Abstract
To understand how small business entrepreneurs respond to government policy one has to know their risk and time preferences. Are they risk averse, or have high discount rates, such that they are hard to motivate? We have conducted a set of field experiments in Denmark that will allow a direct characterization of small business entrepreneurs in terms of these traits. We build on experimental tasks that are well established in the literature. The results do not suggest that small business entrepreneurs are more or less risk averse than the general population under the assumption of Expected Utility Theory. However, we generally find an S-shaped probability weighting function for both small business entrepreneurs and non-entrepreneurs, with entrepreneurs being more optimistic about the chance of occurrence for the best outcome in lotteries with real monetary outcomes. The results also point to a significant difference in individual discount rates between entrepreneurs and non-entrepreneurs: entrepreneurs are willing to wait longer for certain rewards than the general population.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
Field experiments of this kind were first undertaken by Elston et al. (2005) in the United States. They studied risk attitudes of entrepreneurs and non-entrepreneurs at a trade show catering to entrepreneurs. They did not elicit discount rates, and their evaluation of risk attitudes did not consider probability optimism or pessimism. Nor was their control group of non-entrepreneurs as representative of the general population as ours.
Alternative methods for the direct estimation of subjective beliefs about other naturally occurring events, using popular scoring rules and controls for biases due to risk aversion, have been developed. Andersen et al. (2014) review the literature and develop methods that extend the approach we adopt here. These methods could be used to undertake a more holistic evaluation of the subjective beliefs of entrepreneurs about other possible events that might motivate their entry, such as the general state of the economy in the future. For instance, Harrison and Phillips (2013) elicit subjective belief distributions about major global financial risks, such as equities risk, interest rate risk, credit risk, and commodities risk.
There is some evidence that rewarding subjects by selecting one task at random for payment does not distort choices under EUT. On the other hand, there is some evidence that this random lottery payment protocol can affect inferences about risk preferences under RDU: see Harrison and Swarthout (2014). The reason that this protocol could affect preferences under RDU, but not under EUT, is that it relies on the independence axiom, which is precisely the axiom that RDU assumes to be invalid. We assume here that the protocol does not influence inferred risk attitudes.
Coller and Williams (1999), Harrison et al. (2002), and Andersen et al. (2008) provided annual and annual effective interest rates to help subjects compare lab and field investments. This feature may reduce comparison errors, and Coller and Williams (1999) find that providing information on interest rates has a significant negative effect on elicited discount rates.
We assume that the subject does not have access to perfect capital markets, as explained in Coller and Williams (1999, p. 110) and Harrison et al. (2002, 1607 ff.). This assumption not only is plausible, but also subject to checks from responses to the financial questionnaire that Coller and Williams (1999), Harrison et al. (2002), and Andersen et al. (2008) ask each subject to complete. The effects of allowing for field borrowing and lending opportunities on elicited discount rates for risk neutral subjects are discussed by Coller and Williams (1999) and Harrison et al. (2002).
These transactions costs are discussed in Coller and Williams (1999), and they include things such as remembering to pick up the delayed payment as well as the credibility of the money actually being paid in the future. The design of our experiment was intended to make sure that the credibility of receiving the money in the future was high. These considerations may be important in a field context, particularly in less developed countries.
The third task was a laboratory version of the Deal and No Deal game, which always followed the risk aversion and discount rate tasks. We provide instructions for the risk aversion and discount rate tasks in Appendix A, available in the working paper version at http://cear.gsu.edu.
In effect, these 70 subjects allow us to control for possible session effects that might be specific to the field experiments conducted at the Entrepreneurship Fair.
The 97 subjects in the second field experiment were randomly selected from a subsample of the 253 subjects who participated in the first field experiment. These are “artefactual field experiments” in the terminology by Harrison and List (2004), since we essentially took lab experiments to field subjects.
Appendix B provides an overview of the treatments in the risk aversion and discounting tasks across the various experiments.
