1. Introduction.

      This work is an effort to reexamine the topic of rent subsidy program participation and household labor supply. Keane and Moffitt [1998] detailed how the simultaneous choice of multiple transfer programs (including rent subsidies) and household labor supply can be analyzed and a model estimated. Unfortunately, recent work at HUD summarized by Shroder and Martin [1996] indicates that the survey data available to Keane and Moffitt is subject to substantial reporting error. That this reporting error is large, can be seen by the fact that in 1993 the population equivalent of 2.235 million survey respondents informed their interviewers that they lived in separate public housing units, while HUD administrative records show only 1,193,508 occupied public housing units in the United States [Shroder, p. 6]. Recognition of this large discrepancy prompted HUD to conduct several investigations about its causes.

      In the first of several investigations, Casey [1992] at HUD's request re-interviewed a sample of survey respondents and checked their addresses against records of known rent subsidized addresses to produce frequency tables of both false negatives and false positives. She also investigated household's understanding of the survey questions. Fowler's survey methods text [1984] suggests there are several threats to the "face validity" of survey questions. In particular, even ordinary terms of common usage such as "doctor" or "breakfast" may elicit unexpected results without extraordinary efforts to clarify their meaning in the context of the survey. And political/legal terms, like "gun control" are subject to even more disparate interpretation. "Public housing" appears to be precisely such a loaded political term, prompting the population equivalent of 818,000 households who received no rent subsidy of any kind to believe they lived in "public housing." When asked to define "public housing," such households often believed it meant "housing open to the public," or "available to anyone" [Shroder and Martin, p. 10]. Further, HUD found that 37.5% of households who informed interviewers that they received federal rent subsidies were not in any known form of rent subsidy program. That so many households in the survey samples did not face the federal rent subsidy work taxes, may account for the findings of Keane and Moffitt [1995 & 1998] and Painter [1998] that rent subsidies lacked statistically significant effects on labor supply.

      HUD and Congress categorize rent subsidies as being offered in three basic forms: public housing, tenant-based assistance, and project-based assistance. Public housing is defined as being owned by a public housing authority, which is a state or local institution, and is subsidized by the Federal government. Tenant-based assistance, consisting primarily of section 8 certificates and vouchers, is paid on behalf of tenants to private owners whose units the tenants have selected, subject to maximum cost and minimum quality program limits. Project-based assistance is paid to the private owners of particular units on behalf of low-income tenants in conjunction with mortgage insurance or construction subsidies. In all three types of assistance, the tenants make a monthly contribution to rent and utilities based on their income. Which type of rent subsidy is preferable is controversial, both for policy makers and analysts. In particular, public housing has developed a negative reputation for its behavioral effects and a "culture of poverty."

While HUD's research focused on the American Housing Survey (AHS), an examination of the wording of survey questions and interviewer instructions for the Survey of Income and Program Participation (SIPP), Current Population Survey's March Supplement (CPS), and the Panel Study of Income Dynamics (PSID) shows they are identical, and thus prone to the same patterns of erroneous reporting.

Thus, at the suggestion of Keane, I have undertaken to combine HUD administrative data with the survey data and use HUD's research about the characteristics of the mismatch to improve the estimation of a model of labor supply and rental assistance program participation.

      2. Literature.

      The empirical literature on the effects of transfer programs on labor supply has been surveyed by amongst others Danziger, et al. [1981] and Moffitt [1992]. Most of the literature has applied the static labor supply model and has focused on models of female labor supply because a large majority of transfer program recipients are women. A significant portion of the literature has also concerned the proper treatment of the highly nonlinear budget constraints generated by transfer programs [Hausman 1985 and Moffitt 1986]. Most of the literature has analyzed individual transfer programs in isolation from other transfer programs, and has seldom addressed the issues that arise in the analysis of multiple transfer programs. Exceptions include Keane and Moffitt [1995 and 1998]. In particular, Keane and Moffitt point out that work disincentives can be either substantially augmented or unaffected as additional transfer programs are added. The effect of such disincentives and inefficiencies created by transfer programs is one of the most important and oldest issues in the economics of transfer programs in the USA In the USA, it is the norm for households who participate in one program to simultaneously participate in one or more other programs. For non-elderly female headed households in any form of rental assistance program, 64% also participate in AFDC or Food Stamps.

