A substantial amount of international research has documented a statistical relationship between mortality and economic activity at the aggregate level. In many countries, mortality appears to be procyclical, meaning that it tends to increase (relative to long-run trends) during economic expansions.1–8 Procyclical mortality appears concentrated among the elderly and in urban areas.2,3 However, not all causes of mortality are procyclical. Suicides, homicides and purposeful injuries are frequently found to be countercyclical.5,9,10 Morbidities from ischaemic heart disease (including myocardial infarcts in the working aged) and malignant neoplasm (including lung and prostate cancer) are also frequently found to be countercyclical.9,11,12

In New Zealand, a substantial amount of work has examined the relationship between unemployment and suicide.13–15 But there has been little research examining the link between macroeconomic activity and other causes of death, let alone our national mortality rate.

In this paper we aim to progress our understanding of the empirical relationship between mortality and macroeconomic activity in New Zealand. The objective of our analysis is to model the relationship between mortality and aggregate (ie, national) unemployment, including mortality rates for different age groups and morbidities, in order to uncover potentially procyclical and countercyclical features. We use sophisticated time series techniques to identify relevant sample periods for analysis and to establish whether there is short- or long-run covariation between the various mortality rates and unemployment.

We begin by describing the data used in our analysis. We then discuss the empirical approaches taken to model statistical relationships between the variables. This includes a battery of technical diagnostic tests, the results of which inform our empirical strategy.

*Unemployment rate: *Quarterly unemployment rate time series spanning 1948 to 2014 are obtained from Lattimore and Eaqub (2011)17 and updated to 2019 with data from Stats NZ. Annual observations used for analysis are based on within-year averages of the quarterly data.

**Figure 1:** Unemployment rate (%), 1948 to 2016. Shaded regions indicate periods during which the unemployment rate was rising.

We use national unemployment as our measure of macroeconomic activity, rather than alternatives such as real gross domestic product (GDP) or output per capita, for two reasons. First, most explanations of the link between mortality and economic activity focus on (un)employment as a mediating factor.2,3,5,6,8–13 Although our focus remains descriptive, by focussing on the explanatory variables identified in the extant literature we can better illuminate the path forward for understanding the economic factors driving variation in mortality. Second, alternative measures of macroeconomic activity, notably real GDP growth, appear disconnected from unemployment during key periods in New Zealand’s economic history, and remain positive during many episodic increases in unemployment. For example, despite the annual unemployment rate rising in almost every year between 1979 and 1991 (see Figure 1), there were only three short ‘classical’ recessions in which real GDP was decreasing over this period (1982Q3–1983Q1, 1988Q1–Q4 and 1991Q1–Q2).16

*Mortality rates by age group: *Annual mortalities and populations by age group are sourced from the Human Mortality Database (HMD) for the period spanning 1948 to 2013 (available at https://www.mortality.org/). For each age group, mortality rates are constructed by dividing total mortality by population. Figure 2 exhibits the mortality rate for six different age groups: 0 (infants), 1–15 (children), 16–35, 36–65 (middle age), 66+ (elderly) and all ages. Over the sample period, mortality rates are highest among the elderly and infants.

**Figure 2: **Mortality rates across various age groups, 1948 to 2013. Shaded regions indicate periods during which the unemployment rate was rising.

*Mortality rates by morbidity:* Annual age-standardised mortality rates by cause of death are obtained from the Ministry of Health for the 1948 to 2016 period, although some morbidities begin later in the sample period (available at https://minhealthnz.shinyapps.io/historical-mortality/). These data include an age-standardised total mortality rate per 100,000 persons. We divide by 100,000 for comparability to the HMD dataset. Figure 3 depicts the eleven mortality rates available.

**Figure 3: **Age-standardised mortalities by morbidity, 1948 to 2016. Shaded regions indicate periods during which the unemployment rate was rising.

The appropriate approach for capturing potential correlations between the variables of interest depends on the statistical properties of the individual times series. Specifically, we need to establish (a) whether there are any* structural breaks* in the time series, as these will inform the relevant sample period for the statistical analysis, and (b) whether each time series is *stationary *or *non-stationary*, as this will inform the appropriate empirical models for modelling statistical correlations. We describe these concepts and the pre-diagnostic tests used to identify these features of the data. We take natural logs of all variables prior to statistical analysis.

Structural breaks occur when there is discrete change in a specific moment of the data. For example, the mean of a times series may change at a specific point in time. The inflection points evident in many of the mortality rates depicted in Figures 2 and 3 are consistent with a structural break in the average growth rate in the time series. For example, the mortality rate for 66+ trends upwards until the mid-1960s before trending downwards; this inflection point will manifest as a structural change in the average growth rate in per capita mortality from positive to negative.

These long-run secular trends in mortality rates are perhaps driven by changes in medical technology, knowledge and practice and, as such, are unrelated to variation in unemployment. Structural breaks should be identified prior to statistical analysis as they can otherwise obfuscate statistical correlations between the times series. We employ Bai–Perron supF tests20 to identify any breaks in the growth rates (log-differences) of the individual time series. When breaks are found, we restrict the subsequent analysis to the most recent regime after the break.

We must also identify whether each time series is stationary or non-stationary. A non-stationary stochastic process has moments (such as mean and variance) that approach infinity as the number of realisations of the process increases. Non-stationary time series therefore do not (typically) oscillate around a fixed level or trend when plotted over time and instead appear to wander at random. A *unit-root* non-stationary process becomes stationary once it is first-differenced (ie, the first-differenced time series does oscillate around a fixed level over the long run). As an instructive example, Appendix Figure 1 exhibits a simulated unit-root process in levels and first-differences.

Unit-root processes (and non-stationary processes more generally) can pose problems for conventional statistical techniques. For example, two statistically independent unit-root processes can exhibit an estimated correlation that is statistically significant. This is known as the *spurious regression *problem.18

It is therefore critical to first determine whether the time series of interest are stationary or non-stationary by using unit-root tests. We use the conventional Augmented Dickey–Fuller (ADF) unit-root test to establish whether each time series is stationary. To preview our results, we find that each of the time series are unit-root processes, and so we must proceed with caution.

We then test for *cointegration *between each of the mortality rates and the unemployment rate. Two unit-root processes are said to be cointegrated if they follow each other over time. For this reason, cointegrated time series are often described as exhibiting a long-run relationship. (Refer to Figure 4 for an empirical example.) We test for cointegration between each mortality rate and the unemployment rate using the Engle–Granger residual-based t-test. If cointegration holds, the long-run relationship can be consistently estimated using a variety of methods, including ordinary least squares. We use Fully-Modified Ordinary Least Squares (FMOLS) to account for potential endogeneity of the regressor within the cointegrated system.

If we find no evidence of cointegration, we then take first-differences of the time series to ensure stationarity and overcome the spurious regression problem. However, any uncovered correlations between mortality rates and unemployment only capture short-run covariation between the two time series.

In addition, we also test whether changes in the mortality rates differ over periodic increases and decreases in unemployment. For mortality rates that are (now) decreasing over time, this analysis tells us whether reductions in mortality are faster or slower during economic contractions.

We first apply the diagnostic structural-break, unit-root and cointegration tests to the times series. As discussed above, results from these tests then inform the specification and estimation of our empirical models, including whether there is a long-run cointegrating relationship between the mortality rates and aggregate unemployment. To preview our results, we only find evidence of a long-run relationship for self-harm and assault mortalities, meaning that most of our analysis focusses on short-run relationships.

*Age-group mortality rates: *For persons aged 66+, there is weak evidence of an estimated break in 1967 (Bai–Perron supF test-statistic of the null of 0 against a single break is 8.51, 10% critical value = 7.42). For persons aged 36–65, there is strong evidence of breaks in 1957 and 1975 (supF test-statistic of the null of 0 against two breaks is 16.62, 1% critical value = 10.14). We do not find statistical evidence of structural breaks in the remaining age groups.

In the regression analysis to follow, we restrict the sample to 1967–2013 for the mortality rate for persons aged 66+. Note that, if the earlier period 1948–1966 were included, the sample would bias our results in favour of finding that episodic increases in unemployment are associated with decreases in elderly mortality, because unemployment is decreasing and mortality is increasing over the most of the 1948 to 1966 period. Similarly, we restrict regression analysis of the 36–65 mortality rate from 1975 onwards, after the estimated structural break in this time series.

