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Reducing pharmaceutical reimbursement price risk to lower national health expenditures without lowering R&D incentives

  • Hiroshi Nakamura
  • Naohiko WakutsuEmail author
Research article
  • 30 Downloads

Abstract

In Japan, higher reimbursement drug prices give pharmaceutical firms stronger R&D incentives, but they also increase the financial burden on national health insurance and patients. Considering the severe financial situation that the government faces, analyzing how to achieve lower national health expenditures without lowering pharmaceutical firms’ existing R&D incentives is important. In this research, we investigate the effect of reducing the reimbursement price risk that pharmaceutical firms face on their R&D incentives. Theoretically, the presence of output price risks reduces risk-averse firms’ R&D incentives. Therefore, to the extent that pharmaceutical firms exhibit risk aversion, if creating guidelines, accelerating information disclosure and/or enabling public–private dialogue can reduce reimbursement price risks, then maintaining or even increasing R&D incentives is possible, even if the level of reimbursement drug prices is reduced. Specifically, we address (1) by how much a given level of reimbursement price risk reduces pharmaceutical firms’ R&D incentives; (2) by how much reimbursement drug prices can be reduced, keeping pharmaceutical firms’ R&D incentives constant, if one can successfully remove the risk; and (3) how the magnitude of the impact changes with the degree of price risk that firms face and with the level of their risk aversion. To this end, a hypothetical new branded drug is constructed from actual data on the Japanese drug market. Assuming that a pharmaceutical firm is an expected-utility maximizer, that the firm’s instantaneous utility function is in the form of the constant-relative-risk-aversion utility function and that its R&D incentives are quantified by the standard discounted cash flow valuation, we use simulations to compute the certainty equivalent and risk premium associated with various degrees of price risk and risk aversion. Referring to the empirical literature on risk preference, we set the parameter value for the level of relative risk aversion of a pharmaceutical firm to 3.0 and that for the discount rate to 0.08. The following results emerged. (1) In the presence of a 20% price risk regarding a reimbursement price of 100 (i.e., ranging from 80 to 120), a pharmaceutical firm’s certainty equivalent is 96.0. Hence, in the presence of a 20% price risk, a risky reimbursement drug price of 100 is equivalent to a sure reimbursement drug price of 96.0. (2) In the presence of a 20% price risk regarding a reimbursement price of 100, the price premium is 4.0. Therefore, by increasing the predictability of future prices, the reimbursement price may decrease by 4.0, while the firm’s R&D incentives remain unchanged. (3) The magnitude of the impact increases at an increasing rate with the degree of price risk and increases at a decreasing rate with the level of risk aversion.

Keywords

Risk Risk aversion Drug price R&D incentive Simulation 

JEL Classification

I1 

Introduction

In Japan, the government sets the reimbursement price of any pharmaceutical drug or medical device. Higher reimbursement prices contribute to stronger R&D incentives for pharmaceutical firms and medical-device makers, but they also increase the financial burdens on the national health insurance (NHI) system and patients. Lower reimbursement prices reduce the NHI system’s public payers’ and patients cost, but they may hinder patients’ access to innovative drugs and medical devices. Hence, a tradeoff exists between reducing the financial burdens on the NHI system and patients and increasing providers’ R&D incentives.

However, if a successful solution to this tradeoff is found, it will not only reduce the cost of the public payers and patients but also reduce any remaining unmet medical needs. Therefore, analyzing a policy that leads to both lower national health expenditures and stronger R&D incentives of pharmaceutical and medical-device firms is very important.

In this paper, we examine the pharmaceutical industry and focus on the risk that pharmaceutical firms face regarding the reimbursement price level. Theoretically, an increase in the reimbursement price risk reduces a risk-averse firm’s R&D incentives.

