], most studies investigating the effect of acoustic waves on heat transfers typically involve generating such progressive ultrasonic beams with a few hundred watts in a liquid to trigger cavitation and/or drive forced convection.

Over the last few decades, a very different picture has emerged for acoustic streaming in inhomogeneous fluids. Experiments and numerical simulations with standing waves started investigating this regime and reported radically different streaming patterns, in some cases several orders of magnitude faster than the corresponding ones in homogeneous fluids [START_REF] Loh | Acoustic streaming induced by ultrasonic flexural vibrations and associated enhancement of convective heat transfer[END_REF][START_REF] Hyun | Investigation of convective heat transfer augmentation using acoustic streaming generated by ultrasonic vibrations[END_REF][START_REF] Lin | Heat transfer in a rectangular chamber with differentially heated horizontal walls: Effects of a vibrating sidewall[END_REF][START_REF] Nabavi | Influence of differentially heated horizontal walls on the streaming shape and velocity in a standing wave resonator[END_REF][START_REF] Aktas | The effects of acoustic streaming on thermal convection in an enclosure with differentially heated horizontal walls[END_REF][START_REF] Dreeben | Two-dimensional streaming flows in high-intensity discharge lamps[END_REF]. This regime of streaming was rationalized theoretically for gases by Chini et al. [START_REF] Chini | Largeamplitude acoustique streaming[END_REF] and termed baroclinic acoustic streaming. Its most noticeable feature is that the acoustic wave vorticity required to drive streaming no longer results from dissipation but is a consequence of baroclinicity, an inviscid process. This mechanism can be inferred from the curl of the linearized Euler equation describing the leading-order acoustic wave dynamics:

∇ × ρ ∂u ∂t = -∇p ⇒ ∂(∇ × u) ∂t = (∇ρ) × (∇p) ρ 2 , ( 1
)
where ρ is the time-averaged density, u is the acoustic wave velocity and p is the acoustic wave pressure. Whereas inviscid acoustic waves in homogeneous fluids have no vorticity, Eq. ( 1) demonstrates that this no longer holds in the presence of a background stratification as a result of baroclinic production of vorticity. * email: guillaume.michel@upmc.fr

The acoustic force density driving these streaming flows has then been derived in the general case of liquids, for both density and compressibility inhomogeneities [START_REF] Karlsen | Acoustic Force Density Acting on Inhomogeneous Fluids in Acoustic Fields[END_REF]. Since the properties of the acoustic modes (frequency and eigenfunction) depend on these background fields, a subtle two-way coupling takes place: the fast acoustic waves generate a slowly varying mean flow that advects inhomogeneities and feeds back on the acoustic waves. Several applications of this regime of streaming are already documented. It can significantly improve the efficiency of high-intensity discharge lamps, in which the mean temperature varies by thousands of degrees between the center and the walls [START_REF] Dreeben | Two-dimensional streaming flows in high-intensity discharge lamps[END_REF]. In microfluidics, it affects the acoustically-induced mixing of different fluids [START_REF] Karlsen | Acoustic Streaming and Its Suppression in Inhomogeneous Fluids[END_REF]. According to an experiment with water in a microchannel, a local temperature fluctuation of ∼ 0.2 K is sufficient to distort the streaming pattern observed in a homogeneous fluid [START_REF] Qui | Fast Microscale Acoustic Streaming Driven by a Temperature-Gradient-Induced Nondissipative Acoustic Body Force[END_REF]. The baroclinic streaming flow in a stratified gas enclosed between two horizontal walls is characterized in Ref. [START_REF] Michel | Strong wave-mean-flow coupling in baroclinic acoustic streaming[END_REF] and quantitatively fits previous numerical simulations (see also Ref. [START_REF] Koulakis | Convective instability in a stratified ideal gas containing an acoustic field[END_REF] in the limit of small temperature gradients). It suggests a new procedure based on stationary waves to acoustically enhance heat transfers in the absence of natural convection, e.g. for stably stratified or zero-gravity environments [START_REF] Michel | Strong wave-mean-flow coupling in baroclinic acoustic streaming[END_REF][START_REF] Kumar | Heat transfer mechanism driven by acoustic body force under acoustic fields[END_REF]. However, several thermal properties of this system, crucial for assessing the potential of acoustic streaming for practical applications such as cooling electronics aboard spacecraft, are still missing.

