Policy Interventions When Medical Treatment Dynamics Matter: The Case of In Vitro Fertilization∗ Barton Hamilton Emily Jungheim Washington University in St. Louis Washington University in St. Louis Olin Business School School of Medicine Brian McManus Juan Pantano University of North Carolina-Chapel Hill Washington University in St. Louis Department of Economics Department of Economics March 26, 2015 PRELIMINARY AND INCOMPLETE. DO NOT CITE AND DO NOT DISTRIBUTE Abstract As in many medical treatments, decision-making dynamics are central to the In Vitro Fertilization (IVF) treatment process, a technologically advanced infertility treatment for which patients usually pay out-of-pocket. Patients make decisions throughout a single treatment cycle as information about treatment progress is gradually revealed, and they consider the possibility of multiple treatment cycles over time. Patients who choose more aggressive treatment actions reduce the risk of concluding a treatment without a birth, but this comes with an increased likelihood of a high-risk twin or triplet pregnancy. Several policy interventions are possible to increase IVF access while also encouraging patients to take more conservative treatment courses. We use data on treatment choices and outcomes at a single large IVF clinic to estimate technological processes and patient preferences in a dynamic structural model of patients’ choices within and across IVF treatments. The estimated parameters allow us to evaluate the impact of counterfactual policies to directly limit aggressive treatment, extend insurance to all potential patients, and implement new treatment processes that were unavailable in the market during our sample period. All policies have significant impact at the extensive margin and within treatment, and would be diﬃcult or impossible to study using a static framework or less structural methods given practical limitations on data availability. ∗ We thank comments by Flavio Cunha, Liran Einav, Hanming Fang, Donna Gilleskie, Bob Pollak, John Rust, Seth Sanders, Steve Stern, Xun Tang, Ken Wolpin, and participants at several conferences and workshops. All errors remain our own. 1 1 Introduction Many medical ailments require patients and doctors to consider complex or lengthy treatment strategies. Examples include: cancer treatment, which can include some combination of radiation, chemotherapy, and surgery in some sequence as a patient’s response to each therapy is revealed; heart disease treatment, which may begin with pharmaceutical approaches and then progress to diﬀerent sorts of surgery; and treatment of physical injuries or deterioration, which might be addressed with physical therapy, repair-focused surgery, or surgery to replace an aﬀected body part. Common themes across all of these treatments include some scope for choosing how aggressively to treat the ailment, uncertainty about treatment success, and the opportunity to dynamically update treatment strategies as information arrives. When a new public policy or technological advance is implemented that aﬀects one or more treatment avenues for an ailment, we would expect that a patient’s full treatment course could change. The extent of these changes (and their welfare impact) will depend on the precise details of treatment technologies, the decision structure, and patients’ preferences. In this paper we study a form of infertility treatment, In Vitro Fertilization (IVF), which shares many characteristics with the complex therapies described above. IVF is the most technologically advanced infertility treatment available and is widely used, with over 100,000 treatment cycles conducted in the U.S. each year. However, a single IVF cycle will fail for most patients and can require substantial out of pocket payments, on the order of $10,000-$15,000 per attempt. Consequently, patients often tailor their treatment decisions to their financial resources, preferences, and health characteristics. The main avenue for increasing treatment aggressiveness is the number of embryos transferred to the patient, which increases both the probability of pregnancy and the likelihood of a potentially risky high-order birth. Policymakers in the U.S. and abroad have considered a variety of interventions to improve IVF access and reduce treatment risks. One potential avenue is through insurance mandates, which have been implemented in seven U.S. states. Insurance coverage for IVF can reduce the cost of each attempt to $2,000-$3,000, which may lead patients to view failure as less expensive, since future treatment attempts can occur at a lower price. Previous studies at the population or clinic level have provided empirical evidence on the eﬀectiveness of such policies.1 Another potential policy intervention is a cap on the number of embryos transferred during 1 Schmidt (2007), Bitler (2008), and Bundorf, Henne, and Baker (2008) examine the impact of infertility mandates at the population level. Hamilton and McManus (2011), Jain et al (2002), and Henne and Bundorf (2008) investigate the impact of mandates on the number of patients served and birth outcomes at IVF clinics. See also Schmidt (2005), Bitler and Schmidt (2006, 2012) and Buckles (2012). 2 treatment. This restriction is imposed in some Scandinavian countries, and accords with the U.S. medical community’s sentiment that a singleton birth is the best possible outcome of treatment. Finally, policies such as research grants and prizes can push forward technological progress, which aﬀects treatment choices and outcomes. We investigate the impact of these policies by: a) exploiting longitudinal data on individual patients’ decisions at all stages of an IVF treatment cycle, and b) developing an empirical strategy that allows for the investigation of patient actions, outcomes, and surplus in a variety of counterfactual settings. We specify and estimate a dynamic structural model of choices made during IVF treatment by forward-looking patients. We use a novel dataset of 587 women undergoing IVF treatment at an infertility clinic in the St. Louis area (“the Clinic”) from 2001 to 2009. This setting provides a valuable opportunity to understand how prices aﬀect treatment choices: The Clinic serves patients from both Illinois, which mandates insurance coverage of IVF, and Missouri, which does not. Consequently, we are able to analyze the decisions of observationally equivalent patients paying vastly diﬀerent prices ($3,000 for covered patients vs. $11,000 for those without insurance) undergoing the same procedure with the same physicians. Using highly detailed data on the fertility attributes of the patients and their treatment choices and outcomes, we estimate the various stochastic processes that determine success at each stage of an IVF treatment cycle. These processes, together with the specifications of patient preferences over children, delaying treatment, and the disutility of payments, yield a well-specified dynamic optimization problem for choices within and across IVF treatments. We then estimate the patients’ preference parameters to maximize the likelihood of the observed treatment choice histories. Our main empirical model contains three sets of results. The first set is the estimated treatment technologies across the four stages of an IVF cycle. The estimated technologies fit the data well. We see, for example, little diﬀerence between the data and our predictions of transition probabilities for birth outcomes conditional on a patient’s treatment choices and state variables. The second set of results is the structural parameters of our within-clinic patient decision model. These parameters indicate that patients prefer singleton and twin births to the more dangerous triplet births, and the utility from additional children falls in the number of children the patient already has. The model parameters predict patients’ choices at various treatment stages, and we find that our estimates are able to reproduce the data’s main moments fairly well. The final set of results describe the extensive margin for treatment. We construct data on the local population of women “at risk” for infertility treatment, and we use these data together with observed treatment-initiation decisions 3 to estimate a simple auxiliary treatment initiation model that describes the willingness of potential patients to pursue IVF. We use our structural estimates to evaluate a collection of counterfactual policy experiments. First, we explore the impact of restricting patients to transferring a single embryo during treatment. While this policy has a clear eﬀect in nearly eliminating multiple births, we find that active patients are much less likely to conclude treatment with a child, and they are also less likely to begin treatment at all. Second, we illustrate the impact of another potential avenue for improved treatment access and reduced multiple-birth risk: an improvement in treatment technology. We focus on the issue of embryo selection, which is also important to pregnancy failures in natural reproduction. Research is currently underway to understand why some embryos develop into successful pregnancies and others do not. Identification and selection of such embryos before transfer would significantly increase success rates. To capture this, we add an embryo screening stage to treatment, and we allow it to substantially reduce the uncertainty about whether any individual embryo will yield a successful pregnancy. As a result, more patients are willing to start treatment at the current prices (which we hold fixed), and treatments are more likely to end in a birth. In the third counterfactual we estimate the impact of extending insurance coverage to all women in the market. This policy’s primary impact is to substantially increase the number of women who initiate treatment. While insurance reduces the opportunity cost of failed treatment, which could aﬀect embryo transfer rates, we find only a small reduction in treatment aggressiveness as insurance coverage becomes more common. In addition to our main focus on patients’ responses to policy changes, we contribute to literature on understanding responses to changes in medical care prices. The rapid rise in health care expenditures in the United States over the past three decades has generated substantial interest in this area. A growing literature using both experimental and observational data has attempted to empirically measure the relationship between the out-of-pocket price paid by the patient and the utilization and cost of health care. The primary focus of this literature is examining how alternative cost-sharing arrangements in a patient’s health insurance contract (e.g., co-payment rates, deductibles) aﬀect his or her total healthcare expenditures in a given year. Much less attention has been paid to how an individual’s treatment choice for a particular ailment responds to changes in the full price of the treatment. Consequently, little is known about how the composition of medical treatments may change in response to changes in their relative prices. These changes may be especially diﬃcult to study when intensive-margin choices (i.e. the selection of specific treat4 ments options as opposed to extensive margin choice whether to treat or not) and intertemporal substitution are especially salient. Empirical estimation of a patient’s response to the price of medical treatment faces a number of obstacles. First, individuals facing diﬀerent pricing schedules (i.e., insurance co-pays and deductibles) may be directed to diﬀerent healthcare providers, who may not be comparable in terms of quality or available treatments. Second, recent studies have argued that many patients do not even know the prices of treatments, since providers often do not post prices in an accessible or understandable way, making it diﬃcult to infer the eﬀects of prices on choice behavior. Finally, most studies examine the response to the “spot” price of medical care; many medical treatments have uncertain outcomes, meaning that the patient will consider both the current and future price of care. Failure to incorporate the dynamic aspects of treatment may lead to biased estimates of behavioral responses to price changes (Aron-Dine, Einav, Finkelstein, and Cullen 2012). We are able to avoid some of these diﬃculties by studying a market which includes variation in insurance coverage and patients who frequently research prices before selecting treatment. The remainder of the paper proceeds as follows: Section 2 provides an overview of an IVF treatment cycle and state level policies governing insurance coverage of infertility treatment. Section 3 details the stages of an IVF treatment cycle, which are incorporated into our dynamic structural model of treatment choice developed in Section 4. The data we obtained from the Clinic is described in Section 5. Section 6 discusses the empirical specification of our model and Section 7 provides estimation details. Section 8 presents the parameter estimates and measures of model fit and Section 9 contains the results from our counterfactual policy simulations. Conclusions follow. 