Time Preference / Discount Rate (CTB / MPL)

Methods for eliciting individual discount rates and present bias — how much people prefer earlier over later payoffs, and whether that preference is stronger when the earlier option is immediate.

What it is

Time preference elicitation measures how individuals value payoffs at different points in time. The core parameter is the discount rate — the premium a person requires to delay receiving a given amount. A person indifferent between receiving 100 today and 110 in four weeks has a per-period rate of 10% over four weeks. Converting that to an annual rate depends on the convention:

Annualised effective rate (AER, compounded): (1 + 0.10)^(52/4) − 1 ≈ 239% per year. This is the convention in Harrison, Lau and Williams (2002) and most modern field studies.
Simple annualisation: 0.10 × (52/4) ≈ 130% per year. This is less common in published work.

Either is far above bank deposit rates and not unusual in low-income populations (Cohen, Ericson, Laibson & White, 2020). State which convention you use; readers cannot compare numbers across studies without it.

A second parameter of practical importance is present bias: extra discounting applied to any delay from the immediate present, beyond what exponential discounting predicts. A person is present-biased if they prefer 100 today over 110 in four weeks, but prefer 110 in eight weeks over 100 in four weeks — the same four-week delay is valued differently depending on whether it starts now. Laibson’s (1997) quasi-hyperbolic model captures this with a β parameter (originally Phelps & Pollak, 1968): β < 1 indicates present bias and implies that people make plans they later deviate from — directly relevant to savings, commitment devices, technology adoption, and self-control problems generally.

Two elicitation methods dominate the field: the Multiple Price List (MPL) and the Convex Time Budget (CTB). They make different assumptions about utility curvature and produce different estimates; the choice has substantive consequences (Andersen, Harrison, Lau & Rutström, 2008; Andreoni & Sprenger, 2012a).

When to use it

Time preference measurement is appropriate when: discount rates or present bias are a primary outcome of interest; the study evaluates an intervention designed to affect intertemporal behaviour (savings products, commitment devices, insurance, technology adoption); or baseline heterogeneity in time preferences is a plausible moderator of treatment effects.

Ashraf, Karlan and Yin (2006) used a hypothetical time-preference module to show that present-biased individuals in the Philippines were more likely to take up a commitment savings product — a direct validation of the theoretical prediction that people with β < 1 benefit from commitment. Tanaka, Camerer and Nguyen (2010) linked experimentally elicited discount rates to household asset accumulation in Vietnam. Meier and Sprenger (2010) used MPL-with-FED in a US sample to show that present-biased individuals carry more credit card debt.

In field surveys without experimental stakes, time preference is often measured with hypothetical payoffs. Unlike risk preferences (where hypothetical and real elicitations diverge sharply), the empirical pattern for time preferences is broad equivalence between hypothetical and real money elicitations (Cohen et al., 2020). Hypothetical modules such as the Global Preference Survey short form (Falk et al., 2018) are validated and widely used. Note that “hypothetical equivalence” applies to money payoffs; for effort and consumption goods the gap is larger.

How it works

Multiple Price List (MPL). Developed for time-preference elicitation by Coller and Williams (1999). The respondent sees a list of binary choices between a smaller sooner (SS) payment and a larger later (LL) payment. The SS amount stays fixed; the LL amount increases down the list. At some row, the respondent switches from SS to LL. The switching row identifies the interval within which the implied discount rate falls — the rate at which the growing LL amount just compensates for the delay.

To separately identify the level of discounting (δ) and present bias (β), at least two lists are needed: one where the SS option is immediate (“today” vs. “in t weeks”) and one where both options are delayed by the same front-end interval (“in t weeks” vs. “in t + k weeks”, same delay interval k). A respondent who requires a larger premium on the immediate list than on the delayed list is present-biased — the immediate present is discounted more heavily than the same delay in the future. Concretely: present-biased respondents switch at a higher row on the immediate list than on the delayed list (assuming LL increases down the list).

Convex Time Budget (CTB). Developed by Andreoni and Sprenger (2012a). Respondents allocate a budget of tokens between two time periods at different gross interest rates across tasks. Instead of a discrete switch, they can split their allocation, which yields interior solutions. Under a CRRA aggregator the tangency condition gives an Euler equation that identifies utility curvature (α) and the discount factor (δ) jointly. The CTB’s key advantage over the MPL is that it does not require the linear-utility assumption — that is the substantive reason to use it, not its complexity. Andreoni and Sprenger (2012b) argue separately that “risk preferences are not time preferences”, which complicates the joint-estimation story.