*Age-adjusted morbidity mortality rates: *The supF test indicates a break in 1995 for cancer (supF = 13.95, 1% critical value = 13.00); breaks in 1973 and 1982 for cerebrovascular disease (supF = 9.60, 5% critical value = 7.92); breaks in ischaemic heart disease in 1955 and 1968 (supF = 34.88, 1% critical value = 10.14); a break in 1973 for motor vehicle accidents (supF = 9.5321, 5% critical value = 9.1); and a break in 1972 for other heart disease (supF = 11.71, 5% critical value = 9.1). Notably these are all time series that are not cointegrated with the national unemployment rate. Therefore, as with the age group mortality rates above, in the short-run analysis to follow we begin the sample in the year of the final break in the time series. For example, regressions for cancer span 1995 to 2016.

We first apply ADF tests to the time series in log-levels, including a constant in the ADF equation and with automatic lag selection based on the Schwarz criterion. We accept the null of a unit root at a 10% level for each of the time series. We then first-difference the logged time series and reapply the ADF test. We can reject the null of a unit root at the 1% level for each of the mortality time series. For the national unemployment rate, we reject the null at a 5% level (p = 0.024).

We conclude that all the time series are unit-root non-stationary processes, meaning the first difference of each time series is a stationary process.

We only report mortality rates for which we can reject the null hypothesis of no cointegration at the 1% level: self-inflicted harm (Engle–Granger residual ADF t-statistic = -5.0843, p-value < 0.001) and assaults (Engle–Granger residual ADF t-statistic = -6.1199, p-value < 0.001). These two time series are cointegrated with the unemployment rate. Figure 4 plots these times series, illustrating the long-run covariation with the unemployment rate. Unemployment and per capita deaths from assaults and suicides are low in the immediate post-war period until the 1980s. They then increase through to a peak in the early to mid-1990s before declining again.

**Figure 4:** Mortality rates cointegrated with unemployment rate: self-inflicted harm and assault, 1948–2016.

Unemployment is not cointegrated with the majority of the mortality rates. Any statistical relationship with unemployment can therefore only be a short-run phenomenon; this accords with the long-run decline in many mortality rates being driven by factors unrelated to the level of the national unemployment rate. Nonetheless, changes in the unemployment rate may still be correlated with changes in mortality rates over the short run.

To examine these relationships, we run a regression of the log-differenced mortality rate on the log-differenced unemployment rate and a constant. This regression imposes a symmetric relationship between changes in unemployment and changes in mortalities. To account for heteroscedasticity and serial dependence in the error term, we use Newey–West standard errors with a triangular kernel and the bandwidth selected by the data-dependent process suggested by Andrews (1991).19 Tables 1 and 3 illustrate point estimates alongside t-statistics for the null hypothesis that the coefficient is zero.

We also run a regression of the log-differenced mortality rates on a constant and indicators (ie, dummy variables) for periods during which unemployment is rising. The estimated coefficient on the indicator therefore tells us the difference, on average, between the growth in the mortality rate during episodic increases in the unemployment rate relative to the entire sample. Tables 2 and 4 illustrate the point estimates alongside t-statistics.

Table 1 indicates that a 1% increase in the unemployment rate is associated with a contemporaneous 0.043% decrease in the mortality rate of 66+ (one-tailed p-value = 0.0145), a 0.037% decrease in the mortality rate of 36–65 (one-tailed p-value = 0.0145) and a 0.030% decrease in the mortality rate of all ages (one-tailed p-value = 0.042). Note that the sample size for the latter is rather limited and thus use of the normal limiting distribution approximation to the finite sample may be inaccurate. The one-tailed p-value for t-statistic of -2.338 under the t-distribution is nonetheless 0.0124.

**Table 1: **Regressions of log-differenced mortality rates by age on log-differenced unemployment rate.

The estimated slope coefficients in Table 2 tell us whether the growth rate in mortalities is different, on average, during periods when unemployment is rising compared to periods when unemployment is falling. For example, episodic increases in unemployment are associated with a 0.016% reduction in the 66+ mortality rate (one-tailed p-value = 0.0320). Similarly, when unemployment is rising, there is, on average, a 0.011% reduction in the 36–65 mortality rate (one-tailed p-value = 0.034) and an additional 0.016% reduction in the total mortality rate (one-tailed p-value = 0.048).

Comparing the slope coefficients to the constant, the reduction in the all-age mortality rate is about eight times (= (0.0016+0.0112)/0.0016) as large during episodic increases in the unemployment rate. However, the slope coefficient has marginal statistical significance, with a two-tailed p-value of 0.096.

**Table 2:** Regression of log-differenced mortality rates by age on indicators of episodic increases in the unemployment.

Table 3 illustrates that a 1% increase in the unemployment rate is associated with a 0.029% decrease in the age-adjusted mortality rate. However, statistical significance is weak (two-tailed p-value = 0.084). The remaining morbidity mortalities are statistically insignificant in two-tailed tests at the 10% significance level.

**Table 3:** Regressions of log-differenced age-adjusted mortality rates by morbidity on log-differenced unemployment rate.

Table 4 exhibits stronger evidence. Episodic increases in unemployment are associated with a 0.015% reduction in the age-adjusted total mortality rate (one-tailed p-value < 0.001). Comparing this slope coefficient to the estimated constant, the reductions in the age-adjusted mortality rate are 2.5 times (= (0.01+0.015)/0.01) as large during episodic increases in unemployment compared to periods when unemployment is decreasing. This relationship remains statistically significant at the 5% level (two-tailed) when we begin the sample in 1952 (after the sharp drop in mortality over 1951 to 1952 shown in Figure 3) or in 1965 (when the reduction the mortality rate appears to accelerate). (These results are unreported in the interests of brevity.) Among the other morbidities, only chronic lower-respiratory disease appears to be weakly and negatively related to the macroeconomic fluctuations (two-sided p-value = 0.078).

**Table 4: **Regression of log-differenced mortality rates by morbidity on indicators of episodic increases in the unemployment rate.

Unemployment is cointegrated with self-inflicted harm mortality and assault mortality. To estimate the long-run relationship between unemployment and these two mortality time series, we run a regression of the log of the mortality rate (self-inflicted harm or assaults) on the log of the unemployment rate and a constant using Fully-Modified Ordinary Least Squares (FMOLS) to account for potential endogeneity of the regressor within the cointegrated system.

For self-inflicted harm, this yields a point estimate of 0.125 (t-stat = 8.2471, p-value = 0.000). This means that a 1% increase in the national unemployment rate is associated with a permanent 0.125% increase in the self-inflicted harm mortality rate. For assaults, FMOLS yields a larger point estimate of 0.265 (t-stat = 6.9317, p-value = 0.000). This means that a 1% increase in the national unemployment rate is associated with a permanent 0.265% increase in the assault mortality rate.

In this paper we establish both procyclical and countercyclical features in mortality-rate time series in New Zealand. Changes in total mortality rates are negatively correlated with changes in unemployment over the 1948 to 2013 period, indicating a short-run procyclical feature of mortality in New Zealand in the post-war period. Decompositions by age reveal that this relationship is strongest among the elderly (66+).

Although these correlations cannot tell us about the precise nature of any causal channels that drive mortality, they do nonetheless help us to understand where to direct future research to inform policymaking. For example, these findings are similar to US research that shows that elderly mortality is procyclical, a result that is thought to be driven by a decline in the quality of aged-care during economic expansions when aged-care workers have more attractive employment options and aged-care facilities suffer from labour shortages.2 Establishing a similar connection between labour market conditions, aged-care and elderly mortality in New Zealand would have substantive implications for policymakers in New Zealand. For example, it would underscore the need for health, education and training and urban-planning policies to ensure that the industry has sufficient capacity to absorb the baby boomers over the next few decades. It would also have implications for immigration policy, given that the industry has increasingly relied on migrants to fill important roles that have been nonetheless characterised as “low skilled, low paid and low status.”21 Future work may also examine whether the statistical relationship between elderly mortality and macroeconomic conditions has weakened with the increased number of skilled migrants employed in the sector over the past two decades.