In the previous literature, only a few studies examine how (that is, via what policy) to best balance reducing the financial burdens on the NHI system and patients while increasing pharmaceutical firms’ R&D incentives. In a simulation study on the new NHI drug-pricing system in Japan, Wakutsu and Nakamura [22], emphasizing the explicit use of a discount rate in balancing the two opposing tasks, analyze how different price patterns over the product life cycle differently affect a firm’s R&D incentives and the public payers’ financial burden. To the best of our knowledge, no study in the literature focuses on pharmaceutical firms’ reimbursement price risks or analyzes how increased predictability via reduced price risk contributes to lowering the financial burdens on the NHI system and patients and strengthening those firms’ R&D incentives.

Specifically, this paper’s objective is twofold. First, in the theoretical discussion, we show that a reduction in the reimbursement price risk that a risk-averse pharmaceutical firm faces increases the firm’s utility level, thereby strengthening the firm’s R&D incentives. In addition, we show that, by increasing the predictability of future reimbursement price levels, a drug price that is lower than the expected price can increase the firm’s utility level and thereby maintain its existing R&D incentives.

The second objective is to examine this possibility through numerical simulation. Theoretically, the reimbursement price risk is predicted to reduce a pharmaceutical firm’s R&D incentives, but the extent to which such incentives are reduced is not clearly understood. Hence, we first study how much a given level of reimbursement price risk reduces a firm’s R&D incentives. Second, we examine how much a reimbursement drug price can be reduced while keeping the pharmaceutical firm’s R&D incentives unchanged if the price risk is successfully decreased. Lastly, as sensitivity analyses, we examine how the magnitude of the impact changes with the degree of price risk it faces and the level of its risk aversion.

For methodology, in a simulation analysis, a hypothetical new branded drug is constructed from actual data on the Japanese drug market. Assuming that a pharmaceutical firm is an expected-utility maximizer with an instantaneous constant-relative-risk-aversion (CRRA) utility function, and that the R&D incentives are quantified by the standard discounted cash flow valuation, we then conduct numerical simulations and compute the certainty-equivalent drug price and risk premium associated with various degrees of reimbursement price risk.

Referring to the empirical literature on firms’ risk preferences, we set the parameter value for the relative risk-aversion (RRA) level of a pharmaceutical firm to 3.0 and the discount rate to 0.08. From the simulation analysis, the following results emerged.
  1. 1.

    In the presence of a 20% price risk regarding a reimbursement price of 100 (i.e., ranging from 80 to 120), a pharmaceutical firm’s certainty equivalent is 96.0. It follows that a reimbursement price of 100 in the presence of a 20% price risk is equivalent to a reimbursement price of 96.0 with certainty.

     
  2. 2.

    In the presence of a 20% price risk regarding a reimbursement price of 100, the price premium is 4.0. This finding implies that, by increasing the predictability of future prices, the reimbursement price can decrease by 4.0 while maintaining the firm’s existing R&D incentives.

     
  3. 3.

    The magnitude of the impact increases at an increasing rate with the degree of price risk, and increases at a diminishing rate with the level of risk aversion.

     

The rest of the paper is organized as follows. In “Basic idea”, we explain the theory underlying the basic idea of the present study. “Literature on firms’ risk preferences” briefly reviews the empirical literature on firms’ risk preferences. “Methodology” describes the methodology used. “Results” presents the simulation results. Finally, “Conclusion” concludes the paper.

