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Can cost-effective reallocation of inputs increase the efficiency of the public health system in Pakistan?

Heavy investment in many developing countries in the social sector including health is based on the premise that human capital is vital to the growth and development of a nation. However, Pakistan's spending on this sector has been one of the lowest in the region. In the present environment of high budget deficits, one does not expect substantial public funds to be forthcoming and diverted towards the social sector in the intermediate- or medium-term future. The critical issue facing the public sector should then be to design health policies which must be cost-effective and efficient. This study examines these health policy issues within the context of an optimisation framework for public health system, forecasts future upto (2002-03) and discusses an efficient optimal mix of health inputs, outputs, expenditures, and wage policies under alternative scenarios. The study recommends that, first, growth of health infrastructure building in the urban areas be slowed down in the short-term (two to three years), and some of the resources reallocated towards the rural sector either in terms of building new Basic Health Units or upgrading the existing Rural Health Centres. Second, not only attractive wage policies be formulated for health personnel, but the status of nurses in the public health system be also elevated by giving them higher grades, Third, for every rupee of development expenditure incurred, Public Health Department must plan or keep provisions for recurring outlays. All this reallocation of resources is feasible within the projected actual budget and it will lead to efficiency gains in the order of 8 to 10 percent for the entire public health system.


In recent years, many developing countries have invested heavily on the social sector including basic health. This is based on the premise that human capital is vital to the growth and development of a nation. Therefore, keeping the mass healthy is as important as providing them with basic education. Pakistan has had an impressive GDP growth rate of about 8 percent per annum in 1991-92, out of which only a meagre 0.7 percent was spent on the health sector. When this figure is translated in monetary value it amounts to only 7 cents per thousand dollar GNP spent on the health sector. This amount is very little by any standard and, in fact, the picture is even more dismal when this figure is compared with those of other developing countries.

Table 1 shows the percentage of total government expenditure on the health sector in relation to government expenditure and GNP for selected developing countries. Of the eight countries selected for comparison, Bangladesh and Sri Lanka appeared to have spent 4.8 percent of their government expenditure on health as opposed to only 1 percent by Pakistan. Even a small, poor country like Nepal spends more money (4.7 percent) than Pakistan on the health sector. In the list of countries considered, Pakistan's standing in terms of spending on health (either as a proportion of government expenditure or GNP) is the lowest which is very discouraging and disappointing. Although, Pakistan's spending for this sector is one of the lowest in the region, in the present environment of high budget deficits faced by the country, the critical issue facing the public sector should then pertain to designing health policies which must be cost-effective and efficient. A recent study by the World Bank on Pakistan's Health sector 1991) noted:
 ... inefficiency is widely regarded as a central problem in the
 health and population sectors in Pakistan ... (especially) in the
 public sector. Resources are misallocated, in part because no
 investigation has typically been made into the cost-effectiveness
 of various options. Political influence and leakage of equipment
 and supplies further distort public sector allocations. Poor
 management and centralised financial, administrative and management
 authority reduce the efficiency of facility-level staff services.

The major policy debate, in this context, facing the public health system in Pakistan, should then address the problem of re-allocating the limited resources among inputs in the most economical way. In other words, given the limited available budget, should the public health department (PHD) go for a more infrastructure programme (development expenditure) or hire more health personnel (recurring expenditure) or a combination of both so that there is a real improvement in the health services? Or, even more importantly, what type of wage policy should it adopt if more personnel are needed to work in rural health centres (RHCs), basic health units (BHUs) and hospitals, especially when there are shortages of competent nurses and doctors in the country?

Furthermore, if, historically or even in the future, there is more emphasis on development expenditure i.e., rapid expansion of BHUs or RHCs especially under the recently initiated Social Action Programme (SAP), (1) what implications will this programme have on recurring budget? Will the present health system in the country be able or capable of handling such an accelerated expansion of facilities? That is, given the present institutionally fixed wages and inelastic supply of health personnel, will the health system be able to attract enough doctors or nurses? All these public policy issues are critical for the sustainability of the basic health programme in Pakistan and they cannot be addressed in isolation. In this context, a general optimisation framework for the Public Health System (PHS) is needed if the efficient cost-effective input-output linkages consistent with the resource (budget) constraints and institutionally fixed wage policies are to be established.

In view of the above considerations, therefore, the objective of this study is:

(a) To develop a general optimisation framework in order to address the policy issue of cost-effectiveness and efficiency for the public health system;

(b) based on the above theoretical framework, to identify and forecast an optimal mix of cost-effective inputs (doctors, nurses, paramedics), outputs (outdoor and indoor patients) wages and expenditure requirements (both recurring and development) of PHS covering up to the end of the Perspective Plan period, 2002-2003; (2) and

(c) to estimate and compare the extent of efficiency gains/loss for PHS under alternative assumptions.

The organisation of rest of the chapter is as follows. Section 2 develops a simple optimisation model for the public health system and then formulates propositions under alternative assumptions (e.g., constrained strategy etc.). In order get an intuitive insight, we first illustrate the model using a diagram and then in Section 2.1 and 2.2 the analytical derivations and conditions of the model to achieve positive efficiency gains for health facilities are presented. Section 3 presents the discussion on simulation results and ensuing policy implications. Before discussing the simulation results, we also report parameter estimates for input supply and production functions for Punjab in Sections 3.1.1. The discussion on ex-ante simulation results are presented in Sections 3.1.2 while the policy conclusions are given in Section 4.