Joint risk-time identification (Andersen, Harrison, Lau & Rutström, 2008). This is the central modern methodological issue. Under expected utility, the MPL switching row identifies the discount rate only if utility is linear in money over the stake range. If respondents are risk-averse (concave utility), the elicited rate is biased upward — the marginal LL token is worth less in utility terms than the marginal SS token, so the observed indifference overstates the discounting of utility. The Andersen-Harrison-Lau-Rutström (AHLR) approach pairs the time MPL with a Holt-Laury risk task and estimates the CRRA curvature parameter ρ and the discount factor δ jointly via maximum likelihood. The CRRA-adjusted discount factor is δ_adj = (LL/SS)^(−1/ρ). For applied work where the bias matters, run the joint estimation.

Identification assumptions. For the MPL switching row to identify the true discount rate, five conditions must hold:

Linear utility over the stake range — or jointly-estimated CRRA curvature.
Stationarity — the same delay interval is valued identically across horizons under exponential discounting (and not under quasi-hyperbolic).
No transaction-cost differential between SS and LL payments. If SS is delivered in cash on the spot and LL is delivered via mobile money or cheque, the channel difference itself produces a wedge that mimics impatience.
Credibility of the LL payment — respondents trust they will actually receive it.
Monotonic preferences across the list — the basis of the single-switching assumption.

Structural β–δ estimation. For an MPL with multiple horizons, the quasi-hyperbolic parameters β (present-bias) and δ (per-period discount factor) can be estimated by maximum likelihood — given a probabilistic choice model (logit), the choice probabilities are a function of the present discounted value differences, and β and δ are recovered by scipy.optimize.minimize (Python) or nls() / bbmle::mle2 (R). See the Analysis Guide for a pointer.

Key decisions

MPL vs CTB. The MPL is simpler to administer, easier for respondents to understand, and has a larger body of field evidence. Its main cost is the linear-utility assumption — risk-averse respondents have curved utility, and the elicited rate is biased upward unless curvature is jointly estimated (AHLR 2008). The CTB does not require linear utility but is more cognitively demanding and works best with numerate respondents. The practical decision: use MPL paired with a Holt-Laury risk task for joint estimation; use CTB when allocation tasks are feasible in the population.

Real vs hypothetical payoffs. Incentive-compatible (real-stakes) elicitation is theoretically preferred but produces approximately the same money discount rates as hypothetical elicitation (Cohen et al., 2020). For effort or consumption goods the gap is larger and real stakes matter more. Where real payments are used, deliver SS and LL through the same channel (both via mobile money, both via the same agent on a return visit) — see Caveats — and ensure credibility of LL delivery, or the elicitation captures distrust rather than time preference.

Front-end delay (FED). Coller and Williams (1999) introduced FED to remove differential transaction costs between SS and LL: an immediate payment is delivered through a different channel (cash now) than a future payment (mobile money on a later date), and the channel wedge contaminates the elicitation. Adding a small delay to the “sooner” option — comparing “in 1 week” vs “in 5 weeks” rather than “today” vs “in 4 weeks” — controls for this. FED has two distinct motivations worth distinguishing: (a) controlling for transaction-cost confounds (Coller-Williams), and (b) avoiding mistakenly attributing transaction-cost effects to present bias when identifying β. For clean β estimation, run both an immediate (no-FED) list and a delayed (FED) list; the contrast identifies present bias.

Stakes. Elicited discount rates are sensitive to amounts. Very small stakes produce noisy choices; very large stakes shift the consumption-smoothing problem. Standard field practice is stakes equivalent to half a day’s wage to one day’s wage in the local context (Tanaka, Camerer & Nguyen, 2010 used 5,000–500,000 VND in Vietnam, roughly 0.5–3× daily wage; Harrison, Lau & Williams, 2002 used larger Danish stakes).

Number of lists and time horizons. A single MPL identifies only a discount-rate interval; β and δ cannot be separately identified. Minimum: 2 lists (one no-FED, one FED) with 10 rows each. Add a third horizon for a consistency check on stationarity. More than 3–4 lists risks fatigue-driven inattention in later tasks.