Basic idea

Consider a risk-averse firm. Suppose that \( p \) is the reimbursement drug price level that the government sets and that \( S ( p ) \) is the level of sales associated with price level \( p \). Let \( S \) be an increasing function of \( p \). The firm is assumed to expect that \( p \) takes a value between \( p_{a} \) and \( p_{b} \) instead of knowing the exact value of \( p \). Let \( Pro ( p ) \) be the probability distribution according to which each of the values for \( p \) is realized. Also, let \( 0 < p_{a} < p_{b} \). The expected level of sales \( E ( {S ( p )} ) \) is then expressed as follows:
$$ E ( {S ( p )} ) = \mathop \int \limits_{{p_{a} }}^{{p_{b} }} S ( p )Pro ( p )dp. $$
Now, let \( p' \) be a drug price level with certainty, called a certainty-equivalent drug price level, that yields the same expected sales level as the firm obtains in the risky situation described by the probability distribution \( Pro ( p ) \). Then, the following equation holds:
$$ S ( {p^{\prime}} ) = E ( {S ( p )} ) = \mathop \int \limits_{{p_{a} }}^{{p_{b} }} S ( p )Pro ( p )dp. $$
Let \( U \) be the firm’s utility function. Then, the level of utility the firm obtains from the certainty-equivalent drug price \( p' \) is given as follows:
$$ U ( {S ( {p^{\prime}} )} ) = U ( {E ( {S ( p )} )} ) $$
The utility level the firm obtains from the probability distribution \( Pro ( p ) \), on the other hand, is given as follows:
$$ E ( {U ( S )} ) = \mathop \int \limits_{{p_{a} }}^{{p_{b} }} U ( {S ( p )} )Pro ( p )dp. $$
Let us now introduce a risk-averse firm. A risk-averse firm does not prefer price risk. Due to the concavity of \( U \) in \( p \) that represents the firm’s risk aversion, the following holds:
$$ E ( {U ( S )} )) < U ( {S ( {p^{\prime}} )} ). $$
(1)

In words, the level of utility obtained from a risky drug price is strictly lower than that obtained from a drug price with certainty. From (1), the following proposition is derived.

Proposition 1

Reducing the reimbursement price risk that a risk-averse firm faces increases the firm’s utility level.

Let \( p^{*} \) denote a certainty-equivalent drug price level that gives the same utility level as \( E ( {U ( S )} ) \). That is, \( U ( {S ( {p^{*} } )} ) = E ( {U ( S )} ) \). Then, because \( S \) is assumed to be increasing in \( p \) while \( U \) is increasing in \( S \), the following inequality holds:
$$ p^{*} < p^{\prime}. $$
(2)

From (2), the following proposition is derived.

Proposition 2

Reducing the reimbursement price risk that a risk-averse firm faces lowers the drug price which leads to the firm’s existing utility level.

If the level of the firm’s utility increases, the firm’s R&D incentive also increases. Therefore, the implication derived from the two propositions is that, by increasing the predictability of future prices, the R&D incentives can remain unchanged, even if the reimbursement drug price level is lower than the expected price level. Hence, lowering drug expenditures and maintaining R&D incentives can both be achieved.

To make the discussion above more intuitively understood, let us consider a simpler case and present a graphical explanation as in Fig. 1. Suppose that a firm expects that a drug price will take one of the three values, \( p_{a} , p_{b} , p_{c} \), with an equal probability of \( 1/3 \). For the sake of simplicity, let \( p_{c} \) be the median of \( p_{a} \) and \( p_{b} \) so that
$$ Pro ( p ) = \left\{ {\begin{array}{*{20}c} {1/3\; ( {p = p_{a} } )} \\ {1/3\; ( {p = p_{c} } )} \\ {1/3\; ( {p = p_{b} } )} \\ \end{array} } .\quad {\text{with }}\;p_{a} < p_{b} \;{\text{and}}\;p_{c} = \frac{{p_{a} + p_{b} }}{2} . \right.$$
Fig. 1

Effect of price risk on risk-averse firm’s utility level: basic idea

Suppose also that sales increase linearly with \( p \). Under these simple assumptions, the expected reimbursement drug price is \( p_{c} \) (because \( p_{c} \) is the median of \( p_{a} \) and \( p_{b} \), with each having the same probability). Moreover, \( p' = p_{c} \) holds (because sales \( S \) is a linear increasing function of \( p \)).

If the firm knows that \( p \) will take the exact value of \( p^{\prime} ( { = p_{c} } ) \) with certainty, then the firm’s utility is \( U ( {S ( {p'} )} ) \). However, if the firm only knows that \( p \) will take one of the three price levels \( p_{a} , p_{b} , p_{c} \) according to \( Pro ( p ) \), then the firm’s utility is \( E ( {U ( S )} ) \), which is somewhere between the mean of \( U ( {S ( {p_{a} } )} ) \) and \( U ( {S ( {p_{b} } )} ) \) and \( U ( {S ( {p'} )} ) \). Therefore, (1) holds. Hence, as Proposition 1 says, by removing (reducing) the reimbursement price risk that a risk-averse firm faces, the firm’s utility level increases.