In the following, we develop a theoretical optimal allocation model for the health sector under institutionally fixed wage rates for health professionals. In order to keep the analysis simple and, at the same time, realistic, we assume that the health facility produces output [e.g., total patients treated (Q)] using two inputs, namely, infrastructure [represented by beds (B)] and medical professionals [e.g., doctors (D)]. In addition, the supply of personnel is assumed to be inelastic as there does not exist an unlimited inflow of doctors and, especially at the institutionally set low wage rates, many of these health professional are reluctant to offer their services to the public health system. The public sector is assumed to be able to set the wage rates of doctors and other government personnel (supposedly below the market rate) because their share (in terms of total expenditure) within the health sector is very large. Thus, the public sector, represented by the provincial health department (PHD) in this case, can be labelled as a monopsonist. Due to limited public funds allocated to the health and other social sectors, the basic task of PHD (acting as a monopsonist) in this context is to maximise the output of the health facility subject to the available budgeted resources (TC). Assuming a well behaved production technology, c as the unit cost of a hospital bed (B) and as the fixed wage rate for doctors, the optimal health input allocation problem of PHD can be illustrated with the help of a diagram as given in Figure 1.


Essentially, the diagram consists of isoquant (Q) and isocost (*) curves for various combination of Bs and Ds. With institutionally fixed wages for doctors and unit price per beds (c), the initial isocost line is given by [C.sub.0] with slope (=-w/c) in Figure 1. It is, however, important to note that not all points (particularly [E.sub.0], on the broken portion of [C.sub.0]) on this isocost are feasible. Given the inelastic supply of doctors, the number of professionals offering their services will simply not exceed [D.sub.0]. Therefore, the initial equilibrium in this case will be established at [E.sub.0] as shown in Figure 1, which is neither efficient nor optimal even though the available budgeted resources are completely utilised. Here obviously, more beds and fewer doctors are employed to produce an inefficient [Q.sub.0] level of output [i.e., patients treated].

On the other hand, however if PHD adopts a more flexible wage policy and allows the wage rate of doctors to increase from * to [w.sub.1]. then the availability of doctors will increase from [D.sub.o] to [D.sub.1]. It is interesting to note that even though the isocost line has pivoted inwards (due to higher wages) form [C.sub.0] to [C.sub.1], the output (patients treated) however, has increased from [Q.sub.0] to [Q.sub.1]. In fact, the new equilibrium level attained at [E.sub.1] is at a higher isoquant which is both optimal as well as cost effective. (3) The above simple example leads us to make the following proposition that:

Proposition 1: It is possible for the public health policy-maker to be cost efficient and, at the same time, achieve a higher output (in terms of more patients treated) even with the same available budget provided the public sector adopts a flexible wage policy (close to the market wage) for health professionals (be it doctors, nurses or paramedics).

2.1 Optimisation Conditions under a Monoposonistic Public Health System

It was argued earlier that the monopsonistic equilibrium output, such as [E.sub.2] in Figure I, will not be feasible under an institutionally fixed wage system. However, in order to explore alternatives (other than flexible wages) under which the monopsonist PHD may achieve equilibrium at a higher output level, we explicitly need to derive the first order conditions (FOCs) of the present health system. By comparing these FOCs with those of the standard competitive producer we may be able to establish the extent of divergence between them and thus propose the condition(s) which will lead to an improvement in the output for PHD.

Assuming the supply of doctors as a function of wages [D=D(w)] and output [patients treated (Q)] being produced by doctors and beds, the optimisation problem of the monoposonistic PHD will simply entail the maximisation of the following:

Max: Q = Q[D(w);B]; ... (1)

subject to: [bar.C] = wD(w) + (m + c)B; ... (2)

where [lambda] is the unit recurring cost per bed. Other variables in the above model are as defined earlier. Writing the lagrangian function of the above, we get:

P(w,B,[lambda]) = Q|D(w);B|+ [lambda]|[C.sub.0] - wD(w)-(m + c) ... (3)

where [lambda] is the Lagrangian multiplier. The maximisation of the above Lagrangian will yield the following three first order conditions (FOC):


[partial derivative]p/[partial derivative]/B = [partial derivative]Q/[partial derivative]B = [partial derivative]Q/[partial derivative]/D - [lambda](c + m) = 0; ... (5)

[partial derivative]p/[partial derivative]/[lambda] = [bar.C] - wD - (c + m)B = 0; ... (6)

From the first two FOCs, we have


If we define the marginal rate of technical substitution (MRTS) between doctors and beds as:

MRT[S.sub.D,B] = [partial derivative]Q/[partial derivative]/D/[partial derivative]Q/[partial derivative]/B; ... (8)

and the elasticity of supply of doctors with respect to wages ( ) as:

[[xi].sup.S.sub.D] = w/D x [partial derivative]D/[partial derivative]/w; ... (9)

then the above optimisation problem of the monopsonistic PHD will require that

[MRTS.sub.D,B] = w/(c + m) [??] 1 + 1/[[xi].sup.S.sub.d] [??]. ... (10)

The above optimisation condition simply states that, for the monopsonistic PHD, [MRTS.sub.D,B] should not only be equated to the ratio of relative prices [w/Cc+m)], as is the case for the standard competitive producer, but it should now be equated to a weighted relative prices of doctors and beds. The weight factor simply includes the supply elasticity of doctors ( ). It is interesting to note that, depending on the magnitude of ( ), the above optimisation condition for monopsony can be equivalent to that of the competitive producer. This leads us to make our second proposition that:

Proposition 2: The optimal condition (s) for the monopsonistic producer (PHD) can be equivalent to those of the competitive producer as long as the price (wage rate) elasticity of supply of the monopsonistic input (doctors) is infinitely elastic.

Whether or not the above proposition is valid in the case of PHD is a matter of empirical investigation and we relegate this to the next section where we report our results on estimated elasticities for inputs.

2.2 Efficiency Gain/Loss for the Monopsonistic PHD Producer

Based on a simple model constructed earlier we can also analytically compute and compare the efficiency gain/loss (in terms of output) of the monopsonistic PHD under alternative scenarios. Suppose that, at a given point in time, the actual allocation of inputs by PHD is such that the size of the infrastructure in the form of beds (B) is greater than that of the optimal monopsonist. In the following, we can demonstrate that halting or reducing the growth of infrastructure building and optimally reallocating the resources towards health professionals may lead to an improvement in the health facilities. In fact, what is more interesting now is that the monopsonist PHD with fixed beds (named as constrained monopsonit) will be able to achieve an even higher level of output as compared to the standard monopsonist.