Short-form survey modules. The Global Preference Survey (Falk et al., 2018) provides validated short-form modules — a single qualitative question plus a 5-step staircase — that recover discount-rate variation comparable to a full MPL at much lower respondent burden. Use the GPS short form when a full MPL is infeasible.

Caveats & common mistakes

Concavity of the utility function (utility-curvature bias). The MPL switching row identifies the discount rate only if utility is approximately linear in money over the stake range. If respondents are risk-averse (concave utility), the marginal LL token is worth less in utility terms than the marginal SS token, so the observed indifference overstates the rate at which the agent discounts utility — biasing discount rate estimates upward (Andersen et al., 2008; Harrison, Lau & Williams, 2002). Run a paired Holt-Laury risk task and estimate the CRRA parameter ρ to recover the utility-discount-factor: δ_adj = (LL/SS)^(−1/ρ).

Multiple switching points. A non-trivial share of respondents switch back and forth rather than at a single point, violating the monotonicity assumed by the MPL model. These responses may reflect inattention, genuine preference cycles, or treating each row independently. Standard practice: use the first switching row, flag multiple switchers, and run a sensitivity analysis excluding them. A multi-switching rate above 15–20% warrants investigation of the elicitation procedure.

Dominance violations. If the design includes a row where LL strictly dominates SS (LL > SS at zero interest, or with reverse interest making LL the clear choice), respondents who still choose SS commit a dominance violation. Flag and report the violation rate as a comprehension/attention diagnostic.

Channel and transaction-cost contamination. One of the most common implementation errors. If SS is delivered in cash on the spot and LL is delivered via mobile money, cheque, or return visit, the channel difference itself produces a wedge that mimics impatience: respondents may prefer SS because they trust cash now more than a mobile-money transfer next week, not because they discount future utility. The fix is to deliver SS and LL through the same channel wherever possible (both via mobile money with the SS scheduled for tomorrow rather than today; or both via the same agent on a return visit). Use front-end delay to remove the cash-now / mobile-money-later asymmetry (Coller & Williams, 1999).

Trust and credibility. Where institutional trust is low, respondents may prefer immediate payment not because they are impatient but because they doubt future payment will materialise. The bias is acute for longer delays. Comprehension checks and credibility signals — a trusted community figure witnessing the agreement, dated mobile-money receipts, signed documents — reduce but do not eliminate this concern.

Liquidity constraints vs pure time preference. A high elicited discount rate among the poor is often interpreted as impatience, but in liquidity-constrained settings it can equally reflect the marginal value of immediate cash. The MPL does not separately identify pure time preference from the marginal value of liquidity. Bauer, Chytilová and Morduch (2012) and Dean and Sautmann (2021) provide the modern treatment of this identification problem; the latter develops a procedure to separate them using consumption-correlated and consumption-uncorrelated questions.

Domain specificity. Discount rates for money do not generalise cleanly to other domains — health, effort, food, social outcomes. Augenblick, Niederle and Sprenger (2015) show a respondent who is patient in monetary choices can be present-biased in real-effort tasks; Augenblick and Rabin (2019) develop an identification strategy for effort-domain present bias. If the research question concerns a non-monetary domain, money-MPL may not be the most informative measure.

Hypothetical bias (money vs other domains). For money discount rates, hypothetical and real elicitations produce broadly similar estimates (Cohen et al., 2020). For effort, consumption goods, or social rewards, the gap is larger. Match the elicitation domain to the substantive question rather than defaulting to money for everything.

Present-bias share heterogeneity. Imai, Rutter and Camerer (2021) meta-analysis: across studies, mean β ≈ 0.95 in money tasks with around 30% of respondents present-biased; in real-effort tasks the share is substantially higher. Use this as the benchmark when interpreting your sample’s share.

