State Investments in Psychiatric Innovation: Investigating Unmeasured State Factors

Abstract

We apply three separate panel data estimation methods to examine the diffusion of technologies at the state-level. These methods include the Hausman-Taylor random effects model, the fixed effects vector decomposition (FEVD), and generalized estimating equations (GEE). We discuss the assumptions required of each and assess the stability of our policy results across the three models for a longitudinal study of the diffusion of newer psychotropic technologies. We find a reasonable level of consistency among marginal effects for time varying independent variables between our three estimation methods but some discrepancy in the estimated measure of precision in our empirical application. We find a number of policy conclusions are quite stable across estimation methods and may be of interest to state-level mental health policy decision makers.

1 Introduction

Longitudinal analyses frequently use fixed effects to control for unmeasured time-invariant unit or group components when these unobserved group effects have the potential to be correlated with included explanatory variables¹. In health services research, these components could be unmeasured state factors associated with a policy change or utilization measure, facility-specific characteristics that are unobserved by the researcher but not expected to change over time, or even unique effects for individual persons followed over time. It is well known that fixed effect models absorb the effect of observable time-invariant variables as well as unobserved time-invariant effects, rendering the analyst unable to explicitly model the effect of an explanatory variable with only between and no within variation (or time invariant). Recent developments in the applied policy analysis literature have focused attention on methods that allow both unobserved group effects and estimation of observed time-invariant effects under a variety of assumptions. The fixed effects vector decomposition (FEVD) method (Plümper, Troeger 2007) in particular, has experienced a remarkable rate of diffusion in the applied policy literature; this method is not without its skeptics, however (Greene 2011; Breusch et al. 2011).

In this manuscript, we examine the diffusion of technologies, an issue of interest in health services literature. We apply three separate estimation methods: FEVD, the Hausman-Taylor random effects model (HT), as well as generalized estimating equations (GEE). We discuss the assumptions required of each and assess the stability of our policy results across the three methods for a longitudinal study of the diffusion of newer psychotropic technologies in Medicaid programs nationwide. Our results indicate a reasonable level of consistency among estimated marginal effects for time-varying independent variables among our three estimation methods. While HT and GEE are surprisingly similar in their standard error estimates across many rarely changing and time invariant variables despite fairly vast differences in assumptions, the FEVD estimation method results in large standard error estimates for rarely changing variables. In terms of policy results, we confirm previous findings that mental health carve-outs are positively associated with psychotropic medication use across states. Additionally we find that increasing Medicaid capitation is associated with spillovers in psychotropic prescribing, with results varying by drug class. Lastly we find that several state-specific factors, including higher levels of education, urbanization and unionization are generally positively associated with prescriptions for psychotropic medications across states. These results have a number of implications for longitudinal policy analysis.

We begin by providing some background information on the diffusion of psychotropic innovations in order to motivate our research question of interest: Are state-specific characteristics associated with faster diffusion of new innovations in mental health? We provide an overview of empirical studies in diffusion of technology and organize state characteristics broadly into four categories: economic factors, political factors, sociological factors, and health system characteristics to motivate the selection of specific state factors in the diffusion models. We next review the potential estimators available for longitudinal analysis of a continuous dependent variable. We then describe the selected estimation techniques and their underlying assumptions. Finally, we describe our results and provide some conclusions, both in terms of the selected estimation technique as well as the policy findings.

2 Background

2.1 Diffusion of Innovations in Psychiatry

The diffusion of newer psychotropic medications such as second generation antipsychotics and selective serotonin reuptake inhibitor (SSRI) antidepressants occurred relatively rapidly in the decades since the early 1990s, although considerable variation across states and subpopulations in the level of use has been noted (Banthin, Miller 2006; Chen et al. 2008; Kelton et al. 2008; Law et al. 2008; Rawal et al. 2004). Some state policies, such as mental health carve-outs, are reported to have had varying effects on psychotropic medication use (Huskamp 1999, 1998; Ling et al. 2008; Domino 2012), but it is unclear what additional underlying differences across states may predict psychotropic medication use. For example, health policies such as the use of capitated managed care may have direct effects on the use of newer, more costly medications through the direct financial incentives in treatment provision, whereas other state policies such as prioritizing investment in secondary education may indirectly affect the diffusion of novel classes of antidepressants and antipsychotics by changing population preferences for the public provision of health care.

Differences in the use of medical technologies have immediate implications for the quality of care received and subsequent health outcomes. Greater aggregate psychotropic medication use has been shown to be correlated with greater treated prevalence (Frank, Glied 2006; Domino, Swartz 2008). The use of guideline-level care for mental health conditions such as a depression or schizophrenia has been associated with improvements in health (Qaseem et al. 2008). However, unlike the technologies examined previously, the newer psychotropic medications may not have clearly defined advantages over the older classes of medication (Lieberman et al. 2005; Gartlehner et al. 2011). In addition, psychotropic medications are used frequently off-label, which by definition has ambiguous advantages (Maher et al. 2011; Radley et al. 2006). These issues are described in further detail below.

We use nationwide data on psychotropic medication use in fee-for-service state Medicaid programs from 1991 – 2005 to examine the influence of state-specific factors on the diffusion of novel classes of psychotropic medication. This time period is shortly after new entrants in both antidepressant (SSRIs) and antipsychotic (second generation antipsychotics, or atypicals) medications appeared on the market, but before the introduction of Medicare Part D. Both medication classes represented anticipated improvements over the older classes of medication for approved indications. These improvements were generally in terms of more desirable side effect profiles rather than increased efficacy in treating primary symptoms, although this has come into question for the atypical antipsychotics in recent years (Lieberman et al. 2005). We use three empirical techniques to examine the influence of both time varying state characteristics as well as time invariant or rarely-changing characteristics (also referred to as “sluggish” variables in Clark and Linzer, 2013) while controlling for unobserved state-specific factors. Our focus is on state policies that are potentially associated with access to psychotropic medications. Policy results contribute to the knowledge base for building a high-performance mental health system.

