Macroeconomic effects on mortality revealed by panel analysis with nonlinear trends

Abstract

Many investigations have used panel methods to study the relationships between fluctuations in economic activity and mortality. A broad consensus has emerged on the overall procyclical nature of mortality: perhaps counter-intuitively, mortality typically rises above its trend during expansions. This consensus has been tarnished by inconsistent reports on the specific age groups and mortality causes involved. We show that these inconsistencies result, in part, from the trend specifications used in previous panel models. Standard econometric panel analysis involves fitting regression models using ordinary least squares, employing standard errors which are robust to temporal autocorrelation. The model specifications include a fixed effect, and possibly a linear trend, for each time series in the panel. We propose alternative methodology based on nonlinear detrending. Applying our methodology on data for the 50 US states from 1980 to 2006, we obtain more precise and consistent results than previous studies. We find procyclical mortality in all age groups. We find clear procyclical mortality due to respiratory disease and traffic injuries. Predominantly procyclical cardiovascular disease mortality and countercyclical suicide are subject to substantial state-to-state variation. Neither cancer nor homicide have significant macroeconomic association.

Figure 1

National mortality and unemployment. (a) Mortality per 1,000 per year, shown as a dashed line corresponding to the left axis scale; unemployment rate, shown as a solid line corresponding to the right axis scale. (b,c,d) The data in (a) detrended using a linear trend, first difference and Hodrick-Prescott filter (λ = 100) respectively.

Figure 2

Mortality and unemployment for four states. Mortality per 1,000 per year is shown as a dashed line corresponding to the lefts axis scale. The unemployment rate is shown as a solid gray line corresponding to the right axis scale.

Figure 3

Autocorrelation of the residual in four models for total mortality. Points show the sample autocorrelation for each state at each lag. The dashed lines are at $\pm t_{n-2}{\left\{n-2+t_{n-2}^2\right\}}^{-1/2}$ where t_n−2 is the 97.5 percentile of the t distribution on n − 2 degrees of freedom, and n is the number of pairs of time points available to compute the sample autocorrelation at each lag. If the residual series were temporally uncorrelated, approximately 95% of the points should lie between the dashed lines (Moore and McCabe, 1999, Section 10.2). The gray solid line graphs the mean sample autocorrelation at each lag.

Figure 4

The crosscorrelation between residuals for each pair of states, plotted against distance between population-weighted state centers (from the 2000 census) in four models for total mortality. The dashed lines are at $\pm t_{n-2}{\left\{n-2+t_{n-2}^2\right\}}^{-1/2}$ where t_n−2 is the 97.5 percentile of the t distribution on n − 2 degrees of freedom, and n = 27 (for B1, L1, HP1₁₀₀) or n = 26 (for D1). If the residual series were spatiotemporally uncorrelated, approximately 95% of the points should lie between the dashed lines (Moore and McCabe, 1999, Section 10.2). The actual percentages for models B1, L1, D1 and HP1₁₀₀ are 46.1%, 79.3%, 90.9% and 91.3% respectively. The gray solid line shows a local linear regression fit to these crosscorrelations, implemented using the loess function in R2.15.0, with the default parameter settings.

Figure 5

Residual time plots for four states. The top row graphs total state mortality, and subsequent rows graph residuals for each of four models.

Figure 6

State-specific effects of unemployment on mortality. Columns correspond to models, as specified in Table 1 and equation (1). Rows correspond to mortality categories. The estimate of 100α from fitting the model to a single state is plotted against the population of the state. Each state is represented either by its two letter abbreviation or by an open circle.