Analysis Guide

import numpy as np
import pandas as pd
import statsmodels.formula.api as smf

# Convention: choice_1 ... choice_10 are 1 (chose LL) or 0 (chose SS), with LL
# growing down the list. switch_row = first row choosing LL; switch_row = 11
# means never switched (extreme impatience). LOW row = LOW impatience.
# mpl_rate_table is a design-specific lookup: one row per switch_row mapping to
# the implied per-period rate range. Construct it externally from your SS/LL/delay
# parameters before running this analysis.

choice_cols = [f'choice_{i}' for i in range(1, 11)]
cols = df[choice_cols].replace({-99: pd.NA})

# 1. First switching row, robust to all-zero and missing rows
has_any_ll = cols.eq(1).any(axis=1)
first_ll   = cols.eq(1).idxmax(axis=1)
df['switch_row'] = pd.Series(
  np.where(has_any_ll,
           first_ll.str.extract(r'(\d+)').astype('Int64').squeeze(),
           11), index=df.index).astype('Int64')

# 2. Multi-switching diagnostic — count direction changes per respondent; multi-
#    switching violates the MPL's single-crossing assumption and a rate above
#    15-20% warrants a sensitivity analysis excluding multi-switchers
n_switches = cols.diff(axis=1).abs().sum(axis=1, min_count=1)
df['multi_switch'] = (n_switches > 1).astype('Int64')
print('Multi-switching rate:', df['multi_switch'].mean())

# 3. Dominance-violation diagnostic — flag respondents who chose SS on a row
#    where LL strictly dominates (design-specific column index — adjust to your
#    instrument; here assume row 1 is the dominance row)
df['dominance_violation'] = (df['choice_1'] == 0).astype('Int64')
print('Dominance-violation rate:', df['dominance_violation'].mean())

# 4. Merge design table -> implied per-period rate
df = df.merge(mpl_rate_table, on='switch_row', how='left')

# 5. Annualise — chosen convention: Annualised Effective Rate, compounded.
#    AER = (1 + period_rate) ** (52 / delay_weeks) - 1. State this in writeups
df['annual_rate'] = (1 + df['period_rate']) ** (52 / df['delay_weeks']) - 1

# 6. Present bias — present-biased respondents require a LARGER premium on the
#    IMMEDIATE list than on the FED list, so they switch at a HIGHER row on the
#    immediate list (LL growing down). Use > here, NOT <
df['present_biased'] = (df['switch_row_immediate']
                      > df['switch_row_delayed']).astype('Int64')

# 7. CRRA-adjusted discount factor (Andersen et al. 2008) — given an externally
#    estimated CRRA parameter rho from a paired Holt-Laury task, recover the
#    utility-discount-factor rather than the money-discount-factor
# rho = ...   # from Holt-Laury elicitation, see the Holt-Laury MPL guide
# df['delta_adjusted'] = (df['LL'] / df['SS']) ** (-1 / rho)

# 8. Regress annual rate on covariates — HC1 robust SEs; for cluster-randomised
#    designs add cov_type='cluster', cov_kwds={'groups': df['psu']}
fit = smf.ols('annual_rate ~ age + C(female) + log_hh_expenditure',
            data=df).fit(cov_type='HC1')
print(fit.summary())

# 9. Structural quasi-hyperbolic (beta, delta) — define the choice probability
#    under logit and minimise the negative log-likelihood via scipy.optimize.minimize
# def nll(params, df): ...    # log-likelihood given (beta, delta, sigma)
# from scipy.optimize import minimize
# res = minimize(nll, x0=[0.95, 0.99, 1.0], args=(df,), method='L-BFGS-B')

library(estimatr)   # lm_robust with HC1 robust SEs
# library(bbmle)    # mle2 for structural beta-delta estimation

# Convention: c1 ... c10 are 1 (chose LL) / 0 (chose SS), LL grows down the list.
# switch_row = first row choosing LL; 11 = never switched (extreme impatience).
# LOW row = LOW impatience. mpl_rates is a design-specific lookup table.

choice_cols <- paste0("c", 1:10)

# 1. First switching row, robust to all-zero and NA rows
df$switch_row <- apply(df[, choice_cols], 1, function(row) {
sw <- which(row == 1)[1]
if (is.na(sw)) 11L else as.integer(sw)
})

# 2. Multi-switching diagnostic — rate above 15-20% warrants sensitivity analysis
df$n_switches  <- apply(df[, choice_cols], 1, function(r) sum(abs(diff(r)), na.rm = TRUE))
df$multi_switch <- df$n_switches > 1
mean(df$multi_switch, na.rm = TRUE)

# 3. Dominance violation — flag respondents who chose SS on the row where LL
#    strictly dominates (design-specific; here assume row 1 is the dominance row)
df$dominance_violation <- df$c1 == 0
mean(df$dominance_violation, na.rm = TRUE)