3 State-level diffusion of technologies

There is by now a large literature in the diffusion of technologies, some taking a micro or sociological approach by examining factors correlated with specific individuals or organizations who are innovators or “opinion leaders” in their fields, while other studies take a more macro or economics view by examining the factors or barriers associated with greater use of technology. Our study takes the latter approach. In particular, we examine economic factors, political factors, sociological factors, and health system characteristics of states in order to understand which factors are present to a disproportionate degree in states with higher rates of technology adoption. The pathways through which these characteristics affect the use of technologies is complex and our reduced-form approach will not determine the method through which each of these variables affects innovative behavior. Preferences for technology use in Medicaid recipients may not reflect state-level preferences for technology adoption generally, but do shed light on population preferences for adopting innovation among a vulnerable group of individuals, who may have a greater benefit from the adoption of new technologies than other residents because of greater health care needs. Recent work by Skinner and Staiger (2007) examined the influence of state characteristics such as education and income on the uptake of a variety of new practices or innovations. They found that high school graduation rates were highly correlated with rates of diffusion, while state per capita income, a measure of total wealth, lacked correlation with innovation. Their work builds on the classic study by Griliches (1960) which found considerable state-level variation in the diffusion of hybrid corn. Variation across states in the use of policy levers occurs because of underlying differences in resources and preferences by state residents (Skinner, Staiger 2007). Very little is known about the state factors that affect the use of psychotropic medicine in particular and whether the promoters of changes in psychotropic prescribing practices are similar to diffusion of new practices in other medical and non-medical areas. This paper extends the work of Skinner and Staiger (2007) and previous state innovation literature into the area of psychiatric innovation, as measured by the rate of diffusion of new prescribing practices in psychotropic medications.

The list of relevant state characteristics associated with the variation in Medicaid psychotropic prescribing practices is potentially long; therefore we focus on economic, sociological, political and health system characteristics.. Economic characteristics include population income and unemployment. States with greater population wealth, controlling for other factors, may be able to provide better care through the Medicaid program to individuals with mental illnesses. Lower unemployment has also been linked to better health (Ruhm 2000). States with greater wealth, however, may be more focused on concerns of the middle-class, such as higher education and transportation infrastructure, such as roads or highways and thus state wealth may actually have negative effects on programs such as Medicaid, which target the poor and disabled. The net effect wealth is therefore ambiguous and may vary by psychotropic class (e.g., treatments for depression or schizophrenia). Sociological characteristics include education, urbanicity, and union membership. States with more educated residents may have different preferences regarding the provision of health care. States may experience greater diffusion of innovation as a result of better-educated agents of change, such as prescribing MDs or even policy makers, or from demands of a more educated populace. This preference for newer technologies could occur directly though the demand of educated persons for their own health care and trickle down to other patients, such as those on Medicaid, through changes in provider behavior or information, or could occur if more educated people demand greater investments in programs such as Medicaid. Political factors include the size of state government, the percent of state government expenditures devoted to health care, and the ideology of government officials and citizens. More liberal political ideology is hypothesized to be related to investments in Medicaid and other social programs, both in terms of great participation rates and the quality of tools used to manage utilization. Clearly some of these factors span categories; education is a prime example which loaded with social capital in Skinner and Staiger’s (2007) factor analysis.

Finally health system characteristics such as the use of capitation or mental health carve-outs are arguably under state control and can be thought of as state investments in health care that could reasonably affect states’ use of psychotropic medication. Mental health carve-outs help concentrate psychiatric care among participating providers, thus making behavioral health expenditures more predictable and possibly increasing access to less costly outpatient care (Frank et al. 1996; Norton et al. 1999, 1997; Grazier, Eselius 1999; Grazier 1999; Huskamp 1999; Busch et al. 2004). Other factors such as the supply of providers and the Federal Medicaid match rate influence the composition of the health sector.

4 Methods

4.1 Analytic Models

We use three different econometric models to examine the diffusion of psychotropic medications. We examine diffusion both as the number of units of medications (described below) sold in each time period and also as the percent of the market accounted for by newer classes. Each statistical approach has its own assumptions, benefits and limitations, which are summarized in Table 1. We draw on lessons learned across models to improve the robustness of the results in the Discussion section.

Table 1.

A comparison of model assumptions for longitudinal data

Estimator	Assumption about unmeasured group effects	Assumption about correlation between Xs and group effect Ui (endogeneity)	Assumption about correlation between Zs and group effect Ui	Assumptions specific to estimated diffusion model
Hausman-Taylor Random Effects (HT)	Heterogeneous, not estimated	At least some Xs or Zs are correlated with group effect; specified a priori	At least some Xs or Zs are correlated with group effect; specified a priori	State innovation, potentially correlated with at least some variables in the model, specified a priori
Fixed-Effect Vector Decomposition (FEVD)	Heterogeneous, estimated	At least some Xs correlated with group effect.	Consistent if none correlated with group effect	State innovation, potentially correlated with any of the time varying variables but not correlated with the time invariant variables.
Pooled OLS or GEE	Homogenous (no group effect estimated)	NA	NA	No state innovation factor estimated. OLS rejected a priori.
Related models not used in the analysis
Random Effect Models	Heterogeneous, normally distributed, integrated out (not directly estimated)	None endogenous	None endogenous	State innovation not correlated with any included variable. This assumption is likely problematic for current application.
Fixed Effect models	Heterogeneous, estimated but includes effects of time invariant variables	No assumption required	No assumption required	State innovation estimated and potentially correlated with included variables; estimated state innovation includes the effect of time-invariant variables (not estimated); Interest in effects of time-invariant variables makes fixed effect models potentially problematic.