In this letter, we show that baroclinic streaming can significantly enhance heat transfers and characterize this cooling effect as a function of both the acoustic wave properties and the gas stratification. The results are compared with theoretical predictions from dissipation-based streaming [START_REF] Vainshtein | Acoustic enhancement of heat transfer between two parallel plates[END_REF] and baroclinic streaming in Ref. [START_REF] Michel | Strong wave-mean-flow coupling in baroclinic acoustic streaming[END_REF]. Experiment.-The experiment sketched in Fig. 1 consists of a cavity of length L = 10 cm, height H = 5.0 cm and width = 3.0 cm filled with air at atmospheric pressure. Heat is injected at the top wall at a rate P th through an RS Pro silicon heater mat fixed on a metallic plate. The bottom wall is a block of dural laterally cooled by means of water at 5 • C provided by a Lauda Master thermostat. The top and bottom temperatures at the center of these boundaries, measured by type K thermocouples and Keithley 2700 multimeters, are denoted by T h and T c . A Visaton SC-5 tweeter subject to an input sinusoidal signal of frequency f and power P ac constitutes one lateral wall of this cavity, at the opposite end of which a PCB 103A02 sensor is fixed. The signal from this sensor, processed by a PCB 480E09 signal conditioner and a Standford Research Systems SR 830 lock-in amplifier synchronized on the frequency f , yields an accurate measurement of the local amplitude A p of the oscillating pressure field. The remaining boundaries are 10 mm thick PEEK samples, this material being chosen for its thermal insulation properties and heat resistance. The entire setup is surrounded by thermal insulators, and the room itself is air conditioned to further reduce the daily temperature oscillations. Stationary states are reached after a transient of one hour corresponding to thermal diffusion in the lateral PEEK boundaries. Measurements of (T h , T c , A p ) as a function of the input parameters (P th , P ac , f ) are performed during two hours once stationary states are achieved and repeated between 3 and 9 times for statistics, the data reported in this letter summarizing around 2000 hours of acquisition. A first run is performed for various frequencies f , the injected heat P th = 8.8 W and input power in the loudspeaker P ac = 0.5 W being constant. The top to bottom temperature difference, reported in Fig. 2, reaches a minimum at around 1.84 kHz. This frequency corresponds to the first acoustic mode of the cavity, which would read a/(2L) for a homogeneous gas, with a the speed of sound. Under the assumption of a linear temperature stratification and a thin cavity, this eigenvalue problem still allows a simple analytic solution [START_REF] Michel | Strong wave-mean-flow coupling in baroclinic acoustic streaming[END_REF]:

f 0 = a c 2L 1 + T h -T c 2T c , (2)
where the sound speed, no longer uniform, is a c at T c . With a c = 335 m • s -1 and the mean values for this run T c = 16 • C and T h = 105 • C, eq. ( 2) yields f 0 = 1.8 kHz. From Fig. 2, we define the temperature stratification ∆T 0 = 89 K as the low frequency limit of T h -T c and the streaming temperature drop ∆T = 5 K as the variation range of T h -T c . Note that ∆T 0 corresponds to the top to bottom temperature difference in the absence of acoustic waves, when the input power in the speaker is directly converted to heat. The remainder of this investigation details how ∆T 0 and ∆T depend on P th and P ac . The procedure leading to Fig. 2 is repeated for various input acoustic power P ac at fixed heating P th = 8.8 W, the resulting relative temperature drop ∆T /∆T 0 being reported in Fig. 3. A quadratic function 0.4 P 2 ac fits the data in the limit ∆T /∆T 0 → 0, while overestimating those obtained at high acoustic power.

Similarly, the influence of the dimensionless temperature stratification Γ = ∆T 0 /T c is investigated with runs performed for varying P th at fixed P ac = 0.5 W. The relative temperature drop, reported in Fig. 4, increases with Γ and can be approximated by 4×10 8 F (Γ) with F a theoretical function with no fit parameter detailed in the Appendix. The amplitude A p of the oscillating pressure field is found to be (25 ± 2) Pa. It provides the typical acoustic velocity, U ∼ A p /(ρa c ) ∼ 6 cm • s -1 , with ρ the air density.

