The problem and an overview of solutions to it

This chapter considers the problem of estimating the impact of interventions in the presence of selection decisions by agents. For specificity we focus on the problem of estimating the impact of training on earnings when the enrollment of persons into training is the outcome of a selection process. The analysis of training presented here serves as a prototype for the analysis of the closely related problems of deriving selection-bias-free estimates of the impacts of unionism, migration, job turnover, unemployment, and affirmative action programs on earnings.

This chapter investigates the prior restrictions needed to secure consistent estimators of the selection-bias-free impact of training on earnings. We examine their plausibility in the light of economic theory.

We present assumptions required to use three types of widely available data to solve the problem of estimating the impact of training on earnings free of selection bias: (1) a single cross section of post-training earnings, (2) a temporal sequence of cross sections of unrelated people (repeated cross-section data), and (3) longitudinal data in which the same individuals are followed over time. These three types of data are listed in the order of their availability and in inverse order of their cost of acquisition. Assuming random sampling techniques are applied to collect all three types of data, the three sources form a hierarchy: Longitudinal data can be used to generate a single cross section or a set of temporal cross sections in which the identities of individuals are ignored, and repeated cross sections can be used as single cross sections.

In this study we report on a model of the UK economy and tax system which we have used to provide a numerical appraisal of the main impacts of the UK tax/subsidy system. With the basic variant of the model, we concentrate on the distorting effects of taxes and subsidies within a static full employment neo-classical general equilibrium framework, and calculate the resource allocation and distributional effects of alternative tax policy packages. We then consider a sequence of model extensions incorporating intertemporal and labour supply distortions due to taxes, and public good equilibria. In Part I of the study we outline the methods that we used. Both general and particular features are described, along with the functions and parameter values we use. We also summarize the data which give us estimates of tax and subsidy parameters for the model.

The main method of analysis we employ is counterfactual equilibrium analysis. We adopt an assumption that the UK economy achieves an equilibrium in the presence of existing tax/subsidy policies. We use data for a single year drawn from national accounts and other sources which we extend and transform into a form which is consistent with the equilibrium conditions of the model; this we term our benchmark equilibrium. We generate parameter values for the functions in the model such that we can replicate the benchmark equilibrium observation as a model equilibrium solution. The counterfactual analysis then involves the introduction of alternative policy regimes into the model.

Computational Experience with the Model

A substantial amount of computational experience has been acquired with the UK model.

The majority of execution time in solution is spent in function evaluation, particularly in evaluating the market demands for commodities at candidate price vectors. This suggests that execution times are sensitive to the functional forms which are used to describe demand patterns and this seems to be borne out by experience. If steps taken across a simplex have associated with them a fixed number of function evaluations per step, even if the number of steps remain constant for higher dimensional problems (which typically does not happen) the increased time spent in function evaluation per step will cause execution times to rise considerably.

The amount of execution time needed to numerically determine a competitive equilibrium can therefore be directly related to ‘dimensionality’. In its crudest terms, this can be thought of as the overall size of the model, but in practice there are specific dimensions which can be identified as critical.

Two dimensions in the model are especially important.

(i) The Dimensionality of Function Evaluation:

This is the dimension in which calculations underlying market demand and supply functions must be made. On the demand side of the economy the critical features are the twin dimensions of the number of consumers and the number of commodities. In the model of the UK this is a dimension of 103 by 64.

In this chapter we discuss some of the problems involved in selecting elasticities of substitution for industry production functions and household demand functions. We discuss difficulties in interpreting these parameters in light of the empirical estimates we have been able to find, and outline the sources used in our choice of values for the model. We also comment on the reliability of the estimates.

Elasticity values are critical parameters in determining impacts of policy changes generated by the model, and careful discussion of their values is needed prior to presentation of results. We separately report and discuss elasticity values we use for production functions, demand functions, and foreign trade behaviour. In view of the extensions to our basic variant model, we also summarize the elasticities we use in modelling labour supply and savings behaviour.