The Hausman-Taylor (HT) and fixed-effects vector decomposition (FEVD) models (Plümper, Troeger 2007, 2011) explicitly model unobserved heterogeneity. In our application, this heterogeneity consists of unobserved state-specific factors that affect the diffusion of newer psychotropic medications in state Medicaid programs (Table 1). The Hausman-Taylor estimator implements a random effects model using exogenous variables as instruments for the unit (state) effects. These models have the advantage of including time invariant variables (which standard fixed effects models do not) and relax the assumption of a standard random effects model that the unit specific effects are not correlated with the time invariant variables.

We next compare HT models to fixed-effects vector decomposition (FEVD) models (Plümper, Troeger 2007, 2011). These models run standard fixed effects, which estimate unit-specific time-invariant heterogeneity through a set of fixed, or indicator variables. The original FEVD (P&T 2007) process relied on a three-step estimation sequence, where a standard fixed effect model was estimated in the first step, the fixed effects were decomposed into deterministic components as a function of time-invariant and rarely changing variables and the remaining stochastic effect. A third and final stage then regressed the original dependent variable on the time variant, rarely-changing, and time invariant measures and the residual from the second stage regression. This residual reflects the portion of the state fixed effects not accounted for by the observed time invariant and rarely-changing measures, in place of the traditional fixed effects. As noted by Breusch and colleagues (2011), the recent version of FEVD seems to rely only on the first two steps, which are the core of the estimated effects. In our analysis, we use standard errors estimated by the fevd4.0 beta version of the authors’ Stata ado file (Plümper, Troeger 2011), which has been examined by Beck (2011). We note that Clark and Linzer (2013) indicate that with data such as ours, with correlated unit effects and relatively large numbers of units and observations within units, fixed effect models are strongly preferred over random effect models. We follow Plumper and Troeger’s (2007) suggestion to classify variables as largely time invariant according to whether the ratio of the between variance to the within variance is 2.8 or more, but revisit this threshold in sensitivity analyses.

The FEVD is not without its detractors and has been referred to as a specific form of instrumental variables estimation (Greene 2011; Breusch et al. 2011). Both HT and FEVD models rely on the assumption that the unobserved group effects are uncorrelated with at least some of the time invariant variables. In our application, that translates to the assumption that the residual state innovation factors are not correlated with the time invariant variables in the model (Table 1). iIt is important to note that in the case of the FEVD, the unobserved heterogeneity is not synonymous with the fixed effect; but rather is a result of its decomposition into its deterministic and stochastic components. Plümper and Troeger (2011) run a series of Monte Carlo simulations examining the reliability of FEVD in comparison to a shrinkage estimator proposed by Breusch et al. (2011) which combines elements of HT and FEVD. Plümper and Troeger (2011) find largely similar results between the two estimators over 80% of the time, with slightly greater reliability of FEVD, in terms of lower RMSE, than the shrinkage estimator if both time invariant and time varying variables are correlated with the individual unit effects. We therefore use only the FEVD and not the shrinkage estimator, although future research may consider the inclusion of this method as well.

Breusch and colleagues (2011) show that the FEVD is the same as an instrumental variables approach, with the time-invariant variables serving as instruments. Accordingly, the FEVD estimates are inconsistent if any of the time-invariant variables are correlated with the state-specific effects. If all the time varying explanatory variables are endogenous in the sense of being correlated with the unobserved state-specific effect and all time invariant characteristics are exogenous, then the FEVD and HT estimators are equivalent (Breusch et al. 2011). However, Breusch and colleagues (2011) illustrate that both fixed effects models and FEVD are inefficient if any of the time varying variables are exogenous; the HT estimator is more efficient in these cases. Further, Breusch and colleagues (2011) show that neither FEVD nor HT are universally preferred if the loss function is modeled using a standard mean-square error approach.

Finally, both of these models were compared to results from generalized estimating equations (GEE). Unlike either HT or FEVD, GEE models assume no unobserved state-specific effect (Table 1) and thus rely only on observable state characteristics for estimation. While the assumption of no unobserved heterogeneity is counter to our operational framework, GEE models incorporate the error dependence of the repeated state-quarter observations during the estimation process and therefore may be well suited to the long panel used here. For time varying variables, we also include the within-group variable means to better control for between variation (Palta, Seplaki 2002).

4.2 Sensitivity analysis

Since the distinction between time-varying and rarely-changing variables is based on a somewhat arbitrary threshold of between- to within- variation in these variables in the sample, but affects which variables are included in the second stage regression, we also examined the sensitivity of the model to alternative definitions of rarely changing. Specifically, we used a threshold of ≥5.0 for allowing variables to be defined as rarely changing, in contrast to the original threshold of ≥2.8.

5 Data

5.1 Dependent variable

Dependent variables reflect the quarterly use of psychotropic medication paid for on a fee-for-service (FFS) basis in state Medicaid programs. We examine four measures of psychotropic medication use: (1) antidepressant units (described below), (2) antipsychotic medication units, (3) the percent of antidepressants from the SSRI class, and (4) the percent of antipsychotics from the atypical class. The first two measures indicate the amount of each class of medication used by persons on Medicaid in each state, whereas the latter two measures indicate the percent of medication use that is concentrated in the use of newer psychotropic classes. These latter measures may reflect quality if newer medications have greater efficacy or preferential side effect profiles than older medications, or at a minimum, it may reflect the notion of diffusion of new practices. Data on medication use in FFS Medicaid programs are available from the Center for Medicare and Medicaid Services quarterly for the period from 1991 to the present. We limit the sample period through the end of 2005 because the implementation of Medicare Part D in January 2006 may have affected the level and composition of Medicaid medication use.