If we define [O.sub.c.sup.*] and [O.sub.s.sup.*], respectively, as the optimal level of outputs for the constrained and standard monopsonist, then the expression for efficiency gain/loss (E) can be written as:

E = [[O.sub.c.sup.*]/[O.sub.u.sup.*] - 1] x ... (11)

Obviously, a positive value for E will lead to an efficiency gain in favour of the constrained monopsonist and vice-versa. By substituting the optimal values for [O.sub.c.sup.*] and [O.sub.s.sup.*] (obtained from the optimisation model) in the above equation, we can obtain an explicit expression for E.

If the supply elasticity and the share of doctors ([[pi].sup.D]) and nurses (([[pi].sup.B]) are assumed to be fixed in magnitude as a simplifying assumption and the production function is assumed to be Cobb-Douglas, then the two optimal outputs (standard and constrained) and their corresponding input demand functions obtained through the optimisation procedure can be written as : (4)

Standard Monopsonist

[O.sup.*.sub.s] = [A.sub.o][([D.sup.*.sub.s]).sup.[alpha]][([B.sup.*.sub.s]).sup.[beta]]; ... (12)

[B.sup.*.sub.s] = [[PI].sup.B]/(m + c)([bar.C] + c[B.sub.-1]); ... (13)

[D.sup.*.sub.s] = [[[[PI].sup.D]([bar.C] + c[B.sub.-1].sup.Y/1+Y]; ... (14)

Constrained Monopsonist

[O.sup.*.sub.c] = [A.sub.o][([D.sup.*.sub.c]).sup.[alpha]][([bar.B]).sup.[beta]]; ... (15)

[D.sup.*.sub.c] = [([bar.C] - m[bar.B]).sup.Y/1+Y]; ... (16)

where [gamma] is the supply elasticity of doctors and [alpha] and [beta], respectively, are the output elasticities of doctors and beds. Substituting these optimals, we get the following explicit expression for E which contains entities that are either exogenous [e.g., . and [bar.B]] or fixed in values [e.g., share of doctors ([[pi].sup.D]), m, and c]:

E = [[([bar.C] - m[bar.B])/[[PI].sub.D]([bar.C] + c[B.sub.-1])].sup.[alpha]] x [([bar.B]/[B.sup.*]).sup.[beta]]; ... (17)

Thus, for E to be positive (implying positive efficiency gains), the above equation should be written as:

(w[D.sub.c.sup.*]/w[D.sub.s.sup.*] > [([B.sub.s.sup.*]/[bar.B]).sup.[beta]/[alpha]] ... (18)

This leads us to make our third proposition that:

Proposition 3: Constrained monopsonist PHD with fixed infrastructure (beds) may have positive efficiency gains (E>0) relative to those of a standard monopsonist as long as the fixed number of beds (B) exceeds the optimal ([B.sub.s.sup.*) and, at the same time, the total allocation of expenditure on doctors by the constrained monopsonist is greater than that of the standard case.

These three propositions have important implications for public health policies and they are summarised below:

(a) In general, given limited budgeted resources available, a proper cost effective allocation between recurring (health professional) and development expenditures (infrastructure) can lead to higher efficiency gains for health facilities.

(b) In the case where PHD acts as a monopsonist and there is an inelastic supply of health professionals, adopting a flexible wage policy rather than institutionally set wages may not only attract more of these professionals but it is also possible to attain a higher output for the health system which will be both cost effective and efficient.

(c) In the even that the existing allocation of infrastructure (beds) exceeds the optimal level, than a policy of consolidating the infrastructure and diverting the limited available resources towards recurring outlays can lead to efficiency gains which, in fact, will exceed those of the optimal cost effective producer.

In order to test these theoretical propositions and also to obtain the size and magnitude of these efficiency gains for PHD, next section, as an example, develops an empirical simulation model based on combined provincial data for Pakistan.


This section reports simulation forecast results, both historical and ex-ante, based on optimisation strategies subject to available resources for the public health system in Pakistan. Estimated optimal mix of expenditures on inputs in this context will be efficient and also cost effective. Thus, a comparison of the actual available data on health output with the forecasted values will enable us to compute the efficiency gain/loss for alternative optimal health policies. In addition, the simulation forecast results will provide us with an opportunity-to test the validity of the propositions made in the previous section.

Long-term forecasts generated by the model covering up to the end of perspective plan period 2002-03 will be useful for policy-makers in establishing the optimal requirements of physical health inputs (e.g., doctors, nurses, paramedics and beds), expenditure allocations (both development and recurring) and the wage policy under alternative health strategies.

3.1. Simulation Results for the Public Health System

In this section, we report estimated simulation results based on an extended model developed for the public health system. The basic parameters (e.g., elasticities, output share, etc.) used for simulation purposes, in this study, were estimated employing health sector data on Punjab (5). Since there is a plethora of numbers generated by the simulation model, in order to describe these numbers more effectively, only the broad policy oriented results are discussed in the main text.

3.1.1. Estimated Wage Elasticities and Production Functions

Estimated ordinary least squares (OLS) parameter values of the supply function for health professionals based on RHFs and UHFs of Punjab are given in Table 2. The supply function for each professional included its respective wage rate and the number of registered professionals.

Since the function used is in logarithmic form, the parameters estimated in this context simply represent elasticities. For instance, in case of doctors in RHFs, the estimated parameter value of 1.47 in Table 2 represent the doctors' supply elasticity with respect to wage rates. Analysing the results in Table 2, it is interesting to note that health professionals in UHFs have inelastic wage elasticities (less than one). This implies that these professionals, in most cases, will be less than enthusiastic in offering their services in response to a wage rate increase. These wage elasticities (less than one). This implies that these professionals, in most cases, will be less than enthusiastic in offering their services in response to a wage rate increase. These results have important implications in terms of interpreting the propositions made earlier. Obviously, with an inelastic supply of health professionals, an institutionally fixed wage policy will not be copious enough to attract them towards the public health system.