# 4. Merge design table to recover the implied per-period rate
df <- merge(df, mpl_rates, by = "switch_row", all.x = TRUE)

# 5. Annualise to AER (compounded) — state the convention chosen
df$annual_rate <- (1 + df$period_rate) ^ (52 / df$delay_weeks) - 1

# 6. Present bias — present-biased respondents switch at a HIGHER row on the
#    immediate list than on the FED list. Use > here, NOT <
df$present_biased <- df$switch_row_immediate > df$switch_row_delayed

# 7. CRRA-adjusted discount factor (Andersen et al. 2008) — paired Holt-Laury
# rho <- ...   # from Holt-Laury elicitation, see the Holt-Laury MPL guide
# df$delta_adjusted <- (df$LL / df$SS) ^ (-1 / rho)

# 8. Regress annual rate on covariates with HC1 robust SEs — for cluster-
#    randomised designs use clusters = ~ psu, se_type = "CR1"
fit <- lm_robust(annual_rate ~ age + female + log_hh_expenditure,
               data = df, se_type = "HC1")
summary(fit)

# 9. Structural beta-delta via maximum likelihood — define the logit likelihood
#    of choice given (beta, delta, sigma) and call bbmle::mle2 or stats4::mle.
#    apollo (Hess & Palma 2019) implements quasi-hyperbolic discounting natively

SurveyCTO / XLSForm

Pre-load the MPL payoff table as an external CSV loaded via pulldata(). For each choice row, display the SS and LL amounts using ${field} references pulled from the table.

Do not enforce monotonicity in the form. Tempting constraint logic to force respondents to switch only once hides multi-switching, which is itself an important data-quality diagnostic. Capture every row’s choice and detect inconsistency in post-processing.

Store the full response vector — every choice, not just the switching row. Without this you cannot detect multi-switching, dominance violations, or run sensitivity analyses on clean switchers.

For real-payment studies, deliver SS and LL through the same channel where possible (both via mobile money, both via the same return-visit agent). The cash-now / mobile-money-later asymmetry is one of the most common implementation errors: it produces a wedge that mimics impatience. If a delay must be added to the SS payment to make the channel symmetric, that’s the front-end-delay design — see Key Decisions.

Generate a payment record at the end of the session specifying the amount, the payment date, and the transfer channel, and have the respondent confirm it before closing the survey. Persist the design row index, the SS and LL amounts, the delay in weeks, and the realised draw (if the design selects one row at random for payment).

Reading the output

Convention reminder. With LL increasing down the list, a LOW switch row (e.g., row 2–3) means the respondent switched to LL early — they accepted a small premium and are relatively patient. A HIGH switch row (8–10) means they required a large premium and are impatient.
switch_row == 11 (never switched): the respondent always preferred SS regardless of LL. Could be extreme impatience, dominance violation if the bottom row dominated SS, or inattention. Cross-check against the dominance and multi-switching flags before interpreting.
Present bias — present_biased == 1 means the respondent switched at a HIGHER row on the immediate list than on the FED list, i.e., they required a larger premium to delay when the SS option was “today” versus when it was “in t weeks”. Imai, Rutter and Camerer (2021) meta-analysis benchmark: roughly 30% of respondents are present-biased on monetary tasks (substantially higher on real-effort tasks; Augenblick, Niederle & Sprenger, 2015). Shares well above 30% on monetary tasks may indicate comprehension problems or strong field-specific effects.
Multi-switching rate above 15–20% warrants a sensitivity analysis excluding multi-switchers and an investigation of the elicitation procedure (script clarity, enumerator training, respondent fatigue).
Dominance-violation rate above ~5% suggests comprehension problems; consider excluding those respondents or re-training.
Annualised rate: report which convention you used (AER compounded vs simple annualisation). Cohen et al. (2020) note that cross-study comparisons routinely fail because conventions are mixed silently.
Regression interpretation: a positive coefficient on log_hh_expenditure (wealthier = lower discount rate) is the standard field finding. Bauer, Chytilová and Morduch (2012) and Dean and Sautmann (2021) caution that this does not separately identify pure time preference from the marginal value of liquidity.
CRRA-adjusted vs raw rate: if you ran the joint Holt-Laury / time MPL estimation (Andersen et al., 2008), report both the raw and CRRA-adjusted discount factors. A substantial gap between them is evidence that utility curvature was biasing the raw estimate upward.