We also find that self-inflicted harm and assault mortality rates are countercyclical and cointegrated in levels with the unemployment rate, establishing a long-run correlation between these time series. This is consistent with a substantial amount of work that has examined the relationship between unemployment and suicide and suicide ideation at the individual level in New Zealand13–15; but it also establishes that assaults are connected to labour market conditions, which is consistent with extant work on unemployment and crime in the country.26

Given the recent policy focus on addressing mental health problems in New Zealand, these results underscore the role that expanding employment opportunities can play in combatting mental health problems. Successive governments targeted full employment over the 1950–1980 period28 and used a variety of government departments and enterprises to employ people.27 This period is notable for its substantially lower per capita suicide rate (see Figure 4), suggesting that employment programmes not only provided jobs but lowered rates of self-harm. The resurrection of large-scale employment programmes might therefore present a potential policy response to our high rates of suicide. Such programmes might also help address violent crime, given the established relationship between assault fatalities and unemployment.

Future research can shed more light on the nature of the relationship between suicides and macroeconomic conditions. For example, a growing international literature has established asymmetries in the relationship between suicide and unemployment, particularly when suicides are disaggregated by age and sex.22–23 While youth and middle-aged suicides are sensitive to reductions in unemployment in the US, suicides among 55–64 year olds are particularly sensitive to increases in unemployment.22 Future research could examine whether similar asymmetries are present in New Zealand and, given higher rates of suicide among Māori, also examine the relationship between unemployment and suicide across different ethnicities.24 Suicide rates also vary by occupation in New Zealand,25 suggesting that future research on economic conditions within specific sectors of the economy, such as farming, fisheries or forestry and the trades, may provide additional explanatory power and further inform policy to combat suicide through targeted support to at-risk occupations during economic downturns.

**Appendix Figure 1: **Simulated unit-root process in levels (left) and after first-differencing (right). The unit-root process is a random walk with a drift generated by summing a sequence of normally distributed random variables with a mean of 0.1 and variance of one. Note that, after first-differencing, the process oscillates around a fixed level.

1. Ruhm, C. J. (2016). The Health Effects of Economic Crises. Health Economics 25(2), 6-24.

2. Stevens, A. H., Miller, D. L., Page, M. E., & Filipski, M. (2015). The best of times, the worst of times: understanding pro-cyclical mortality. American Economic Journal: Economic Policy, 7 (4), 279-311.

3. Sameem, S., & Sylwester, K. (2017). The business cycle and mortality: Urban versus rural counties. Social Science & Medicine 175, 28-35.

4. Haaland, V. F., & Telle, K. (2015). Pro-cyclical mortality across socioeconomic groups and health status. Journal of Health Economics 39, 248-258.

5. Granados, J. A. T. (2005). Recessions and mortality in Spain, 1980–1997. European Journal of Population/Revue européenne de Démographie, 21 (4), 393-422.

6. Van den Berg, G. J., Gerdtham, U. G., von Hinke, S., Lindeboom, M., Lissdaniels, J., Sundquist, J., & Sundquist, K. (2017). Mortality and the business cycle: Evidence from individual and aggregated data. Journal of Health Economics, 56, 61-70.

7. Regidor, E., Vallejo, F., Granados, J. A. T., Viciana-Fernández, F. J., de la Fuente, L., & Barrio, G. (2016). Mortality decrease according to socioeconomic groups during the economic crisis in Spain: a cohort study of 36 million people. The Lancet, 388 (10060), 2642-2652.

8. Gerdtham, U. G., & Ruhm, C. J. (2006). Deaths rise in good economic times: evidence from the OECD. Economics & Human Biology, 4 (3), 298-316.

9. Economou, A., Nikolaou, A., & Theodossiou, I. (2008). Are recessions harmful to health after all? Journal of Economic Studies Journal of Economic Studies 35(5):368-384

10. Lin, S-J. (2009) Economic fluctuations and health outcome: a panel analysis of Asia-Pacific countries, Applied Economics, 41:4, 519-530

11. Svensson, M. (2007). Do not go breaking your heart: do economic upturns really increase heart attack mortality? Social Science & Medicine 65 (4), 833-841.

12. Maruthappu, M., Watkins, J., Taylor, A., Williams, C., Ali, R., Zeltner, T., & Atun, R. (2015). Unemployment and prostate cancer mortality in the OECD, 1990–2009. ecancer 9 538.

13. Blakely, T., Collings, S., Atkinson, J. (2003). Unemployment and suicide. Evidence for a causal association? Journal of Epidemiology & Community Health 57 594-600.

14. Fergusson D.M., Boden J.M., Horwood L.J. (2007).Unemployment and suicidal behaviour in a New Zealand birth cohort: A fixed effects regression analysis. CRISIS 28(2), 95-101

15. Fergusson D.M., Horwood L.J., Woodward L.J. (2001) Unemployment and psychosocial adjustment in young adults: causation or selection? Social Science and Medicine 53, 305–320

16. Hall, V.B. & McDermott, C. J. (2016). Recessions and recoveries in New Zealand's post-Second World War business cycles, New Zealand Economic Papers, 50:3, 261-280

17. Lattimore, R. & Eaqub, S. (2011) THE NEW ZEALAND ECONOMY: AN INTRODUCTION. Auckland University Press: Auckland.

18. Phillips, P.C.B. (1986). Understanding Spurious Regressions in Econometrics, Journal of Econometrics 33(3), 311-340

19. Andrews, D. W. K. (1991). Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation. Econometrica 59, 817-858.

20. Bai, J and P. Perron (2003). Computation and analysis of multiple structural change models. Journal of Applied Econometrics 18 (1), 1-22

21. Badkar, J., Callister, P., & Didham, R. (2009). Ageing New Zealand: The growing reliance on migrant caregivers. Institute of Policy Studies Working Paper 09/08.

22. Lin, Y-H. & Chen, W-Y. (2018). Does unemployment have asymmetric effects on suicide rates? Evidence from the United States: 1928–2013, Economic Research Ekonomska Istraživanja, 31:1, 1404-1417

23. Wu, W-C., & Cheng, H-P. (2010). Symmetric mortality and asymmetric suicide cycles, Social Science & Medicine, 70:12, 1974-1981.

24. Beautrais, A. L. & Fergusson, D. M. (2006) Indigenous Suicide in New Zealand, Archives of Suicide Research, 10:2, 159-168,

25. Gallagher, L.M., Kliem, C., Beautrais, A.L., & Stallones, L. (2008) Suicide and Occupation in New Zealand, 2001–2005. International Journal of Occupational and Environmental Health, 14:1, 45-50.

26. Papps, K. & Winkelmann R. (2000) Unemployment and crime: New evidence for an old question, New Zealand Economic Papers 34(1), 53-71

27. Bridgman, B. & Greenaway-McGrevy, R. (2018) The fall (and rise) of labour share in New Zealand, New Zealand Economic Papers, 52:2, 109-130

28. Endres, T. (1984). ARTICLE: The New Zealand Full Employment Goal: A Survey of Changing Views 1950 to 1980. New Zealand Journal of Industrial Relations, 9(1).

communications@nzma.org.nz

A substantial amount of international research has documented a statistical relationship between mortality and economic activity at the aggregate level. In many countries, mortality appears to be procyclical, meaning that it tends to increase (relative to long-run trends) during economic expansions.1–8 Procyclical mortality appears concentrated among the elderly and in urban areas.2,3 However, not all causes of mortality are procyclical. Suicides, homicides and purposeful injuries are frequently found to be countercyclical.5,9,10 Morbidities from ischaemic heart disease (including myocardial infarcts in the working aged) and malignant neoplasm (including lung and prostate cancer) are also frequently found to be countercyclical.9,11,12

In New Zealand, a substantial amount of work has examined the relationship between unemployment and suicide.13–15 But there has been little research examining the link between macroeconomic activity and other causes of death, let alone our national mortality rate.

In this paper we aim to progress our understanding of the empirical relationship between mortality and macroeconomic activity in New Zealand. The objective of our analysis is to model the relationship between mortality and aggregate (ie, national) unemployment, including mortality rates for different age groups and morbidities, in order to uncover potentially procyclical and countercyclical features. We use sophisticated time series techniques to identify relevant sample periods for analysis and to establish whether there is short- or long-run covariation between the various mortality rates and unemployment.