Overall, these results demonstrate that, in a stratified gas, a significant temperature drop can be obtained by forcing a standing wave at resonance even for acoustic powers P ac < 1 W orders of magnitude below the ones typically used for cooling in liquids (a few hundred watts [START_REF] Legay | Enhancement of Heat Transfer by Ultrasound: Review and Recent Advances[END_REF]). This cooling is found to increase with both the acoustic power and the thermal stratification. Discussion.-These results are compared with theoretical predictions based on Rayleigh streaming [START_REF] Vainshtein | Acoustic enhancement of heat transfer between two parallel plates[END_REF] and baroclinic streaming [START_REF] Michel | Strong wave-mean-flow coupling in baroclinic acoustic streaming[END_REF]. Both models apply to an ideal gas enclosed in a thin cavity and subject to the following main assumptions: the dynamics is two-dimensional, the top and bottom walls are at fixed temperature, parameters such as µ, κ and c p are assumed independent of temperature (see Tab. I) and, most importantly, gravity is neglected. Although this last assumption precludes any quantitative comparison with the present experiment in which gravity acts as a strong restoring force, it is of interest to investigate if the associated scaling laws hold.

From the dimensional parameters used to model this experiment and listed in Tab. I, several dimensionless numbers can be defined, see Tab. II. The multiple scales theory of baroclinic streaming expands the various fields as series of ε 1 and scales h, Re s , P e s and Γ as O(1). The smallness of ε in this experiment supports such multiple scales analysis. In the limit ∆T ∆T 0 where the background density field can be approximated by the one at rest, the constant power and constant temperature boundary conditions become equivalent and the following temperature drop is derived:

∆T ∆T 0 = F (Γ)(A 2 Re s P e s h 4 ) 2 , (3)
where A is the dimensionless amplitude of the wave, assumed of O(1) in the analysis and related to A p through

A p = εp atm Aγ π 1 + Γ 2 , (4)
with p atm = 10 5 Pa the ambient pressure and γ = 1.4 the specific heat ratio.

It is instructive to compare eq. ( 3) with the temperature drop that would be achieved by forced convection with a fan of fixed rotation rate, ∆T ∝ ∆T 0 : baroclinic acoustic streaming is such that ∆T ∝ F (Γ)∆T 0 with F (Γ) an increasing function in the range Γ ∈ [0, 1.05], evidencing that increasing the temperature stratification ∆T 0 also affects the streaming flow. With the dimensionless parameters listed in Tab. II, an arbitrary constant amplitude A = 0.55 makes the right hand sides of eq. ( 3) become 4 × 10 8 F (Γ), corresponding to the dashed line plotted in Fig. 4 that fits our data for Γ 0.2. Inferring A from (4) with Γ 0.2 and A p = 25 Pa instead leads to A 1.8 that overestimates the temperature drop.

In comparison, the temperature drop resulting from Rayleigh streaming driven by dissipation in the boundary layers and dominant for homogeneous fluids is [START_REF] Vainshtein | Acoustic enhancement of heat transfer between two parallel plates[END_REF] (∆T ) R ∆T 0 = 6.2 × 10 -5 (εA 2 P e s h 2 ) 2 .