      Prior to the implementation of the 1995 welfare reform, marginal tax rates for AFDC were 100% on gross wages. Food Stamps levied an additional 30% marginal tax. Rental Assistance, however, levies an "after tax and transfer" marginal tax rate of 30% (except it ignores Food Stamps). Further, Medicaid for this group was largely a fringe benefit of AFDC receipt, and was typically cut off abruptly with the end of AFDC eligibility. While the 1995 welfare changes have altered some of these dynamics, the overall effect is still one of a highly nonlinear budget constraint with kinks, jumps, and steep marginal tax rates.

      While theory implies such disincentives are very important, few studies other than Keane and Moffitt [1995 and 1998] have addressed the labor supply effects of multiple program participation. Keane and Moffitt cite two reasons for this lack of empirical work. "First, the existence of self-selection into different program combinations on the basis of unobserved heterogeneity factors, such as welfare stigma, implies that the labor supply equation must be estimated jointly with a set of program participation equations." Until recently, such joint estimation of large numbers of equations with limited dependent variables was computationally in feasible. "Second, imposing a utility structure on the problem results in a choice problem whose analytic solution is intractable because the region of the error space within which different program combinations are optimal is too complex to derive." [1995, pg. 554]

      Keane and Moffitt solved these two problems using "simulation estimation" methods. "Simulation estimation" simulates choice probabilities by Monte Carlo methods rather than evaluating the choice probabilities by conventional numerical methods Keane and Moffitt [1998] showed that simulation solves not only the first problem of evaluating multiple integrals arising from sets of limited dependent-variable equations, but also the second problem of the intractable analytic solution to the choice problem. The second problem is solved because "the estimation of the relevant choice probabilities through simulation does not require an analytic derivation of the boundaries of the error space within which different program combinations are optimal." Further, they extended the literature on simulation methods by investigating the special issues that arise in selection models [1991, 1994, 1995 and 1998].

      The primary simulation methods are simulated maximum likelihood, or SML [Albright et al., 1977, Lerman and Manski 1981] and the method of simulated moments, or MSM [McFadden 1989, Pakes and Pollard 1989]. Keane and Moffitt compared the performance of the SML method with a modified MSM method suggested by McFadden and Ruud [1994] and extended this to a two-step estimator in which first-stage wage-equation estimates are used in a second stage MSM estimation [Keane and Moffitt 1998]. They found that for their model the modified MSM involving joint estimation was considerably more burdensome than the SML method, while the two-step MSM was much simpler and gave similar parameter estimates.

      Keane and Moffitt estimated their model with 1984 data from the Survey of Income and Program Participation, SIPP. Unfortunately, at the time they did their work, HUD's documentation of the severe reporting error for such surveys was not yet known. Thus, my work will extend their model to account for the HUD findings. Ideally this reexamination would combine the same 1984 SIPP data with HUD findings and administrative data for 1984. Unfortunately 1984 administrative data is unavailable. The first year for which administrative data is available is 1995. Thus, while I am unable to use the same data, I will endeavor to estimate a model following methods and data as similar as possible to facilitate comparison of results.

     In line with this goal, I will first attempt to replicate Keane and Moffitt's methods using the 1995 SIPP, and compare those results with a model that replaces the portion of SIPP containing self-reported rent subsidized households with a sample from HUD administrative data on households truly in rent subsidized housing. Following Keane and Moffitt, the base model will select female heads of families who choose from among the most common transfer programs - AFDC and subsidized rental housing. The method employed generalizes to any number of programs, and extensions of the basic model will allow choice of Food Stamps as a separate program and choice of the type of subsidized housing program (tenant-based, project-based, or public housing).

     2.5. Data.

      The ideal combination of administrative records and survey data would match a household identifier, such as social security numbers and would allow for direct correction of most false reports. Unfortunately, none of the existing surveys track social security numbers, and access to identifying characteristics that would permit such a match are tightly restricted - the HUD researchers would re-interviewed survey households had to be sworn census officers. Lacking such access, I propose to use the known characteristics of the correct and false reports found in the HUD studies, and reported here in Tables 1 and 2. In each Table scanning down the columns the reflect the true number (or percentages) of household's with a given rent subsidy status, while scanning across the rows reflect the population equivalent numbers (or percentages) with the given survey reported status. The population, and population equivalent numbers are in thousands.