With respect to Proposition 2, the suppositions that \( S \) is an increasing function of \( p \) and that \( U \) is an increasing function of \( S \) ensures (2). Hence, a lower drug price exists that does not reduce the firm’s utility level, once the reimbursement price risk that a risk-averse firm faces is successfully removed (reduced).

Risk and uncertainty

In the above description, we use the term “risk” because we consider a situation in which the probability distribution is known. However, in reality, firms encounter situations in which the probability distribution for the reimbursement drug price is unknown, which reduces a risk-averse firm’s utility level further.

Therefore, for risk-averse firms that face price uncertainty, increasing the predictability of future prices increases the firm’s utility level further and thereby strengthens the R&D incentives further, even in the presence of lower reimbursement drug prices.

Literature on firms’ risk preferences

In this section, the empirical literature on firms’ risk preferences and on risk and R&D investment is briefly reviewed. As presented below, the vast majority of empirical studies on firms’ risk attitudes are in agricultural or financial industries, and none is in the pharmaceutical industry. In addition, almost all attempts to empirically estimate firms’ risk attitudes are related to firm production or portfolio selection, and none is related to R&D investment.

Attitudes toward risk are usually classified into three categories: risk averse, risk neutral, and risk loving. Although a firm can theoretically fall within any of these categories, a large body of empirical literature that examines firms’ risk attitudes shows that in many fields firms have risk-averse attitudes. See, for instance, Pope and Just [17], Saha [19], Kumbhakar [12], Mosnier et al. [14] in agriculture; Appelbaum [1] in the textile industry; Appelbaum and Ullah [2] in printing and publishing and the stone, clay and glass industry; Satyanarayan [20] in the chemical industry; Appelbaum and Woodland [3] in the production sector; and Huang and Kao [10] in finance.

Two of the most fundamental risk-aversion measures in the literature are the Arrow–Pratt measure of absolute risk aversion (ARA) \( \theta_{A} \) and relative risk aversion (RRA) \( \theta_{R} \). The measure \( \theta_{A} \) of ARA is defined as follows:
$$ \theta_{A} = - U'' ( x )/U' ( x ) $$
where \( U \) is the utility function; prime \( ' \) and double prime ″ are the first-order and second-order partial derivatives, respectively; and \( x \) is a random variable.

With this measure, the structure of risk aversion is classified into three categories: constant absolute risk aversion (CARA: \( \theta_{A} \) is constant with \( x \)), increasing absolute risk aversion (IARA: \( \theta_{A} \) increases with \( x \)), and decreasing absolute risk averse (DARA: \( \theta_{A} \) decreases with \( x \)). Many researchers have empirically examined whether firms are CARA, IARA, or DARA, and most have found supportive evidence for DARA (e.g. [2, 12, 14, 17, 19].

The measure \( \theta_{R} \) of RRA is defined as follows:
$$ \theta_{R} = - xU'' ( x )/U' ( x ). $$

Analogous to the measure of ARA, the measure of RRA divides risk-averse structure into three categories: constant relative risk aversion (CRRA: \( \theta_{R} \) is constant with \( x \)), increasing relative risk aversion (IRRA: \( \theta_{R} \) increases with \( x \)), and decreasing relative risk aversion (DRRA: \( \theta_{R} \) decreases with \( x \)). The two measures of risk aversion are related to each other, so DARA implies CRRA or IRRA. A number of empirical studies have investigated this sub-classification. Many have found support for CRRA (e.g. [14, 19].