We begin by describing the data used in our analysis. We then discuss the empirical approaches taken to model statistical relationships between the variables. This includes a battery of technical diagnostic tests, the results of which inform our empirical strategy.

*Unemployment rate: *Quarterly unemployment rate time series spanning 1948 to 2014 are obtained from Lattimore and Eaqub (2011)17 and updated to 2019 with data from Stats NZ. Annual observations used for analysis are based on within-year averages of the quarterly data.

**Figure 1:** Unemployment rate (%), 1948 to 2016. Shaded regions indicate periods during which the unemployment rate was rising.

We use national unemployment as our measure of macroeconomic activity, rather than alternatives such as real gross domestic product (GDP) or output per capita, for two reasons. First, most explanations of the link between mortality and economic activity focus on (un)employment as a mediating factor.2,3,5,6,8–13 Although our focus remains descriptive, by focussing on the explanatory variables identified in the extant literature we can better illuminate the path forward for understanding the economic factors driving variation in mortality. Second, alternative measures of macroeconomic activity, notably real GDP growth, appear disconnected from unemployment during key periods in New Zealand’s economic history, and remain positive during many episodic increases in unemployment. For example, despite the annual unemployment rate rising in almost every year between 1979 and 1991 (see Figure 1), there were only three short ‘classical’ recessions in which real GDP was decreasing over this period (1982Q3–1983Q1, 1988Q1–Q4 and 1991Q1–Q2).16

*Mortality rates by age group: *Annual mortalities and populations by age group are sourced from the Human Mortality Database (HMD) for the period spanning 1948 to 2013 (available at https://www.mortality.org/). For each age group, mortality rates are constructed by dividing total mortality by population. Figure 2 exhibits the mortality rate for six different age groups: 0 (infants), 1–15 (children), 16–35, 36–65 (middle age), 66+ (elderly) and all ages. Over the sample period, mortality rates are highest among the elderly and infants.

**Figure 2: **Mortality rates across various age groups, 1948 to 2013. Shaded regions indicate periods during which the unemployment rate was rising.

*Mortality rates by morbidity:* Annual age-standardised mortality rates by cause of death are obtained from the Ministry of Health for the 1948 to 2016 period, although some morbidities begin later in the sample period (available at https://minhealthnz.shinyapps.io/historical-mortality/). These data include an age-standardised total mortality rate per 100,000 persons. We divide by 100,000 for comparability to the HMD dataset. Figure 3 depicts the eleven mortality rates available.

**Figure 3: **Age-standardised mortalities by morbidity, 1948 to 2016. Shaded regions indicate periods during which the unemployment rate was rising.

The appropriate approach for capturing potential correlations between the variables of interest depends on the statistical properties of the individual times series. Specifically, we need to establish (a) whether there are any* structural breaks* in the time series, as these will inform the relevant sample period for the statistical analysis, and (b) whether each time series is *stationary *or *non-stationary*, as this will inform the appropriate empirical models for modelling statistical correlations. We describe these concepts and the pre-diagnostic tests used to identify these features of the data. We take natural logs of all variables prior to statistical analysis.

Structural breaks occur when there is discrete change in a specific moment of the data. For example, the mean of a times series may change at a specific point in time. The inflection points evident in many of the mortality rates depicted in Figures 2 and 3 are consistent with a structural break in the average growth rate in the time series. For example, the mortality rate for 66+ trends upwards until the mid-1960s before trending downwards; this inflection point will manifest as a structural change in the average growth rate in per capita mortality from positive to negative.

These long-run secular trends in mortality rates are perhaps driven by changes in medical technology, knowledge and practice and, as such, are unrelated to variation in unemployment. Structural breaks should be identified prior to statistical analysis as they can otherwise obfuscate statistical correlations between the times series. We employ Bai–Perron supF tests20 to identify any breaks in the growth rates (log-differences) of the individual time series. When breaks are found, we restrict the subsequent analysis to the most recent regime after the break.

We must also identify whether each time series is stationary or non-stationary. A non-stationary stochastic process has moments (such as mean and variance) that approach infinity as the number of realisations of the process increases. Non-stationary time series therefore do not (typically) oscillate around a fixed level or trend when plotted over time and instead appear to wander at random. A *unit-root* non-stationary process becomes stationary once it is first-differenced (ie, the first-differenced time series does oscillate around a fixed level over the long run). As an instructive example, Appendix Figure 1 exhibits a simulated unit-root process in levels and first-differences.

Unit-root processes (and non-stationary processes more generally) can pose problems for conventional statistical techniques. For example, two statistically independent unit-root processes can exhibit an estimated correlation that is statistically significant. This is known as the *spurious regression *problem.18

It is therefore critical to first determine whether the time series of interest are stationary or non-stationary by using unit-root tests. We use the conventional Augmented Dickey–Fuller (ADF) unit-root test to establish whether each time series is stationary. To preview our results, we find that each of the time series are unit-root processes, and so we must proceed with caution.

We then test for *cointegration *between each of the mortality rates and the unemployment rate. Two unit-root processes are said to be cointegrated if they follow each other over time. For this reason, cointegrated time series are often described as exhibiting a long-run relationship. (Refer to Figure 4 for an empirical example.) We test for cointegration between each mortality rate and the unemployment rate using the Engle–Granger residual-based t-test. If cointegration holds, the long-run relationship can be consistently estimated using a variety of methods, including ordinary least squares. We use Fully-Modified Ordinary Least Squares (FMOLS) to account for potential endogeneity of the regressor within the cointegrated system.

If we find no evidence of cointegration, we then take first-differences of the time series to ensure stationarity and overcome the spurious regression problem. However, any uncovered correlations between mortality rates and unemployment only capture short-run covariation between the two time series.

In addition, we also test whether changes in the mortality rates differ over periodic increases and decreases in unemployment. For mortality rates that are (now) decreasing over time, this analysis tells us whether reductions in mortality are faster or slower during economic contractions.

We first apply the diagnostic structural-break, unit-root and cointegration tests to the times series. As discussed above, results from these tests then inform the specification and estimation of our empirical models, including whether there is a long-run cointegrating relationship between the mortality rates and aggregate unemployment. To preview our results, we only find evidence of a long-run relationship for self-harm and assault mortalities, meaning that most of our analysis focusses on short-run relationships.

*Age-group mortality rates: *For persons aged 66+, there is weak evidence of an estimated break in 1967 (Bai–Perron supF test-statistic of the null of 0 against a single break is 8.51, 10% critical value = 7.42). For persons aged 36–65, there is strong evidence of breaks in 1957 and 1975 (supF test-statistic of the null of 0 against two breaks is 16.62, 1% critical value = 10.14). We do not find statistical evidence of structural breaks in the remaining age groups.

In the regression analysis to follow, we restrict the sample to 1967–2013 for the mortality rate for persons aged 66+. Note that, if the earlier period 1948–1966 were included, the sample would bias our results in favour of finding that episodic increases in unemployment are associated with decreases in elderly mortality, because unemployment is decreasing and mortality is increasing over the most of the 1948 to 1966 period. Similarly, we restrict regression analysis of the 36–65 mortality rate from 1975 onwards, after the estimated structural break in this time series.

*Age-adjusted morbidity mortality rates: *The supF test indicates a break in 1995 for cancer (supF = 13.95, 1% critical value = 13.00); breaks in 1973 and 1982 for cerebrovascular disease (supF = 9.60, 5% critical value = 7.92); breaks in ischaemic heart disease in 1955 and 1968 (supF = 34.88, 1% critical value = 10.14); a break in 1973 for motor vehicle accidents (supF = 9.5321, 5% critical value = 9.1); and a break in 1972 for other heart disease (supF = 11.71, 5% critical value = 9.1). Notably these are all time series that are not cointegrated with the national unemployment rate. Therefore, as with the age group mortality rates above, in the short-run analysis to follow we begin the sample in the year of the final break in the time series. For example, regressions for cancer span 1995 to 2016.