      For Table 1, Let H ( {0,1}, denote reported rent subsidy status, with H = 1 indicating a report of a rent subsidy, and let T( {0,1}, denote the true rent subsidy status. Then let P(H ( T) denote the probability of a household reporting status H, given that their true status is T, and P(T( H) denote the proportion of households with true status, T, given that their reported status is H.

Table 1.

      Table 2 increases the detail to show the substantial differences in reporting by true public housing residents versus participants in other rent subsidies. Let A denote the set of alternatives, A={N,PH,TBorPB}, where N denotes a report of no rent subsidy, PH indicating a report of public housing, and TorPB denoting a report of other rent subsidies. As before let H denote reported status and T denotes true status.

Table 2.

      A method that replaces all survey reports of PH status, would remove the population equivalent of 2685 thousand or 17% of the sample, while the administrative records replace those with only 1138 thousand true PH residents or 7.2% of the eligible population. Due the high degree of accuracy in true PH residents correctly reporting they are in PH 94% of the time, those who are truly in PH and remain in the survey are only 64/13111 or 0.3% of the remaining survey sample. An increased weighting of the survey sample by (74.3+18.5)/(65.8+17.2) = 92.8/83 = P(T=PH)/P(H=PH) = 1.118 is required to reflect the discard of records of households reporting H=PH, while T=N or TorPB.

More problematic is how to correct for the errors in reports of TorPB rent subsidies.

     Replacing the population equivalent of 2715 thousand households reporting other TorPB rent subsidies or 17.2% of the survey sample, with the administrative records for 2916 thousand true TorPB households or 18.5% of the eligible population. This leaves (34+647)/10396 = 6.5% of the remaining survey sample with records of households reporting no rent subsidies, who in fact are in either PH or TorPB rent subsidies programs. However, we now have a data set where all of the records claiming PH, or TB, or PB rent subsidies are in fact in those respective rent subsidy programs, and we have not increased the proportion of the remaining survey records who claim no rent subsidy, but in fact do receive rent subsidies (it remains at 6.5%). To reflect the true proportions of program participants requires weighting those remaining in the survey by P(T=N)/P(H=N) = 74.3/65.8 = 1.12918.

Section 3 explains the problem, and section 4 explains the solution method using simulation techniques.

     Proposed further sections to be forwarded to you upon completion are as follows. Section 5 will discuss the use of mixed data sets, while Section 6 will discuss how the budget constraints for individuals in the sample are constructed. Section 7 will present results from the simulations and discuss the meaning of parameters. Section 8 will present simulations of the effects of implementing changes in transfer programs associated with the 1995 welfare reform, along with estimates of the associated changes in subsidy costs for subsidized housing.

     3. The estimation problem in a model of labor supply and multiple program participation with mixed data sets.

     In general I will consider the availability of M different transfer programs for households to consider as they chose whether to take paid employment. Each program bases its payment to a recipient on a particular 'base' amount - the payment to a family with no income from any other source - and on a set of 'tax rates' that denote the amount by which the payment is reduced for each extra dollar of income. These tax rates typically differed based on whether the source of additional income is earnings, non-earned income, or from other transfer programs. Further the tax rates on particular sources of income also differ across programs.

      At first glance, the analysis of labor supply response in this environment could use a simple conventional form of utility U*(H,Y), where H is hours of work (which reduces leisure), and Y is disposable income. Then computation of the budget constraint Y(H) for each of the 2M possible program combinations, at the available wage, w, with the appropriate taxes permits derivation of the envelope of these constraints. Labor supply choice could then be estimated by appropriate methods for finding the locus on the envelope constraint. Unfortunately, such a model would perform very poorly, because many households are eligible for benefits that could enlarge their net income without changing work hours and yet do not participate in those programs. Thus, their choices are not located on the envelope of the constraints. Such behavior has been attributed to welfare stigma [Moffitt 1983], or it may arise from a general disutility of dealing with welfare bureaucracies, or from time and money costs of program participation [see Moffitt 1992 for a review of explanations]. The econometric difficulty this phenomenon creates arises in part because the unobservables affecting program participation are likely to be correlated with the unobservables affecting labor supply - in particular those most likely to participate may have lower tastes for work. As a result, labor supply choice cannot be estimated conditional on an assumed exogenous choice of programs in which the individual participates. Rather, the program participation choice must be treated jointly with labor supply choice, and so the labor supply equation must be estimated jointly with a set of program participation equations.