Medications were identified from National Drug Codes and/or drug names. We translated the reported number of medication units (e.g., pills) from the CMS data into their defined daily dose (DDD) equivalents using the ATC/DDD system developed by the World Health Organization (World Health Organization Collaborating Center for Drug Statistics Methodology 2006). One DDD is defined as the minimum recommended amount of a medication an individual would take on a maintenance basis: 50 DDDs indicate the amount of medication that a typical individual would use for 50 days or 50 individuals for one day. We use standardized dosing as indicated by the WHO in the year the medications were prescribed. For a small number of medications, WHO changed their standardized dosing system during the study period and we used the dosing information which would have been available to providers at the time of prescriptions². Individual user characteristics are unavailable in this aggregated data, so, the DDD conversion may be inappropriate in instances of use for children, elderly, off-label indications, and initiating (as opposed to maintenance) prescriptions. We prefer the DDD measure over other units such as prescriptions or sales for two reasons. First, prescription lengths are not standardized across state Medicaid programs and may vary even within states (Domino et al. 2009). The variation in prescription lengths may be one tool that states use to control medication use, as explained above, and therefore the number of prescriptions may be higher in states with shorter days’ supply, ceteris paribus. Second, sales, as measured by dollars spent by Medicaid prior to rebates disproportionately weigh prescriptions of newer medications, which tend to cost more per daily dose. We therefore rely on DDDs to measure prescription drug use across drug products within psychotropic categories. Over the study period, the average state used 4.5 million antidepressant DDDs and 2.7 million antipsychotic DDDs per quarter (Table 2). SSRIs accounted for an average of 59.8% of the antidepressant market while atypical antipsychotics accounted for an average of 49% of the antipsychotic market.

Table 2.

Variable means and between/within ratio for state characteristics

Variable	Mean / Percent	Between / Within variation
Dependent variables (in thousands of DDDs per quarter)
Antidepressant DDDs	4,523.9
Antipsychotic DDDs	2,726.6
SSRIS as a Percent of antidepressant DDDs	59.8 %
Atypicals as a Percent of antipsychotic DDDs	49.1
State characteristics – time variant
The percent of the state’s general fund devoted to Medicaid	13.1	2.6
Medicaid mental health carve-out	0.25	1.7
Unemployment rate	5.1	0.9
Percent of Medicaid enrollees under capitated plans	22.9	1.2
Total state expenditures per capita (2005 dollars)	3936.1	2.7
State characteristics – rarely changing
Federal Medicaid matching rate	60.6	15.5
Medicaid FFS population (in thousands)	528.4	3.1
Median income (thousands of $2005 dollars)	44.0	3.5
Percent of the population living under 100% of the federal poverty level (FPL)	12.4	3.3
Percent of the population living under 200% of the federal poverty level (FPL)	31.5	4.1
Physician supply (partially imputed; in thousands)	2.4	4.3
State characteristics – time invariant
Percent of population graduated high school (1990)	76.3
Percent of population with bachelor’s degree (1990)	19.8
Percent urbanized (1990)	51.8
Percent unionized (1990)	15.1
Citizen ideology measure (1990)	48.7
Government ideology measure (1990)	53.1
Putnam’s Social Capital index (2000), excludes AK, HI (x100)	2.8

5.2 State characteristics

State-level variable means and the between/within ratio for independent variables are provided in Table 2. Time varying measures include the percent of all state Medicaid expenditures paid for by the Federal government, total state expenditures per capita; two measures of state Medicaid policies that changed over the study period: the use of mental health carve-outs and the use of capitation in Medicaid, and the annual state unemployment rate. While drugs for individuals in capitated Medicaid programs are not included in the dependent variables, the percent of the Medicaid enrollees in capitated programs is included as an additional covariate to reflect changes in prescribing practices due to managed care that may have spilled over to FFS Medicaid patients (Baker 1999; Domino 2012), with a stronger “signal” from managed care expected in states/years that have a higher level of capitation. It should be noted that there is not a strong evidence base for the greater cost-effectiveness of newer psychotropic medications; their costs are higher and they have not been found to deter other types of medical or psychiatric use (Duggan 2005; Rosenheck et al. 2006) to compensate for these greater costs. We therefore might not necessarily expect greater use of newer medications to be desirable to capitated plans, since the overall health care costs are not expected to decrease.

Variables with a higher between to within variation are classified as rarely-changing and include measures of state wealth (median per capita income, and the percent of the population living under 100% and separately 200% of the Federal Poverty level (FPL)), the size of the Medicaid fee-for-service population, the Federal Medicaid matching rate, and the physician supply per capita.

Finally, we use a set of time-invariant variables from immediately prior to our study period in our analyses, largely to reduce the endogeneity bias. These variables include two measures of population education from 1990: the percent of state residents that have a high school diploma (or higher) and the percent of state residents that have a bachelor’s degree (or higher)³. We similarly control for the percent of the population who belonged to a labor union in 1990, the percent of the state that was urbanized in 1990, and two measures of political ideology (citizens and governmental institutions)(Berry et al. 1998). Both of the later measures reflect the degree of liberalism, such that states with more liberal citizens and government representatives have higher scores. The correlation between these two measures is fairly high (0.77), as one might expect. We can make the heroic assumption that these latter two measures are exogenous to the unmeasured state innovation variable, but will revisit this when we discuss the results.