2 IVF overview A couple is defined to be medically infertile if they are unable to conceive after attempting to do so for 12 months. Initial treatment for infertility often includes the use of the drug clomiphene to induce ovulation, or the use of hormone shots. While such treatments are relatively low cost, they also may be: less eﬀective than more technologically advanced treatments as the woman ages, more likely to lead to higher order pregnancies, and less eﬀective for couples with male factor infertility. Due to these limitations, couples may choose to undergo IVF. The US market for IVF has grown substantially in recent years. Between 1992 and 2009, the annual number of IVF treatment cycles increased from 38,000 to 142,000. Treatments in 2009 lead to the births of 51,700 children. While 5 the use of IVF has grown, a cycle of treatment is still more likely to fail than to succeed. Live birth rates range from 10% to 45% depending on the age of the woman and the health status of the couple. Once a patient has decided to use IVF, the treatment cycle unfolds in stages. First, the woman takes drugs to stimulate egg production. The doctor monitors the response to these drugs and may choose to cancel the cycle and choose a diﬀerent drug dosage to generate more eggs. If the cycle is not cancelled, the eggs are retrieved during a minor surgical procedure. The eggs are fertilized in the laboratory. The doctor may recommend the use of intracytoplasmic sperm injection (ICSI), in which a single sperm is injected into the egg. ICSI was initially used to address male-factor infertility problems, but has become more widely used. Depending on the number of fertilized eggs that develop, the patient decides how many embryos to implant in the womb. At this point the patient faces an important tradeoﬀ: the probability of a live birth increases with the number of embryos transferred, but so does the likelihood of a potentially costly multiple birth. For example, the expected medical cost of a triplet birth may be more than 10 times that of a singleton, due in large part to a shorter gestation period resulting in the need for the infants to be admitted to neonatal intensive care at birth. If the IVF cycle does not result in a live birth, the patient then must decide whether to attempt another cycle of treatment. Because fertility declines with age, subsequent cycles are less likely to be successful, all else equal, and couples potentially incur substantial out-of-pocket cost if they try again. 2.1 Insurance and IVF A key feature of the market for IVF is the presence of state-level mandates regarding whether and how insurers must oﬀer coverage for infertility treatment, including IVF. During the period of our study, 2001-2007, seven states had mandates requiring some form of insurance coverage for IVF. Illinois, Massachusetts, and Rhode Island had the strongest mandates for IVF, requiring insurers to cover a certain number of IVF treatment cycles.2 Prior research has found that these mandates increase the number of IVF treatment cycles at clinics in covered states, reduce the number of embryos transferred, and reduce multiple birthrates.3 These studies have generally examined data 2 Arkansas, Hawaii, Ohio, and West Virginia had mandates requiring insurers to oﬀer plans that include IVF coverage. Nothing prevents insurers, however, from charging substantially higher prices for plans that include this coverage. 3 When looking at multiple birthrates, it is important to distinguish, the intensive and extensive margins. Among existing IVF patients insurance mandates reduce multiple birth rates by facilitating less agressive treatment. But the overall number of multiple births may increase if enough new patients can pursue IVF treatment under the mandated coverage. 6 aggregated at the population or clinic level. We contribute to the literature by accounting for variation in insurance status at the individual level. This strategy helps us to recover the price elasticity of demand for IVF. For patients in our study residing in Illinois and working for an employer covered by the mandate, insurance plans are required to pay for up to 4 cycles of IVF if the woman has no children.4 As noted in the Introduction, this insurance coverage pays the cost of the IVF procedure, but may not cover the full cost of drugs used during treatment. These drugs generally cost approximately $3,000 dollars. For patients paying out-of-pocket for IVF in our sample, the Clinic charged about $8,000 per treatment cycle throughout the sample period. The Illinois mandate exempts firms with fewer than 25 employees and organizations, such as the Catholic Church, that may object to IVF for religious reasons. These individuals pay the full price of IVF. Our study exploits the fact that The Clinic draws patients from the greater St. Louis metro area, which includes both Illinois, which has an IVF insurance mandate, and Missouri, which does not. However, an interesting feature in our data is that some patients residing in Missouri have private insurance covering their IVF cycle, even in the absence of a mandate. Some employers may choose to oﬀer IVF coverage as a means to attract and retain better employees. In addition, some firms operating in the St. Louis metro area have locations in both Illinois and Missouri. Rather than oﬀer IVF coverage only to their Illinois employees, many of these firms choose to oﬀer insurance coverage to all their workers in order to reduce administrative costs and eliminate inequality in benefits. The Clinic has found that the insurance plan characteristics covering Missouri patients are very similar to those of plans under the Illinois mandate. The patient-level information on insurance status allows us to exploit both cross-sectional and longitudinal variation in the out-of-pocket prices paid by individuals in our sample. 3 IVF treatment technologies We consider two timing concepts in the model below. First, there are decision periods when potential patients choose whether to start or delay an IVF cycle. Second, there are treatment stages during which patients in an IVF treatment cycle make a sequence of choices. Conditional on starting IVF treatment, a patient makes a series of choices regarding the aggressiveness of her treatment and whether the treatment continues at all. Along the way, the patient 4 If the woman already has children, the mandate on.ly covers up to 2 cycles of IVF. 7 uses information that is known at the start of treatment (e.g. age, current number of children, basic fertility diagnoses) and information that is collected incrementally as treatment progresses (e.g. the numbers of eggs retrieved and embryos available for transfer). In order to describe how a patient makes her choices throughout the IVF process, we must describe the stages of IVF treatment fully, including assigning notation, etc. We divide the patient’s choices into four stages, which we describe below. See Figure 1 for an illustration of the IVF treatment stages described below. The Figure contains some notation on utility payoﬀs that are introduced in the following section. 3.1 Initial information A patient who is considering treatment is aware of several personal characteristics that aﬀect treatment eﬀectiveness and utility. We track a patient’s age, her wealth, number of prior children, and insurance status in the state vector . In addition to these characteristics, we assume that the patient will learn some of her own biological characteristics, , if she initiates treatment. The characteristics in include the women’s antral follicle count (AFC score), whether she has one or more specific infertility diagnoses (e.g. endometriosis), and whether her partner has malefactor infertility. At treatment initiation decision, the patient considers the possible values of she may have using the population frequency of these characteristics conditional on her age, ( |0 ), where 0 is the patient’s age at the time she decides to pursue IVF treatment. Once the value of is realized we consolidate notation and refer to the full collection of state variables as = [ ] In addition to acting as a state variable which influences treatment outcomes, patient age also functions as a time index for decision periods, so we add an ‘’ subscript to where appropriate. During an arbitrary age, we have = [ ], and at treatment initation the state variables have the value 0 Our assumptions on include a few simplifications that we impose to maintain tractability. First, we do not allow patients to receive a detailed fertility screening before deciding to initiating treatment, which could be used to reveal While such screenings are feasible in actual treatment markets, we make this simplification in order to reduce the dimensions of potential patient heterogeneity prior to treatment. Second, we assume that patients (and their doctors) use no other biological data in choosing a treatment path for patients. Although fertility doctors collect information on patients’ pre-treatment follicle-stimulating hormone (FSH) and estradiol (E2) levels, we do not observe these items in our data. We eﬀectively assume that the patient’s observed biological 8 state variables along with her age fully capture her relevant fertility characteristics. We assume that the doctor knows how the variables in aﬀect the outcome probabilities that we describe below. Each patient receives this information from her doctor and also knows her preferences over treatment outcomes. In addition the patient receives taste shocks as she moves through the treatment stages, and the realizations of these shocks are not known in advance. With the patient’s knowledge of her choice problem at every stage within treatment, the stochastic processes that determine outcomes, and her preferences over these outcomes, we have suﬃcient structure to write down a well-specified dynamic optimization problem for the patient. 3.2 Stage 1: Start treatment vs. delay Conditional starting IVF treatment, the patient pays the price ( ) out of pocket and begins a regimen of pharmaceuticals to promote egg production. The patient’s price depends on because the treatment may or may not be covered by the patient’s insurance, which is recorded in . We assign = 3000 for patients without insurance coverage, and = 1000 for patients with insurance. The positive price for insured patients is due to deductibles, co-payments, and co-insurance charges. The patient’s personal characteristics and drug regimen will yield a realization of the patient’s Peak E2 score () at the start of the next treatment stage. During the first stage, however, the patient knows only the distribution over possible values, which take integer values in our data and range from 0 to 10196 with a mean of 1694 and median of 1577. 99% of all values are below 4500. Let (| ) represent the probability of a patient with characteristics receiving a score with value . Diﬀerent realizations of aﬀect the choices and success probabilities of later stages of IVF, so the distribution has an important role in a patient’s decision whether to start treatment. 3.3 Stage 2: Continue vs. cancel The patient makes her next significant choice after the value of is realized. During the second treatment stage, she considers and her personal characteristics ( ) while deciding whether to cancel or continue treatment. A larger value of is generally associated with a larger number of eggs that are ready for retrieval from the patient’s ovaries. If the patient cancels treatment, she pays no additional treatment fees, and she is able to consider starting treatment again in the future. If the patient continues treatment, she pays the additional fee ( ) and undergoes a process in which eggs are retrieved. We assume that patients with insurance pay the price = 2000 if they choose to continue treatment, while uninsured patients pay = 6000. 9 We denote as (| ) the probability of successfully retrieving eggs from a patient with Peak E2 score and personal characteristics . The patient knows her value of and the probability distribution when she makes her decision whether to continue treatment. In the data, takes integer values from 0 to 38 with a mean of 106 and median of 10. The 90th percentile is at = 18, and 99% of all values are below 27 3.4 Stage 3: Fertilization If treatment is not cancelled, the patient’s eggs are retrieved and she observes the realized value of . The patient’s next choice is how to fertilize the eggs. The fertilization method is represented by the variable , and the patient’s options are: natural fertilization (1 ) or with ICSI (2 ). While the options “full ICSI” and “partial ICSI” are separated in the data, we group them together in our model. The patient’s characteristics ( ), her number of eggs (), and her fertilization choice () will determine the number of viable embryos generated for the patient. We assume that insured patients pay 2 = 0 for ICSI if they choose to use it, while uninsured patients pay 2 = 2000 Let represent a possible realization for the number of embryos. Possible values of are in {0 1 2 3 4+}. We cap the maximum value of at 4 because this is the greatest number of embryos that we see transferred to patients during the final treatment stage. In the data, the mean of the distribution is 625 and the median is 6 About 75% of patients have 4 or more embryos available for transfer. In practice, patients may choose to freeze excess embryos for potential later use, but we do not examine that decision in this paper. Frozen-embryo cycles account for only 12% of the clinic’s treatments. When making her choice over fertilization method, the patient considers the probability of receiving embryos: (| ). 