In contrast to these agreements on the qualitative nature of the structure of risk aversion, the literature reaches relatively less agreement regarding the quantitative nature of the level of risk aversion. Table 1 lists some of the estimates for firms’ levels of RRA in previous studies.1 As can be seen, the estimates vary across the studies, ranging from 0.35 to 6.07.2 In financial economics, much larger positive values around 50 have also been reported. See, for instance, Mehra and Prescott [13]. However, such substantially higher RRA’s have rarely been observed in more recent studies. In summary, it seems safe to say from these casual observations that more plausible estimates for the firms’ RRA’s may be single-digit estimates rather than extremely large values although the exact value is far from known.
Table 1

Estimates for the level of relative risk-averse in previous studies

Articles

Relative risk aversion

Area

Chavas and Holt [7]

6.07

Agriculture

Bar-Shira et al. [4]

0.61

Agriculture

Pope et al. [18]

0.35

Agriculture

Kumbhakar [12]

3.36

Fishery

Mosnier et al. [14]

2.38

Stock raising

Orea and Wall [16]

2.88

Dairy firming

Normandin and St-Amour [15]

3.07

Finance

Bliss and Panigirtzoglou [6]

4.41

Finance

Guo and Whitelaw [9]

3.52

Finance

Chiappori and Paiella [8]

5.16

Finance

Koijen [11]

5.16

Finance

Mean

3.36

The RRA values in the table are average values. All of the values are reported in the studies. An exception is Bliss and Panigirtzoglou [6]. The above RRA value of 4.41 in their paper is calculated for “All Observations” in Table VI by the authors

Methodology

For numerical simulation, a hypothetical new branded drug is constructed from actual data on the Japanese drug market. A new branded drug is launched at time \( t = 1 \). Its entire sales period is 30 years. Its generic products are launched in its 13th year and thereafter. Its initial reimbursement drug price is \( p_{1} = 100 \), and the government then revises the drug price every odd year. The resulting price pattern is in the left panel of Fig. 2.3 The associated sales pattern appears in the right panel of Fig. 2. Specifically, the level of sales at time \( t \), \( S_{t} \), is expressed by the parsimonious Bass [5] diffusion model
$$ S_{t} = a \left[ {\frac{{x ( {x + y} )^{2} \exp ( { - ( {x + y} )t} )}}{{ ( {x + y\exp ( { - ( {x + y} )t} )} )^{2} }}} \right] $$
for a given set of the parameter values of \( x \), \( y \), and \( a \).4 Given these price and sales patterns, the quantities sold \( q_{t} \) of the new branded drug at time \( t \) are defined as \( q_{t} = S_{t} /p_{t} \). For the sake of simplicity, doctors’ behaviors in prescribing drugs are assumed to be based on scientific evidence. Therefore, the demand for the drug is mostly determined by its efficacy, the number of potential patients, and the number of available competing drugs in the market rather than by its price.
Fig. 2

Price (left) and sales patterns of a hypothetical new branded drug

Suppose that there is a reimbursement price risk on initial entry price \( p_{1} \). In this paper, the R&D incentives in the presence of the reimbursement price risk are captured by the present value of the flow of future expected utility from sales. We assume that a pharmaceutical firm’s utility function U is time-additive, and that its instantaneous utility function u is in the class of CRRA utility function. That is,
$$ U ( {S_{1} ,S_{2} , \ldots ,S_{30} } ) = \mathop \sum \limits_{t = 1}^{30} \frac{{u ( {S_{t} } )}}{{ ( {1 + r} )^{t} }} = \mathop \sum \limits_{t = 1}^{30} \frac{{S_{t}^{1 - \theta } / ( {1 - \theta } )}}{{ ( {1 + r} )^{t} }} $$
where \( r \) is the discount rate, and \( \theta \) is the level of RRA (θ ≠ 1).5

Here, the \( r \) value is set to \( r = 0.08 \), while the \( \theta \) value is set to \( \theta = 3.0 \). We choose the value of \( r \) in reference to the findings from our original interviews with research-oriented pharmaceutical firms in Japan.6 We choose the value of \( \theta \) in reference to the extant empirical literature on a firm’s RRA level including those appearing in Table 1. Since no direct evidence is available on a pharmaceutical firm’s RRA level, other \( \theta \) values are also considered such as \( \theta = 1.0 \) and \( \theta = 5.0 \) in sensitivity analyses.