We first apply ADF tests to the time series in log-levels, including a constant in the ADF equation and with automatic lag selection based on the Schwarz criterion. We accept the null of a unit root at a 10% level for each of the time series. We then first-difference the logged time series and reapply the ADF test. We can reject the null of a unit root at the 1% level for each of the mortality time series. For the national unemployment rate, we reject the null at a 5% level (p = 0.024).

We conclude that all the time series are unit-root non-stationary processes, meaning the first difference of each time series is a stationary process.

We only report mortality rates for which we can reject the null hypothesis of no cointegration at the 1% level: self-inflicted harm (Engle–Granger residual ADF t-statistic = -5.0843, p-value < 0.001) and assaults (Engle–Granger residual ADF t-statistic = -6.1199, p-value < 0.001). These two time series are cointegrated with the unemployment rate. Figure 4 plots these times series, illustrating the long-run covariation with the unemployment rate. Unemployment and per capita deaths from assaults and suicides are low in the immediate post-war period until the 1980s. They then increase through to a peak in the early to mid-1990s before declining again.

**Figure 4:** Mortality rates cointegrated with unemployment rate: self-inflicted harm and assault, 1948–2016.

Unemployment is not cointegrated with the majority of the mortality rates. Any statistical relationship with unemployment can therefore only be a short-run phenomenon; this accords with the long-run decline in many mortality rates being driven by factors unrelated to the level of the national unemployment rate. Nonetheless, changes in the unemployment rate may still be correlated with changes in mortality rates over the short run.

To examine these relationships, we run a regression of the log-differenced mortality rate on the log-differenced unemployment rate and a constant. This regression imposes a symmetric relationship between changes in unemployment and changes in mortalities. To account for heteroscedasticity and serial dependence in the error term, we use Newey–West standard errors with a triangular kernel and the bandwidth selected by the data-dependent process suggested by Andrews (1991).19 Tables 1 and 3 illustrate point estimates alongside t-statistics for the null hypothesis that the coefficient is zero.

We also run a regression of the log-differenced mortality rates on a constant and indicators (ie, dummy variables) for periods during which unemployment is rising. The estimated coefficient on the indicator therefore tells us the difference, on average, between the growth in the mortality rate during episodic increases in the unemployment rate relative to the entire sample. Tables 2 and 4 illustrate the point estimates alongside t-statistics.

Table 1 indicates that a 1% increase in the unemployment rate is associated with a contemporaneous 0.043% decrease in the mortality rate of 66+ (one-tailed p-value = 0.0145), a 0.037% decrease in the mortality rate of 36–65 (one-tailed p-value = 0.0145) and a 0.030% decrease in the mortality rate of all ages (one-tailed p-value = 0.042). Note that the sample size for the latter is rather limited and thus use of the normal limiting distribution approximation to the finite sample may be inaccurate. The one-tailed p-value for t-statistic of -2.338 under the t-distribution is nonetheless 0.0124.

**Table 1: **Regressions of log-differenced mortality rates by age on log-differenced unemployment rate.

The estimated slope coefficients in Table 2 tell us whether the growth rate in mortalities is different, on average, during periods when unemployment is rising compared to periods when unemployment is falling. For example, episodic increases in unemployment are associated with a 0.016% reduction in the 66+ mortality rate (one-tailed p-value = 0.0320). Similarly, when unemployment is rising, there is, on average, a 0.011% reduction in the 36–65 mortality rate (one-tailed p-value = 0.034) and an additional 0.016% reduction in the total mortality rate (one-tailed p-value = 0.048).

Comparing the slope coefficients to the constant, the reduction in the all-age mortality rate is about eight times (= (0.0016+0.0112)/0.0016) as large during episodic increases in the unemployment rate. However, the slope coefficient has marginal statistical significance, with a two-tailed p-value of 0.096.

**Table 2:** Regression of log-differenced mortality rates by age on indicators of episodic increases in the unemployment.

Table 3 illustrates that a 1% increase in the unemployment rate is associated with a 0.029% decrease in the age-adjusted mortality rate. However, statistical significance is weak (two-tailed p-value = 0.084). The remaining morbidity mortalities are statistically insignificant in two-tailed tests at the 10% significance level.

**Table 3:** Regressions of log-differenced age-adjusted mortality rates by morbidity on log-differenced unemployment rate.

Table 4 exhibits stronger evidence. Episodic increases in unemployment are associated with a 0.015% reduction in the age-adjusted total mortality rate (one-tailed p-value < 0.001). Comparing this slope coefficient to the estimated constant, the reductions in the age-adjusted mortality rate are 2.5 times (= (0.01+0.015)/0.01) as large during episodic increases in unemployment compared to periods when unemployment is decreasing. This relationship remains statistically significant at the 5% level (two-tailed) when we begin the sample in 1952 (after the sharp drop in mortality over 1951 to 1952 shown in Figure 3) or in 1965 (when the reduction the mortality rate appears to accelerate). (These results are unreported in the interests of brevity.) Among the other morbidities, only chronic lower-respiratory disease appears to be weakly and negatively related to the macroeconomic fluctuations (two-sided p-value = 0.078).

**Table 4: **Regression of log-differenced mortality rates by morbidity on indicators of episodic increases in the unemployment rate.

Unemployment is cointegrated with self-inflicted harm mortality and assault mortality. To estimate the long-run relationship between unemployment and these two mortality time series, we run a regression of the log of the mortality rate (self-inflicted harm or assaults) on the log of the unemployment rate and a constant using Fully-Modified Ordinary Least Squares (FMOLS) to account for potential endogeneity of the regressor within the cointegrated system.

For self-inflicted harm, this yields a point estimate of 0.125 (t-stat = 8.2471, p-value = 0.000). This means that a 1% increase in the national unemployment rate is associated with a permanent 0.125% increase in the self-inflicted harm mortality rate. For assaults, FMOLS yields a larger point estimate of 0.265 (t-stat = 6.9317, p-value = 0.000). This means that a 1% increase in the national unemployment rate is associated with a permanent 0.265% increase in the assault mortality rate.

In this paper we establish both procyclical and countercyclical features in mortality-rate time series in New Zealand. Changes in total mortality rates are negatively correlated with changes in unemployment over the 1948 to 2013 period, indicating a short-run procyclical feature of mortality in New Zealand in the post-war period. Decompositions by age reveal that this relationship is strongest among the elderly (66+).

Although these correlations cannot tell us about the precise nature of any causal channels that drive mortality, they do nonetheless help us to understand where to direct future research to inform policymaking. For example, these findings are similar to US research that shows that elderly mortality is procyclical, a result that is thought to be driven by a decline in the quality of aged-care during economic expansions when aged-care workers have more attractive employment options and aged-care facilities suffer from labour shortages.2 Establishing a similar connection between labour market conditions, aged-care and elderly mortality in New Zealand would have substantive implications for policymakers in New Zealand. For example, it would underscore the need for health, education and training and urban-planning policies to ensure that the industry has sufficient capacity to absorb the baby boomers over the next few decades. It would also have implications for immigration policy, given that the industry has increasingly relied on migrants to fill important roles that have been nonetheless characterised as “low skilled, low paid and low status.”21 Future work may also examine whether the statistical relationship between elderly mortality and macroeconomic conditions has weakened with the increased number of skilled migrants employed in the sector over the past two decades.

We also find that self-inflicted harm and assault mortality rates are countercyclical and cointegrated in levels with the unemployment rate, establishing a long-run correlation between these time series. This is consistent with a substantial amount of work that has examined the relationship between unemployment and suicide and suicide ideation at the individual level in New Zealand13–15; but it also establishes that assaults are connected to labour market conditions, which is consistent with extant work on unemployment and crime in the country.26

Given the recent policy focus on addressing mental health problems in New Zealand, these results underscore the role that expanding employment opportunities can play in combatting mental health problems. Successive governments targeted full employment over the 1950–1980 period28 and used a variety of government departments and enterprises to employ people.27 This period is notable for its substantially lower per capita suicide rate (see Figure 4), suggesting that employment programmes not only provided jobs but lowered rates of self-harm. The resurrection of large-scale employment programmes might therefore present a potential policy response to our high rates of suicide. Such programmes might also help address violent crime, given the established relationship between assault fatalities and unemployment.