      The resulting choice problem remains relatively simple, but the estimation problem does not. For example, consider the utility function U(H,Y,P), where P is a M by 1 vector, and each element of the vector, Pm, is a dummy variable equal to 1 if the individual participates in program m and 0 if not. The presence of participation indicators in the preference function can be interpreted as representing either stigma influences or, more generally, as costs of participation (as neither money nor time costs are directly measured in most data sets any combination of such interpretations is possible). Assume (U/(H < 0, (U/(Y0, (U/(Pm<0. For purposes of illustration consider the separable case:

     (1) U(H,Y,P1,...,Pm,...,PM) = U*(H,Y) - ('P

     where (' is a 1 by M vector, and each (m element of (' denotes the marginal disutility of participating in program m. Thus if (m is sufficiently large, a particular program may not be chosen even though participation increases U*.

      It is convenient both analytically and empirically to consider the choice of discrete H points rather than continuous H. Therefore, consider the choice of H equal to 0, 20, or 40 hours per week, taken as the choice of no market work, part-time work, or full-time market work respectively. This approach, taken before in the transfer program literature [Zabalza et al. 1980, Fraker and Moffitt 1988] avoids the task of computing the locations of the numerous segments and kinks of each of the 2M budget constraints that would be required if continuous H were modeled. In the present context, discrete H is particularly convenient because it allows us to model agents as facing a multinomial choice problem with a set of discrete participation hours alternatives.

      With three H points and M transfer programs there are J = 3*2M discrete choices available to the individual. The budget constraint gives disposable income for each possible choice as:

(2) Y(H,P) = w H + OthInc + P'B(H) - T(H)

     where w is the hourly wage rate, OthInc is any non-transfer non-labor income, B(H) is a M by 1 vector and each element, Bm(H), is the benefit function for program m, and T(H) is the positive tax function. For notational simplicity I have suppressed the dependence of Bm(H) and T(H) on OthInc, w, and the benefits of other transfer programs in which the individual might participate (as well as other individual and family characteristics that may affect taxes or transfers).

     Denote the choice set by C = {1,...,J} such that J = 3*2M, and let j ( C denote the combination of choices in a particular alternative from the choice set, {H j, P 1,j,..., P m, j,..., P M, j}. Further, I order the choice set C, such that j = 1 denotes the alternative {H 1, P 1,1,..., P m,1,..., P M,1} = {0,0,...,0,...,0}, and j = J denotes the alternative {H J, P 1,J,..., P m, J,..., P M,J} = {40,1,...,1,...,1}. Define attainable utilities U j, (j ( C, and differences in utilities between alternatives j and k in C as follows:

     (3a) U j ( U(H j, P 1,j,..., P m, j,..., P M, j);

(3b) (U j, k ( U j - UK.

     Thus, U j is the evaluation of U for combination j in C obtained by inserting (2) evaluated at that combination into U, and by setting H and P to their appropriate values for combination j. And (U j, k is the difference in utility between alternatives j and k. Then the choice problem is simply: (3)

Choose alternative j(C ({(U j, k ( U j - U k 0, (k(C}.

While this framework is squarely in the tradition of the single decision-maker static model, it is worth emphasizing some of the limitations of that model.

(I) One is the downplay of joint decisions of different household members, which, though less important for female heads than for married couples, is relevant even for the former if there are other family members with earnings present in the household (in this empirical work, I will test various specifications including and excluding such households).

(II) Another is the assumption that family size, marital status, and the number of children are all exogenous and unaffected by welfare benefits, whereas the literature in this area indicates some significant effects of this kind. (III)

     Perhaps a more important drawback of the static model is its failure to incorporate dynamic considerations that might be important in the welfare participation decision. For example, an individual may choose to stay off welfare, even at the cost of current income, if she is investing in private market search or human capital and that such investment could not be conducted while on welfare. This is an explanation for non-participation of eligible households that differs significantly from the pure stigma explanation. Future work on these models should address these issues.