Table 3 reports the estimated parameter values for health output (patients treated) production functions of both RHFs and UHFs. These estimated regression results in Table 3 indicate that, for both RHFs and UHFs, the role of infrastructure (in terms of large parameter values for beds as compared to other inputs) in the production process is more dominant than other remaining inputs, namely, health professionals. Analysing the health problem on the basis of production function alone, in this case, may suggest that resources be diverted towards building of infrastructure in order to improve health facilities. However, it should be noted that a production function approach may tell us only about the technical efficiency of the inputs.

Whether a technically efficient input is also cost-effective from the entire health system point of view can be established if the problem is analysed within a broader optimisation framework where the available cost constraints are also considered. Inputs derived from the optimisation approach will not only be optimal but, more importantly, they will be cost-effective. Distribution of health inputs through this optimisation principle will ensure the allocative efficiency of the health system. In the next section, we first discuss the historical optimisation simulation results and then present the ex-ante results.

3.1.2. Ex-ante Forecast and Efficiency Gain/Loss (1992-2003)

Based on the estimated supply and output elasticities from Tables 2 and 3, respectively, and exogenously given profile for total cost and total stock of registered health professionals, we can now directly compute the optimal expansion paths for inputs, and output for both UHFs and RHFs using the reduced form expressions derived from the optimisation problem. (6)

Tables 4-6 show that there were more beds for urban hospitals than they should have had in 1992 if the system had operated under a cost-efficient approach. A pertinent public policy question that may arise in this context is what should the PPHD do or what options are available to them so that there is a real improvement in the system in terms of positive efficiency gains? Obviously, one thing PPHD possibly cannot or should not do, is to dismantle its existing infrastructure. In fact, in future, the growth in infrastructure building programmes (in terms of new hospital beds) undertaken by PPHD should be slowed down or perhaps halted at the current level. Adopting such a policy will enable the PPHD to achieve the optimal mix of inputs in due course of time so that with each year gone by the population growth and the normal wear and tear of capital will gradually bring the existing number of beds closer to the optimal value.

In the following we present ex-ante simulation results, relying on two strategies: (a) standard strategy based on normal optimisation approach adopted earlier; and (b) constrained strategy based on an optimisation problem in which the beds in UHFs are now fixed at the baseline year 1992 level until they become equal to those of the standard strategy. The simulation results for health personnel and infrastructure, wage structure and efficiency gain/loss based on both standard as well as constrained strategies are reported in Tables 4-6.

It should be noted that the future data under the headings of actual in Tables 4-6, do not exist in published documents. They are, however, generated in this study by simply taking the annual compound growth rates of the past five to ten years of actual historical data on these variables. The underlying behaviour in projecting these actual data is predicated on the presumption that the Public Health Department continues to follow the future course of actions based on their health policies and practices of the recent past in matters concerning setting wages, hiring health professionals, annual development plans, etc. Comparing these actual data with the simulated ones generated by our optimisation model will not only enable us to examine the extent of divergence between optimal and sub-optimal health inputs within and across different health facilities but, more importantly, the above analysis will allow us to compute the size of ex-ante efficiency gain/loss of the optimal approach by simply calculating the yearly percentage deviation between optimal and actual outputs of a given health facility.

Considering 1991-92 as the baseline year, future projections are made up to the end of the Perspective Plan period (2002-03). In addition, forecasts for all monetary variables are measured in current rupees. Having computed the actual projected data on health inputs (between 1992-93 to 2002-03) based on the methodology explained above, the corresponding actual health output variable is generated using the underlying estimated production technology parameters reported in Table 3. (7)

Focusing on the board policy issues, the ex-ante simulation results reported in Tables 4-6, reveal several interesting facts that have important implications for public Health Policies in Pakistan. The salient features of the results are summarised below:


* Actual number of beds in UHFs in the baseline year 1991-92 appeared to be greater than what an optimal optimisation strategy would stipulate by over 13 percent. However, by the end of the perspective plan period (2002-03), this figure may come down to about 10 percent as shown in Table 4. It is important to note that if the public Health Department (PHD) were to adopt a policy of slowing down the growth of health infrastructure (in terms of beds) and re-allocate the existing resources then our results suggest that it is possible for the PHD to attain an efficiency gain of about 11 percent for UHFs in 1994 as reported in Table 6.

* Furthermore, the re-allocation of resources from urban health development expenditure may take place not only towards other urban recurring activities (e.g., more medicine and health personnel) but, interestingly enough, these resources can now he diverted towards rural health facilities. In fact, our analysis suggests that some of these funds Could be transferred towards the development of rural infrastructure (in terms of either upgrading BHUs to RHCs or outright construction of new BHUs).

Health Personnel

* In terms of health personnel, the optimisation model predicted a faster growth for doctors in RHFs during the entire plan period (about 11.1 percent p.a.), which is to be induced by raising their salaries by a substantial amount particularly in the earlier years (over 15 percent in 1993) as shown in Table 5. However, once enough doctors are attracted towards RHFs, the model predicts modest salary increases towards the latter part of the plan for the health system to be cost-effective.

* As for the doctors in the UHFs, cost-effective strategy suggests roughly the same number of doctors as the actual but with significantly higher salaries by the end of the plan period by about 11 percent as shown in Table 5. This result can be rationalised since, in urban areas, enough opportunities and alternatives are available to the doctors (in private hospitals or clinics). Thus, to improve urban health facilities in the long run, PHD should hire fewer good-quality doctors and pay them well.

* If PHD were to pursue its wage policies for nurses at the existing pattern, then the optimisation model predicts severe shortages of nurses to the extent of over forty-two percent in 1992 as reported in Table 4. Shortages will persist even at the end of the plan period 2002-2003. This excruciating situation of nurses in the present set-up in Pakistan is due to a combination of many factors. Obviously, one of the important reasons is the present low salary structure and, in this regard, the optimisation model suggests an immediate boost in nurses' salary by over 26 percent as shown in Table 5. Another reason is the social stigma attached to this profession particularly in the public sector health system in Pakistan. It needs to be emphasised that, even in the Defence Medical Services in Pakistan, nurses are not only paid reasonable salaries but, more importantly, they are accorded an honourable status in the military hierarchy. For instance, a nurse would begin her career in the Armed Forces as a commissioned officer while, in the public health system, the starting level is only at the BSP grade 11 that is far below the category of an officer (BSP-17).