3.5 Stage 4: Embryo transfer At the start of the fourth and final treatment stage, the patient learns her number of viable embryos, . The patient chooses , the number of embryos to transfer during the final treatment stage, subject to ≤ A patient’s treatment outcome is influenced by her number of embryos () and her personal characteristics (). As a result of treatment, children are born with probability (| ). Possible values of are in {0 1 2 3}. There is no price for this treatment stage. 10 3.6 After IVF When a patient cancels her IVF cycle in stage 2 or has = 0 as an outcome of stage 4, she may begin another IVF cycle during the following decision period, i.e. three months later. A patient who has 0 in stage 4 must wait for one year before considering her next IVF cycle. 4 Patient decision model 4.1 Timing We assume that potential patients’ decisions begin with an exogenous event which prompts them to consider having children. Women who are able to reproduce naturally (or with lower-tech infertility treatments) are immediately removed from the process we study in this paper. The remaining women have reproductive diﬃculties that can only be solved by IVF. These women, who constitute our “at risk” population, evaluate the expected benefit of beginning IVF relative to an outside option, which we parameterize below. If the woman does not begin IVF at this critical moment, we assume she exits the model permanently. We track patient’s decisions in three-month periods (i.e. quarters). The exogenous event to consider reproduction begins when the patient is of age 0 , which we assume to be not smaller than a lower limit min In our data we observe patients with 0 between their late twenties and early forties. If at that point she opts to pursue IVF treatment, the patient will continue to make decisions up to, possibly, the fourth quarter of age max . At this age the IVF clinic will no longer treat the patient and her birth probability (via IVF or naturally) is zero.5 This allows a maximum of 4 × (max − 0 ) periods.6 In addition to the age index, a time index () us useful for describing the data sample and econometric procedure. Let 0 represent the period during which we first observe patient . We see a patient for the last time in , which might be equal to max (defined below) or the end of the sample period. We assume that all treatment stages that follow from a treatment starting in period also occur in period Once a patient’s total number of children reaches 3 (or more), she automatically stops making decisions within the model. Alternatively, the patient’s fertility outcomes can llow her to continue making decisions until the end of the year in which her age is max . Once she reaches max she 5 We assume this age upper bound for tractability. The clinic does not have a preset age limitation and, instead, evaluates each patient on a case by case basis. 6 We use min = 28 and max = 44. Therefore the number of periods is 68 11 receives the terminal payoﬀ (max ) at age max + 1 4.2 Patients’ preferences and options In the (potential) patient’s first decision period she chooses whether to pursue IVF or forego the treatment forever. Conditional on starting IVF at age 0 for all subsequent decision periods the (now active) patient will choose between start () or delay () IVF. Patients have preferences over birth outcomes, and these preferences can depend on the patient’s existing number of children (e ) at the start of stage 1 and other personal characteristics. Possible values of are in {0 1 2 3}, and e takes values in {0 1 2}. (These values for e cover 98% of the patient population at the Clinic). We allow patients to have permanent unobservable heterogeneity, indexed by . Let (|e ) represent the lump-sum utility payoﬀ from a treatment cycle that ends in children conditional on e and . We assume that treatment outcomes with = 0 always result in = 0 for all patients. In addition to payoﬀs through which may be received at the end of IVF treatment, patients undergoing treatment experience disutility, scaled by , from paying positive prices. When a patient pays within treatment, she has the immediate utility loss of . We allow the value of to depend on a patient’s demographic characteristics, so we write () An additional potential source of disutility is in a patient’s choice to violate American Society for Reproductive Medicine (ASRM) guidelines for embryo transfers. During our sample period the ASRM generally recommended against four-embryo transfers for all patients, and single-embryo transfers for older patients. We assume that a patient’s utility falls by ( ) if she violates the guidelines. We write as a function of state variables to capture shifts in ASRM guidelines within our sample period and their dependence on patient age. We assume that all ASRM rule changes come as a surprise to decision-makers. At each treatment node, the patient’s benefit from the available options includes an additional taste shock, , which represents heterogeneity in patient’s circumstances and preferences. For computational ease, we specify that values of are distributed extreme value across patients, time periods, and treatment stages. The remaining parts of patients’ preferences concern a terminal value for patients and the value of delaying treatment. To maintain consistency with the zero payoﬀ from non-treatment that we implicitly assume for patients before treatment begins, we normalize the baseline delay and terminal value payoﬀs to zero. Relative to the delay baseline of zero, we assume that patients receive the 12 flow benefit of () during any period she begins treatment in stage 1. Patients’ terminal payoﬀs are captured by the parameter vector (max ). The patient receives at age max + 1 regardless of whether she remains active in the model up until max or if her decision process ends due to ≥ 3 at some earlier . Finally, we assume that patients discount future decision periods by the factor . We assume that all discounting occurs across periods, and not across treatment stages. Treatment options and outcomes that occur periods into the future are discounted by . We do not estimate in this paper, so we set its value equal to = 097. 4.3 Value functions We combine our assumptions on patient’s preferences, the timing of their decisions, and the IVF technology described above to write value functions for the patients. The patients’ optimal dynamic decisions include two components. There are optimal decisions across time periods, when active patients decide whether to start or delay treatment during any particular period . The second is optimal decisions within a treatment cycle but across its stages. We begin by considering the value functions of patients who have already learned their state variables. For these patients, let [1 ( 1 )] represent the expected value of beginning a period with the characteristics . Patients’ values of [1 ( 1 )] with vary due to their realization of but we suppress this term and the subscript for notational simplicity. In contrast to the expected value [1 ( 1 )] the patient’s realized value of 1 depends, in part, on the realized values of that the patient observes during the first treatment stage. Within a treatment stage , the patient selects a discrete option from the set . Let [ ( )] represent the value from an optimal decision within treatment stage . We add a subscript for the choice-specific value of option in stage and denote by the systematic component (i.e. net of of the preference shock ) of the age-, alternative- and stage-specific value function. We then have ( ) = ( ) + (1) When a patient reaches age max + 1, she receives the terminal value (max ) = (max ) and exits the model. 13 4.3.1 Stage 1: Start treatment vs. delay Consider the stage 1 decision of a patient who already started IVF in an earlier time period. The patient decides whether to start () or delay () IVF. Therefore the set of available choices is 1 = { } The value from starting treatment is 1 , and it includes the expected value from continuing to the second stage of treatment ( [2 ( 2 )]); the utility normalization relative to delay, ; the price of starting treatment; and a taste shock 1 . The value of the second stage depends on the realization of (the peak estradiol score), but this is not known during stage 1. The full expected benefit from starting treatment is then 1 ( 1 ) = 1 ( ) + 1 X = [2 ( 2 )] (| ) + ( ) − ( ) ( ) + 1 (2) The value of delaying the IVF decision until the start of the next period is: 1 ( 1 ) = 1 ( ) + 1 (3) = 0 + [1 (+1 1+1 )] + 1 Changes in across periods will account for the patient becoming older, her number of covered IVF cycles may decline, her stock of children may increase, etc. The expected value [1 (+1 1+1 )] accounts for the expectation over and the eﬀects of these shocks on a patient’s optimal choices and payoﬀs. Combining terms, the patient’s value at the start of the period (after observing the shocks ) is 1 ( 1 ) = max{1 ( 1 )} = max{ 1 ( ) + 1 } ∈1 ∈1 (4) and the expected value [1 ( 1 )] accounts for the expectation over and the eﬀects of these shocks on a patient’s optimal choices and payoﬀs. Due to the extreme value assumption for , we can write [1 ( 1 )] with the inclusive value expression: [1 ( 1 )] = log{exp[ 1 ( )] + exp[ 1 ( )]} (5) Now consider the decision of a potential patient at age 0 who is considering whether to start 14 IVF for the very first time. This is somewhat diﬀerent than the decision to begin a new cycle, by an already active patient. This potential patient does not yet know her values of , but she knows the population distribution of values conditional on age. Let (0 |0 ) represent this discrete distribution. The potential patient’s expected value from starting treatment is: ¡ ¢ £ ¤ X 1 (0 0 ) (0 |0 ) 0 = 1 (0 )|0 = 0 where we make the distinction between the state variables known prior to treatment (0 ) and ¡ ¢ those learned after treatment begins. The potential patient compares 0 to the utility from foregoing treatment, which we specify as + . The potential patient becomes a patient (i.e. enters the clinic to pursue her first IVF cycle) if ¢ ¡ 0 ≥ + and exits the model otherwise. 4.3.2 Stage 2: Continue vs. cancel Every time a patient starts an IVF cycle (whether for the first time or in subsequent attempts), she learns her realized value of and considers whether to continue treatment. Her options are to stop () or continue () treatment. The available options are 2 = { }. A patient who continues treatment must pay the additional price If the patient continues treatment, she will learn how many eggs () are retrieved at the beginning of the next stage. While she does not observe before making her continuation decision, the value of serves as a imperfect signal of her eventual value of . If the patient decides to stop treatment, she receives the value 2 ( 2 ) = 2 ( ) + 2 (6) = 0 + 1 (+1 ) + 2 The value of continuing treatment includes an expectation taken over values of conditional on 15 the realized signal and other patient characteristics: 2 ( 2 ) = 2 ( ) + 2 ! Ã X [3 ( 3 )] (| ) − ( ) ( ) + 2 = (7) The full value of the second stage is the maximum of these two options: 2 ( 2 ) = max{2 ( 2 )} = max{ 2 ( ) + 2 } ∈2 ∈2 (8) and we write [2 ( 2 )] for the expected value of this stage before the shocks are realized. [2 ( 2 )] = log{exp[ 2 ( )] + exp[ 2 ( )]} 4.3.3 (9) Stage 3: Fertilization After the patient has learned , she must decide how to fertilize the eggs. The variable represents her fertilization method, with = 1 if no ICSI is used and = 2 when ICSI is used. Thus 3 = {1 2 }. When = 2 , the patient pays the additional price . Her choice of will influence her realization of the number of cleavage-stage embryos that will be available for transfer during the 4th treatment stage. 