Production Function Elasticities

Our model incorporates CES value added functions for each industry. We therefore need to specify a separate value for the elasticity of substitution between capital and labour for each industry in the model.

Since the introduction of the CES function in the early 1960's, there has been a continuing debate as to whether the elasticity of substitution for manufacturing industry is approximately unity. If unity is a correct value, the more complex CES form can be replaced by the simpler Cobb-Douglas form which has unitary elasticity of substitution. This debate has concentrated primarily on substitution elasticities for aggregate manufacturing rather than component industries as specified in the model.

Introduction

In analyzing discrete choices made over time, two arguments favor the use of continuous time models: (1) In most economic models there is no natural time unit within which agents make their decisions and take their actions. Often it is more natural and analytically convenient to characterize the agent's decision and action processes as operating in continuous time. (2) Even if there were natural decision periods, there is no reason to suspect that they correspond to the annual or quarterly data that are typically available to empirical analysts, or that the discrete periods are synchronized across individuals. Inference about an underlying stochastic process that is based on interval or point sampled data may be very misleading, especially if one falsely assumes that the process being investigated operates in discrete time. Conventional discrete choice models such as logit and probit when defined for one time interval are of a different functional form when applied to another time unit, if they are defined at all. Continuous time models are invariant to the time unit used to record the available data. A common set of parameters can be used to generate probabilities of events occurring in intervals of different length. For these reasons the use of continuous time duration models is becoming widespread in economics.

Introduction

In the UK, as in other countries, there has been substantial discussion in recent years of tax reform. Many of the problems and difficulties encountered by the UK economy have, at times, been attributed to the structure of the tax system, and over the years both politicians and academic economists have produced a number of alternative proposals for tax reform. The Report of the Royal Commission on Taxation (1966), and more recently the Meade Report (1978), are evidence of this continuing interest. In spite of pressure for change, however, quantitative analysis of the effects which taxes and subsidies produce (especially those on resource allocation) remains surprisingly sparse, both in the UK and elsewhere.

In this study we use a conceptual approach, widely explored in theoretical literature in public finance, to analyze the impacts of the UK tax/subsidy system on the allocation of resources and the distribution of income using 1973 data. We explore general equilibrium efficiency and incidence effects of taxes and subsidies, emphasizing a numerical, empirically oriented version of this well-known approach. In Part I of the study we describe the structure of the model we use. Part II reports our empirical results.

The approach used is to build a general equilibrium model using explicit demand and production functions. In the model all markets clear in equilibrium. Demands equal supplies for both goods and factors, and no industry does any better than break even in terms of profitability.

This manuscript was originally prepared in camera ready copy in 1981, at which point the original publisher withdrew due to concerns over the small market for such a specialized research monograph. Since this date there have been many developments both within the field of applied general equilibrium analysis, and in UK tax policies.

Recent developments in applied general equilibrium are reflected in two conference volumes [Scarf and Shoven (1983) and Piggott and Whalley (forthcoming)]. A recent survey paper by Shoven and Whalley (1984) provides an up to date summary. On the tax front, developments in the UK have continued with the usual round of budget and other changes.

We decided not to revise our manuscript to reflect all of these developments. Not only does this involve a large volume of work, but we were concerned not to interrupt the flow of the present draft with a series of inserts. Even without any revisions we believe that our book makes a significant contribution to the applied general equilibrium literature by focussing applied modelling heavily towards results, and their ultimate policy applicability. While some of the model structure has been extended in subsequent work (particulary in dynamic sequenced models used to analyze taxation and savings issues), there are features of our model which are still not present in other modelling efforts. Among these are the incorporation of public goods as a model variant, and household detail on the demand side.

