Academic journal article Economic Inquiry

The Dual-Process Drift Diffusion Model: Evidence from Response Times

Academic journal article Economic Inquiry

The Dual-Process Drift Diffusion Model: Evidence from Response Times

Article excerpt

I. INTRODUCTION

Economists are increasingly interested in connecting choice behavior with response time. (1) One source of inspiration for the economics literature is the "dual-process" approach, which draws on a psychological tradition of contrasting rapid "automatic" decisions with more time-consuming "considered" decisions. (2) For instance, Rubinstein (2007) posits that in some matrix games "choices that require more cognitive activity will result in longer response times than choices that involve an instinctive response."

A second source of inspiration for the economics literature is the drift diffusion model (DDM) introduced by Ratcliff (1978), which maps the gradual accretion of evidence up to a decision-inducing threshold. (3) Clithero and Rangel (2013) show that the DDM, when calibrated with response times, is better at predicting out-of-sample choices than the standard Logistic approach.

We introduce a dual-process DDM that borrows from both psychological traditions. As in the dual-process approach, individuals make either automatic decisions or considered decisions. Automatic decisions are rapid and based only on general features of the choice environment. Considered decisions involve waiting for a threshold decision quality to be achieved, as in the DDM. We follow much of this literature in treating the parameters of the DDM as fixed for a given level of perceptual difficulty. Hence, choice accuracy and the distribution of response times do not change unless the perceptual difficulty changes.

The key innovation in our model is that individuals choose whether to make automatic or considered decisions. (4) In making this choice, they face the following trade-off; while making a considered decision can produce better choices, it also involves an "attentional" cost. (5) In our model, this cost is stochastic, but broadly follows idiosyncratic features of the subject and the situation. For example, the distribution of costs shifts to the right when the decision maker is tired or evidence becomes more difficult to process. The individual decides which type of decision to make after a quick appraisal of the realized level of such costs.

Our model is designed for settings in which considered decisions involve substantial attentional costs. While this may not be the case in traditional applications in psychology (quick perceptual tasks), it is certainly true for most economic applications. Thus, our dual-process extension may prove useful in applying the DDM to a range of economic choices.

We conduct an experiment the results of which validate our modeling strategy. Subjects have available three actions, one and only one of which yields a prize, but determining which is best requires considerable cognitive effort. Because prior beliefs directly impact the value of automatic decisions, our central point of treatment variation is the probability each action is best. (6)

Our model provides a cogent interpretation of five key properties of the experimental data:

1. There is a clear bimodal distribution of decision times. Averaging across experiments, almost 40% of all decisions are made very rapidly: within the first 8 seconds. It is these that we label automatic decisions. When the decision is not made within 8 seconds, it typically takes far longer. For the 60% of decisions that take more than 8 seconds, the mean decision time is fully 69 seconds. These are the considered decisions.

2. As the model predicts, automatic decisions appear to reflect no information beyond prior beliefs (independent of the experimental round):

a. The likelihood of each option being best is the same for automatic and considered decisions.

b. Nearly all automatic decisions involve choosing the a priori best option.

c. Automatic decisions are no better in quality than can be guaranteed by picking the prior best option.

3. …

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