3 ( 3 ) = 3 ( ) + 3 Ã ! X = [4 ( )] (| ) − ( ) ( ) + 3 (10) The full value of the third stage is 3 ( 3 ) = max {3 ( 3 )} = max { 3 ( ) + 3 } ∈3 ∈3 (11) with [3 ( 3 )] as the expected value. [3 ( 3 )] = log{exp[ 31 ( )] + exp[ 32 ( )]} 16 (12) 4.3.4 Stage 4: Embryo transfer At the start of the 4th stage, the patient learns her number of transferable embryos, , which constitute her choice set in the final treatment stage. She then chooses a number of embryos, , with ≤ . At the end of this stage the patient realizes the number of children from her treatment. If treatment fails she moves to the start of the next period, but if treatment is successful she waits for three additional periods (i.e. 9 months) before making her next reproductive decision. When the patient elects to transfer embryos, she receives an expected benefit of 4 ( 4 ) = 4 ( ) + 4 (13) = (0| ) [1 (+1 1+1 )] Ã ! n o X 4 + (| ) (|e ) + [1 (+4 1+4 )] (14) 0 +( ) + 4 (15) This expression includes the possibilities of failed treatment ( = 0) and successful treatment ( 0). The future value of a patient’s decision, [1 ( 1 )], will depend on the realization of the current treatment. If the treatment is successful, will evolve to a value +4 which reflects that the patient is one full year older and has additional children. Moreover, this future value is discounted at 4 . If treatment fails, then the next decision’s value is discounted by and +1 relects that the patient is just three months older. The full value of the fourth stage is: 4 ( 4 ) = max{4 ( 4 )} = max{ 4 ( ) + 4 } ∈ ∈ (16) with the expected value [4 ( 4 )] [4 ( 4 )] = log ⎧ ⎨X ⎩ ≤ 17 ⎫ ⎬ exp[ 4 ( )] ⎭ (17) 5 Data 5.1 Clinic data Our primary data cover individual patient histories at the Clinic during 2001-09. We observe all treatment cycles conducted during this period for patients who underwent their first IVF cycle after 2001. While these data allow us to describe a patient’s IVF history from the start of her treatments, we do not observe whether a patient returns to the clinic after 2009 or visits a diﬀerent clinic after her final visit at the Clinic. We handle this potential right-censoring by assuming that patients may choose to continue their treatment after they appear for the final time in our data. The main data sample contains treatment histories for 587 patients who use only fresh embryos (i.e. not frozen) and have complete data on their personal characteristics and treatment details. We supplement these observations with data from an additional 519 patients for whom we have data on all state variables and most treatment choices. We refer to the expanded data as the “first-stage sample.” In Table 1 we display some basic characteristics of the patients, their treatment choices, and their outcomes; we separately report statistics for the main sample of 587 patients and the 1106 patients in the full first-stage sample. The average patient in the main sample is 34 years old at the time of her first cycle in the clinic, and over half of all patients have insurance. Most patients’ homes are in a zip code with a median house price above $100,000, which we use as a proxy for patient wealth ( ). The patients in the main sample have no children (0 = 0) when they initiated treatment, but some patients in the first-stage sample have prior children. The biological variables ( ) exhibit some minor diﬀerences between the main and first-stage samples, with the former set of patients displaying slightly worse fertility characteristics. At the bottom of Table 1 we display patient-level statistics on treatment choices and outcomes. Patients in the main sample average 175 treatments during the sample period, and about half experience at least one birth during their full treatment history. In Table 2 we report summary statistics on choices and outcomes within treatment stages. Most patients at stage 2 choose to continue treatment, with only 2 = 014 as the cancellation rate. Most patients (60%) fertilize their eggs with ICSI; this rate is closer to 90% when male-factor infertility is present. Finally, patients take 2.3 embryos on average during a treatment. The embryo transfer choices are most often made with a choice set of 4+ embryos, due to over 6 embryos being generated during an average cycle. At the bottom of Table 2 we report treatment-level outcomes. To obtain the main sample’s average of 0.51 children born per cycle, we include all stage 4 decisions with 0 and 18 birth outcomes in {0 1 2 3} A singleton birth occurs in 27% of cycles, and twins occur in an additional 12%. While we observe no triplet births in the main sample, they occur at a rate of about 1% in the larger first-stage sample; this allows us to account for triplet risk when estimating the structural model. Some correlations among patient characteristics and treatment sequences suggest the role of dynamics and the importance of the state variables in patients’ decision-making. Conditional on having one successful cycle at the Clinic, 8% of patients return to start another cycle. Patients who receive Peak E2 scores in the lowest quartile chose to cancel treatment in 40% of all cases, while patients with scores in the 25 − 75 percentile cancel only 4% of cycles. Patients who are 35 or older take an average of 26 embryos in their first cycle, while younger patients take 2 embryos on average. Uninsured patients take more embryos (24) during their first cycle than uninsured patients (22), but this diﬀerence shrinks in the second and third cycle, as insurance coverage is drawn down. 5.2 Market data We also use several pieces of market data to get a sense of how large the set of potential patients for our clinic is and what it might look like. These data are used in a separate estimation step that deals with the model of treatment initiation. To characterize potential patients we focus on an area of 75 miles around our clinic. This captures the geographic area from which the clinic draws most of its patients. The area includes the City of St. Louis along with its suburban rings as well as rural towns further away from the metro area, but still within a 75-miles radius from the clinic. We collect information from birth certificates (Vital Statistics) on the distribution of maternal age among first births occurring in this region. These, along with estimates of infertility rates by age allows us to derive an estimate of the distribution of age among the potential patients at risk of initiating treatment in our clinic. We also use zip code level data on the percent of each zip code’s population with private insurance. We take these data from the 2012 American Community Survey (ACS) and combine it with other sources of information to derive insurance coverage rates for IVF at the zip code level. We also collect data on the median home value for each zip code in the area, taken from 2000 Decennial Population Census. This allows us to provide an estimate for the distribution of our wealth measure. Combining the zip code level data on home values and IVF insurance coverage we can then come up with an estimate of the joint distribution of IVF insurance coverage and our 19 measure of wealth. We also collect data from CDC on the number of cycles conducted at each infertility clinic in the area to assess how many in the pool of potential patients would rely on our clinic, if deciding to pursue IVF.7 Appendix B provides more details on how these and other sources of market data are used to characterize the pool of potential patients. 6 Empirical specification In this section we describe some of the assumptions that we make about functional forms and how outcomes and utility may vary with patients’ observable characteristics. 6.1 State variables and transitions There are two types of state variables in the model. First, there are the state variables in , which remain constant within decision periods but may transition between them. Second, there are state variables which are revealed during the stages of treatment but do not carry over between periods. The state variables in the second category, which are the values, , , and , are described fully above so we do not provide additional details here. The state vector contains a diverse group of variables which pertain to a patient’s demographic characteristics, her health, and her family composition as of age . Some elements in are fixed across the entirety of the patient’s decision sequence, while others evolve exogenously, and a final group evolve endogenously due to a patient’s choices. The fixed variables include: the patient’s initial wealth, which we model with zipcode-level data on housing values, and the patient and her partner’s diagnosed fertility problems, which can include endometriosis, tubal issues, and low sperm counts. A patient’s age is part of , and it evolves exogenously as the patient moves through decision periods. The endogenous state variables are: the number of children entering the current period, an indicator for whether the patient has paid full price for IVF during an earlier period, and the number of remaining insured cycles. We observe the patient’s number of children when she first visits the clinic, plus the outcome of any treatment cycles, so the evolution of this variable is clear in the data. Regarding insurance, we observe whether a patient ever uses insurance to pay for treatment. We initialize the number of insured cycles to four (the Illinois mandate value) for all 7 All our policy experiements are assumed to apply equally to all clinics in the area. Therefore, the clinic’s market share, which we compute using CDC reports, is invariant in our counterfactual experiments. 20 patients who ever use insurance, and this number falls by one whenever an insured patient chooses “continue” in the second stage of treatment.8 Most insured patients are from Illinois but not all; likewise most Illinois patients are insured but not all of them. 6.2 Treatment technologies During each treatment stage, a patient makes her choice while considering a probability distribution over outcomes that will be realized at the stage’s conclusion. We now describe the functional forms and data assumptions that describe the distributions. In the first stage, a woman knows some basic facts about her fertility including , and takes drugs to stimulate egg production. While we observe drug dosage, we do not model the choice, so we assume that dosage is selected deterministically based on the patient’s characteristics. The woman’s characteristics and (unmodeled) drug decision aﬀect a stochastic process that determines her Peak E2 score, . We model the probability of a particular with a multinomial logit model for (| ). We assume that the possible realizations of are 0-500, 500-1000, 1000-1500, 15002000, 2000-2500, and over 2500. We include variables for a woman’s age, the average of any AFC scores she receives over the entire treatment history, and her initially diagnosed fertility problems. The age variables we include are indicators for whether the patient’s age is: 28 or under, 29-31, 32-34, 35-37, 38-40, 41-43, or 44+. (We exclude age 35-37 for the empirical implementation.) We separate the patient’s AFC score into categories for scores from 1-5, 6-10, 11-15, 16-25, and 26+, with the highest category excluded for the empirical implementation. For patient fertility problems, we include an indicator for whether the patient has two or more distinct diagnosed issues. We use a multinomial logit model here rather than an ordered one because especially high values of can be seen as bad for the patient. In the second stage, the patient observes her realized value of and considers the number of eggs, , that might be retrieved if she continues treatment. The distribution of depends on and . We use an ordered probit model for this distribution, with possible values of as 0-4, 5-10, 11-20, and 21+. The variables that can aﬀect the realization of are: indicators for possible values of , split as they are in the model for ; the same age categories in ; the AFC score categories from ; and the indicator for whether a patient has one more more documented fertility problems. 8 In practice, the Illinois insurance code is more complicated. When an Illinois resident has a successful treatment cycle (for the first time), her number of remaining insured cycles is automatically set to two. This implies that an Illinois resident can have as few as three or as many as six cycles, depending on when or whether she has a successful cycle. We abstract away from these details in our model. 21 In the third stage, the patient observes her realized value of and selects a fertilization method (). The patient’s number of transferable (cleavage-stage) embryos will depend on , , and the patient’s characteristics. We model the process determining with an ordered probit. We include as regressors: the possible values of as described in the model for ; the patient’s age, AFC score, and fertility problems as described above; and the patient’s choice of plus the interaction of with an indicator for male-factor infertility. In the final stage of treatment, the patient is subject to the stochastic process which determines her number of live births. We model as a multinomial logit, with the probability of each outcome determined by the number of transferred embryos, the patient’s age, and the indicator for female fertility problems. Some patient and treatment characteristics, like AFC score or male factor infertility, are not relevant here because their role in determining outcomes is finished once the patient has her collection of transferable embryos. 