Expenditure Pattern

* The critical public policy issue that deserves some discussion in this context is the availability of funds to meet the future recurring expenditure obligations for the health system. Our optimisation model predicts recurring outlays of over 5 and 2.5 times that of development expenditures for UHFs and RHFs, respectively, in 1992-93. These figures are expected to remain high until the end of the Perspective Plan period. Many plans formulated in the past emphasised the establishment of infrastructure in terms of opening new hospitals, RHSs, and BHUs without giving due consideration towards the recurring expenditures [e.g. health personnel and other inputs (medicine, x-ray films, etc.)]. What is crucial for the long-term sustainability of the Public Health System is the commitment from the policy-makers for provision of steady inflow of funds to meet recurring expenditure.

Efficiency Gains

* A crucial part of our analysis in this study is to investigate whether by becoming more cost-effective it is possible for the Public Health Departments to improve their provision of basic health facilities. The optimisation results in Table 6 suggest that about ten percent efficiency gains can be made in UHFs and RHFs. In fact, our simulation results in Table 6 clearly supports the proposition made earlier that, by reallocating resources within UHFs from development to recurring expenditures, reasonable efficiency gains of over ten percent were attained in 1994. The efficiency gains for the combined health system were also in the order of eight to nine percent.


Pakistan's share of total health expenditure to gross national product has never exceeded 0.8 percent per annum [Economic Survey 1992-93], which is significantly lower than many of its neighbouring countries in the region. If the future is any reflection of past history, then one does not expect substantial public funds to be forthcoming and diverted towards this sector in the immediate or medium term future especially when the country is already experiencing large increasing budgetary deficits. Prudent public policy research in this context, based on a realistic pragmatic approach, should then be geared towards an investigation into measures to improve the present Public Health system (PHS) through an efficient, cost-effective reallocation of health inputs within the existing limited budget. This study has examined these health policy issues within the context of an optimisation framework for PHS and forecasted future (up to 2002-03) efficient optimal mix of health inputs (doctors, nurses, paramedics), outputs (patients treated for urban and rural health facilities), expenditures (development and recurrent) and wage policies (health personnel) under alternative scenarios. Comparing the projected actual health output (based on historical growth rates) with those of optimal values, efficiency gains were also computed. Based on these simulation results, this study makes policy recommendations for PHS and some of the important ones are summarised below:

* Our optimisation model predicts an excess build-up of infrastructure (measured in terms of beds) in the present urban health facilities while, in the rural areas, there is a paucity of RHCs and BHUs. We recommend that the growth of health infrastructure building in the urban areas be slowed down in the short-run (two to three years) and some of the resources be reallocated toward the rural sector either in terms o building new BHUs or upgrading the existing RHCs.

* Our optimal forecasts suggest that both more nurses and doctors should be hired in UHFs and RHFs, respectively, during the entire plan period though in terms of percentage, the demand for nurses will exceed that of doctors in RHFs. We recommend that not only attractive wage policies be formulated for these personnel but, more importantly, like the Armed Forces, the status of nurses in the Public Health System be elevated by giving them higher BSP.

* There is a shift in focus from development towards recurring expenditure a predicted by the optimisation model. It is, therefore, recommended that for every rupee of development expenditure incurred, PHD must plan or keep provisions for recurring outlays. This is critical from the point o view of long-term sustainability of PHS.

It is important to note that all this reallocation of resources is feasible within the projected actual budget and, interestingly enough, it will also lead to efficiency gains in the order of 8 to 10 percent for the entire Public Health System.


I commend the authors for attempting to analyse rigorously the economics the public health sector in Pakistan. The main conclusions are that channelling more resources to personnel, nurses, and doctors and less to infrastructure for the same total cost will result in more output of about 8-10 percent. I do not necessarily disagree with the authors' conclusions, but I recommend that we should treat these conclusions with extreme caution and as highly tentative. This is because the study suffers from several conceptual problems and employs highly questionable assumptions and data set.

The paper starts out by lamenting on the meager resources that are devoted to the public health sector. Statistics on health as a percentage of GNP for some neighbouring and other countries are provided with the purpose of showing the dismal state of relative expenditures on health in Pakistan. At this point I was expecting that the authors would go on to forcefully argue for more expenditures be allocated to public health. Instead, the authors' objective turns out to be of finding whether the health sector is economically efficient with the meager resource that it gets.

The framework employed is the neoclassical optimisation problem whereby the health sector maximises output with respect to the various inputs subject to a budget constraint. Remember we are talking about the public sector here and not the private sector. The equilibrium solution to this problem determines the optimal amounts of health personnel and output in each time period. While the framework employed is more elaborate, it is the same one that I used in my paper entitle, "Optimal Resource Utilisation in Pakistan Agriculture" presented at the third PSDE Meetings, Khilji (1986). There are some methodological differences though among these papers. My paper focussed on the private agricultural sector and not on the public sector. It allowed equilibrium to be reached over several periods instead of assuming that equilibrium is reached in each period as in this paper. My paper allowed the output elasticities, with respect to the various inputs, to vary over time instead of the constant elasticities assumed in this paper.

In terms of efficiency, the authors are never clear of what type of inefficiency they are referring to. According to the quotation from the World Bank study which they present on the first page, inefficiency is due to, "Political influence and leakage of equipment and supplies.... Poor management and centralised financial, administrative and management authority..." These notions of inefficiency are different than what the authors model, The paper talks about allocative inefficiency due to the monopsonistic power of the public health sector, which is assumed rather than proved. Employing isoquant and isocost curves in Figure 1, the authors painstakingly explain that a fixed wage for doctors below a market determined wage would bring in fewer doctors. This will result in less output for the same cost. All this is familiar to undergraduate students in economics. There are many ways the same point is normally made. Price and wage ceilings result in misallocation of resources. This is a proposition that we teach our first year students and is not as novel as is presented in Proposition I of the paper. However, the question arises, what is the source of inefficiency? Is it an institutionally fixed wage or is it the monopsonistic power of the public health sector. Instead of worrying about isoquants and isocosts, which are rather cumbersome, the point can be equally made by using the familiar supply and demand diagrams. Figure 1 below does just that.