      The estimation problem in the simple static model that I am using can be seen by assuming a stochastic specification in which the labor supply preference parameter ( varies across the population and the M parameters (m vary across the population as well; the parameters vary for reasons unobserved to the investigator but known to the individuals. Hence utility is U(H*,Y,P1,...,PM;(,(1,...,(M). Estimation of the resulting M+1 equations of the model by conventional ML methods must confront two problems.

(1st) First, a well-known problem of evaluating integrals of order (M+1) for the computation of the probabilities; such evaluation is in general infeasible with typical quadrature methods if the covariance matrix of the errors is unrestricted.

      Keane and Moffitt [1995] explain how both of these problems are solved by simulation estimation. While it was well known that simulation estimation solves the first problem, it was less recognized in the literature on welfare programs and similar problems that it solves the second problem as well. Rather than analytically deriving the regions of the space over which integration is taken, simulation of choice probabilities merely determines, for each draw from the distribution of the errors, which of the participation possibilities has greatest utility. The details of the computational algorithm are discussed below.

     4. Empirical Application and Estimation Method.

For the utility function in (1) above, I follow Keane and Moffitt, with:

(4)

     U(H,Y,P1,P2,...,PM) = ( H + Y - ( h H2 - ( y Y2 - ( ((m=1M (m Pm) - (1-()Max{(1P1,...,(MPM}. [mwl1]

     The marginal utility of Y at Y = 0 is normalized to 1; the remaining parameters are therefore in dollar terms. The ( parameter on program participation will be less than 1 if the implicit cost of multiple program participation differs from the simple sum of the costs of participating in each singly (e.g., if the stigma or other costs of participation are less than proportionate to the number of programs). In particular, (1-() permits the preference for a combination to be dominated by the program for which the household has the strongest preference. This multinomial choice model therefore consists of (4) and (2), with solution (3).

Our stochastic structure permits ( and the (m to vary in the population conditional on a set of observable socioeconomic characteristics: (5)

( = X'(bar + (a; (6)

     (m = X'(bar m + (m, (m = 1,...,M; [mwl2]

     where X is a vector of household characteristics and (bar and (bar m are vectors of coefficients. The parameter ( represents the marginal disutility of work at H=0, and each parameter (m represents the marginal disutility, or cost, of program participation if there are no higher-order interactions in the preference function. I choose these parameters to be stochastic because they appear linearly in the pair-wise utility differences among the J=3*2M alternatives. That is, differencing (4) across alternatives with the same P m but different H and Y gives choice equations for H that are linear in (, and differencing (4) across alternatives with the same H but different P m and Y gives choice equations for P m that are linear in (m. While linearity in errors is not necessary for computation when simulation methods are used, it does increase the comparability of this specification to past work.

      The full model, therefore, can be derived by inserting (2), (5), and the M equations in (6) into (4). There are J possible combinations of the choice variables, and hence J of the "U j" attainable utilities referred to in (3a), and there are M+1 error terms. Our model is 'structural' in the sense that it has a particular factor structure of the errors, that arises from the imposition of a particular utility function (albeit one with a flexible form), and a presumption that the major source of variation in choices arises from the heterogeneity in a selected set of preference parameters.

Since wage rates are unobserved for non-workers, I specify a log wage equation as: (7)

ln(w) = X'(bar + (w

     I initially will estimate (7) jointly with the labor supply participation choice model. However, I also estimate models which use predicted wages from first-stage estimates of (7) in a second-stage estimation of the choice model alone.

     Further sort alternatives in C into two sets C0 = {1,...,J0}, and C r = {J0+1,...,J0+J1}, such that 1 through J0 are alternatives without subsidized housing, and J0+1 through J0+J1=J are alternatives which include participation in subsidized housing. Let P(j«(, X i) denote the probability of participation-hours combination j conditional on a vector of observed characteristics, X i, for individual i, and a vector of all parameters in the model, (, where j = 1,...,J. In the baseline model M=2 so that J= 3*2M = 12. Let, h0 = P(T=N)/P(H=N) denote the weight assigned to observations reporting no rent subsidy in the survey sample. Then randomly draw observations from the administrative data to reflect the true population distribution of rent subsidy participants, and use these observations to replace the survey reported rent subsidized households. Then let P(j«(, X i, w i,) denote the probability of the same choice j, but conditioned additionally on the observed wage, w i. Letting d i, j be an indicator equal to 1 if person i chooses participation-hours combination j and 0 otherwise, the log likelihood function for our model (assuming the wage equation is estimated jointly with the choice model) is:

(8) ln[L(()] = ( i(En ( j(C0 h0 d i, j {ln[P(j«(, X i, w i,)] + ln[((w i «(, X i,)]} +

+ ( i(En ( j(C0 d i, j {ln[P(j«(, X i, w i,)] + ln[((w i «(, X i,)]} +

+ ( i(U n ( j(C0 h0 d i, j ln[P(j«(, X i)] + ( i(U n ( j(C0 d i, j ln[P(j«(, X i)]

     where En and U n are the sets of observations of individuals who are employed and not-employed in market work, and ( is the normal p.d.f. The score of the log likelihood is then:

(9) ((ln[L(()] = ( i(En ( j(C0 h0 d i, j {((ln[P(j«(, X i, w i,)] + ((ln[((w i «(, X i,)]} +

+ ( i(En ( j(C0 d i, j {((ln[P(j«(, X i, w i,)] + ((ln[((w i «(, X i,)]} +

+ ( i(U n ( j(C0 h0 d i, j ((ln[P(j«(, X i)] + ( i(U n ( j(C0 d i, j ((ln[P(j«(, X i)]

      To estimate the parameters of the model I will use either the method of Simulated Maximum Likelihood, SML [Albright et al., 1977; Lerman and Manski 1981], or Keane and Moffitt's two-step MSM method. The SML method involves directly evaluating the log likelihood function by simulating the probabilities P(j«(, X i, w i,) and P(j«(, X i,) and inserting the simulated values into (8). I denote the simulated probabilities by probabilities f(j«(, X i, w i,) and f(j«(, X i,) respectively. This procedure does not give an unbiased estimator of the log likelihood because, for a finite number of Monte Carlo draws,

(10)

E{ln[f(j«(, X i, w i,)]} ( ln[P(j«(, X i, w i,)]

and (11)

E{ln[f(j«(, X i)]} ( ln[P(j«(, X i)].

     The simulated log likelihood is only asymptotically unbiased as the number of draws used to simulate the choice probabilities grows large. Thus, an estimator of ( obtained by maximizing the simulated log-likelihood function obtains consistency only as simulation size goes to infinity. An alternative method that obtains consistency for finite simulation size would be a modified version of the Method of Simulated Maximum likelihood, MSM [McFadden 1989, and Keane and Moffitt 1995]. Keane and Moffitt's [1995] comparison of SML and MSM methods and found that as MSM requires that the (w's drawn must be independent of the draws for (a, (A and (R, the total number of draws required for a simulation by MSM is the square of those required for SML. Thus, although the MSM estimator has the advantage of being consistent in sample size for a fixed simulation size, its computational advantage over the SML method is greatly reduced. Hence, in this context MSM is computationally more burdensome than SML.

     Implementing either simulation estimator is eased considerably by using simulators that are smooth functions of (, for this permits the use of standard gradient optimization procedures [see McFadden, 1989]. The importance of smoothing methods for sampling proposed by McFadden are not particularly desirable for our problem because those methods require that the dimension of the vector of utility differences equal the number of error terms in the model. In our model, a factor structure of errors of smaller dimension underlies the vector of utility differences. Therefore, I instead adopt an alternative kernel smoothing procedure discussed by McFadden which adds an i.i.d. extreme value error term to the utility of each alternative. The resulting choice probabilities are multinomial logit conditional on the normal error terms contained in the UK (see equation (3a)) and are of the form:

(12)

P(k«() = Exp[U k(()/(]/{(j(C Exp[U j(()/(]}, (k(C.

     where C is the set of alternatives and where ( is the standard deviation of the extreme value errors. The probability simulator is unbiased as ( approaches zero, for as that occurs the simulator P(k«() approaches a step function. In practice, I set ( at a value close to zero.

      A critical feature of this smoothing method -- which is not a feature of other methods -- is that it allows us to simulate the choice probabilities without knowing the boundaries of the regions of integration that generate those probabilities. Equation (12) can be evaluated by calculating the U k(() at simulated values of the stochastic terms. This property is important because, as I noted previously, the relevant integration boundaries are intractable in this and similar applications.