The four sets of prizes (in kroner) are as follows, with the two prizes for lottery A listed first and the two prizes for lottery B listed next: (A1: 2000, 1600; B1: 3850, 100), (A2: 2250, 1500; B2: 4000, 500), (A3: 2000, 1750; B3: 4000, 150), and (A4: 2500, 1000; B4: 4500, 50).
The two asymmetric treatments offered probabilities of (0.3, 0.5, 0.7, 0.8, 0.9, and 1) and (0.1, 0.2, 0.3, 0.5, 0.7, and 1), respectively. These treatments vary the cardinal scale of the multiple price list and yield six decision rows in each treatment.
The two asymmetric treatments offered annual interest rates of (15, 25, 35, 40, 45, and 50 %) and (5, 10, 15, 25, 35, and 50 %), respectively. The symmetric treatment offers 10 rows with annual interest rates between 5 and 50 %.
We review the estimation procedures in Appendix C.
The CRRA specification we use is \({\textit{U}(\textit{M})}=\textit{M}^{(1-{r})}/(1-{r})\) for \(r \ne 1\), where r is the CRRA coefficient. With this functional form r \(=\) 0 denotes risk neutral behavior, \(r > 0\) denotes risk aversion, and \(r < 0\) denotes risk seeking behavior.
The Expo-Power function is defined as \(U(M) = [1-\mathrm{exp}(-\alpha {M}^{1-{r}})]/\alpha \), where \(\alpha \) and r are parameters to be estimated. RRA is then r + \(\alpha (1-{r}){M}^{1-{r}}\), so RRA varies with income if \(\alpha \ne 0\). This function nests CRRA (as \(\alpha \ne 0\)) and CARA (as \(r \ne 0\)).
Table C1 in Appendix C shows ML estimations of the same model with control for employment status instead of firm ownership. The results suggest that self-employed are less risk averse than full-time employed subjects. The estimated coefficient is equal to \(-\)0.295 with a p-value of 0.099.
Prelec (1998) offers a two-parameter probability weighting function that exhibits considerable flexibility. This function is \(w(p) = \mathrm{exp}\{-\eta (-\hbox {ln}{p})^{\varphi }\)}, and is defined for \(0< {p} <1, \eta >0\) and \(\varphi >0\).
Table 4 Risk attitudes assuming RDU with Prelec probability weighting We also find that the probability weighting function generally has an S-shape when we control for employment status instead of firm ownership.
Prizes in the discount rate tasks are only one-tenth of those in the first field experiment, so we cannot rule out the hypothesis that individual discount rates are falling over the range of income considered in all experiments. This result is consistent with the so-called “magnitude effect” on individual discounting. Andersen et al. (2013) provide direct evidence against this hypothesis and magnitude effect in later experiments with Danes.
The discount factor for the Quasi-Hyperbolic specification is defined as \({D}^{\mathrm{QH}}{(t)} = 1\) if t \(=\) 0 and \({D}^{\mathrm{QH}}{(t)} = \beta /(1+\delta )^{{t}}\) if \({t}>0\), where \(\beta <1\) implies quasi-hyperbolic discounting, and \(\beta =1\) is exponential discounting.
We find similar results in the model with control for employment status. Table C3 reports estimates of the quasi-hyperbolic discounting function assuming RDU. We cannot reject the hypothesis that \(\beta =1\) when we control for employment status. It is possible to condition our core parameters on individual demographic covariates, just like we consider treatment variables. We consider total demographic effects of sex, age (below and above 40 years of age), short and long education, and low and high income. Our main results are robust to controls for observable individual characteristics: we find a significant effect of firm ownership on subjective probability weighting, a negative association with the level of discounting, and no evidence of Quasi-Hyperbolic discounting. The only demographic covariate to have a significant effect on the estimated parameters is age. Table C4 shows that younger subjects below 40 years of age have a significantly more concave utility function and a lower implied discount rate than those above 40 years of age.