This chapter will discuss models for longitudinal data in which a sample of individuals or firms is followed over time. A primary advantage of such data is that they allow us to test and relax assumptions that are implicit in a cross-sectional analysis. Section 1 considers the main issue in the context of the familiar linear model. Here a basic specification test is a comparison of a regression based on changes with a cross-sectional regression. This test is put in a general framework that relates it to tests for strict exogeneity in time series analysis. We show that the failure of strict exogeneity may be due to heterogeneity, which suggests a reformulation in which there is a mixture of strictly exogenous processes. The assumption of strict exogeneity in a mixture model is itself testable, and such tests should be routine whenever the standard analysis-of-covariance estimator is used.

The treatment of heterogeneity leads to the statistical problem of incidental parameters. Since the typical panel has a large number of individuals observed over a short time period, the relevant limiting distributions have the number of individuals increasing but not the time dimension. If we allow for individual specific parameters, then maximizing the joint likelihood function does not in general provide a consistent estimator of the parameters common to all individuals. We discuss procedures that are valid in general, based on conditional, marginal, and posterior likelihood functions.

The aim of this chapter is to present a survey of how the statistical theory of multivariate counting processes can be useful when studying labor market dynamics. Throughout it will be assumed that longitudinal data are available on some sample S of individuals during a fixed calendar time interval I =[to,t1].

We shall be working with the basic three-state model illustrated in Figure 1. The state “unemployed” will be denoted 0, the state “employed” will be denoted 1, and the state “out of labor force” will be denoted 2. The number of individuals in state i (i = 0,1,2) at time t — (t ϵ I) is denoted Yi (t) . The requirement of having longitudinal data implies that for each individual v ϵ S and for each time t ϵ I the state to which v belongs at t is known and thus that Y0 (t), Y1 (t) and Y2 (t) are known and that the numbers Nij(t) of direct transitions from i to j before t are known. These stochastic processes Ntj (t) counting the transitions between the states are the basic observations, and in the rest of this chapter statistical models for these counting processes will be discussed. In the presentation, only references to the statistical literature where these methods have been developed will be given. The methods will, however, be related to the specific problem of studying unemployment, and as far as possible terminology from econometrics will be used. Also, in the final section of the chapter the models will be related to various models suggested previously in the econometric literature.

As indicated in Chapter 2 all major taxes and subsidies operating in the UK (post April 1973) enter our model. This chapter discusses the treatment of each, and outlines their major discriminatory features. Numerical values used for tax rates are reported in Chapter 5.

An overview of the 1973 Tax/Subsidy System in the Model

In the 1973 public sector accounts used in the model gross tax revenues are £25.0 billion and expenditures on subsidies are £5.3 billion. UK NNP in our data for 1973 is £69.8 billion. 35.8% of NNP is collected in taxes and 7.6% paid in subsidies. The major taxes are income tax (£7.3 billion in 1973), specific excises (chiefly on hydrocarbon oil, tobacco, and drink; a combined total of £3.9 billion), national insurance and related contributions (£3.9 billion), corporation tax (£3.2 billion), rates (£2.6 billion), and value added tax (£2.2 billion). The major subsidies are those to local authority housing (£3.1 billion) and nationalized industries (£1.4 billion). These are listed in Table 3.1 along with the major features of each and their treatment in the model.

Each of these is treated as an ad valorem tax or subsidy. Some are treated as taxes on factor use with differential rates by industry, some are production taxes on intermediate use, some are consumer taxes on commodity purchases, and some tax incomes of consumers. The model treatment adopted for each tax and subsidy is motivated primarily by the discriminatory features which each introduces.

Introduction

Much of the empirical work on labor supply ignores life cycle theory, and practically none of it admits the possibility that consumers are uncertain about future events. A natural question that arises concerns the implications of these factors when evaluating and interpreting estimates of wage and income effects found in the existing literature. This study provides an answer to this question. While the discussion here concentrates on hours of work behavior, it fully applies to the analysis of consumption behavior as well.