6.3 Utility assumptions We must make functional form assumptions for several expressions that are relevant for patients’ utility. In addition to the restriction that all patients have the payoﬀ of = 0 from zero-birth outcomes, we assume that outcomes with 0 provide utility according to: 0} + × 1{ = 2} (|e ) = + × 1{e The vector (1 2 3 ) contains parameters that (respectively) capture the lump-sum payoﬀ from a singleton, twin, and triplet birth to a patient with no prior children (e = 0). Given the health risks and other challenges for triplets, we anticipate that 3 2 and 3 1 , but these parameters are unrestricted in estimation. The parameter captures any diﬀerence in the marginal benefit of a birth to patients with prior children; diminishing marginal utility from children would imply that the is negative. For patients who violate ASRM guidelines, we assume a constant utility penalty ( ) = 0 × 1{ }, where 1{ } is an indicator function that is equal to one when embryos violates ASRM guidelines for a patient with state variables We assume a simple two-type structure for patients’ permanent unobserved heterogeneity. A share of patients (of type = 1) has preferences for birth outcomes represented only by (1 2 3 ), while the remaining share has (with type = 2) has, in addition, its utility payoﬀ shifted by the scalar parameter 0. A patient’s probability of being of type = 2 depends on her state 22 values at the time she initiated treatment, 0 . Along with 0 , the patient’s age when she started treatment, we allow the distribution of to depend on a measure of her wealth level ( defined above), her initial number of insurance-covered cycles (0 ), and a dummy (0 ) for the ASRM guideline regime in place when treatment started. We assume that the probability of high type ( = 2) is Pr( = 2|0 ) = exp(0 + 1 0 + 2 + 3 0 + 4 0 ) 1 + exp(0 + 1 0 + 2 + 3 0 + 4 0 ) During estimation we restrict 0 0 for computational purposes, but this adds no real restrictions on the utility parameters. For notational convenience, let represent the vector of values. As the patient makes her choice between starting treatment and delay, she considers the additional flow benefit ( ) which she receives (or pays) when she begins treatment. In the current specification, is a scalar to be estimated, = 0 . The value of will be identified, in part, by the frequency with which Clinic patients return for additional treatment cycles following their first cycle. The patient’s utility from foregoing treatment takes the simple form (0 ) = The first three stages of IVF treatment include () the disutility from paying a price for some treatment component. We specify () so that it is allowed to vary with a patient’s initial wealth. We assume () = 0 + . Since the eﬀect of price is subtracted from within-stage value functions above, we expect 0 to be positive to be consistent with downward-sloping demand. If wealthier patients are less price sensitive, this will be captured through 0 Finally, we assume that the terminal payoﬀ is a function of the patient’s cumulative payments for treatment. Children born due to treatment are not included here because those benefits are included in . We add the variable as an indicator for whether a patient ever paid full price for a treatment cycle. We assume = which includes the normalization = 0 for patients who have never paid the full price of treatment. There is a total of 16 utility-related parameters to estimate, given the specifications above. Let represent a vector of all of the parameters except and , and define = ( ). We estimate separately from so it is convenient for us to distinguish between the two. 23 7 Estimation 7.1 Treatment technologies We estimate the model in three stages. We estimate the treatment technologies, , , , and in the first stage. These models are easy to estimate using conventional statistics packages. We use the parameter estimates from this stage to calculate predicted values of the technologies for each possible unique value of the state vector. We implicitly assume that we as econometricians have all of the same information on outcome probabilities as the patient and her doctor. Also within this stage we estimate the distribution of ( |0 ) non-parametrically using frequencies of realizations from within the population of women who initiate treatment. In the second stage we estimate the parameters in using data exclusively from the population of 587 patients who are observed within the clinic. The clinic data are stronger than our data on the overall at-risk population, and we want to rely on it alone to estimate the taste parameters ¤ £ in . In the final stage we estimate using our estimates of 1 (0 )|0 together with the market-level data. 7.2 Within-clinic choices Given the predicted treatment technologies, a guess at the value of the structural parameters in ( ) and the distributional assumptions on we are able to calculate the value of [ ( ; )] for each . We perform this calculation by backward induction separately for each type . For each potential state that might be reached in period when the patient is age max , we use ( ) to compute the terminal payoﬀ plus the logit inclusive value for the expected value of optimal behavior in each potential treatment stage. We then move to the second-to-last period and use the final period’s expected utility values as part of a new set of logit inclusive value terms to calculate the expected value of optimal decisions in period − 1. The procedure continues back to the first potential decision period for all possible IVF clinic patients. We then use the calculated values of [ ( ; )] for all and to compute choice probabilities for each observed decision in our data. Conditional on a patient’s type , calculating this probability is a straightforward task due the i.i.d. extreme value assumption for the terms. For example, conditional on a patient reaching at age a stage-2 decision over whether to continue () or cancel () treatment, her probability of cancelling treatment is: 24 Pr(2 = | ; ) = exp[ 2 ( ; )] exp[ 2 ( ; ) + 2 ( ; )] (18) The values of 2 ( ; ) and 2 ( ; ) are relatively simple functions of the the estimated transition and the calculated values of [3 ( 3 )] and [1 (+1 1+1 )] We calculate a probability like this one for each observed decision by each patient, including the implicit choices to delay treatment which occur during periods when the patient does not appear in the data despite starting treatment during some earlier period. A patient’s permanent unobserved type, , aﬀects every period and stage of her decision problem. Let Pr( | ; ) represent the predicted probability that patient took her observed action during stage of period when she was at age if she were of type The patient is observed starting in period 0 and ending in . For periods in which a patient does not reach stage 1, let Pr( | ; ) = 1 for that stage. Conditional on and , the type-specific joint probability of observing patient ’s sequence of choices is: ( ) = Y 4 Y =0 =1 Pr( | ; ) With ’s true type unobserved, the likelihood of observing her choices requires integration over , which is simply () = Pr( = 1|0 ) ( = 1 0) + Pr( = 2|0 ) ( = 2 ) The log-likelihood of observing the choices of all patients in the clinic data is L() = X log[ ()] We estimate by maximizing the value of L(). We compute standard errors following the “outer product of the score” method for only. In computing standard errors we do not account the multiple-step nature of our estimation strategy. 7.3 Treatment initiation To get a sense of how the population that comes into the clinic may diﬀer across multiple counterfactual scenarios, we need a model of treatment initiation. In other words, we need a model 25 that determines who, among the set of potential clinic patients, actually becomes a patient in each environment. Counterfactual scenarios that make IVF treatment more attractive (less expensive, more eﬀective, etc.), will induce more potential patients to initiate treatment. Scenarios that make it more unattractive will draw fewer patients into the clinic. Given the size of the pool of potential patients and an estimate of the joint distribution of their state variables, this model will tell us how many patients initiate treatment and what is the distribution of their observed and unobserved characteristics. Therefore this model will allow us to adjust the number as well as the mix of patients that come to the Clinic under alternative scenarios. We estimate this model in a 3rd step, taking the within-clinic estimates from the second step b = (b b b ) as given. To construct the pool of potential patients we take the following steps. Assuming stationarity and stable cohort sizes, at any given point in time (quarter) there are stl couples in the St. Louis region who have optimal life cycle fertility plans that induce them to pursue their first pregnancy. Therefore, every quarter there is a distribution of age at first (attempted) birth for these women () Some of them will succeed immediately, some will take some more time. If, after 12-months of attempts, the woman does not get pregnant, the couple is diagnosed with clinical infertility. Let (inf |) be an age-specific infertility rate, which increases with age. Together ¡ ¢ () (inf |) tell us the number of women of each age that realize that they are having diﬃculty to conceive. These inf women constitute the risk set (i.e. the set of women who may potentially seek IVF treatment in the St. Louis region). It is the set of potential clinic patients. To make the econometric problem more explicit, we write the value associated with starting a very first cycle as 1 (0 ), where refers to the policy environment in place at that time.9 The index captures elements such as pricing, insurance, technology, regulations, etc. It should then be clear that under alternative environments 0 the value of 1 will change and therefore initiation decisions will be aﬀected. While 1 depends on and all 0 a potential patient knows her type and a subset of the state variables 0 = { 0 0 0 }. She does not know her 3 “biological” state variables but she can form expectations about them conditional on her age using ( |0 ) Therefore, couples actually make treatment initiation decisions based not on 1 but on ¢ £ ¤ X ¢ ¡ ¡ 1 0 ( |0 ) 0 = 1 (0 ) |0 = (19) 9 Note that there is no 1 for this very first cycle. 26 We assume the value of not pursuing IVF is given by = + where is a parameter to be estimated and is an idiosyncratic heterogeneity shifter. explains why women with the same ¡ ¢ 0 make diﬀerent choices with respect to pursuing IVF. One possible interpretation of is that of a sunk utility cost that must be paid to pursue IVF. There is a continuous distribution () of this cost in the population of potential patients and the realizations of are i.i.d. Moreover, we assume ¢ ¡ is independent of infertility problems and everything else in our model, so F | in risk set, 0 = () We assume ∼ so we have () = Λ () = exp() 1+exp() Let be an indicator which is equal to one when a potential patient decides to show up at the clinic (i.e. initiate treatment) and zero otherwise. Then we have ¢ ¢ ¡ ¡ ¢ ¡ Pr = 1|0 = Pr 0 ¢ ¢ ¡ ¡ = Pr 0 + ¢ ¢ ¡ ¡ = Λ 0 − Let = inf (20) be the percentage of potential patients who walk into the Clinic and be- come patients. We estimate so as to match this treatment initiation share. That is, solves ³ ´ ³ ´ = where b ; b is the predicted share of potential patients that become b ; b clinic patients under environment according to the treatment initiation model. To compute the ¡ ¢ empirical initiation share we need to know both, how many patients came into the clinic ¡ ¢ and how many could had come inf . We observe that = 828 new patients showed up and initiated treatment at the clinic during the period 2001-2007.10 But we can only approximate the number of potential patients inf through assumptions. There are multiple clinics in the St Louis area, so we deflate inf to match the market share of the Clinic observed in our data. We provide details of the approximation in Appendix B. Using those assumptions and after the market share deflation, we estimate inf ≈ 2146 and therefore, can be approximated by ≈ 828 = 039 = inf 2146 (21) which means that 39% of the clinic’s potential IVF patients decided to pursue treatment. The remaining 1318 potential patients could be induced to seek IVF treatment through large enough increases in 1 A particular policy or regime change will only induce some of them to seek 10 We use the 587 with complete data in estimation, but have records for 828 patients initiating treatment over this period. 