(

) 5
With A ∼ 2, the streaming temperature drop (∆T ) R ∼ 10 -6 ∆T 0 is negligible. This confirms that dissipationbased streaming is irrelevant in the presence of large temperature inhomogeneities. Note that the scaling ∆T /∆T 0 ∝ P 2 ac observed in Fig. 3 as P ac → 0 is consistent with both Rayleigh and baroclinic streaming. In this limit, the two theories predict that both the relative temperature drop and the power transferred by the waves to the streaming flow scale as A 4 . The injected acoustic power P ac is then mainly balanced by the dissipation of energy in the oscillating boundary layers (proportional to A 2 ), hence A ∝ √ P ac and ∆T /∆T 0 ∝ A 4 ∝ P 2 ac . Conclusion.-Acoustic streaming resulting from inhomogeneities in the mean density field rather than dissipation processes recently emerged as an efficient mechanism to drive mean flows. Such setups typically stem from the use of different liquids [START_REF] Karlsen | Acoustic Force Density Acting on Inhomogeneous Fluids in Acoustic Fields[END_REF][START_REF] Karlsen | Acoustic Streaming and Its Suppression in Inhomogeneous Fluids[END_REF] or from large temperature fluctuations in a gas [START_REF] Loh | Acoustic streaming induced by ultrasonic flexural vibrations and associated enhancement of convective heat transfer[END_REF][START_REF] Hyun | Investigation of convective heat transfer augmentation using acoustic streaming generated by ultrasonic vibrations[END_REF][START_REF] Lin | Heat transfer in a rectangular chamber with differentially heated horizontal walls: Effects of a vibrating sidewall[END_REF][START_REF] Nabavi | Influence of differentially heated horizontal walls on the streaming shape and velocity in a standing wave resonator[END_REF][START_REF] Aktas | The effects of acoustic streaming on thermal convection in an enclosure with differentially heated horizontal walls[END_REF][START_REF] Dreeben | Two-dimensional streaming flows in high-intensity discharge lamps[END_REF][START_REF] Fand | Acoustic Streaming near a Heated Cylinder[END_REF]. This affects not only the pattern of the streaming flow, but also its velocity. Indeed, whereas Rayleigh streaming is of velocity O(U 2 /a), with U the typical acoustic velocity and a the sound speed, baroclinic streaming in strongly stratified systems can be O(U ) [START_REF] Michel | Strong wave-mean-flow coupling in baroclinic acoustic streaming[END_REF]. Such strong streaming flow could enhance diffusive heat transfers observed in stably-stratified gas on earth or close to hot electronic devices aboard spacecraft. The present experiment confirms this potential, by decreasing the temperature difference across a stably-stratified gas by almost 10 • C with low-power stationary acoustic waves (P ac < 1 W), in qualitative agreement with theoretical predictions [START_REF] Michel | Strong wave-mean-flow coupling in baroclinic acoustic streaming[END_REF] in which gravity is neglected, and several orders of magnitude above estimates based on Rayleigh streaming. This outlook is even more promising since the temperature drop increases more than linearly with the temperature difference, as measured by the right hand side of eq. ( 3): since F (1) 2.2 F (0.32), a setup with {T c = -62 • C, T h = 150 • C} should for instance be associated with a relative temperature drop ∆T /T 0 120 % higher than the one described Fig. 2 with

{T c = 16 • C, T h = 103 • C}.
At least two perspectives emerge from this work. First, the experimental investigation of more intense acoustic waves, associated with streaming Reynolds numbers Re s 1 for which the streaming flow would presumably involve jets and/or turbulence [START_REF] Lighthill | Acoustic Streaming[END_REF]. The theoretical approach of such setups remains challenging and requires numerical simulations accounting for two-way coupling between the acoustic waves and the streaming flow [START_REF] Chini | Largeamplitude acoustique streaming[END_REF][START_REF] Michel | Strong wave-mean-flow coupling in baroclinic acoustic streaming[END_REF]. Second, similar large-amplitude streaming flows should be expected wherever stationary acoustic waves develop in inhomogeneous fluids, as for instance in thermoacoustic devices [START_REF] Daru | Acoustically induced thermal effects on Rayleigh streaming[END_REF] and in acoustically-trapped spherical plasma bulbs [START_REF] Koulakis | Convective instability in a stratified ideal gas containing an acoustic field[END_REF][START_REF] Koulakis | Trapping of plasma enabled by pycnoclinic acoustic force[END_REF].

This work is supported by CNES. CG acknowledges financial support from the French program 'JCJC' managed by Agence Nationale de la Recherche (Grant ANR-19-CE30-0025-01).