References

Andersen, S., Harrison, G. W., Lau, M. I., & Rutström, E. E. (2008). Eliciting risk and time preferences. Econometrica, 76(3), 583–618. https://doi.org/10.1111/j.1468-0262.2008.00848.x

Andreoni, J., & Sprenger, C. (2012a). Estimating time preferences from convex budgets. American Economic Review, 102(7), 3333–3356. https://doi.org/10.1257/aer.102.7.3333

Andreoni, J., & Sprenger, C. (2012b). Risk preferences are not time preferences. American Economic Review, 102(7), 3357–3376. https://doi.org/10.1257/aer.102.7.3357

Ashraf, N., Karlan, D., & Yin, W. (2006). Tying Odysseus to the mast: Evidence from a commitment savings product in the Philippines. Quarterly Journal of Economics, 121(2), 635–672. https://doi.org/10.1162/qjec.2006.121.2.635

Augenblick, N., Niederle, M., & Sprenger, C. (2015). Working over time: Dynamic inconsistency in real effort tasks. Quarterly Journal of Economics, 130(3), 1067–1115. https://doi.org/10.1093/qje/qjv020

Augenblick, N., & Rabin, M. (2019). An experiment on time preference and misprediction in unpleasant tasks. Review of Economic Studies, 86(3), 941–975. https://doi.org/10.1093/restud/rdy019

Bauer, M., Chytilová, J., & Morduch, J. (2012). Behavioral foundations of microcredit: Experimental and survey evidence from rural India. American Economic Review, 102(2), 1118–1139. https://doi.org/10.1257/aer.102.2.1118

Cohen, J., Ericson, K. M., Laibson, D., & White, J. M. (2020). Measuring time preferences. Journal of Economic Literature, 58(2), 299–347. https://doi.org/10.1257/jel.20191074

Coller, M., & Williams, M. B. (1999). Eliciting individual discount rates. Experimental Economics, 2(2), 107–127. https://doi.org/10.1023/A:1009986005690

Dean, M., & Sautmann, A. (2021). Credit constraints and the measurement of time preferences. Review of Economics and Statistics, 103(1), 119–135. https://doi.org/10.1162/rest_a_00872

Falk, A., Becker, A., Dohmen, T., Enke, B., Huffman, D., & Sunde, U. (2018). Global evidence on economic preferences. Quarterly Journal of Economics, 133(4), 1645–1692. https://doi.org/10.1093/qje/qjy013

Frederick, S., Loewenstein, G., & O’Donoghue, T. (2002). Time discounting and time preference: A critical review. Journal of Economic Literature, 40(2), 351–401. https://doi.org/10.1257/002205102320161311

Harrison, G. W., Lau, M. I., & Williams, M. B. (2002). Estimating individual discount rates in Denmark: A field experiment. American Economic Review, 92(5), 1606–1617. https://doi.org/10.1257/000282802762024674

Imai, T., Rutter, T. A., & Camerer, C. F. (2021). Meta-analysis of present-bias estimation using convex time budgets. The Economic Journal, 131(636), 1788–1814. https://doi.org/10.1093/ej/ueaa115

Laibson, D. (1997). Golden eggs and hyperbolic discounting. Quarterly Journal of Economics, 112(2), 443–478. https://doi.org/10.1162/003355397555253

Meier, S., & Sprenger, C. (2010). Present-biased preferences and credit card borrowing. American Economic Journal: Applied Economics, 2(1), 193–210. https://doi.org/10.1257/app.2.1.193

Phelps, E. S., & Pollak, R. A. (1968). On second-best national saving and game-equilibrium growth. Review of Economic Studies, 35(2), 185–199. https://doi.org/10.2307/2296547

Read, D. (2001). Is time-discounting hyperbolic or subadditive? Journal of Risk and Uncertainty, 23(1), 5–32. https://doi.org/10.1023/A:1011198414683

Tanaka, T., Camerer, C. F., & Nguyen, Q. (2010). Risk and time preferences: Linking experimental and household survey data from Vietnam. American Economic Review, 100(1), 557–571. https://doi.org/10.1257/aer.100.1.557