27 treatment. Our estimates of (0 ) and ( |0 ) will determine the observed and unobserved characteristics of those who seek treatment under any alternative environment in our counterfactual experiments. Note that, similar to our clinic patients, the inf potential patients will be heterogenous in terms of 0 and . There is a joint distribution of characteristics 0 for these potential patients given ¡ ¢ by 0 and a distribution of types ( |0 ) If we have these, then we can integrate out the ¢ ¡ probabilities of initiating treatment across the distribution of 0 and . Note that |0 = 1 ¡ ¢ will in general be diﬀerent from |0 . In other words, the distribution of types among potential patients is diﬀerent from that of actual patients within the clinic. Even if is independent of (as we assume), by having diﬀerent preferences for children, the two types will have diﬀerential propensities to initiate treatment, holding everything else (i.e. the 0 ) equal. ¢ ¡ In the previous sections we described how we use to parameterize |0 = 1 as ¢ ¡ Λ 0 + 0 . Then given for any 0 we will know the prevalence of type 2 (and thus type 1) ¢ ¡ ¡ ¢ ¢ ¡ in the clinic data. Then, Λ 0 + 0 along with Λ 0 − for = 1 2 can be used ¡ ¢ to back out |0 the unconditional (on treatment initiation) prevalence of the types for each 0 among potential patients. Appendix A provides details on how we do this. We obtain ⎛ ⎡ 1−Λ(0 +0 ) ⎤⎞−1 ¡ ¢ ⎜ ⎢ Λ( (0 =1)−) ⎥⎟ = 2|0 = ⎝1 + ⎣ ⎦⎠ Λ(0 +0 ) Λ( (0 =2)−) (22) ¡ ¢ ¡ ¢ and = 1|0 = 1 − = 2|0 Note that if both types were to select into the clinic at the same rate (i.e. they did not really had diﬀerent preferences for children), we will have ¢ ¡ ¢ ¡ Λ( ( =1)−) 0 = 1 = 0 = 2 so Λ 0 =2 − = 1 and the distribution of types ( ( 0 ) ) ¢ ¡ ¢ ¡ within the clinic and among potential patients would be the same, = 2|0 = = 2|0 = 1 We also need an estimate of the unconditional distribution of 0 among potential patients ¢ ¡ ¢ ¡ 0 but we only have the within-clinic joint distribution 0 | = 1 and, in general, ¢ ¡ ¢ ¡ ¡ ¢ 0 6= 0 | = 1 So an important issue is how to approximate 0 . Appendix B provides details on this. ¡ ¢ ¡ ¢ Now, having estimates for |0 and 0 allows us to to derive ( ) the model-predicted share of potential patients who walk into the clinic (i.e. the share of potential patients who actually become patients). To obtain (; ) under the status quo ( = ) we 28 ¡ ¢ integrate Pr = 1|0 over the distribution of 0 and among potential patients ³ ´ ´ ³ b ; b = Pr = 1|b = # " ´ ´ ³ ´ X X ³ ³ ¡ ¢ b b Λ 0 b − |0 0 0 (23) We then estimate as the value that solves ´ ³ =0 − b ; b 8 (24) Results 8.1 Technology estimates In this subsection we discuss our estimates of the four treatment stages’ technologies. These technologies are dependent on a patient’s characteristics, and a patient’s knowledge of them is a crucial part of how she solves her personal dynamic optimization problem. Rather than providing parameter estimates for each treatment technology, we use a collection of figures to discuss both model fit and the role each technology plays in the choice process. One of our overall goals is to emphasize the importance of allowing forward-looking dynamic behavior at each treatment stage. During the first treatment stage, the (potential) patient decides whether to start or delay an IVF cycle. She is aware of her full state vector, , which includes her AFC score. At this point in the decision process, she considers her probable peak estradiol score (), which will be revealed in Stage 2 if she starts treatment. In Figure 2 we display probability distributions over for a low AFC score (below 5) and one that is not low. The Figure shows that having an AFC score below 5 substantially shifts to the left the distribution of values of that the patient can expect to realize at the beginning of stage 2. The patient cares about her value of because it aﬀects outcomes in later stages. In Figure 3 we show that the realized value of influences the distribution of the number of eggs that will be successfully retrieved () in stage 3. Indeed, if is low (e.g. in the 500-1000 range) the mode of the distribution of eggs is 6-10 whereas if is relatively high (2000-2500) the mode of the distribution of eggs is 11-20. Moreover, if is high the probability of having a low retrieved egg count (1-5) is almost zero. This strong diﬀerence in outcomes at diﬀerent values of justifies our treatment of as a within-period state variable that is critical to continuation/cancellation decisions in stage 2. 29 In treatment stage 3, a patient chooses her fertilization method (). This choice, interacted with the patient’s state variables, can influence the distribution of available embryos () in stage 4. In Figure 4 we display the distributions of with (2 ) and without (1 ) ICSI for patients with male-factor infertility. The Figure shows that the more technologically advanced fertilization method (ICSI) shifts the distribution to the right, increasing the probability of having 4 or more viable embryos and substantially reducing the probability of having a small count of viable embryos. Once the patient has realized her value of , she chooses number of embryos () to transfer back into the uterus subject to ≤ . In Figure 5 we display evidence on how aﬀects the distribution of births (). Transferring 3 embryos instead of 2 reduces the chance of no birth, but the probabilities of twins and triplets increases. It is important to notice, however, that the probability of having no live births is fairly high regardless of whether 2 or 3 embryos are transferred. Finally, in Figure 6 we explore the eﬀects of age. We focus on patients who transfer = 3 embryos in stage 4. As expected the distribution for older (35) women shifts to the left, noticeably increasing the odds of no live birth. 8.2 Utility parameters Taking as inputs the technology parameters described above, we estimate the model’s structural taste parameters. In Table 3 we display our estimates of (|e ), , and Our estimates of 1 2 and 3 represent payoﬀs from diﬀerent birth outcomes to patients with = 0 and no prior children. These estimates show that patients receive a positive payoﬀ from a singleton or twin birth, with the latter valued slightly more. Triplet births, by contrast, have a negative utility payoﬀ for patients. The estimate of indicates that patients with 1 or 2 prior children have their utility from births shifted downward substantially. For example, for a patient with e 0 and = 0, the estimated implies that the patient would prefer no additional children. The taste shifter , however, is suﬃcient to increase the utility from additional births to be positive for patients with e 0 We estimate that about half of the patient population has this preference type given their values. To interpret the individual parameters, consider the case of patient wealth. The negative coeﬃcient (2 ) on wealth indicates that a high-wealth person selected from the treated population is less likely to have type = 2 than a random low-wealth person. This accords with intuition because we expect that treatment expenses are most likely to discourage low-wealth individuals with relatively small payoﬀs from children. The final utility parameter on Table 2 is the utility shifter from violating ASRM embryo transfer guidelines. We recover a negative value for this parameter, indicating a 30 penalty for deviating from the guidelines. In Table 3 we display the remaining utility parameters. The results indicate that the baseline price disutility is significantly diﬀerent from zero for all patients, but this disutility is smaller for patients in the top portion of the wealth distribution. (Recall that we subtract from patient utility, so a negative coeﬃcient on indicates reduced price sensitivity.) We recover a significantly negative estimate for the start/delay parameter 0 , which plays a large role in determining whether a patient returns for additional treatment cycles after her first. The negative value of 0 may represent the physical or psychological stress in undergoing IVF. Finally, we estimate values of for a patient’s terminal payoﬀ . We find that there is no significant diﬀerence between the utility of patients who have paid out-of-pocket for a treatment and those who have not. Finally, in a third estimation step we recover b0 = −133 This value of ensures that the initiation model generates treatment initiation decisions such that, as estimated from our data, 39% of potential clinic patients indeed choose to become clinic patients and undergo at least one IVF cycle. 8.3 Model fit We conduct two procedures to evaluate model fit. First, we contrast the estimated model’s predicted choice probabilities to those we observe in the data. This provides a straightforward way to examine choice probabilities at the four stages of IVF treatment. Comparisons of the predicted and observed choice probabilities are displayed in Figures 7 − 10. We omit the patient’s initial choice to begin her first cycle at the clinic. All predictions match the data fairly well. Start/delay decisions, which are observed most frequently in the data have the tightest fit. Stage 2 and 3 predicted decisions also follow the data fairly closely but there are noticable diﬀerences in the rate of treatment cancellations (stage 2) and ICSI use (stage 3). Our predicted stage 4 choice succeeds in matching = 2 as the most common choice, followed by = 3. Transfers of 1 and 4 embryos are rare in the data (and model) because of the utility penalty from violating ASRM guidelines and the negative payoﬀ from a triplet birth (in the case of = 4). In a second set of exercises, we evaluate the predicted choice and outcome histories for the population of 587 observed patients. These histories begin with the same state variables () as the patients in the data, but then random draws on medical outcomes and taste shocks determine choices and outcomes over time. We focus on two critical measures of eﬀectiveness and eﬃciency of IVF treatment. First we ask: What proportion of patients eventually succeed in delivering at least 31 one live birth through IVF, regardless of the number of attempted cycles required to do so? We find that 59% of our simulated patient histories include a birth, which is reasonably close to the empirical value of 53% reported on Table 1. Second, we investigate how many cycles an individual patient receives at the clinic. In our simulation, 53% of patients are observed taking a single cycle, 28% undergo two cycles, and 20% receive three or more cycles. These results compare very well to the data, in which we see 54%, 27%, and 19% of patients receive one, two, or three or more cycles, respectively. 9 Counterfactual experiments We conclude by considering a set of counterfactual policy experiments which analyze potential IVF patients’ responses to changes in their decision environment (). Extensive-margin choices are crucial for this analysis, so we employ the full “at risk” population of inf = 2146 potential patients described above. For each patient, we draw age, wealth, insurance, and ASRM regime values that are consistent with the empirical distributions of these values. Along with the distribution of biological state variables (not yet revealed to potential patients), we use the estimated model ´ ³ ´ ³ b b for each simulated patient. The values of 0 b b diﬀer to construct 0 across policy experiments. We then allow patients to elect whether to begin treatment by comparing ´ ³ b b to the population-wide utility parameter and a simulated value for the patient’s 0 taste shock For patients who start treatment, we simulate decision histories in the same way we described above for evaluating model fit. Patients who do not start treatment at 0 exit the model forever. We assume that the inf simulated patients arrive at the fertility decision uniformly over the 2001-07 window during which the 587 observed clinic patients began treatment. As in the data used for estimation, the simulated patients are observed from their initiation decision through 2009. To maintain consistency with our empirical model, we focus on counterfactual outcomes during 2001-09, and we continue to refer to this window as the “sample period.” Across all experiments we hold fixed the clinic’s prices. While substantial changes in the policy environment may prompt the clinic to adjust its prices, we do not oﬀer a model of how new equilibrium prices would be set. We note that during the full sample period the clinic elected to keep its prices fixed at the same level. We report our results in Figures 11-14 and in Table 5. Because the Figures contain results 32 from all experiments collected together, it is worthwhile to introduce them briefly and define terms. First, we calculate histories for inf potential patients under the observed choice environment; the results of this simulation are labeled ‘Baseline.’ The first policy experiment is one which limits patients to a single embryo, and this is identified as ‘Embryo cap’ on the Figures. The second policy experiment examines the impact of an improvement in the eﬃcacy of embryo screening and births; this is labeled ‘Technology shift.’ Finally, we examine the impact of extending Illinois-style insurance to all potential patients in the market. We use the label ‘Universal insurance’ to identify this experiment on the Figures. Before describing the individual policy experiments, we describe some of the results that come from our Baseline scenario, which we denote . Under the observed prices and constraints, we find that 835 of 2146 potential patients (39%) elect to begin treatment. Of the patients who start treatment, 56% have at least one child via IVF during the sample period (22% unconditional on starting ³ ´ b b −(+ ) treatment). For each patient who begins treatment we calculate ∆ = 0 which is a measure of the net utility gain from initiating IVF above the outside option. Patients who elect to forego treatment receive ∆ = 0 We use to obtain a patient-specific dollar-valued surplus measure, ( ) = ∆ . Across all potential patients in the Baseline scenario, the average ( ) = $4 670 from the option to initiate IVF. For patients who elect to start treatment, the average surplus is $12 003 We use the simulated population to calculate price elasticity as well. We inflate all non-zero out-of-pocket prices by 5% and compute the impact on initiated treatments and total patient cycles. This price increase, which aﬀects both insured and uninsured patients, leads to a 2.4% decrease in the number of patients who take one or more IVF cycles, or an elasticity of −048 at the extensive margin. Under the empirical prices, patients receive a total of 1242 cycles, but with the 5% price increase the total falls to 1212. This is again a 2.4% decrease in activity, and therefore implies an overall elasticity of −048. While elasticities above −1 are inconsistent with profit maximization, the clinic may have diﬀerent objectives than a traditional firm. The elasticities we recover are comparable to others from the healthcare literature. 