The chapter begins with the development of an economic model of consumption and labor supply behavior in an intertemporal environment in which the consumer is uncertain about his future income, the future relative prices of consumption and leisure, and variables influencing his future preferences. A consumer making decisions in this model reacts differently to changes in variables than he would in a deterministic setting. In response to a change in the current wage rate, for example, the adjustment the consumer makes in his consumption and in hours of work depends on how much of this change was anticipated and how it alters expectations concerning future wages. Because the economic model considered here explicitly addresses such issues, it provides some direction on how to account for the various aspects of uncertainty when specifying empirical relations.

Introduction

In this part of the monograph we report our findings on the allocative and redistributive effects of the UK tax/subsidy system using the model described in preceding chapters. We simulate a number of counterfactual equilibria for the economy under alternative policies from those associated with the 1973 benchmark equilibrium. We compare counterfactual and the benchmark equilibria to arrive at our evaluation of the impacts of the tax/subsidy system.

In these comparisons we concentrate on various summary indices. In our welfare analysis we stress Hicksian compensating and equivalent variations. The compensating variation (CV) for a single household is the sum of money that would need to be taken away from a household so as to restore its original utility level prevailing before the change. The Hicksian equivalent variation (EV) is the sum of money which would need to be given to a household to increase its welfare to a level equivalent to that which it would have enjoyed had some proposed policy change been enacted. The compensating variation is a measure at the new equilibrium prices; the equivalent variation is measured at the prechange prices. These definitions imply that a positive equivalent or compensating variation indicates a welfare gain from moving to the counterfactual equilibrium from the benchmark. As Kay [1980] points out, in a sequence of wise comparisons between alternative counterfactual equilibria and the same benchmark equilibrium, the sequence of comparisons using EV's uses the same price data, since the EV is based on original benchmark prices.

Introduction

This chapter presents results from our analysis of the static industry and commodity distortions in the UK tax/subsidy system using 1973 data. Distortions of labour supply, savings decisions, those attributable to a non-indexed tax system, and analysis involving public goods are all left until Chapter 9. In this chapter, we concentrate on one central counterfactual experiment from the model and explore the results in detail.

The characteristics of this central case are as follows:

1. 1. Fixed factor static formulation. Aggregate factor supplies are fixed; household savings do not vary with the rate of return on capital. A single period static equilibrium is assumed in the presence of alternative policy regimes.

2. 2. Equal yield tax replacement of all existing taxes and subsidies. All existing taxes and subsidies are abolished and replaced by a non-distorting yield preserving single rate sales tax. The size of the public sector is preserved in real terms. The replacement follows Musgrave's (1959) concept of “differential incidence”.

3. 3. Terms of trade neutralizing surtax/subsidy. Because of the nature of the tax system and the trade elasticities used, terms of trade effects accompany tax changes in the model. UK trade elasticities are low, and since high effective tax rates apply to the production and sale of exports in the model, the tax system produces a terms of trade gain to the economy. Without a terms of trade neutralizing tax we find that the welfare gains to the UK are smaller than they would be with such a tax.

Introduction

In this chapter we consider additional features of public sector activity in the UK by extending our basic variant model in a number of directions. We analyze both the tax distortion of the labour-leisure choice and the distortion of savings. We also evaluate the distorting effects of the tax system through its interaction with inflation. We next consider the income effects associated with the transfer mechanism on the expenditure side of government activity and briefly discuss some stylized calculations associated with welfare reform. We also examine an alternative solution concept for our model in which the level of provision of public services is endogenously determined as part of the optimizing procedure. Finally a particular tax reform experiment associated with the changes introduced in the UK is reported, in order to demonstrate the applicability of our approach to more practical situations where explicit tax reform proposals are being considered.

Tax Distortions and Labour Supply

Our central case analysis in Chapter 7 assumes the supply of factors is fixed as changes occur in taxes and subsidies. In this section we use a factor supply model in which labour supply depends on taxes.

We consider households to have utility functions which are defined not only over the commodities in the model, but also over consumption of leisure. We augment the labour endowment of households so that households repurchase a portion of their labour endowment in the form of leisure, with their purchase decision following directly from utility maximization.