Future research can shed more light on the nature of the relationship between suicides and macroeconomic conditions. For example, a growing international literature has established asymmetries in the relationship between suicide and unemployment, particularly when suicides are disaggregated by age and sex.22–23 While youth and middle-aged suicides are sensitive to reductions in unemployment in the US, suicides among 55–64 year olds are particularly sensitive to increases in unemployment.22 Future research could examine whether similar asymmetries are present in New Zealand and, given higher rates of suicide among Māori, also examine the relationship between unemployment and suicide across different ethnicities.24 Suicide rates also vary by occupation in New Zealand,25 suggesting that future research on economic conditions within specific sectors of the economy, such as farming, fisheries or forestry and the trades, may provide additional explanatory power and further inform policy to combat suicide through targeted support to at-risk occupations during economic downturns.

**Appendix Figure 1: **Simulated unit-root process in levels (left) and after first-differencing (right). The unit-root process is a random walk with a drift generated by summing a sequence of normally distributed random variables with a mean of 0.1 and variance of one. Note that, after first-differencing, the process oscillates around a fixed level.

1. Ruhm, C. J. (2016). The Health Effects of Economic Crises. Health Economics 25(2), 6-24.

2. Stevens, A. H., Miller, D. L., Page, M. E., & Filipski, M. (2015). The best of times, the worst of times: understanding pro-cyclical mortality. American Economic Journal: Economic Policy, 7 (4), 279-311.

3. Sameem, S., & Sylwester, K. (2017). The business cycle and mortality: Urban versus rural counties. Social Science & Medicine 175, 28-35.

4. Haaland, V. F., & Telle, K. (2015). Pro-cyclical mortality across socioeconomic groups and health status. Journal of Health Economics 39, 248-258.

5. Granados, J. A. T. (2005). Recessions and mortality in Spain, 1980–1997. European Journal of Population/Revue européenne de Démographie, 21 (4), 393-422.

6. Van den Berg, G. J., Gerdtham, U. G., von Hinke, S., Lindeboom, M., Lissdaniels, J., Sundquist, J., & Sundquist, K. (2017). Mortality and the business cycle: Evidence from individual and aggregated data. Journal of Health Economics, 56, 61-70.

7. Regidor, E., Vallejo, F., Granados, J. A. T., Viciana-Fernández, F. J., de la Fuente, L., & Barrio, G. (2016). Mortality decrease according to socioeconomic groups during the economic crisis in Spain: a cohort study of 36 million people. The Lancet, 388 (10060), 2642-2652.

8. Gerdtham, U. G., & Ruhm, C. J. (2006). Deaths rise in good economic times: evidence from the OECD. Economics & Human Biology, 4 (3), 298-316.

9. Economou, A., Nikolaou, A., & Theodossiou, I. (2008). Are recessions harmful to health after all? Journal of Economic Studies Journal of Economic Studies 35(5):368-384

10. Lin, S-J. (2009) Economic fluctuations and health outcome: a panel analysis of Asia-Pacific countries, Applied Economics, 41:4, 519-530

11. Svensson, M. (2007). Do not go breaking your heart: do economic upturns really increase heart attack mortality? Social Science & Medicine 65 (4), 833-841.

12. Maruthappu, M., Watkins, J., Taylor, A., Williams, C., Ali, R., Zeltner, T., & Atun, R. (2015). Unemployment and prostate cancer mortality in the OECD, 1990–2009. ecancer 9 538.

13. Blakely, T., Collings, S., Atkinson, J. (2003). Unemployment and suicide. Evidence for a causal association? Journal of Epidemiology & Community Health 57 594-600.

14. Fergusson D.M., Boden J.M., Horwood L.J. (2007).Unemployment and suicidal behaviour in a New Zealand birth cohort: A fixed effects regression analysis. CRISIS 28(2), 95-101

15. Fergusson D.M., Horwood L.J., Woodward L.J. (2001) Unemployment and psychosocial adjustment in young adults: causation or selection? Social Science and Medicine 53, 305–320

16. Hall, V.B. & McDermott, C. J. (2016). Recessions and recoveries in New Zealand's post-Second World War business cycles, New Zealand Economic Papers, 50:3, 261-280

17. Lattimore, R. & Eaqub, S. (2011) THE NEW ZEALAND ECONOMY: AN INTRODUCTION. Auckland University Press: Auckland.

18. Phillips, P.C.B. (1986). Understanding Spurious Regressions in Econometrics, Journal of Econometrics 33(3), 311-340

19. Andrews, D. W. K. (1991). Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation. Econometrica 59, 817-858.

20. Bai, J and P. Perron (2003). Computation and analysis of multiple structural change models. Journal of Applied Econometrics 18 (1), 1-22

21. Badkar, J., Callister, P., & Didham, R. (2009). Ageing New Zealand: The growing reliance on migrant caregivers. Institute of Policy Studies Working Paper 09/08.

22. Lin, Y-H. & Chen, W-Y. (2018). Does unemployment have asymmetric effects on suicide rates? Evidence from the United States: 1928–2013, Economic Research Ekonomska Istraživanja, 31:1, 1404-1417

23. Wu, W-C., & Cheng, H-P. (2010). Symmetric mortality and asymmetric suicide cycles, Social Science & Medicine, 70:12, 1974-1981.

24. Beautrais, A. L. & Fergusson, D. M. (2006) Indigenous Suicide in New Zealand, Archives of Suicide Research, 10:2, 159-168,

25. Gallagher, L.M., Kliem, C., Beautrais, A.L., & Stallones, L. (2008) Suicide and Occupation in New Zealand, 2001–2005. International Journal of Occupational and Environmental Health, 14:1, 45-50.

26. Papps, K. & Winkelmann R. (2000) Unemployment and crime: New evidence for an old question, New Zealand Economic Papers 34(1), 53-71

27. Bridgman, B. & Greenaway-McGrevy, R. (2018) The fall (and rise) of labour share in New Zealand, New Zealand Economic Papers, 52:2, 109-130

28. Endres, T. (1984). ARTICLE: The New Zealand Full Employment Goal: A Survey of Changing Views 1950 to 1980. New Zealand Journal of Industrial Relations, 9(1).

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A substantial amount of international research has documented a statistical relationship between mortality and economic activity at the aggregate level. In many countries, mortality appears to be procyclical, meaning that it tends to increase (relative to long-run trends) during economic expansions.1–8 Procyclical mortality appears concentrated among the elderly and in urban areas.2,3 However, not all causes of mortality are procyclical. Suicides, homicides and purposeful injuries are frequently found to be countercyclical.5,9,10 Morbidities from ischaemic heart disease (including myocardial infarcts in the working aged) and malignant neoplasm (including lung and prostate cancer) are also frequently found to be countercyclical.9,11,12

In New Zealand, a substantial amount of work has examined the relationship between unemployment and suicide.13–15 But there has been little research examining the link between macroeconomic activity and other causes of death, let alone our national mortality rate.

In this paper we aim to progress our understanding of the empirical relationship between mortality and macroeconomic activity in New Zealand. The objective of our analysis is to model the relationship between mortality and aggregate (ie, national) unemployment, including mortality rates for different age groups and morbidities, in order to uncover potentially procyclical and countercyclical features. We use sophisticated time series techniques to identify relevant sample periods for analysis and to establish whether there is short- or long-run covariation between the various mortality rates and unemployment.

We begin by describing the data used in our analysis. We then discuss the empirical approaches taken to model statistical relationships between the variables. This includes a battery of technical diagnostic tests, the results of which inform our empirical strategy.

*Unemployment rate: *Quarterly unemployment rate time series spanning 1948 to 2014 are obtained from Lattimore and Eaqub (2011)17 and updated to 2019 with data from Stats NZ. Annual observations used for analysis are based on within-year averages of the quarterly data.

**Figure 1:** Unemployment rate (%), 1948 to 2016. Shaded regions indicate periods during which the unemployment rate was rising.