9.1 Embryo transfer restrictions We explore the impact of restricting patients to transferring only a single embryo during treatment; we assign the index to this experiment. To accomplish this we solve the model again at the same estimated parameters but now imposing the restriction ∈ {0 1} instead of 0 ≤ ≤ in stage 33 4 (the embryo transfer stage). We also remove the utility penalty for single-embryo transfers for circumstances when these would violate ASRM guidelines. We then use the new policy functions together with the same history of and medical technology shocks to simulate counterfactual patient histories under the 1-embryo cap. The restriction on embryo transfers entails a large utility penalty for patients considering IVF. Only 367 potential patients choose to begin treatment, therefore the share of inf who begin treatment falls from 39% in the Baseline to just over 17%. (See Figure 11.) The cap has a very large mechanical eﬀect on the distribution of embryos transferred (Figure 12), which in turn yields a substantial shift in the distribution of births (Figure 13). Individual cycles fail to deliver a child in 74% of all treatments. The low birth probabilities of active patients translates into a low success rate for the overall at-risk population. As illustrated on Figure 14, around 4% of inf experience a birth within the sample period. This is due to a combination of frequently-unsuccessful treatments and potential patients avoiding treatment altogether. The Embryo Cap leads to a large reduction in consumer surplus, reported in Table 5. For the overall population, the average ( ) = $974, a reduction of $3700 from the Baseline value. Patients who begin IVF are aﬀected strongly as well, with a surplus of $5 693 on average. In summary, the Embryo Cap achieves its primary goal of reducing multiple births, but this comes at substantial expense in terms of patient surplus and even single-birth outcomes. 9.2 Technology shifts The risk of failure is the central motivation behind patients’ choices to transfer multiple embryos under current IVF technology. In this counterfactual experiment, which we denote by , we explore the impact of an improvement in IVF technology on patient choices and utility. Specifically, we alter IVF stages 3 and 4 to be roughly consistent with new advances in screening embryos for success. The technology shift requires two steps. First, we add a screening process to stage 3’s technology, which generates a number of embryos, ∈ {1 2 3 4+}, for the patient given her number of retrieved eggs (), the selected fertilization method (), and her state variables (). We specify that some number of embryos, , will be identified as “good” while the remaining embryos will have no chance of generating a successful pregnancy. We assume that each embryo has an independent probability, (), of being good, where is a declining function of patient age. Given embryos, the probability (), and the independence assumption, we can use the binomial distribution to calculate the probability of obtaining . To implement this step we 34 must address the possibility that a patient has 4 embryos, which we previously collected into the “4+” category. The primary determinant of a patients’ total number of embryos is her number of retrieved eggs, , which we track through 4 categorial variables. For patients in the = 4+ group with the lowest realized value of , we assume that = 4. Patients in the remaining categories are assigned = 6, 9, or 13 in increasing order of their categories. While we consider 4 in the pre-screening part of stage 3, the final collection of values is again restricted to {1 2 3 4+} Ultimately, we are able to compute a distribution over values as ( | ) = ( | ()) (| ), where is the binomial distribution function. In a final set of assumptions for stage 3, we assign () = 03 for the youngest patients, () = 01 for the oldest, and a uniform rate of decline for age categories in between. For the second step in altering the treatment technology, we adjust stage 4 to reflect the improved success probability for each good embryo. For women with = 0, we assume that each embryo has an independent probability ( ) = 085 of generating a successful pregnancy. Women with = 1 have ( ) = 070 for each embryo. We make use of the binomial distribution again to calculate the probability that a women who transfers ≤ embryos achieves births. Together across stages 3 and 4, the probabilities and generate choice sets that are usually much smaller than the empirical ones (and contain zero good embryos fairly frequently), but patients procede with the understanding that each transferred embryo is very likely to result in a child. Technology improvements have a substantial impact on patients’ choices and welfare, although we do not consider the cost of implementing . 49% of potential patients (1058) now initiate treatment (Figure 11), and single embryo transfers are now more common relative to given the improved prospects for success with a single embryo (Figure 12). (The increase in zero-embryo transfers is due to the increased frequency of = 0 outcomes in stage 3.) The improved technology together along with less aggressive embryo transfer choices lead to a substantial increase in singleton birth outcomes. Twin births are also fairly common also, which is due to the positive utility value patients receive from twin deliveries. Across the full patient population, the share of women with at least one birth increases to over 50%. It is not surprising that the improved technology with constant prices leads to a substantial improvement in patient surplus. The average surplus in the full population, reported in Table 5, increases to $6 942, or about $2 300 greater than the Baseline value. Over the full sample period, this is $4.9M in additional patient surplus in the St. Louis region, which can be adjusted 35 to account for the relative size of the full US market (of which the observed clinic is about 0.4%). This additional potential patient surplus of over a billion dollars can be compared to the likely expenses of scientific research that focuses on improving treatment technology. 9.3 Expanding insurance coverage In our final counterfactual we consider a policy, , which endows all potential patients with 4 insured IVF cycles, as under Illinois’ infertility insurance mandate. In the simulated population only 20% of potential patients have insurance in , so this policy aﬀects a large share of the population. The eﬀective reduction in treatment expense is about 70% for women who gain insurance under . We find that insurance leads to a substantial increase in the share of women who initiate treatment, which is 69% under . The proportional change in treatment in initiation is 77% greater than , which is larger than would be expected from the price elasticity described above. Despite a reduction in the price of treatment, the distribution of embryos transferred is very similar under and (Figure 12). The distribution of births (Figure 13), shows little diﬀerence between and . This suggests that the patients who select treatment have roughly the same fertility characteristics in the two settings. As might be expected, the widespread expansion of insurance leads to many more potential patients experiencing a birth through IVF (about 40%) The consumer surplus benefits of universal insurance are substantial. The average ( ) = $8 658 for the full patient population. The average conditional on treatment is $4,000 greater — a smaller diﬀerence than in the other policy experiments due to the large share of the risk set who start treatment. For the full at-risk population, the diﬀerence in aggregate consumer suplus is just over $8.5M for relative to . To fully account for the net welfare benefit of , we need to calculate the total insurance payments under and . In there are 419 insured cycles and 823 uninsured cycles, implying an insurance cost of $34M (= 581 × $8000) if all patients use ICSI and complete a full cycle In all 2285 cycles are insured, which requires $18.3M in insurance payments when all cycles use ICSI and are executed to completion. Therefore the additional consumer surplus is about $64M less than the additional insurance cost. This diﬀerence is to be expected considering the traditional “moral hazard” incentive of patients to take insured treatment when their willingness to pay is less than the price for uninsured patients. The expansion of insurance coverage, therefore, must be defended through arguments about fairness or equal access. 36 10 Conclusions To be written.... References [1] Bitler, Marianne P. (2008): “Eﬀects of Increased Access to Infertility Treatment on Infant Health Outcomes: Evidence from Twin Births”, mimeo, University of California-Irvine. [2] Bitler, Marianne P. and Schmidt, Lucie (2006), Health Disparities and Infertility: Impacts of State-Level Insurance Mandates", Fertility and Sterility, 85(4), April, pp. 858-65. [3] Bitler, Marianne P. and Schmidt, Lucie (2012), "Utilization of Infertility Treatments: The Eﬀects of Insurance Mandates," Demography 49(1), pp. 124-149 [4] Buckles, Kasey (2012) "Infertility Insurance Mandates and Multiple Births", Health Economics, forthcoming. [5] Bundorf, M.K., Henne, M. and Baker L. (2008). Mandated Health Insurance Benefits and the Utilization and Outcomes of Infertility Treatments. NBER Working Paper #12820. [6] Aron-Dine, A. Einav, L. Finkelstein, A. and Cullen, M. (2012) "Moral hazard in health insurance: How important is forward looking behavior ?", mimeo, Stanford University. [7] Einav, L. Finkelstein, A. and Schrimpf, M. (2010) "Optimal Mandates and the Welfare Cost of Asymmetric Information: Evidence from the U.K. Annuity Market, Econometrica, Vol. 78, No. 3 (May), 1031—1092 [8] Hamilton, B. and McManus, B. (2011), "The Eﬀects of Insurance Mandates on Choices and Outcomes in Infertility Treatment Markets", Health Economics, forthcoming. [9] Henne, M. B. and M. K. Bundorf (2008): “Insurance Mandates and Trends in Infertility Treatments,” Fertility and Sterility 89 (1), 66-73. [10] Jain, T. , Harlow B. L. and Hornstein, M. D. (2002): “Insurance Coverage and Outcomes of In Vitro Fertilization” New England Journal of Medicine 347 (9), 661-666. 37 [11] Rust, J. (1987) "Optimal Replacement of GMC Bus Engines: An Empirical Model of Harold Zurcher", Econometrica, Vol 55, No 5, September, 999-1033 [12] Schmidt, L. (2005): “Infertility Insurance Mandates and Fertility”, American Economic Review, Papers and Proceedings 95 (2), 204-208. [13] Schmidt, L. (2007), “Eﬀects of Infertility Insurance Mandates on Fertility”, Journal of Health Economics 26(3): 431-446. 38 Appendix A: Distribution of Types Among Potential Patients ³ ´ After estimating the model of decision-making within the clinic, we know b and therefore b We also know ¢ ¡ ¢ ¡ =Λ b 0 + b 1 0 Pr = 2|0 = 1,b (25) In addition, from the treatment initiation model we know, for each possible and 0 the initiation rate among potential patients of each type. That is, we know ´ ´ ³ ³ b b − for = 1 2 Λ 0 (26) For each 0 we also know the total (i.e. unconditional on type) number of women with charac¡ ¢ Together with Pr = 1|0 = 1, teristics 0 who came into the clinic. Let this number be N 0 we then have an estimate of the number of patients of type 1 with characteristics 0 who came () where into the clinic, say 0 1 £ ¡ ¢¤ () = × 1 − Pr = 2|0 = 1 0 0 1 (27) Similarly for type 2, we get ¡ ¢ () = × Pr = 2|0 = 1 0 0 2 Note that while 0 (28) ∙ ¸ is just data, () () depend on and is identified by the 0 1 0 2 diﬀerential behavior of the two types in the (within-clinic) patient histories. is estimated in our second step along with ( ) ¢ ¢ ¡ ¡ Given from the initiation model we know that 100×Λ 0 − percent of potential patients with initial non-biological state 0 and type will choose to initiate treatment. We also () patients. Then it must be the case that the number of know that they ended up being 0 potential patients of each type among is given by inf = inf = 0 1 0 2 £ ¡ ¢¤ 1 − Λ 0 + 0 0 1 ¡ ¡ ¢ ¢ = ¡ 0 ¡ ¢ ¢ Λ 0 = 1 − Λ 0 = 1 − ¡ ¢ () Λ 0 + 0 0 2 ¡ ¡ ¢ ¢ = ¡ ¡ 0 ¢ ¢ Λ 0 = 2 − Λ 0 = 2 − () 39 (29) (30) Then we can estimate the unconditional prevalence of type 2 among potential patients with state 0 as ¡ ¢ Pr = 2|0 ≈ inf 0 2 inf 1 0 + inf 2 0 ⎛ ⎡ ⎜ ⎢ = ⎝1 + ⎣ 1−Λ(0 +0 ) Λ( (0 =1)−) Λ(0 +0 ) Λ( (0 =2 )−) ⎤⎞−1 ⎥⎟ ⎦⎠ (31) Note that for given , everything in the RHS is known, so Pr ( = 2| ) is known. ¡ ¢ Appendix B: Approximating inf and 0 To come up with a model-predicted IVF initiation rate among potential patients we must use an ¡ ¢ estimate of 0 . Note that since the expected value of initiation depends on 0 the distri- bution of 0 among clinic patients will diﬀer from that among potential patients. In particular, we expect women who we observe as patients at the clinic to be older, more likely to be covered by ¡ ¢ insurance and wealthier. To approximate 0 among potential patients we use the following assumptions: • Assumption 0 (Exogenous ASRM Guidelines): the particular ASRM guidelines in place are independent of everything else in the model ¢ ¡ asrm ⊥ 0 0 (32) • Assumption 1 (Conditional Independence): conditional on age, the 3 biological state variables related to infertility are independent of insurance and wealth: ⊥ (0 ) | 0 (33) Note that Assumption 1 and the fact that the value of these 