6 Results

Coefficient and standard error estimates from all three estimation approaches are reported in Tables 3–4; because all three estimators are linear models these estimates represent the marginal effects for each estimator. In general, we find that coefficient estimates on time-varying variables are remarkably similar across all three approaches, but standard errors are considerably higher from FEVD models than in either of the other two models. Estimates on rarely-changing and time invariant variables are quite similar between HT and GEE but exhibit somewhat more variation in coefficient estimates between FEVD and either HT or GEE; FEVD are generally more conservative. Standard error estimates are again considerably larger in FEVD models than in HT or GEE models for rarely changing variables, but are smaller than either alternative for time-invariant variables.

Table 3.

Estimated Marginal Effect of state characteristics on levels of psychotropic use: a comparison of longitudinal methods

	Antidepressant DDDs (thousands)			Antipsychotic DDDs (thousands)
	Hausman-Taylor estimates	FEVD estimates	GEE estimates	Hausman-Taylor estimates	FEVD estimates	GEE estimates
Time Varying Measures
Percent of state’s general fund given to Medicaid	37.87* (19.63)	36.08 (43.13)	35.07* (19.81)	−17.19 (11.14)	−18.32 (24.39)	−18.90* (10.88)
Total state government expenditures per capita	−0.592*** (0.094)	−0.59*** (0.14)	−0.592*** (0.095)	−0.428*** (0.054)	−0.430*** (0.080)	−0.430*** (0.053)
Medicaid mental health carve-out	2294.38*** (202.74)	2185.28*** (462.29)	2262.71*** (204.42)	1166.00*** (115.21)	1107.53*** (235.36)	1151.39** (112.43)
Percent in capitated managed care	−8.16** (4.08)	−9.62 (8.23)	−7.38* (4.09)	7.74*** (2.31)	6.92 (4.39)	8.18*** (2.25)
Unemployment rate	−64.54 (80.40)	−51.97 (245.77)	−80.38 (81.01)	−103.60** (45.62)	−95.45 (128.88)	−111.17** (44.50)
Rarely changing variables
Physician supply per capita	−2360.66*** (357.07)	28.37 (1114.19)	−2342.42*** (358.19)	−1187.80*** (202.19)	118.89 (560.16)	−1178.00*** (196.34)
Federal Medicaid matching rate	−138.36*** (36.00)	−123.31* (67.15)	−144.42*** (36.06)	−60.06*** (20.26)	−62.03 (33.86)	−62.26*** (19.72)
Medicaid FFS population (1000s)	−4.32*** (0.30)	3.54*** (0.61)	−4.28*** (0.30)	0.20 (0.17)	4.12*** (0.30)	0.20 (0.17)
Median income (1000s)	−104.51*** (30.63)	−103.45 (101.97)	−104.93*** (30.75)	−52.99*** (17.43)	35.12 (51.24)	−53.43*** (16.92)
Percent of the population < 100% FPL	−195.45*** (43.34)	−132.92 (138.41)	−195.31* (43.51)	−81.41*** (24.65)	−124.12* (71.08)	−88.36*** (23.91)
Percent of the population < 200% FPL	127.32*** (35.46)	103.09 (108.07)	126.55*** (35.64)	74.81*** (20.13)	129.02** (53.57)	74.02*** (19.57)
Time Invariant Variables
Percent of population graduated from high school in 1990	−824.17*** (226.11)	−130.38 (108.08)	−767.62*** (200.27)	−401.70*** (112.86)	−89.50* (54.18)	−353.23*** (107.95)
Percent of population graduated college in 1990	586.38 (377.01)	−37.72 (201.88)	614.12** (300.24)	435.87*** (188.28)	73.56 (101.49)	398.15** (161.86)
Percent urban (1990)	10684.48** (4934.51)	1442.38 (2399.02)	7191.14 (4678.28)	4294.84* (2468.64)	−1168.66 (1218.75)	4622.26* (2522.08)
Percent union membership (1990)	399.98* (212.41)	127.00 (91.06)	305.66* (176.62)	299.64*** (105.92)	151.93*** (45.61)	239.98** (95.19)
Citizenship ideology (1990)	36.06 (111.79)	18.33 (54.40)	42.36 (90.26)	10.65 (55.76)	8.74 (26.96)	24.80 (48.65)
Government ideology (1990)	−52.17 (62.29)	19.77 (25.91)	−41.84 (50.23)	−42.97 (31.04)	−9.50 (12.77)	−35.62 (27.07)
State fixed effects	No	Yes	No	No	Yes	No
Quarterly indicator variables	Yes	Yes	Yes	Yes	Yes	Yes
N	2729	2729	2729	2727	2727	2727

^***p<0.01;

^**p<0.05;

^*p<0.10.

Estimated standard errors are in parentheses. All models control for nationwide non-linear time trends through the use of quarterly indicator variables. GEE models also control for state-specific means of time varying variables (not reported).

Table 4.