Appendix In this appendix is derived the function F (Γ) introduced in Eq. ( 3) from the multiple scales model of Ref. [START_REF] Michel | Strong wave-mean-flow coupling in baroclinic acoustic streaming[END_REF]. Following their notations, the dimensionless mean temperature field Θ0 (x, y, Γ) is a solution of their equation (4.8), (1+Γy)∂ yyyyyy Θ0 +3Γ∂ yyyyy Θ0 = -2A 2 Γ 2 Re s P e s h 4 π(2 + Γ) 2 cos(2x), (6) complemented with six boundary conditions, setting to zero Θ0 , ∂ yy Θ0 and ∂ yyy Θ0 at y = 0 and y = 1 (whatever x). The solution is found to be Θ0 (x, y, Γ) = -2A 2 Γ 2 Re s P e s h 4 π(2 + Γ) 2 G Γ (y) cos(2x), [START_REF] Lin | Heat transfer in a rectangular chamber with differentially heated horizontal walls: Effects of a vibrating sidewall[END_REF] where G Γ (y) is only reported in Ref. [START_REF] Michel | Strong wave-mean-flow coupling in baroclinic acoustic streaming[END_REF] for Γ = 1. Here, G Γ (y) is computed with Mathematica and reads

G Γ (y) = A + B + C D , (8)
Following (4.19) of Ref. [START_REF] Michel | Strong wave-mean-flow coupling in baroclinic acoustic streaming[END_REF], the function F (Γ) is then

F (Γ) = Γ 2 π 2 (2 + Γ) 4

FIG. 1 .

 1 FIG. 1. Experimental setup.A driven by a harmonic signal of frequency f and power Pac, generates an acoustic wave of local amplitude Ap measured at the opposite end. The cavity of height H and length L is heated at the top (power P th , temperature T h ) and cooled at the bottom (temperature Tc). The width is not displayed. Gray areas represent dural samples and hatched areas represent thermal insulators.

FIG. 2 .

 2 FIG. 2. Top to bottom temperature difference T h -Tc as a function of the forcing frequency f for Pac = 0.5 W and P th = 8.8 W. The corresponding temperature stratification ∆T0 and streaming temperature drop ∆T are also reported.

1 FIG. 3 .FIG. 4 .

 134 FIG. 3. Relative temperature drop ∆T /∆T0 as a function of the injected power in the loudspeaker Pac for P th = 8.8 W.

  speed ac (at Tc) 335 m • s -1 Typical acoustic velocity U 6 cm • s -1 Horizontal wave number k π/L = 31 m -1 Height of the cavity H 50 mm Air density ρ (at Tc) 1.25 kg • m -1 Dynamic viscosity µ (indep. of T ) 18 µPa • s Thermal conductivity κ (indep. of T ) 28 mW • K -1 Isobaric specific heat cp (indep. of T ) 1.0 kJ • kg -1 • K -1

where A = Γ 2 9 )-( 9 +

 299 (y -1)y{45 + Γ[46 + 3Γ + y + 3Γy (7Γ)y 2 + 3(2 + Γ)y 3 ]} -30Γ ln(1 + Γy), (10) B = 3Γ 2 (Γ + 1)y -7 + 10y -5y 3 + 2y 4 ln(Γ) + 30(1 + Γ)(1 + 2Γ)y ln(1 + Γ) -30 ln(1 + Γy), (11) C = -3Γ 2 (1 + Γ)y[-7 + y 3 (-5 + 2y)] ln (Γ(1 + Γ)) + 20 ln(1 + Γy) + 10Γy ln (Γ(1 + Γy)) ,(12)D = 1080Γ 3 [Γ(2 + Γ) + 2(1 + Γ) ln(Γ) -2(1 + Γ) ln (Γ(1 + Γ))] .

1 0GFIG. 5 .F 2

 152 FIG.5. Function F (Γ) associated with cooling by baroclinic streaming and the approximation for Γ < 0.4 used in the present study.

TABLE I .

 I Dimensional parameters used to model this experiment.

	Dimensionless parameters	Definition	Value
	Inverse Strouhal number ε Aspect ratio h	U/ac kH/ √ ε	1.8 × 10 -4 1.2 × 10 2
	Streaming Reynolds number Res ερU/(kµ)	2.4 × 10 -2
	Streaming Peclet number P es ερcpU/(kκ) 1.5 × 10 -2
	Temperature gradient Γ	∆T0/Tc 0.1 Γ 0.3
	TABLE II. Dimensionless parameters describing the stream-
	ing flow.