3 state variables only becomes observable after deciding to start a first cycle, imply that these variables will have the same conditional (on age) distribution in the risk set and in the clinic ¢ ¡ ¢ ¡ |0 = | 0 = 1 (34) • Assumption 2 (Surprise): among the women attempting their first pregnancy at age 0 finding out about the infertility problem is a complete surprise. Therefore, the joint dis40 tribution of wealth and insurance coverage among women of that age should be independent of whether they have any infertility problem (i.e. independent of whether they are among the potential patients or not). Therefore, Pr (0 |0 ) is the same in and out of the set of potential patients. We further assume that Pr (0 |0 ) = Pr (0 ) for all 0 Using these assumptions we can approximate the joint distribution of all state variables among ¡ ¢ ¡ ¢ ¡ ¢ potential patients as (0 ) = 0 = |0 0 ¡ ¢ First note that by Assumptions 0 and 1 |0 = ( |0 ) = ( |0 = 1) and we can then easily construct an estimate b ( |0 = 1) using patient data. So we only need ¡ ¢ to focus on 0 which is the critical input for the share matching procedure described in Section 7.3. By Assumption 0 ¡ ¢ ¡ ¢ 0 = 0 0 (0 0 ) 0 (35) To estimate 0 0 (0 0 ) = 0 (0 ) 0 (0 ) we rely on Assumption 2 which means that we don’t need to restrict ourselves to the unobservable set of potential patients. Distribution of age among potential patients. We first estimate 0 (0 ) using data from the St. Louis region on (first) births and the maternal age associated with those births. Also because of Assumption 2, this gives us the distribution of age at first attempted birth (regardless of whether the attempt was successful or not). These, along with estimates of infertility rates by age, gives the age distribution for our potential patients. Joint distribution of IVF coverage and wealth. Finally we collect data on the joint distribution of IVF coverage and wealth, ( ). To estimate ( ) we consider ( ) = (| ) ( )and develop a strategy at the zip-code level for estimating (| ) and ( ) using information from zip codes whose center is located within 75 miles from our clinic. To estimate ( ) we assume patients from same zip code are homogenous regarding ( ). In particular, we know whether each zip code in the St. Louis area is considered "wealthy" or not by construction: we defined = 1 if zipcode ’s median home value is above $100,000. This is consistent with the way we are defining a patient to be "wealthy" or not (i.e. whether she comes from a zip code where the median home value is above $100,000. So within a zip code everyone is either wealthy 41 or not wealthy. We can estimate ( ) by Pr ( = 1) = X ∈ { = 1} = X (36) : =1 where is a population weight that measures how important zip code is within the St. Louis region in terms of population. We have the population by age for each zip code so we can construct easily. The results are as follows. We estimate that 39 percent of the potential patients are wealthy. To estimate Pr (|) we take the following steps: we have the % of population who has private insurance for each zip code within the St. Louis area: (priv ). We obtain this from the 2012 American Community Survey (ACS) 5-year estimate. A 2005 Mercer Survey of Employer Health Insurance reported that 19 percent of those with large (500+ employees) employer-provided health insurance have IVF coverage (and 11 percent of those working for small employers do so). We assume the same rates apply to Missouri zip codes. We then use figures from Census’s Business Dynamics Statistics as reported by Moscarini & Postel Vinay (2012) and estimate the employment share of large employers to be 48%11 . Therefore we use the following adjustment factor = 052 × 011 + 048 × 019 = 015 to adjust the raw insurance coverage rates we obtain from ACS. Then the IVF coverage for each Missouri zip code is given by ( ) = (priv ) × Regarding Illinois counties, we know that there is a mandate. But small employers ( 25 employees) and self-insured employers (regardless of size) are excluded.12 According to a Kaiser Family Foundation (2007) report, 55% of workers nationally are covered by plans that are partially or fully self-insured.13 So we adjust the raw county-level employer-sponsored health insurance coverage rate by the % of large employers and the % not self-funded and assume that no firm with less than 25 employees provides IVF coverage. we obtain the following adjustment factor for Illinois counties = (0215 × 0 + 0785 × [045 × 1 + 055 × 019]) = 0435. Then the IVF coverage for each Illinois zip code is given by: IVF (IVF ) = (priv ) × 11 See Table 1 in Moscarini & Postel-Vinay (2012) Under this alternative definition of small employer, we interpolate the numbers in Moscarini adn Postel-Vinay and find that 21.5% of employment is accounted for by firms with less than 25 employees. 13 We assume that in these self-funded plans the same rate found in the Mercer survey (19%) for large employers applies. This is probably an upper bound because large employers here also include firms with 25 to 499 employees, not just those with 500+ as in the Mercer study definition. 12 42 We then compute the aggregate IVF coverage rate for the region conditional on wealth. First, we condition on = 0 and compute Pr ( = 4| = 0) = X IVF (IVF ) : =1 Ã P : =1 ! (37) Regarding coverage conditional on high wealth ( = 1) we take a diﬀerent approach. Since most of the wealthy zip codes are in the Missouri side but is very low relative to if we pool zip codes together in the aggregation we would end up with a spurious negative correlation. Therefore we compute Pr ( = 4| = 1) in the following way. b Pr ( = 4| = 1) = Pr ( = 4| = 0) + ∆ where b = ∆ ÃP : =1∈ P : =1 ! b + ∆ ÃP : =1∈ P : =1 ! b ∆ (38) b gives the estimated average increase in IVF coverage observed for state when one moves and ∆ from poor zip codes to wealthy zip codes within that state. ⎡ b = ⎣ ∆ X : =1∈ ( ) Ã P : =1∈ !⎤ ⎡ ⎦−⎣ X ( ) : =0∈ Ã P : =0∈ !⎤ ⎦ for = IL, MO The results indicate that IVF insurance coverage rate depends of wealth Distribution of IVF Coverage Conditional on Wealth =0 =4 poor 83% 17% wealthy 75% 25% Size of Potential Patient Pool. In addition to the joint distribution of characteristics among potential patients, we need the size of the potential patient pool inf . We count the number of women of each age in the St. Louis region that give birth naturally to a first birth in any given quarter. Let this number be . We get this from Vital Statistics. At any given time then the total number of women who attempt their first pregnancy is comprised of those women who succeed and have a birth whose certificate we see in Vital Statistics and those who fail, realize they have an infertility problem and become part of our set of potential patients. 43 Therefore = + inf Then using infertility rates by age among women who are attempting to get pregnant, inf (inf |) we can back out inf = inf (inf |) [1−inf (inf |)] According to Vital Stats the larger counties in and around the St. Louis region have an average of 28−44 = 1172 first births each quarter distributed among mothers aged 28 to 44. To capture births occurring in the more rural areas, but still within our 75-mile radius area, we also estimate the births occurring in smaller counties within this area. An additional 10.4% of births come from these counties.14 So 75 28−44 = 1172 × 1104 = 1294Using infertility rates by age and summing across ages, we can then determine that there are inf = 198 × 1104 = 219 new potential patients, on average, each quarter.15 Since there are 28 quarters between 2001 and 2007, the size of the potential patient pool inf = 28 × inf = 28 × 219 = 6132 All this was assuming our for our sample period is then 2001−07 clinic to be a monopolist, though. But our clinic only has a market share, s 116 Then we inf for this, and obtain a final estimated pool size of inf = 2146 potential patients. adjust 2001−07 14 Births occuring in smaller counties are combined and reported into a single residual county for each state in Vital Stats. So we know how many first births occured in these "residual" counties. We also know how important (in terms of number of households) the zipcodes belonging to small counties but located within the 75-mile radius are as a share of the each state specific residual county. Therefore we can augment the number of births in the relevant area by assuming that the same share of births comes from these zipcodes. 15 We interpolate between ages 28 to 39 and extrapolate for ages 40-44 the 12-month infertility estimates reported in Dunson et al (2004). 16 Clinic share is computed based on CDC data on the number of cycles conducted at each of the clinics in the St. Louis area. 44 Figure1:IVFtreatmentstages Stage1/ Periodstart Stage2 Stage3 Stage4 Patientlearns diagnoses,AFCcount Delay Start ud–ps+s d+EW1(Za+1) LearnPeakE2 Gotonextpd. Cancel c–pc nc+EW1(Za+1) Gotonextpd. Learn#eggs(r) NoICSI 3,1 ICSI 3,2–pm2 Learnembryos(X) ChoosexX 45 Continue k>0fk(k|x)[U(k)+4EW1(Za+4)] +fk(0|x)EW1(Za+1)+x Gotonextdecisionpd. Figure2:DistributionofPeakE2Probabilities 0 .1 .2 .3 VariationinPeakE2byAFC 0‐500 500‐1000 1000‐1500 1500‐2000 2000‐2500 LowAFC 2500+ HighAFC Figure3:DistributionofRetrievedEggCount 0 .2 .4 .6 VariationinRetrievedEggsbyPeakE2 1‐4 5‐10 11‐20 LowPeakE2 21+ HighPeakE2 46 Figure4:DistributionofEmbryosAvailable 0 .2 .4 .6 .8 EmbryosObtainedbyICSIUse,MaleFactorPatients 0 1 2 NoICSI 3 4+ WithICSI Figure5:DistributionofBirthsbyEmbryosTransferred 0 .2 .4 .6 BirthOutcomesbyEmbryosTransferred,Age34‐36 0 1 2 2Embryos 3 3Embryos 47 Figure6:DistributionofBirthsbyPatientAge(3embryos) 0 .2 .4 .6 BirthOutcomesbyPatientAge 0 1 2 Age<35 3 Age35+ Figure7:PredictedStage1Decisions 0 .2 .4 .6 .8 1 StartorDelayafterInitiation Start Delay Observed Predicted 48 Figure8:PredictedStage2Decisions 0 .2 .4 .6 .8 CancelorContinueTreatment Cancel Continue Observed Predicted Figure9:PredictedStage3Decisions 0 .2 .4 .6 FertilizationMethod NoICSI ICSI Observed Predicted 49 Figure10:PredictedStage4Decisions 0 .1 .2 .3 .4 .5 DistributionofEmbryosTransferred 0 1 2 Observed 3 4 Predicted Figure11:Treatmentinitiationincounterfactualexperiments 0 .2 .4 .6 .8 ShareWhoInitiateTreatment Baseline Embryocap Techshift 50 Univ.insurance Figure12:Embryotransfersincounterfactualexperiments 0 .2 .4 .6 .8 1 DistributionofEmbryosTransferred 0 1 2 Baseline TechShift 3 4 EmbryoCap UnivInsurance Figure13:Birthsincounterfactualexperiments 0 .2 .4 .6 .8 ChildrenBornatEndofCycle 0 1 2 Baseline TechShift EmbryoCap UnivInsurance 51 3 Figure14:Birthsincounterfactualexperiments 0 .1 .2 .3 .4 .5 SharewithChildrenDuringSamplePeriod Baseline Embryocap Techshift Univ.insurance 52 Table1:Patient‐levelCharacteristics Mainsample N=587 First‐stagesample N=1106 Mean Std.dev. Patientageatinitiation 34.30 Insuredatinitiation?(Y=1) Mean Std.dev. 4.02 33.31 4.70 0.54 0.50 0.59 0.49 Wealthyzipcode?(Y=1) 0.82 0.39 0.79 0.41 Priorchildrenatinitiation 0.00 0.00 0.30 0.56 AFCscore 14.37 7.96 14.61 8.13 Femalefertilityproblem?(Y=1) 0.80 0.40 0.69 0.46 Malefertilityproblem?(Y=1) 0.34 0.48 0.30 0.46 Totalcycles 1.75 1.02 1.97 1.21 Birthduringsampleperiod?(Y=1) 0.53 0.50 0.55 0.50 Demographicstatevariables(ZD) Biologicalstatevariables(ZB) Aggregateactionsandoutcomes The“Mainsample”isusedinsecond‐stageestimationofpatients’choices.The“First‐stage sample”isusedtoestimatetreatmenttechnologies. 53 Table2:ActionsandOutcomeswithinTreatment Mainsample First‐stagesample Std. N Mean dev. N Mean Std. dev. Canceltreatment?(Y=1) 1027 0.14 0.35 1859 0.14 0.35 Fertilizationmethod?(ICSI=1) 879 0.60 0.49 1597 0.59 0.49 Numberofembryostransferred 875 2.29 0.81 1592 2.32 0.82 PeakE2score 1027 16.82 9.73 1905 17.19 9.77 Eggsretrieved 879 10.60 5.46 1697 10.87 5.60 Embryosgenerated 881 6.11 3.75 1687 6.34 3.86 4+embryos?(Y=1) 881 0.74 0.44 1687 0.76 0.43 Childrenborn 848 0.51 0.70 1632 0.55 0.75 Singletonbirth?(Y=1) 848 0.27 0.45 1632 0.27 0.45 Twinbirth?(Y=1) 848 0.12 0.32 1632 0.12 0.33 Tripletbirth?(Y=1) 848 0.00 0.00 1632 0.01 0.10 Stage1‐4actions Stage1‐3outcomes Stage4outcomes The“Mainsample”isusedinsecond‐stageestimationofpatients’choices.The“First‐stagesample” isusedtoestimatetreatmenttechnologies. 54 Table3:EstimatedUtilityfromChildren 5.147 Utilityof1birth(u1) Preferenceshifter (0.932) (0.855) 5.967 Utilityof2births(u2) Typedistr.constant(0) (1.690) ‐1.318 (0.556) ‐14.063 Utilityof3births(u3) 9.631 0.044 (4.372) Typedistr.age(1) (0.013) Utilityshiftwhen >0() ‐11.698 (0.955) Typedistr.weath(2) ‐0.861 (0.458) PenaltyforviolatingASRM embryoguidelines ‐3.049 (0.194) Typedistr.insurance(3) Typedistr.ASRMregime(4) ‐0.073 (0.370) 0.442 (0.339) Standarderrorsareinparentheses. Table4:AdditionalUtilityParameters 0.311 Terminalpayoff (0.071) XPrev.payment(p) PricesensitivityXwealth(w) ‐0.125 Start/delayconstant(0) (0.067) (0.098) Pricesensitivityconstant(0) Standarderrorsareinparentheses. 55 0.221 (0.633) 4.917 Table5:CounterfactualSimulationResults Policysetting(g) Ninitiating (of2146) %initiating AverageCS, fullpop.($) AverageCS, clinicpop.($) TotalCS,full pop.($) Baseline 835 38.9% $4,670 $12,003 $10,022,280 Embryocap 367 17.1% $974 $5,693 $2,089,160 Technologyshift 1058 49.3% $6,942 $14,082 $14,898,380 Universalinsurance 1470 68.5% $8,658 $12,640 $18,580,930 56

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