In practice then, observations in the set C0 which involve no rent subsidies will come from the SIPP and are weighted to compensate for the discarded observations and reflect the true population distribution of eligible households not in rent subsidy programs, while observations in the set C1 will are randomly drawn from the HUD administrative data to reflect the appropriate population proportions of rent subsidy program participants.

      Please feel free to respond to this draft in anyway. If you have particular concerns about anything that is confusing, ambiguous, incomplete, or that you would like to see summarized better please let me know. I don't yet have any empirical results to report, though I have been working on that and hope to have preliminary results in the next few weeks. I have just completed a move back to MN from Washington, DC and received my HUD administrative data extract today at my local HUD office. I realize that I have a lot of work left to do on this, but would appreciate any preliminary comments you might want to make. Thanks for your consideration.

Sincerely,

Mark Lutterman

email: lutt@atlas.socsci.umn.edu

phone: 612:827-3531

Papers on Transfer Programs and Female Labor Supply:

     Danziger, S., R. Haveman, and R. Plotnick. "How Income Transfers Affect Work, Savings, and the Income Distribution." Journal of Economic Literature 19 (September 1981): 975-1028.

     Fraker, T., and R. Moffitt. "The Effects of Food Stamps on Labor Supply: A Bivariate Selection Model." Journal of Public Economics 35 (February 1988): 1-24.

     Housman, J. "The Econometrics of Non-Linear Budget Sets." Econometrica (November 1985): 1255-1282.

     Keane, M. "A New Idea for Welfare Reform: How best to get people off the welfare rolls and into the labor market." Quarterly Review, Research Department of the Federal Reserve Bank of Minneapolis v. 19 n. 2 (Spring 1995): 2-28.

     Keane, M., and R. Moffitt. "A Structural Model of Multiple Welfare Program Participation and Labor Supply." International Economic Review 39 (Aug. 1998): 553-590.

     Leonesio, M. "In-Kind Transfers and Work Incentives." Journal of Labor Economics 6 (Oct. 1988): 515-530.

     Moffitt, R. "An Economic Model of Welfare Stigma." American Economic Review 73 (December 1983): 1023-1035.

     _______. "The Econometrics of Piecewise-Linear Budget Constraints." Journal of Business and Economic Statistics 4 (July 1986): 317-328.

     _______. "Incentive Effects of the U.S. Welfare System: A Review." Journal of Economic Literature 30 (March 1992): 1-61.

     Moffitt, R., and B. Wolfe, "The Effect of the Medicaid Program on Welfare Participation and Labor Supply." Review of Economics and Statistics 74 (1992): 615-626.

     Painter, G. "Low-Income Housing Assistance: Its Impact on Labor Force and Housing Program Participation." Unpublished paper from the author at University of Southern California, School of Public Administration, 1998.

     Zabalza, A., C. Pissarides, and M. Barton. "Social Security and the Choice Between Full-Time Work, Part-Time Work, and Retirement." Journal of Public Economics 14 (October 1980): 245-276.

Papers on Econometrics and Simulation Methods:

     Albright, R., S. Lerman, and C. Manski. "Report on the Development of an Estimation Program for the Multinomial Probit Model." Report Prepared by Cambridge Systematics for the Federal Highway Administration, 1977.

     Geweke, J., M. Keane, and D. Runkle. "Alternative Computational Approaches to Inference in the Multinomial Probit Model." Review of Economics and Statistics 76 (November 1994): 609-632.

     Greene, W. Econometric Analysis, PrenticeHall, NJ. 3rd Edition, 1997.

     Lerman, S. and C. Manski. "On the use of Simulated Frequencies to Approximate Choice Probabilities." In Structural Analysis of Discrete Data with Econometric Applications, Eds. C. Manski and D. McFadden. Cambridge: MIT Press, 1981.

     McFadden, D. "A method of Simulated Moments for Estimation of Discerate Response Models without Numerical Integration." Econometrica 57 (September 1989): 995-1029.

     McFadden, D. and P. Ruud. "Estimation by Simulation." Review of Economics and Statistics 76 (November 1994): 591-608.

     Pakes, A. and D. Pollard. "Simulation and the Asymptotics of Optimization Estimators." Econometrica 57 (September 1989): 1027-1057.