The figure presents the market for doctors. D is the demand curve by the public health sector for doctors and S is the supply of doctors at various wage rates W. The wage [W.sub.pc] is the market clearing wage where supply is equal to demand. It would result in [N.sub.pc] amount of doctors hired per period of time. Since D is also the Value Marginal Product (VMP) of Doctors = [Price.sup.*] Marginal Product of Doctors, [N.sub.pc] amount of doctors coincides with [D.sub.1] in Figure 1 of the paper. Output would be [Q.sub.1] which is optimal. The problem with a monopsonist is that he faces an upward sloping supply curve. This means that when he hires additional doctors, he has to raise the wage, not only for the additional doctor, but also for all doctors in his employment. This gives rise to a marginal factor cost (MFC) for him which is higher than the supply price of doctors. In order to maximise output for a given cost, he will equate the VMP of doctors not to the wage rate but rather additional cost of hiring them which is MFC. This occurs at point c in Figure 1. The wage that corresponds to MFC at point c is [W.sub.m] which is what the monopsonist will pay. At this wage only [N.sub.M] doctors will be willing to work. [N.sub.M] doctors corresponds to [D.sub.0] in Figure 1 of the paper where the wage rate < VMP of doctors resulting in sub-optimal amounts (from the economy's stand-point) of doctors and output. The reason here for allocative inefficiency in the economy is the monopsonistic power of the producer.

The point of presenting all this is to show that both institutionally fixed wages below the market clearing wages or monopsony elements lead to inefficient allocation of resources. For example, [W.sub.m] could be either institutionally fixed or can be the result of the monopsonist's optimisation behaviour The effects will be the same. The paper moves back and forth between these two. Moreover this is a far cry from what the World Bank study had in mind about leaks, political influence, and poor management. These types of inefficiencies would be hard to put in the optimisation framework employed in the paper.

I wander why the paper wastes so much time proving Propositions 2 and 3. We all know that if a monopsonist faces an infinitely elastic supply curve he would not be, by definition, a monoposonist but a perfect competitor in that factor market. Proposition 3 is also well known. If you are stuck with a fixed factor higher than the optimal amount than keeping it fixed and increasing other inputs will result in higher output than a situation where you start with an optimal combination of inputs. This has to do with higher marginal products of the relatively scarce factors.

Let me turn now to the econometrics, solution algorithm, and simulations in the paper. Unfortunately the paper is not very forthcoming about any of these matters. In fact it does not even elaborate on the data employed except to state that it is the health sector data on Punjab. The other thing we know is that this data is for the period 1977-1992.

Essentially there are two outputs, one is an index of patients treated in Rural Health Facilities, and the other is an index of patients treated in Urban Health Facilities. These outputs are related to inputs through production functions which are statistically estimated with inputs as doctors, paramedics, hospital beds, and registered paramedics. Given these estimated production functions and an exogenous budget to be allocated for a year, constrained optimisation of output leads to demand equations for medical personnel for each year. The supply equations of doctors nurses and paramedics are statistically estimated. Equating these factors' supplies to their demands for a particular year provides equilibrium solutions for the amounts of factors employed and their wage rates for that year. Substituting these solution values of inputs into the respective production equations generates values for the two outputs tot the year. This solution algorithm is repeated each year based on a new budget allocation. The solution algorithm calculates equilibrium amounts of inputs employed, wage rates, and outputs each year.

In standard forecasting there are two types of simulations. These are ex-post and ex-ante simulations. Historical simulations (or ex-post simulations) involve the comparison of predicted values of inputs and outputs in the past with the actual values of these variables The purpose is to check on the forecasting accuracy of the estimated model. Ex-ante simulations (or forecasts) involve projecting the endogenous variables into the future based on expected values of all exogenous variables. Since the future has not happened, it is not possible to check whether the ex-ante forecasts are accurate or not.

The paper performs ex-ante simulations with a twist. The twist is that it also projects forward, from 1992 to 2003, what the likely values of the endogenous variables (inputs, wage rates, and outputs) are going to be based on past growth rates. These are compared with the values generated from the solution algorithm. This is absolutely bizarre! The questions is that, are not the estimated input elasticities, and supply equations based on historical values of the same endogenous variables? One can understand the use of the word optimal in the ex-ante simulations. It can be rationalised as follows: Given the existing structure of production, budget allocation to health, input supply equations, and assuming that the public health sector wants to maximise output, then the optimal amounts of inputs, wage rates, and outputs are the ones that are reported as optimal in Tables 4, 5, and 6. Actual has no meaning here. except for 1992, since the values are not observed.

If the purpose were to show efficiency gains, would not ex-post simulations be more relevant? Even if we were to accept the procedure adopted in the paper, we find that the actual amounts of doctors employed are higher than optimal for UHFs and for RHFs (for most years) in Table 4. I thought that the point of the exercise was to show that because wages of doctors were lower than the competitive wages due to monopsonistic elements, less doctors were employed than optimal. Finally, comparison of actual output to optimal output in Table 6 shows efficiency gains in output of the order of 8-10 percent. This is not much given that most of the important parameters are statistically estimated. It would be useful to present the standard errors associated with these efficiency gains to assess their significance. Even if these were not calculable, some qualifications about these point estimates would make sense.