We use national unemployment as our measure of macroeconomic activity, rather than alternatives such as real gross domestic product (GDP) or output per capita, for two reasons. First, most explanations of the link between mortality and economic activity focus on (un)employment as a mediating factor.2,3,5,6,8–13 Although our focus remains descriptive, by focussing on the explanatory variables identified in the extant literature we can better illuminate the path forward for understanding the economic factors driving variation in mortality. Second, alternative measures of macroeconomic activity, notably real GDP growth, appear disconnected from unemployment during key periods in New Zealand’s economic history, and remain positive during many episodic increases in unemployment. For example, despite the annual unemployment rate rising in almost every year between 1979 and 1991 (see Figure 1), there were only three short ‘classical’ recessions in which real GDP was decreasing over this period (1982Q3–1983Q1, 1988Q1–Q4 and 1991Q1–Q2).16

*Mortality rates by age group: *Annual mortalities and populations by age group are sourced from the Human Mortality Database (HMD) for the period spanning 1948 to 2013 (available at https://www.mortality.org/). For each age group, mortality rates are constructed by dividing total mortality by population. Figure 2 exhibits the mortality rate for six different age groups: 0 (infants), 1–15 (children), 16–35, 36–65 (middle age), 66+ (elderly) and all ages. Over the sample period, mortality rates are highest among the elderly and infants.

**Figure 2: **Mortality rates across various age groups, 1948 to 2013. Shaded regions indicate periods during which the unemployment rate was rising.

*Mortality rates by morbidity:* Annual age-standardised mortality rates by cause of death are obtained from the Ministry of Health for the 1948 to 2016 period, although some morbidities begin later in the sample period (available at https://minhealthnz.shinyapps.io/historical-mortality/). These data include an age-standardised total mortality rate per 100,000 persons. We divide by 100,000 for comparability to the HMD dataset. Figure 3 depicts the eleven mortality rates available.

**Figure 3: **Age-standardised mortalities by morbidity, 1948 to 2016. Shaded regions indicate periods during which the unemployment rate was rising.

The appropriate approach for capturing potential correlations between the variables of interest depends on the statistical properties of the individual times series. Specifically, we need to establish (a) whether there are any* structural breaks* in the time series, as these will inform the relevant sample period for the statistical analysis, and (b) whether each time series is *stationary *or *non-stationary*, as this will inform the appropriate empirical models for modelling statistical correlations. We describe these concepts and the pre-diagnostic tests used to identify these features of the data. We take natural logs of all variables prior to statistical analysis.

Structural breaks occur when there is discrete change in a specific moment of the data. For example, the mean of a times series may change at a specific point in time. The inflection points evident in many of the mortality rates depicted in Figures 2 and 3 are consistent with a structural break in the average growth rate in the time series. For example, the mortality rate for 66+ trends upwards until the mid-1960s before trending downwards; this inflection point will manifest as a structural change in the average growth rate in per capita mortality from positive to negative.

These long-run secular trends in mortality rates are perhaps driven by changes in medical technology, knowledge and practice and, as such, are unrelated to variation in unemployment. Structural breaks should be identified prior to statistical analysis as they can otherwise obfuscate statistical correlations between the times series. We employ Bai–Perron supF tests20 to identify any breaks in the growth rates (log-differences) of the individual time series. When breaks are found, we restrict the subsequent analysis to the most recent regime after the break.

We must also identify whether each time series is stationary or non-stationary. A non-stationary stochastic process has moments (such as mean and variance) that approach infinity as the number of realisations of the process increases. Non-stationary time series therefore do not (typically) oscillate around a fixed level or trend when plotted over time and instead appear to wander at random. A *unit-root* non-stationary process becomes stationary once it is first-differenced (ie, the first-differenced time series does oscillate around a fixed level over the long run). As an instructive example, Appendix Figure 1 exhibits a simulated unit-root process in levels and first-differences.

Unit-root processes (and non-stationary processes more generally) can pose problems for conventional statistical techniques. For example, two statistically independent unit-root processes can exhibit an estimated correlation that is statistically significant. This is known as the *spurious regression *problem.18

It is therefore critical to first determine whether the time series of interest are stationary or non-stationary by using unit-root tests. We use the conventional Augmented Dickey–Fuller (ADF) unit-root test to establish whether each time series is stationary. To preview our results, we find that each of the time series are unit-root processes, and so we must proceed with caution.

We then test for *cointegration *between each of the mortality rates and the unemployment rate. Two unit-root processes are said to be cointegrated if they follow each other over time. For this reason, cointegrated time series are often described as exhibiting a long-run relationship. (Refer to Figure 4 for an empirical example.) We test for cointegration between each mortality rate and the unemployment rate using the Engle–Granger residual-based t-test. If cointegration holds, the long-run relationship can be consistently estimated using a variety of methods, including ordinary least squares. We use Fully-Modified Ordinary Least Squares (FMOLS) to account for potential endogeneity of the regressor within the cointegrated system.

If we find no evidence of cointegration, we then take first-differences of the time series to ensure stationarity and overcome the spurious regression problem. However, any uncovered correlations between mortality rates and unemployment only capture short-run covariation between the two time series.

In addition, we also test whether changes in the mortality rates differ over periodic increases and decreases in unemployment. For mortality rates that are (now) decreasing over time, this analysis tells us whether reductions in mortality are faster or slower during economic contractions.

We first apply the diagnostic structural-break, unit-root and cointegration tests to the times series. As discussed above, results from these tests then inform the specification and estimation of our empirical models, including whether there is a long-run cointegrating relationship between the mortality rates and aggregate unemployment. To preview our results, we only find evidence of a long-run relationship for self-harm and assault mortalities, meaning that most of our analysis focusses on short-run relationships.

*Age-group mortality rates: *For persons aged 66+, there is weak evidence of an estimated break in 1967 (Bai–Perron supF test-statistic of the null of 0 against a single break is 8.51, 10% critical value = 7.42). For persons aged 36–65, there is strong evidence of breaks in 1957 and 1975 (supF test-statistic of the null of 0 against two breaks is 16.62, 1% critical value = 10.14). We do not find statistical evidence of structural breaks in the remaining age groups.

In the regression analysis to follow, we restrict the sample to 1967–2013 for the mortality rate for persons aged 66+. Note that, if the earlier period 1948–1966 were included, the sample would bias our results in favour of finding that episodic increases in unemployment are associated with decreases in elderly mortality, because unemployment is decreasing and mortality is increasing over the most of the 1948 to 1966 period. Similarly, we restrict regression analysis of the 36–65 mortality rate from 1975 onwards, after the estimated structural break in this time series.

*Age-adjusted morbidity mortality rates: *The supF test indicates a break in 1995 for cancer (supF = 13.95, 1% critical value = 13.00); breaks in 1973 and 1982 for cerebrovascular disease (supF = 9.60, 5% critical value = 7.92); breaks in ischaemic heart disease in 1955 and 1968 (supF = 34.88, 1% critical value = 10.14); a break in 1973 for motor vehicle accidents (supF = 9.5321, 5% critical value = 9.1); and a break in 1972 for other heart disease (supF = 11.71, 5% critical value = 9.1). Notably these are all time series that are not cointegrated with the national unemployment rate. Therefore, as with the age group mortality rates above, in the short-run analysis to follow we begin the sample in the year of the final break in the time series. For example, regressions for cancer span 1995 to 2016.

We first apply ADF tests to the time series in log-levels, including a constant in the ADF equation and with automatic lag selection based on the Schwarz criterion. We accept the null of a unit root at a 10% level for each of the time series. We then first-difference the logged time series and reapply the ADF test. We can reject the null of a unit root at the 1% level for each of the mortality time series. For the national unemployment rate, we reject the null at a 5% level (p = 0.024).

We conclude that all the time series are unit-root non-stationary processes, meaning the first difference of each time series is a stationary process.

We only report mortality rates for which we can reject the null hypothesis of no cointegration at the 1% level: self-inflicted harm (Engle–Granger residual ADF t-statistic = -5.0843, p-value < 0.001) and assaults (Engle–Granger residual ADF t-statistic = -6.1199, p-value < 0.001). These two time series are cointegrated with the unemployment rate. Figure 4 plots these times series, illustrating the long-run covariation with the unemployment rate. Unemployment and per capita deaths from assaults and suicides are low in the immediate post-war period until the 1980s. They then increase through to a peak in the early to mid-1990s before declining again.

