Happiness Matters: Productivity Gains from Subjective Well-Being

Abstract

This article studies the link between subjective well-being and productivity at the aggregate level, using a matched dataset from surveys and official statistics. Well-being and productivity are measured, respectively, by life satisfaction and total factor productivity. The analysis, which applies non-parametric frontier techniques in a production framework, finds that life satisfaction generates significant productivity gains in a sample of 20 European countries. These results confirm the evidence of a positive association between the variables of interest found at the individual and firm level, and support the view that promoting subjective well-being is not only desirable per se, but it is conducive to higher productivity and improved countries’ economic performances.

Appendices

Appendix 1: The DEA Method

DEA rests on a theoretical framework where, given certain levels of inputs use and the available technology, there exists a level of output that cannot be exceeded—and might not be attained—by the operating economic units (Farrell 1957). Operating units can be firms, industries, or countries. These maximal levels of output define the so-called efficient (or best-practise) frontier. The distance between the frontier and the level of production recorded for each operating unit gives a measure of the productive inefficiency of that unit. For more details on the method, one can see Färe et al. (1994a). These authors present the theoretical foundation of the approach, while Coelli et al. (2005) provide an accessible introduction to efficiency measurement.

Formally, let ${\mathbf {y}}$ and ${\mathbf {x}}$ denote, respectively, the vectors of outputs and inputs to production. Assume convexity, free disposability of inputs and outputs, and constant returns to scale (CRS).¹⁶ Computing measures of operating units’ productive efficiency requires solving, for each unit j and each period t, linear programs (LP) formulated as follows:

$$\begin{aligned}&Max_{\theta , \lambda } \, \theta _j^t \end{aligned}$$

(8)

$$\begin{aligned}&s.t. \, \sum _{k=1}^K \lambda _k^t y_{mk}^t \ge y_{mj}^t \theta _j^t \quad m=1, \dots ,M \end{aligned}$$

(9)

$$\begin{aligned}&\sum _{k=1}^K \lambda _k^t x_{nk}^t \le x_{nj}^t \quad n=1,\dots ,N \end{aligned}$$

(10)

$$\begin{aligned}&\lambda _k^t \ge 0 \quad k=1,\dots ,K \end{aligned}$$

(11)

(Here, units are indexed by k, inputs by n and outputs by m; the $\lambda$s denote a set of weights.) The linear program constructs a virtual technology given by linear combinations of inputs and outputs used/produced. The goal is to maximize the output of unit j, under the constraint that no unit can operate beyond a convex set defined by the virtual technology and that weights are non negative. The value taken by $\theta$ tells to what extent a unit could increase its produce by using available resources more efficiently.

$$\begin{aligned} \theta ^{-1}=D^{t}\left( {\mathbf {x}}^{t},{\mathbf {y}}^{t}\right) \end{aligned}$$

(12)

the parameter $\theta ^{-1}$ represents the distance of an operating unit to the frontier. It takes values between zero and one. If a unit is efficient, then $\theta ^{-1}=1$, meaning that the unit cannot attain higher levels of production without increasing the use of inputs. In contrast, values of $\theta ^{-1}$ below unity could produce more using more efficiently its existing resources. Thus, D provides an estimate of the producing units’ efficiency at time t; it is interpreted as a measure of TFP, as it compares output to inputs to production.

DEA technologies are time specific. TFP growth rates are computed by linking the efficiency scores $\theta$s computed for two adjacent time periods. Developing an idea first suggested by Malmquist (1953), Caves et al. (1982) defines the (Malmquist) productivity index as follows:

$$\begin{aligned} M^{t+1}= \frac{D^{t}\left( x^{t+1},y^{t+1}\right) }{D^{t}\left( x^{t},y^{t}\right) }; \end{aligned}$$

(13)

For each operating unit k, this index is the ratio of the distances to the efficient frontier at time t computed comparing output and inputs of two subsequent periods (t and $t+1$). Thus, the Malmquist index indicates how the efficiency of operating units evolves between two periods. Doing so requires “fixing” the technology (expressed by the frontier) at a certain point in time. Clearly, it is also possible to write the same index using the technology in $t+1$. To avoid the arbitrary choice of a reference technology, Färe et al. (1994a) propose to use a geometric average of the Malmquist indices obtained using the technologies available in t and $t+1$:

$$\begin{aligned} M^{t,t+1}= \left[ \left( \frac{D^{t}\left( x^{t+1},y^{t+1}\right) }{D^{t}(x^{t},y^{t})} \right) \left( \frac{D^{t+1}\left( x^{t+1},y^{t+1}\right) }{D^{t+1}\left( x^{t},y^{t}\right) } \right) \right] ^{\frac{1}{2}}; \end{aligned}$$

(14)

Equation 15 considers how much a unit could produce using the inputs available in $t+1$, if it used the technology at time t, and how much a unit could produce using the inputs available in t, if it used the technology available in $t+1$, and takes the geometric mean of the answers to these two questions. If, for example, the output resulting from the use of inputs in $t+1$ were halved when using as reference technology the frontier in t, and the output from the use of inputs in t were doubled when using as reference technology the frontier in $t+1$, the index above would show that a substantial technology progress has occurred from period t to $t+1$. Here, the CRS assumption is crucial to the interpretation of the Malmquist index as a TFP index (Grifell-Tatje and Lovell 1985).

Equations 12 and 14 are used in this study to compute measures of productivity and productivity changes.

The second part of the study establishes whether an additional input to production, life satisfaction, is an output or an input to production.

To this purpose, a test developed by Pastor et al. (2002) is implemented. The test proves to perform well under most situations (Nataraja and Johnson 2011). This procedure is as follows. Firstly, we compute efficiency indices using the linear program of Eq. 8. This is done twice, one time with life satisfaction included in the input set, another time with sLS included in the output set. Then, we compute the level of output that would be attained if countries were efficiently using their inputs. (This is done by multiplying the efficiency scores by the observed values of output.) Finally, we re-calculate efficiency scores by comparing the optimal values of output to physical inputs, capital and labour, thus omitting life satisfaction in the set of inputs (or outputs). This allows us to interpret any resulting loss of efficiency as the effect of (omitted) life satisfaction. If a country is close to the frontier, then results indicate that subjective well-being does not generate significant efficiency gains. In contrast, if a country is displaced from the frontier and experience “large” efficiency losses, results suggest that subjective well-being plays a significant role in the production framework of that country.

To test significance of the results, Pastor et al. (2002) suggest to perform a simple binomial test. Assume to assign a value of 1 when efficiency changes by more than 10% and 0 otherwise. The sum of such 1s over the countries in the sample follows a Binomial distribution. Therefore,

$$\begin{aligned} T=\sum _{j=1}^N T_j \sim \, Binomial \, (N-1,p_0=0.15) \end{aligned}$$

(15)

where:

$$\begin{aligned} \begin{array}{rl} T_j = 1&\quad {\text {if}}\, {\text {change}}\, {\text {in}}\,{\text {efficiency}} > 0.1 \\ 0&\quad {\text {otherwise}}, \,\, j=1,\dots ,N \end{array} \end{aligned}$$

Following Pastor et al. (2002), a change in efficiency of more than 10% obtained for at least 15% of countries would signal a significant role of well-being as an input (or output) to production.

Appendix 2: TFP Growth

See Table 5.

Table 5 Average TFP growth and country rankings.