Effect of state characteristics on market share of new psychotropic classes: a comparison of longitudinal methods

	SSRIS as a percent of all antidepressant DDDs			Atypicals as a Percent of all Antipsychotic DDDs
	Hausman-Taylor estimates	FEVD estimates	GEE estimates	Hausman-Taylor estimates	FEVD estimates	GEE estimates
Time Varying Measures
Percent of state’s general fund given to Medicaid	0.00058 (0.00036)	0.00066 (0.00063)	0.00067* (0.00037)	−0.00190*** (0.00044)	−0.00201** (0.00081)	−0.00189*** (0.00045)
Total state government expenditures per capita	2.36e-06 (1.73e-06)	1.49e-06 (2.23e-06)	1.84e-06 (1.80e-06)	−5.07e-06** (2.10e-06)	−6.82e-06** (2.78e-06)	−6.32e-06*** (2.18e-06)
Medicaid mental health carve-out	−0.0015 (0.0038)	−0.0038 (0.0062)	−0.0024 (0.0038)	0.0034 (0.0046)	0.0061 (0.0073)	0.0041 (0.0046)
Percent in capitated managed care	−0.000373*** (0.000077)	−0.00038*** (0.00012)	−0.000352*** (0.000076)	0.000555*** (0.000092)	0.00063*** (0.00014)	0.000538*** (0.000092)
Unemployment rate	−0.0087*** (0.0015)	−0.0096*** (0.0033)	−0.0095***\ (0.0015)	−0.0012 (0.0018)	−0.0031 (0.0039)	−0.0013 (0.0018)
Rarely changing variables
Physician supply per capita	−0.0077 (0.0066)	−0.005 (0.013)	−0.0052 (0.0065)	−0.0494*** (0.0080)	−0.024 (0.016)	−0.0456*** (0.0078)
Federal Medicaid matching rate	−0.00092 (0.00061)	0.00104 (0.00083)	−0.00107* (0.00060)	−0.00472*** (0.00075)	−0.0022** (0.0010)	−0.00418*** (0.00072)
Medicaid FFS population (1000s)	−5.03e-05*** (5.23e-06)	−2.94e-05*** (7.50e-06)	−5.17e-05*** (5.13e-06)	2.44e-05*** (6.36e-06)	−8.37e-06 (8.81e-06)	2.05e-05*** (6.17e-06)
Median income (1000s)	−0.00240*** (0.00058)	−0.0025* (0.0012)	−0.00256*** (0.00057)	−0.00212*** (0.00070)	−0.0010 (0.0015)	−0.00227*** (0.00069)
Percent of population < 100% FPL	−0.00138* (0.00082)	0.0010 (0.0018)	− 0.00126 (0.00082)	0.0002 (0.0010)	0.0049** (0.0021)	0.00036 (0.00098)
Percent of population < 200% FPL	−0.00224*** (0.00067)	−0.0021 (0.0014)	−0.00248 *** (0.00066)	−0.00138* (0.00081)	−0.0018 (0.0015)	−0.00159** (0.00080)
Time Invariant Variables
Percent of population graduated from high school in 1990	0.0002 (0.0017)	0.0030** (0.0013)	0.0019 (0.0015)	0.0036* (0.0021)	0.0037** (0.0016)	0.0045** (0.0018)
Percent of population graduated college in 1990	−0.0005 (0.0029)	−0.0001 (0.0025)	−0.0015 (0.0024)	0.0004 (0.0035)	0.0009 (0.0029)	−0.0010 (0.0028)
Percent urban (1990)	0.105*** (0.039)	0.122*** (0.030)	0.110*** (0.036)	−0.237*** (0.047)	−0.165*** (0.036)	−0.196*** (0.043)
Percent union membership (1990)	0.0004 (0.0015)	0.0003 (0.0011)	−0.0007 (0.0013)	−0.0024 (0.0020)	−0.0004 (0.0013)	−0.0039** (0.0016)
Citizenship ideology (1990)	0.00062 (0.00084)	0.00062 (0.00066)	0.00104 (0.00068)	0.0026** (0.0010)	0.00186** (0.00077)	0.00290*** (0.00081)
Government ideology (1990)	−0.00044 (0.00046)	−0.00012 (0.00031)	0.00037 (0.00037)	−0.00016 (0.00056)	−0.00040 (0.00037)	−0.00045 (0.00044)
State fixed effects	No	Yes	No	No	Yes	No
Quarterly indicator variables	Yes	Yes	Yes	Yes	Yes	Yes
N	2729	2729	2729	2727	2727	2727

^***p<0.01;

^**p<0.05;

^*p<0.10.

Estimated standard errors are in parentheses. All models control for nationwide non-linear time trends through the use of quarterly indicator variables. GEE models also control for state-specific means of time varying variables (not reported).

In terms of policy findings, we find a number of state characteristics are associated with greater rates of psychotropic medication use (Table 3). Greater government expenditures per capita are negatively associated with number of psychotropic DDDs, as are physicians per capita, Federal Medicaid matching rate and greater high school graduation rate. Consistent with other studies, we find that mental health carve-outs are associated with greater use of psychotropic medications, possibly because of the explicit incentives to increase use. Greater use of capitation in the state was associated with lower levels of antidepressant use but greater levels of antipsychotic use. Greater proportion of residents with a college degree, greater urbanization, and greater unionization were all generally positively correlated with psychotropic medication use. Wealth had mixed effects on use, with greater median income and greater population under 100% of FPL associated with lower levels of use, while greater population below 200% of FPL is positively associated with use.

Fewer of the state characteristics were associated with the market share of newer classes of psychotropic medication (Table 4) and results were often mixed between the two classes. Only two of the wealth variables, median income and the proportion of the population under 200% FPL, were consistently (and negatively) associated with the market share of newer psychotropic medications. The size of the state government per capita and the proportion of spending devoted to the Medicaid program was negatively associated with use of atypicals, but not correlated with SSRI use. Carve-outs had no effect on composition of use in either class, but capitated care was negatively associated with SSRI use but positively associated with atypical use, possibly reflecting the remaining FFS population as noted below. Greater unemployment and a larger Medicaid program were negative associated with innovation in antidepressants, but positively associated with innovation in antipsychotics. The number of physicians per capita had no effect on the market share of SSRIs but was negatively associated with use of newer antipsychotics. High school education was generally positively associated with greater innovation, consistent with Staiger and Skinner’s (2007) findings. College education had no effect on innovation. Urbanization had surprisingly large effects on innovation, with greater urbanization associated with greater innovation in antidepressants but lower innovation in antipsychotics.

