DESARROLLO DE ACTIVIDADES

To test whether disclosure laws and damage caps are significantly related to ex ante expected damages, the following random effects linear model with an AR(1) distur-bance was estimated:

ln(P REMit)=α+φ1DISCL_it+φ2CAP_it+φ3(DISCLit∗CAP_it)+λY EARit+νi+it

i= 1, ..., N ; t = 1, ..., Ti

where

2003) (effective July 1, 2001)

20Data on the number of physicians in patient care by state and by year were collected from the American Medical Association [2]. Data from 1991 were not available, however. An estimate for each state was formed by taking the average of the number of physicians in patient care in 1990 and the number of physicians in patient care in 1992.

Trends in Insurance Premiums

Mean Median Minimum Maximum 1991 $9,503 $9,471 $1,513 $18,918 1992 $9,314 $9,610 $1,567 $17,708 1993 $9,018 $8,636 $1,329 $17,295 1994 $9,462 $9,089 $2,429 $15,904 1995 $9,075 $8,659 $1,391 $15,580 1996 $8,489 $7,938 $1,294 $15,194 1997 $7,785 $7,274 $1,304 $13,786 1998 $7,941 $7,868 $1,524 $13,284 1999 $7,651 $7,549 $1,733 $12,924 2000 $7,360 $7,116 $1,840 $13,519 2001 $7,595 $7,316 $2,142 $15,727

Table 4.2: This table provides descriptive statistics on trends for medical malprac-tice insurance premiums per non-federal physician in patient care. Premiums are reported in 1990 dollars.

P REMit = aggregated medical malpractice insurance premiums earned (in 1990 dollars) normalized by the number of non-federal physicians in patient care in state i during year t,

α = the intercept,

φ1, φ2, φ3 and λ represent estimated coefficients of the model,

DISCLit = 1 if state i had a disclosure law in effect during year t and 0 otherwise, CAPit = 1 if state i had a damage cap of any sort in effect during year t and 0 otherwise,

YEARitrepresents each observation’s year (i.e., YEARit= 1 for 1991 observations, 2 for 1992 observations, etc.),

νi = state-specific disturbances,²¹

it = ρi,t−1+ ηit= non-state-specific disturbances, where ρ = the autocorrelation

21The random-effects model assumes that νi are realizations of an independent and identically distributed process with mean 0 and variance σν².

parameter²² and ηit is distributed as N (0, σ²_η) and is independent of other errors over time (as well as being independent of ).

Functional Form. Logarithmic transformations of the dollar-dependent variables, PREM and LOSS, are used to correct for their skewed distributions. This transfor-mation also decreases the effect that outliers might have on the estitransfor-mation results and accounts for the fact that the distribution of premiums is naturally truncated (i.e., all observations on premiums are strictly positive).

Dynamic Nature of Premiums. A particular state’s prior year premiums per physi-cian is likely a good predictor of the current year’s premiums per physiphysi-cian. Events affecting premiums, such as changes in the law and the competitive environment of the insurance industry, tend to occur slowly over time. Therefore, the set of condi-tions in a particular state affecting premiums are likely to be very similar from one year to the next. Typically a lagged dependent variable is used to control for this feature when time-series data are used. With panel-data sets, however, the inclusion of a lagged dependent variable can be quite problematic.²³ Therefore, to account for the dynamic nature of premiums, a variable for the year, YEARit, is included as an independent variable. The coefficient on this variable (λ) represents the general time trend in the data. Specifically it will capture the average percentage change in premiums from year to year.

Heterogeneity Across States. When using panel data, it is possible that the distur-bances include a component common to all states (which is time-invariant and orthog-onal to the regressors). Using a random effects estimator controls for these effects.²⁴

22This parameter measure the correlation between it and _i,t−1.

23See Hsiao [51] for a discussion of dynamic models with variable intercepts (describing why es-timates are bias under these conditions). The bias of coefficients worsens as the number of time periods decreases. Note that Gius [41] employs a random effects specification with a lagged depen-dent variable, but does not account for the issues described here. His coefficients are possibly biased due to the specification of his model. His data set, however, includes 15 time periods; thus, the bias might be minimal.

24Virtually identical results were obtained when estimates were computed using a fixed effects estimator. A Hausman specification test (Hausman [47]) indicated that the difference in coefficients estimated using a random-effects model are not systematically different from the coefficients esti-mated using a fixed-effects model (i.e., the state-specific disturbances are not correlated with the regressors). Therefore, the random-effects specification seems appropriate. In addition, the Breusch and Pagan [17] lagrangian multiplier test results indicate the presence of random effects.

Most other empirical studies of medical malpractice insurance premiums account for differences between states by adding several control variables to the empirical model (e.g., differences in tort reforms, insurance regulations, access to lawyers, age distri-bution of the population, etc.). The theories regarding how these variables interact with one another and how they should enter the empirical model, however, are not well developed. When using a relatively small number of observations, including a large number of independent variables calls into question the model’s results. There-fore, rather than specifying a model with several independent variables, the present study employs a random-effects model to account more generally for variations across states.

Serial Correlation of the Disturbances. Given the nature of data on premiums, serial correlation of the disturbances is expected.²⁵ First, the lag in closing claims might induce strong correlation across years. Also, insurers might not be able to set premiums freely in any given year. Insurance regulations in some states might restrict changes to premiums from year to year. That insurance regulations are not included in the empirical model might cause serial correlation of the disturbances.²⁶ To account for this feature of the data, a linear model with an AR(1) disturbance was used.²⁷

It should be noted that estimation from first differences was attempted but un-successful. The minimal variation in independent variables during the time period under consideration probably led to this result (e.g., of 550 observations on change in disclosure law, only 21 observations indicate a change).

Interaction Term. The interaction term, DISCLit∗CAPit, captures the fact that caps might affect premiums differently for states with disclosure laws in place than

25In fact, a Breusch [18] – Godfrey [42] test indicates significant autocorrelation in the disturbances when premiums are regressed on the independent variables.

26Other studies correct for autocorrelation in the presence of controls for random effects. See, e.g., Baltagi and Griffin [6], Jalan and Ravallion [55] and Egger [31].

27An AR(1) disturbance specification assumes that the disturbance term is first-order autoregres-sive. Under this specification, each disturbance embodies the entire past history of the η’s with the most recent observations receiving greater weight than those in the distant past. This is the most widely used assumption for serial correlation. See Baltagi and Li [7] for a description of the transformation that circumvents the problem of autocorrelation in an error component model.

for states not mandating disclosure. The interaction term allows for estimation of this effect. For example, the percentage change in premiums caused by implementing a damage cap along with a disclosure law can be calculated as follows:

∂ln(P REMit)

∂CAPit

= φ₂+ φ₃

Similarly, the interaction term can be used to estimate the percentage change in premiums caused by implementing a disclosure law in the presence of a damage cap by considering φ₁+ φ₃.