Recently Anne Krueger (1997) remarked that when economists present empirical results that are favourable to one point of view, politicians, whose side is flavoured, exploit this result claiming it to be gospel truth. They do not heed all the qualifications, conditions, and assumptions the economists may have employed and stated when presenting their results. Unfortunately no qualifications are put in this paper making it easier for people to claim that the health sector is inefficient. There need to be several qualifications put in this paper. These have to do with the limited data employed, the definition of output, the statistical estimations of coefficients which are assumed to stay constant in the future and their associated standard errors. Additionally, the arbitrary nature of the assumptions about the future course of budget allocations, and expected inputs, wage rates and outputs should be emphasised

While this is an elegant and elaborate piece of work, I am sure the authors would agree that, we should be extremely careful in using the results reported in this study, especially for policy purposes.

Nasir M. Khiiji

U.S. Bureau of the Census and Economic Adviser

U.S./Saudi Arabian Joint Commission on Economic Cooperation (JECOR)



Khilji, N. M. (1986) Optimum Resource Utilisation in Pakistan's Agriculture. The Pakistan Development Review 25:4 469-487.

Krueger, A. O. (1997) Trade Policy and Economic Development: How We Learn. The American Economic Review March.

Authors' Note: This study was initiated Aynul Hasan was visiting the Social Policy and Development Centre, Karachi as Senior Technical Adviser on behalf of the Canadian International Development Agency (CIDA). He wishes to thank the Agency for providing financial support for the study. Research assistance and primary data collection were conducted by Zahid Hasnain, Naveed Hanif, Nooreen Mujahid, and Nasrul Eman. Any errors are the responsibilities of the authors.


Pakistan, Government of (Various Issues) Economic Survey. Islamabad: Finance Division, Economic Advisors Wings.

Punjab, Government of (Various Issues) Demand for Grants Current Expenditure.

Punjab, Government of (Various Issues) Punjab Development Statistics. Lahore Bureau of Statistics.

The World Bank Report (1991) Pakistan Health Sector Study: Key Concerns and Solution. New York: The World Bank Report.

World Development Report (1991) The Challenge of Development. New York: Oxford University Press.

(1) In response to donor agencies' insistence, the Government of Pakistan recently initiated an accelerated Social Action Programme (SAP), whereby the policy-makers have committed to revamp public expenditures in certain key areas namely, primary education, basic health, public health, population planning etc.

(2) In order to undertake long-run planning, Government of Pakistan prepared a fifteen-year perspective plan covering a period between 1988-89 to 2002-2003, wherein it stipulated targets for all key economic and social variables including basic health.

(3) It should be noted that [E.sub.2] on the old isocost line [C.sub.0] is also an equilibrium point for a fixed monosonistic wage rate which is both efficient and at a higher output level. However, to attain such a level of output, the producer (PHD) must be able to exert enough monopsony power to hire the required level of doctors. Here we argue that such a situation will be difficult if not impossible to achieve particularly when there are alternatives available to superior qualified health professionals within (in the private sector) and outside the country.

(4) Note that the case of constrained monopsonist, since the number of beds are fixed at [bar.B] ([B.sub.-1]), the budget constraint will now be changed to * = wD + m [bar.B].

(5) A discussion on data sources, definition of variables, and ensuing problems and anomalies are reported in a technical Appendix, which is available on request the authors.

(6) The detailed reduced form for the optimisation problem is available from the authors on request.

(7) Forecasting the actual health outputs based on the estimated production function, reported in Table 3, will not be unreasonable as the predictive power of these equations are very high (99 percent).

M. Aynul Hasan is Professor of Economics, Acadia University, Wolfville, Nova Scotia, Canada. Hafiz A. Pasha was Deputy Chairman of the Planning Commission, Government of Pakistan, Islamabad. Ajaz M. Rasheed is Senior Systems Analyst, Social Policy and Development Centre, Karachi.
Table 1
Expenditure on Health for Selected Developing Countries

 % of Total Govt. % of GNP Spent
Country Expenditure on Health on Health

Pakistan 1 0.002
Bangladesh 4.8 0.007
Nepal 4.7 0.009
India 1.6 0.003
Sri Lanka 4.8 0.014
Indonesia 2.4 0.005
Egypt 2.8 0.011
Philippines 4.2 0.008

Source: World Development Report, 1991-92.

Table 2
Estimated Supply Functions of Health Personnel

 Rural Health Facilities

Variables Doctors Paramedics

Intercept -15.450 -8.108
 (-3.572) * (-8.585) *
Doctors 1.472 --
Nominal Wage (1.761) *
Nurses -- --
Nominal Wage
Paramedics -- 1.078
Nominal Wage (3.239) *
Registered 0.759 --
Doctors (1.849) *
Registered -- --
Registered -- 0.715
Paramedics (2.021) *
[R.sup.2] 0.969 0.987
DW-test 1.690 1.570
Observations 1977-92 1977-92

 Urban Health Facilities
Variables Doctors Nurses Paramedics

Intercept 0.295 -3.917 -1.587
 (0.202) (-3.182) * (-2.149) *
Doctors 0.659 -- --
Nominal Wage (2.258) *
Nurses -- 0.253 --
Nominal Wage (0.440)
Paramedics -- -- 0.498
Nominal Wage (2.909) *
Registered 0.127 -- --
Doctors (0.780)
Registered -- 0.9792 --
Nurses (1.956) *
Registered -- -- 0.271
Paramedics (2.737) *
[R.sup.2] 0.949 0.932 0.976
DW-test 2.386 1.837 2.44
Observations 1977-92 1977-92 1977-92

Notes: 1. Numbers in Parentheses are t-values.

2. Paramedics in RHFs include Nurses and Paramedics.

3. Asterisk indicates significance of the estimated parameters at 10
percent or less level of significance.

Table 3

Estimated Production Functions for RHFs and UHFs

 Rural Health Urban Health
Variables Facilities Facilities
 (RHFs) (RHFs)

Intercept 1.373 -6.449
 (5.205) * (-12.97) *
Doctors 0.129 0.353
 (0.929) (8.024) *
Paramedics 0.360 0.290
 (3.095) * (4.836) *
Hospital Beds -- 0.701
 (6.194) *
RHFs 0.561 --
 (1.948) *
Registered Paramedics 0.715
 (2.021) * --
[R.sup.2] 0.995 0.999
DW-test 2.297 1.961
Observations 1977-92 1977-92

Notes : (1.) Numbers in parenthesis are t-values.