**Figure 4:** Mortality rates cointegrated with unemployment rate: self-inflicted harm and assault, 1948–2016.

Unemployment is not cointegrated with the majority of the mortality rates. Any statistical relationship with unemployment can therefore only be a short-run phenomenon; this accords with the long-run decline in many mortality rates being driven by factors unrelated to the level of the national unemployment rate. Nonetheless, changes in the unemployment rate may still be correlated with changes in mortality rates over the short run.

To examine these relationships, we run a regression of the log-differenced mortality rate on the log-differenced unemployment rate and a constant. This regression imposes a symmetric relationship between changes in unemployment and changes in mortalities. To account for heteroscedasticity and serial dependence in the error term, we use Newey–West standard errors with a triangular kernel and the bandwidth selected by the data-dependent process suggested by Andrews (1991).19 Tables 1 and 3 illustrate point estimates alongside t-statistics for the null hypothesis that the coefficient is zero.

We also run a regression of the log-differenced mortality rates on a constant and indicators (ie, dummy variables) for periods during which unemployment is rising. The estimated coefficient on the indicator therefore tells us the difference, on average, between the growth in the mortality rate during episodic increases in the unemployment rate relative to the entire sample. Tables 2 and 4 illustrate the point estimates alongside t-statistics.

Table 1 indicates that a 1% increase in the unemployment rate is associated with a contemporaneous 0.043% decrease in the mortality rate of 66+ (one-tailed p-value = 0.0145), a 0.037% decrease in the mortality rate of 36–65 (one-tailed p-value = 0.0145) and a 0.030% decrease in the mortality rate of all ages (one-tailed p-value = 0.042). Note that the sample size for the latter is rather limited and thus use of the normal limiting distribution approximation to the finite sample may be inaccurate. The one-tailed p-value for t-statistic of -2.338 under the t-distribution is nonetheless 0.0124.

**Table 1: **Regressions of log-differenced mortality rates by age on log-differenced unemployment rate.

The estimated slope coefficients in Table 2 tell us whether the growth rate in mortalities is different, on average, during periods when unemployment is rising compared to periods when unemployment is falling. For example, episodic increases in unemployment are associated with a 0.016% reduction in the 66+ mortality rate (one-tailed p-value = 0.0320). Similarly, when unemployment is rising, there is, on average, a 0.011% reduction in the 36–65 mortality rate (one-tailed p-value = 0.034) and an additional 0.016% reduction in the total mortality rate (one-tailed p-value = 0.048).

Comparing the slope coefficients to the constant, the reduction in the all-age mortality rate is about eight times (= (0.0016+0.0112)/0.0016) as large during episodic increases in the unemployment rate. However, the slope coefficient has marginal statistical significance, with a two-tailed p-value of 0.096.

**Table 2:** Regression of log-differenced mortality rates by age on indicators of episodic increases in the unemployment.

Table 3 illustrates that a 1% increase in the unemployment rate is associated with a 0.029% decrease in the age-adjusted mortality rate. However, statistical significance is weak (two-tailed p-value = 0.084). The remaining morbidity mortalities are statistically insignificant in two-tailed tests at the 10% significance level.

**Table 3:** Regressions of log-differenced age-adjusted mortality rates by morbidity on log-differenced unemployment rate.

Table 4 exhibits stronger evidence. Episodic increases in unemployment are associated with a 0.015% reduction in the age-adjusted total mortality rate (one-tailed p-value < 0.001). Comparing this slope coefficient to the estimated constant, the reductions in the age-adjusted mortality rate are 2.5 times (= (0.01+0.015)/0.01) as large during episodic increases in unemployment compared to periods when unemployment is decreasing. This relationship remains statistically significant at the 5% level (two-tailed) when we begin the sample in 1952 (after the sharp drop in mortality over 1951 to 1952 shown in Figure 3) or in 1965 (when the reduction the mortality rate appears to accelerate). (These results are unreported in the interests of brevity.) Among the other morbidities, only chronic lower-respiratory disease appears to be weakly and negatively related to the macroeconomic fluctuations (two-sided p-value = 0.078).

**Table 4: **Regression of log-differenced mortality rates by morbidity on indicators of episodic increases in the unemployment rate.

Unemployment is cointegrated with self-inflicted harm mortality and assault mortality. To estimate the long-run relationship between unemployment and these two mortality time series, we run a regression of the log of the mortality rate (self-inflicted harm or assaults) on the log of the unemployment rate and a constant using Fully-Modified Ordinary Least Squares (FMOLS) to account for potential endogeneity of the regressor within the cointegrated system.

For self-inflicted harm, this yields a point estimate of 0.125 (t-stat = 8.2471, p-value = 0.000). This means that a 1% increase in the national unemployment rate is associated with a permanent 0.125% increase in the self-inflicted harm mortality rate. For assaults, FMOLS yields a larger point estimate of 0.265 (t-stat = 6.9317, p-value = 0.000). This means that a 1% increase in the national unemployment rate is associated with a permanent 0.265% increase in the assault mortality rate.

In this paper we establish both procyclical and countercyclical features in mortality-rate time series in New Zealand. Changes in total mortality rates are negatively correlated with changes in unemployment over the 1948 to 2013 period, indicating a short-run procyclical feature of mortality in New Zealand in the post-war period. Decompositions by age reveal that this relationship is strongest among the elderly (66+).

Although these correlations cannot tell us about the precise nature of any causal channels that drive mortality, they do nonetheless help us to understand where to direct future research to inform policymaking. For example, these findings are similar to US research that shows that elderly mortality is procyclical, a result that is thought to be driven by a decline in the quality of aged-care during economic expansions when aged-care workers have more attractive employment options and aged-care facilities suffer from labour shortages.2 Establishing a similar connection between labour market conditions, aged-care and elderly mortality in New Zealand would have substantive implications for policymakers in New Zealand. For example, it would underscore the need for health, education and training and urban-planning policies to ensure that the industry has sufficient capacity to absorb the baby boomers over the next few decades. It would also have implications for immigration policy, given that the industry has increasingly relied on migrants to fill important roles that have been nonetheless characterised as “low skilled, low paid and low status.”21 Future work may also examine whether the statistical relationship between elderly mortality and macroeconomic conditions has weakened with the increased number of skilled migrants employed in the sector over the past two decades.

We also find that self-inflicted harm and assault mortality rates are countercyclical and cointegrated in levels with the unemployment rate, establishing a long-run correlation between these time series. This is consistent with a substantial amount of work that has examined the relationship between unemployment and suicide and suicide ideation at the individual level in New Zealand13–15; but it also establishes that assaults are connected to labour market conditions, which is consistent with extant work on unemployment and crime in the country.26

Given the recent policy focus on addressing mental health problems in New Zealand, these results underscore the role that expanding employment opportunities can play in combatting mental health problems. Successive governments targeted full employment over the 1950–1980 period28 and used a variety of government departments and enterprises to employ people.27 This period is notable for its substantially lower per capita suicide rate (see Figure 4), suggesting that employment programmes not only provided jobs but lowered rates of self-harm. The resurrection of large-scale employment programmes might therefore present a potential policy response to our high rates of suicide. Such programmes might also help address violent crime, given the established relationship between assault fatalities and unemployment.

Future research can shed more light on the nature of the relationship between suicides and macroeconomic conditions. For example, a growing international literature has established asymmetries in the relationship between suicide and unemployment, particularly when suicides are disaggregated by age and sex.22–23 While youth and middle-aged suicides are sensitive to reductions in unemployment in the US, suicides among 55–64 year olds are particularly sensitive to increases in unemployment.22 Future research could examine whether similar asymmetries are present in New Zealand and, given higher rates of suicide among Māori, also examine the relationship between unemployment and suicide across different ethnicities.24 Suicide rates also vary by occupation in New Zealand,25 suggesting that future research on economic conditions within specific sectors of the economy, such as farming, fisheries or forestry and the trades, may provide additional explanatory power and further inform policy to combat suicide through targeted support to at-risk occupations during economic downturns.

**Appendix Figure 1: **Simulated unit-root process in levels (left) and after first-differencing (right). The unit-root process is a random walk with a drift generated by summing a sequence of normally distributed random variables with a mean of 0.1 and variance of one. Note that, after first-differencing, the process oscillates around a fixed level.

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