Papers on survey and administrative data for rent subsidized households:

     Casey, C. Characteristics of HUD-Assisted Renter and their Units in 1989, United States Department of Housing and Urban Development, Office of Policy Development and Research (PD&R), U.S. Government Printing Office, March 1992.

     Fowler, F. Survey Research Methods, Sage Publications, Beverly Hills, 1984.

     McGough, D. Characteristics of HUD-Assisted Renters and Their Units in 1993, United States Department of Housing and Urban Development, Office of Policy Development and Research (PD&R), U.S. Government Printing Office, May 1997.

     Shroder, Mark and Marge Martin. "NEW RESULTS FROM ADMINISTRATIVE DATA: HOUSING THE POOR, OR, WHAT THEY DON'T KNOW MIGHT HURT SOMEBODY" Office of Policy Development and Research, U.S. Department of Housing and Urban Development, Paper presented at the 1996 Mid-Year meeting of the American Real Estate and Urban Economics Association, May 29, 1996, available at "http://www.huduser.org/publications/smallgrants/index.html" or contact HUD USER, PO Box 6091, Rockville, MD 20849, 1-800-245-2691, TDD: 1-800-483-2209, Fax: 1-301-519-5767, E-mail: huduser@aspensys.com, and from U.S. Government Printing Office.

     United States Department of Housing and Urban Development. "Nationwide Sample of Assisted Households to Estimate Unreported Income, Excessive Housing Assistance and the Effects on HUD Subsidies, Calendar Year 1996, Phase I." A Joint Project of the Office of Public and Indian Housing, the Office of Housing, the Chicago Asset Recovery Center, Office of the Chief Financial Officer, and the Office of Information Technology. Washington, DC, June 1998, 20pp.

Papers on in-kind transfers:

     Cage, R. "Does Rental Assistance Influence Spending Behavior." Monthly Labor Review 117: 17-28.

     Crews, A. "Self Selection, Administrative Selection, and Aggregation Bias in the Estimation of the Effects of In-Kind Transfers." Unpublished Ph.D. dissertation, University of Virginia, 1995.

     Crews, A. "Do Housing Programs for Low-Income Households Improve Their Housing?" Center for Policy Research, Maxwell School of Citizenship and Public Affairs, Syracuse University, April 1996.

     Hanushek, E., and J. Quigley, "Consumption Aspects of Housing Allowances." In Do Housing Allowances Work? Eds. K. Bradbury and A. Downs. Brookings Institution. Washington, DC (1985): 185-240.

     Moffitt, R. "Estimating the value of an in-kind transfer: The case of Food Stamps." Econometrica 57 (March): 385-409.

     Moffitt, R., and B. Wolfe, "A New Index to Value In-Kind Benefits." Review of Income and Wealth 37 (1991): 387-408.

     Murray, M. "The Distribution of Tenant Benefits in Public Housing." Econometrica 43 (1975): 773-787.

     Olsen, E., and A. Crews. "Are Section 8 Housing Subsidies Too High?" Presented at the New Orleans Meetings of the AEA, January 1997.

     Painter, G. "Does Variation in Public Housing Waiting Lists Induce Intra-Urban Mobility?" Journal of Housing Economics 6 (1997): 248-276.

     United States General Accounting Office (GAO). "Housing Allowances: An Assessment of Program Participation and Effects." Program Evaluation and Methodology Division, No. 86-3, 1986.

     I would also like to acknowledge the financial support of the U.S. Dept. of Housing and Urban Development for employment as a student intern working in their Policy Development and Research Division under Dr. Jill Khadduri, and Economist Mark Shroder in Washington, DC and continuing at the local HUD office in Minneapolis, MN. Access to the HUD administrative data is restricted to HUD employees. Hence, the HUD internship support is what has made this project possible. Thanks also to Peter Angelides for discussions of simulation techniques and sample programs of SML methods using Visual Numerics, Inc.'s IMSL Math/Library - FORTRAN Subroutines for Mathematical Applications. And thanks to Mike Keane for suggesting this line of research, and his ongoing support. Thanks to John Geweke for help directing me to Digital's Visual FORTRAN package for a PC with Visual Numerics, Inc. IMSL. Thanks to Anh Nguyen for help decoding and extracting HUD's administrative databases stored under a vintage Unisys UNIVAC operating system on 28 poorly documented tapes.