About the reimbursement price risk on initial entry price \( p_{1} \), three different cases are considered. One is a 20% price risk regarding the initial entry price of 100, which is the risky situation described by the following probability distribution:
$$ Pro ( {p_{1} } ) = \left\{ {\begin{array}{*{20}c} {1/3\; ( {p_{1} = 80 } )} \\ {1/3\; ( {p_{1} = 100} )} \\ {1/3\; ( {p_{1} = 120} )} \\ \end{array} } .\right. $$

The other cases are its mean-preserving spreads: a 10% price risk and a 30% price risk. In each case, the certainty-equivalent drug price (the price level corresponding to \( p^{ *} \) in Fig. 1) and the risk premium (the price difference corresponding to \( p^{\prime} - p^{ *} \) in Fig. 1) are calculated to address how much the given reimbursement price risk reduces the firm’s R&D incentives (Proposition 1) and how much the reimbursement drug price can be reduced while keeping the firm’s R&D incentives the same (Proposition 2).

Results

How much does reimbursement price risk reduce R&D incentives?

Table 2 presents the simulation result for the case of a 20% price risk about the initial entry price of 100 as well as those for a 10% price risk and a 30% price risk. In the presence of a 20% price risk, the certainty-equivalent drug price is 96.0. That is, the initial reimbursement drug price of 100 in the presence of a 20% price risk is equivalent to the initial reimbursement drug price of 96.0 with certainty.
Table 2

Simulation results

 

Certainty equivalent

Risk premium

Relative risk aversion: θ = 3

 Price risk (%)

  ± 10

99.0

1.0

  ± 20

96.0

4.0

  ± 30

90.8

9.2

Relative risk aversion: θ = 1

 Price risk (%)

  ± 10

99.6

0.4

  ± 20

98.7

1.3

  ± 30

96.9

3.1

Relative risk aversion: θ = 5

 Price risk (%)

  ± 10

98.4

1.6

  ± 20

93.5

6.5

  ± 30

85.9

14.1

How much can the reimbursement drug price be reduced without reducing R&D incentives by increasing the predictability of future prices?

As Table 2 shows, the risk premium is 4.0 in the presence of a 20% price risk regarding the initial entry price of 100. This finding implies that, by increasing the predictability of future prices, the reimbursement price can be reduced by 4% without lowering the firm’s R&D incentives. Note that this price difference closely corresponds to a 5% premium in the similar efficacy comparison method, a pricing method that the government uses to determine a new drug’s initial entry price, if a similar drug is available in the market with the same effectiveness as the drug concerned.

Sensitivity analysis

How do these results change with the degree of price risk? To investigate this, we consider two different cases of a 10% price risk and a 30% price risk. Both of them are mean-preserving spreads of the 20% price risk discussed above. As summarized in Table 2, the certainty-equivalent drug price is 99.0 in the presence of a 10% price risk, while the certainty-equivalent drug price is 90.8 in the presence of a 30% price risk. Hence, these results imply that the negative impact of the reimbursement price risk on the firm’s R&D incentives increases at an increasing rate.

Consequently, the risk premium is 1.0 in the presence of a 10% price risk, and the risk premium is 9.2 in the presence of a 30% price risk. Thus, by increasing the predictability of future prices, the reimbursement price can decrease by (at most) 1% and 9.2%, respectively, without damaging the firm’s R&D incentives.

How do the results change with a firm’s RRA level? To investigate this, we use two different \( \theta \) values of \( \theta = 1.0 \) and \( \theta = 5.0 \). Table 2 presents the results. We find that the negative impact of the reimbursement price risk on the firm’s R&D incentives increases with the RRA level at a diminishing rate.

Conclusion

In the present paper, a theoretical and simulation analysis shows that, by reducing the price risk of future reimbursement drug prices, maintaining or increasing a firm’s R&D incentives is possible, even in the presence of a lower reimbursement price level.