These were losses from earnings in an unrelated, prior experimental task.
References
Andersen, S., Fountain, J., Harrison, G. W., & Rutström, E. E. (2014). Estimating subjective probabilities. Journal of Risk and Uncertainty (in press).
Andersen, S., Harrison, G. W., Lau, M. I., & Rutström, E. E. (2008). Eliciting risk and time preferences. Econometrica, 76(3), 583–618.
Andersen, S., Harrison, G. W., Lau, M. I., & Rutström, E. E. (2011). Discounting behavior: A reconsideration. Working Paper 2011–03, Center for the Economic Analysis of Risk, Robinson College of Business, Georgia State University, January 2011.
Andersen, S., Harrison, G. W., Lau, M. I., & Rutström, E. E. (2013). Discounting behavior and the magnitude effect: Evidence from a field experiment in Denmark. Economica, 80, 670–697.
Coller, M., & Williams, M. B. (1999). Eliciting individual discount rates. Experimental Economics, 2, 107–127.
Dohmen, T., Falk, A., Huffman, D., Sunde, U., Schupp, J., & Wagner, G. G. (2011). Individual risk attitudes: New evidence from a large representative, experimentally-validated survey. Journal of the European Economic Association, 9(3), 522–550.
Elston, J. A., Harrison, G. W., & Rutström, E. E. (2005). Characterizing the entrepreneur using field experiments. Working Paper 05–30, Department of Economics, College of Business Administration, University of Central Florida.
Harrison, G. W., Johnson, E., McInnes, M. M., & Rutström, E. E. (2005). Risk aversion and incentive effects: Comment. American Economic Review, 95(3), 897–901.
Harrison, G. W., Lau, M. I., & Rutström, E. E. (2007). Estimating risk attitudes in Denmark: A field experiment. Scandinavian Journal of Economics, 109(2), 341–368.
Harrison, G. W., Lau, M. I., & Williams, M. B. (2002). Estimating individual discount rates for Denmark: A field experiment. American Economic Review, 92(5), 1606–1617.
Harrison, G. W., & List, J. A. (2004). Field experiments. Journal of Economic Literature, 42(4), 1013–1059.
Harrison, G. W., Phillips, R. D. (2013). Subjective beliefs and statistical forecasts of financial risks: The Chief Risk Officer Project. Working Paper 2013–08, Center for the Economic Analysis of Risk, Robinson College of Business, Georgia State University.
Harrison, G. W., & Swarthout, J. T. (2014). Experimental payment protocols and the bipolar behaviorist. doi:10.1007/s11238-014-9447-y.
Hey, J. D., & Orme, C. (1994). Investigating generalizations of expected utility theory using experimental data. Econometrica, 62(6), 1291–1326.
Holm, H. J., Opper, S., & Nee, V. (2013). Entrepreneurs under uncertainty: An economic experiment in China. Management Science, 59(7), 1671–1687.
Holt, C. A., & Laury, S. K. (2002). Risk aversion and incentive effects. American Economic Review, 92(5), 1644–1655.
List, J. A., & Mason, C. F. (2011). Are CEO’s expected utility maximizers? Journal of Econometrics, 162(1), 114–123.
Saha, A. (1993). Expo-power utility: A flexible form for absolute and relative risk aversion. American Journal of Agricultural Economics, 75(4), 905–913.
Acknowledgments
We thank the Danish Social Science Research Council for research support under project 275-08-0289 and 12-130950, and the Carlsberg Foundation under grant 2008-01-0410.
Author information
Authors and Affiliations
Corresponding author
Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Andersen, S., Di Girolamo, A., Harrison, G.W. et al. Risk and time preferences of entrepreneurs: evidence from a Danish field experiment. Theory Decis 77, 341–357 (2014). https://doi.org/10.1007/s11238-014-9446-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11238-014-9446-z