 (2.) Paramedics in RHFs include Nurses and Paramedics.

 (3.) Asterisk indicates significance of the estimated
 parameters at 10 percent or less level of significance.

Table 4

Health Personnel and Physical Infrastructure:
Ex-ante Forecasts for Standard and Constrained


 1992 1994 2003

 Urban Health Facility (UHF)

 Variables Baseline Standard


 Actual 23,5528 26,620 45,989
 Optimal 22,044 24,842 24,533
 % Change -6.31% -6.68% -7.51%


 Actual 10,981 12,990 27,421
 Optimal 15,634 18,249 36,609
 % Change 42.37% 40.48% 33.51%


 Actual 31,350 34,372 54,572
 Optimal 33,458 37,462 62,305
 % Change 6.72% 8.99% 14.17%


 Actual 50,138 54,800 81,028
 Optimal 43,196 47,480 73,038
 % Change -13.85% -13.36% -9.86%

 Rural Health Facility (RHF)


 Actual 10,083 11,913 25,001
 Optimal 9,605 11,755 29,179
 % Change -4.74% -1.33% 16.71%


 Actual 20,900 25,718 64,820
 Optimal 22,726 27,273 61,988
 % Change 8.74% 6.05% -4.37%


 Actual 1,274 1,442 2,499
 Optimal 1,465 1,656 2,879
 % Change 14.99% 14.84% 15.21%


 1994 2003

 Urban Health Facility (UHF)

 Variables Constrained


 Actual 26,620 45,989
 Optimal 24,499 42,533
 % Change -7.97% -7.51%


 Actual 12,990 27,421
 Optimal 18,120 36,609
 % Change 39.49% 33.51%


 Actual 34,372 54,572
 Optimal 37,016 62,305
 % Change 7.69% 14.17%


 Actual 54,800 81,028
 Optimal 50,138 73,038
 % Change -8.51% -9.86%


 Actual 11,913 25,001
 Optimal 11,516 29,179
 % Change -3.33% 16.71%


 Actual 25,718 64,820
 Optimal 26,782 61,988
 % Change 4.14% -4.37%


 Actual 1,442 2,499
 Optimal 1,599 2,879
 % Change 10.89% 15.21%

Table 5

Wage Structure for Health Facilities: Ex-ante Forecasts for
Standard and Constrained Optimisation


 1992 1994 2003

Variable Urban Health Facility (UHF)

 Actual Standard


 Actual 54,303 61,208 103,954
 Optimal 49,862 58,070 115,286
 % Change -8.18% -5.13% 10.90%


 Actual 24,438 28,376 55,091
 Optimal 30,801 34,630 58,680
 % Change 26.04% 22.04% 6.51%


 Actual 17,975 20,703 38,753
 Optimal 16,155 18,936 38,702
 % Change -10.13% -8.53% -0.13%

 Rural Health
 Facility (RHF)


 Actual 42,114 47,620 82,041
 Optimal 51,389 55,107 75,463
 % Change 22.02% 15.72% -8.02%


 Actual 16,651 20,240 48,274
 Optimal 23,049 25,207 37,698
 % Change 38.42% 24.54% -21.91%


 1994 2003

Variable Urban Health Facility (UHF)


 Actual 61,208 103,954
 Optimal 56,858 115,286
 % Change -7.11% 10.90%


 Actual 28,376 55,091
 Optimal 33,678 58,680
 % Change 18.68% 6.51%


 Actual 20,703 38,753
 Optimal 18,505 38,702
 % Change

 Rural Health
 Facility (RHF)


 Actual 47,620 82,041
 Optimal 54,316 75,463
 % Change 14.06% -8.02%


 Actual 20,240 48,274
 Optimal 24,786 37,698
 % Change 22.46% -21.91%

Note: Wages are reported in current Pakistani rupees (Rs).

Table 6
Efficiency Gain/Loss for Health Facilities:
Ex-ante Forecasts for Standard and Constrained


 1992 1994 2003

Variables Urban Health Facility (UHF)

 Actual Standard
Health Output
(Composite Index)
 Actual 13,182 17,703 65,288
 Optimal 14,288 19,145 71,713
Efficiency (gain/loss) 8.39% 8.15% 9.84%

 Rural Health Facility (RHF)
Health Output RHFs
(Patient Treated)
 Actual 35,027 41,351 86,448
 Optimal 38,055 44,948 95,450
Efficiency (gain/loss) 8.65% 8.70% 10.40%

 Combined Health Facilities
Total Health Output
(Composite Index)
 Actual 20,664 29,411 74,288
 Optimal 22,422 31,882 81,794
Total Efficiency
 (gain/loss) 8.51% 8.40% 10.10%


 1994 2003

 Urban Health Facility (UHF)


Health Output
(Composite Index)
 Actual 17,703 65,288
 Optimal 19,572 71,713
Efficiency (gain/loss) 10.56% 9.8417

 Rural Health Facility (RHF)
Health Output RHFs
(Patient Treated)
 Actual 41,351 86,448
 Optimal 43,703 95,450
Efficiency (gain/loss) 5.69% 10.40%

 Combined Health Facilities
Total Health Output
(Composite Index)
 Actual 26,154 7,429e+09
 Optimal 28,322
Total Efficiency
 (gain/loss) 8.29% 10.10%
COPYRIGHT 1997 Reproduced with permission of the Publications Division, Pakistan Institute of Development Economies, Islamabad, Pakistan.
No portion of this article can be reproduced without the express written permission from the copyright holder.
Copyright 1997 Gale, Cengage Learning. All rights reserved.

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Author:Hasan, M. Aynul; Pasha, Hafiz A.; Rasheed, Ajaz M.
Publication:Pakistan Development Review
Article Type:Report
Geographic Code:9PAKI
Date:Dec 22, 1997
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