An important policy implication derived from this research is that by creating appropriate guidelines, enhancing information disclosure and/or enabling public–private dialogue, among other things, the reduced price risk enables us to achieve both lower financial burdens on the NHI system and patients and stronger R&D incentives for pharmaceutical firms.

The question then arises: “What kind of guidelines and information disclosure are then appropriate?” In Japan, the government determines all reimbursement drug prices. For new drugs, it uses either the similar efficacy comparison method (if a similar drug is available in the market with the same efficacy) or the cost accounting method (otherwise). Some aspects of these pricing methods are well understood by pharmaceutical firms, but other aspects are not. For instance, pharmaceutical firms understand the formulae in these methods very well. However, they often do not fully understand how a comparable “similar” drug is defined in the similar efficacy comparison method, especially when two or more similar drugs exist in the market; or they do not fully understand how “indirect” cost is defined and proportionally divided among projects in the cost accounting method. As in these examples, if pharmaceutical firms do not know the scientific guidelines on which the government bases its decisions, then this becomes a source of the reimbursement price risks for pharmaceutical firms. In that case, the appropriate guidelines and information disclosure may be those that fill this information gap between pharmaceutical firms and the government.

Remaining issues for future research, on the other hand, are investigations of the attitudes toward price risk of pharmaceutical firms, and on the use of particular forms of utility function. Are pharmaceutical firms risk averse? If so, what does the structure of their risk aversion look like? In particular, do they have DARA and CRRA as assumed in this paper? And what is the level of their risk aversion? Because the above results do not hold if pharmaceutical firms are not risk averse, and because the magnitude of the results changes with the level of risk aversion, investigations of the attitudes toward price risk of pharmaceutical firms are essential to advance this line of research further.

Footnotes

  1. 1.

    An advantage of the RRA measure is that it is a unit-free measure. By rearranging the definition above, an elastic form is derived as follows: \( \theta_{R} = \frac{\partial U'/U'}{\partial x/x}. \)

  2. 2.

    Concerning the level of RRA, more positive values are associated with greater degrees of risk aversion. whereas the zero and more negative values are related to risk neutrality and greater degree of risk loving, respectively.

  3. 3.

    The formula for price revision considered here is the one used in 2012. The discrepancy rate from the market price is set to 0.06 before generic entries, to 0.1 at the time of generic entries, and to 0.18 after generic entries. The value for the weighted-average market discrepancy rate is 0.08. In this setting, the price remains at the initial level before generic entries and decreases at two-year intervals as depicted in Fig. 2. A similar price pattern is considered in Wakutsu and Nakamura [22]. Although the current formula is somewhat different from the one in 2012, the analysis presented in this paper is still applicable.

  4. 4.

    A bell-shaped sales curve is ensured if \( x < y \) holds. While the height of peak drug sales depends on the values of \( x \) and \( a \), its timing is determined by the value of \( y \). Here the values are determined by an ordinary-least-square regression and set to \( x = 0.006 \), \( y = 0.32 \), and \( a = 12,500 \) as in Wakutsu and Nakamura [22].

  5. 5.

    In the case of \( \theta = 1 \), we consider \( u ( {S_{t} } ) = \ln ( {S_{t} } ) \). See Wakker [21].

  6. 6.

    We interviewed 17 research-oriented pharmaceutical firms in Japan between late March and early July in 2017 and collected data on the discount rate they used to evaluate an R&D project in early stages of clinical drug development such as proof-of-concept. We found that the median is 0.08 and the mean is 0.071. We tried \( r = 0.07 \) but the results were similar.

Notes

Acknowledgements

This work was partially supported by the grant from the Health Care Science Institute and JSPS Grant-in-Aid for Scientific Research (C) (Grant number: 16K03700).

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Copyright information

© Japan Economic Policy Association (JEPA) 2018

Authors and Affiliations

  1. 1.Keio UniversityYokohamaJapan
  2. 2.Nagoya City UniversityNagoyaJapan

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