In the sensitivity analyses, we found that the definition of rarely changing variables mattered substantially in the model estimates (Table 5). Variables with ratios of between to within variation that were between the two thresholds examined (2.8–5.0) and thus were classified as rarely changing in the original models but reclassified as time varying in the sensitivity analysis had substantially different estimates in the FEVD models, often changing signs and retaining significance or loosing significance in the sensitivity analyses.

Table 5.

Comparison of FEVD models with different definitions of rarely-changing variables

	Antidepressant DDDs (thousands)		Antipsychotic DDDs (thousands)		SSRIS as a percent of all antidepressant DDDs		Atypicals as a Percent of all Antipsychotic DDDs
	Original	Sensitivity	Original	Sensitivity	Original	Sensitivity	Original	Sensitivity
Time Varying Measures (original and sensitivity)
Percent of state’s general fund given to Medicaid	36.08 (43.13)	36.08 (80.74)	−18.32 (24.39)	−18.32 (45.28)	0.00066 (0.00063)	0.00066 (0.00069)	−0.00201** (0.00081)	−0.00201** (0.00090)
Total state government expenditures per capita	−0.59*** (0.14)	−0.59** (0.24)	−0.430*** (0.080)	−0.43*** (0.13)	1.49e-06 (2.23e-06)	1.49e-06) (2.35e-06)	−6.82e-06** (2.78e-06)	−6.82-06** (2.96e-06)
Medicaid mental health carve-out	2185.28*** (462.29)	2185.28** (877.40)	1107.53*** (235.36)	1107.53*** (422.60)	−0.0038 (0.0062)	−0.0038 (0.0068)	0.0061 (0.0073)	0.0061 (0.0080)
Percent in capitated managed care	−9.62 (8.23)	−9.62 (13.26)	6.92 (4.39)	6.92 (6.92)	−0.00038*** (0.00012)	−0.00038*** (0.00012)	0.00063*** (0.00014)	0.00063** (0.00015)
Unemployment rate	−51.97 (245.77)	−51.97 (412.04)	−95.45 (128.88)	−95.45 (209.83)	−0.0096*** (0.0033)	−0.0096*** (0.0032)	−0.0031 (0.0039)	−0.0032 (0.0037)
Variables that were rarely changing in original model that become time varying in sensitivity model
Physician supply per capita	28.37 (1114.19)	−2380.02 (1682.29)	118.89 (560.16)	−1194.45 (885.72)	−0.005 (0.013)	−0.006 (0.013)	−0.024 (0.016)	−0.050*** (0.016)
Medicaid FFS population (1000s)	3.54*** (0.61)	−4.69*** (0.89)	4.12*** (0.30)	−0.04 (0.47)	−2.94e-05*** (7.50e-06)	−5.78e-05*** 8.55e-06)	−8.37e-06 (8.81e-06)	3.57e-05*** (1.06e-05)
Median income (1000s)	−103.45 (101.97)	−105.54 (110.36)	35.12 (51.24)	−54.73 (60.45)	−0.0025* (0.0012)	−0.00253*** (0.00095)	−0.0010 (0.0015)	−0.0022* (0.0012)
Percent of the population < 100% FPL	−132.92 (138.41)	−193.23 (115.39)	−124.12* (71.08)	−86.48 (57.16)	0.0010 (0.0018)	−0.0013 (0.0011)	0.0049** (0.0021)	0.0002 (0.0012)
Percent of the population < 200% FPL	103.09 (108.07)	121.45 (101.04)	129.02** (53.57)	70.49 (57.16)	−0.0021 (0.0014)	−0.00267*** (0.00099)	−0.0018 (0.0015)	−0.0014 (0.0012)
Rarely changing variables (original and sensitivity)
Federal Medicaid matching rate	−123.31* (67.15)	−247.12* (129.94)	−62.03 (33.86)	−136.30** (65.36)	0.00104 (0.00083)	0.00141 (0.00094)	−0.0022** (0.0010)	−0.0013 (0.0011)
Time Invariant Variables (original and sensitivity)
Percent of population graduated from high school in 1990	−130.38 (108.08)	−847.80*** (217.50)	−89.50* (54.18)	−430.18*** (108.55)	0.0030** (0.0013)	−0.0002 (0.0016)	0.0037** (0.0016)	0.0049*** (0.0019)
Percent of population graduated college in 1990	−37.72 (201.88)	414.10 (387.33)	73.56 (101.49)	346.99* (194.81)	−0.0001 (0.0025)	0.0014 (0.0028)	0.0009 (0.0029)	0.0031 (0.0033)
Percent urban (1990)	1442.38 (2399.02)	11419.28** (4670.73)	−1168.66 (1218.75)	4209.28* (2339.58)	0.122*** (0.030)	0.163*** (0.034)	−0.165*** (0.036)	−0.202*** (0.041)
Percent union membership (1990)	127.00 (91.06)	354.03* (193.91)	151.93*** (45.61)	272.86*** (97.44)	0.0003 (0.0011)	0.0014 (0.0014)	−0.0004 (0.0013)	−0.0014 (0.0016)
Citizenship ideology (1990)	18.33 (54.40)	66.45 (108.37)	8.74 (26.96)	24.06 (53.92)	0.00062 (0.00066)	0.00050 (0.00077)	0.00186** (0.00077)	0.00226** (0.00091)
Government ideology (1990)	19.77 (25.91)	−69.45 (54.66)	−9.50 (12.77)	−51.47* (26.66)	−0.00012 (0.00031)	−0.00046 (0.00038)	−0.00040 (0.00037)	0.00016 (0.00044)
N	2729	2729	2727	2727	2727	2727	2725	2725

^***p<0.01;

^**p<0.05;

^*p<0.10.

Estimated standard errors are in parentheses. Origina models are those reported in Tables 3 and 4 in the FEVD columns. Quarterly indicators variables are included in all models.

7 Discussion

This paper examined three potential estimators for a longitudinal study on state-factors associated with innovation: Hausman-Taylor random effect models, fixed effect vector decomposition models, and generalized estimating equations. Each has a number of assumptions the applied researcher needs to be comfortable with; many of these assumptions are not easily verified (Plümper, Troeger 2011) but are essential for the incorporation of empirical estimates into further theoretical development (Breusch et al. 2011). While our specific example examines the diffusion of innovation in mental health, these methods are likely to be considered by health services researchers analyzing many other topics using longitudinal data with both time-varying and time-invariant variables. Several lessons may be drawn from this work.

First, the considerably larger standard error estimates in FEVD models compared to HT and GEE models for rarely changing variables is notable. In their 2011 paper, P&T state “there cannot be any doubt that FEVD is more efficient than the fixed effects and Hausman-Taylor models (for time-invariant, rarely changing and exogenous time-varying variables) and less biased than pooled-OLS and random effects (for endogenous time-varying variables in finite samples).” While this is not a Monte Carlo study and therefore we cannot comment on the biasedness of any of the estimators, our findings on estimates from rarely-changing variables is somewhat at odds with this statement. Breusch et al. (2011) note the difference between the 2011 and 2007 P&T papers in terms of their focus on advantages for rarely changing variables in particular. Rarely changing variables can pose problems in fixed effect models, as the (small) amount of within variation allows for identification separately from model fixed effects, but identification comes mostly through between variation. In addition, substantial differences in the sensitivity analyses depending on the definition of rarely changing variables for FEVD models are troubling. Further work is clearly in order to put more science behind the definition of rarely changing variables if FEVD-type models are to be adopted in the future.

Second, given the focus in our example on the unobserved heterogeneity across states, there is surprising consistency between HT and GEE models (Tables 3 & 4). One of the primary differences between these two models is HT’s estimation of unobserved state-level innovation factors in contrast to GEE’s reliance only on observable factors. If these group effects were correlated with included variables (endogeneity), we might expect to see substantial differences between the two estimation techniques. The lack of difference across both types of diffusion models (Tables 3 & 4) indicates that either there is little remaining heterogeneity after controlling for the rich set of state characteristics included here, or any remaining state heterogeneity is not correlated with any of the included variables. Either may indicate that GEE, which better incorporates repeated observations at the group level, may be an appropriate model when a rich set of covariates are available.

Finally, the estimated models have a number of policy conclusions that may be of interest to mental health policy makers. The fact that larger state governments had consistent lower levels of psychotropic medication use seems to indicate that psychotropic medications are a necessity rather than a luxury good. Mental health carve-outs had the expected positive effects on quantity of medications used found elsewhere (Huskamp 1998), confirming that psychotropic medications are an important part of creating an efficient predictable mental health system, but that newer medications are not necessarily preferred. The finding that states with a greater presence of capitated managed care programs have lower levels of antidepressant use but higher levels of antipsychotic use may reflect the composition of persons covered by Medicaid capitation plans, with more severely mentally ill persons more likely to stay in the FFS program, thus proportionately increasing antipsychotic medication use. We cannot rule out spillover effects from capitation settings to FFS, however (Baker 1997, 1999; Domino, Salkever 2003). The finding that states with a greater federal share of spending had lower levels of medication use may indicate the substitutability of medications in states with greater mental health manpower shortages, if states use greater Federal resources for higher service rather than medication reimbursements. The fact that urbanization had surprisingly large effects on innovation, and in different directions for each of the two psychotropic classes examined here may indicate that information on SSRIs is more readily diffused through urban settings in contrast to information on antipsychotics, that marketing efforts may be more efficient in urban areas, or could reflect underlying state preferences in each of these classes.

A number of limitations of our empirical example should be noted. First, we are not able to distinguish medications that are appropriately versus inappropriately prescribed. We cannot link prescriptions to individuals, so characteristics of medication users are unknown. Others have previously employed GEE models to explore the diffusion of newly introduced antipsychotics in the Veterans Health Administration (VHA) by patient and facility level factors and have found many of these factors important predictors (Valenstein et al. 2006). Similarly, we cannot ascertain medication switching among individuals which has been shown to be common (Leslie, Rosenheck 2002). Our data also include only prescriptions reimbursed through fee-for-service programs, which were still the modal reimbursement method during our study period, but have been declining over time. Because prior literature has found a strong correlation between greater aggregate psychotropic medication use and greater treated prevalence (Frank, Glied 2006; Domino, Swartz 2008), we can possibly interpret greater medication use as an indicator of quality or outreach, although the aggregated data used herein cannot directly address this question.

In summary, we find remarkable similarity in estimated marginal effects among the three longitudinal methods selected here, but large differences in efficiency. Researchers should ensure the assumptions of their framework match the assumptions of the estimation technique and may want to examine more than one estimation technique when applicable in order to better determine the robustness of estimates. In terms of policy findings, we do find evidence that a number of state-specific factors affect diffusion of newer psychotropic medications.