Introduction to Quantitative Policy Analysis with GAMS

Introduction to Quantitative Policy Analysis with GAMS

Technical issues

Maria Sassi

1

Basic concepts for quantitative policy analysis

1.1. Introduction

1.2.

Quantitative policy analysis involves quantitative methods to:

- Define a policy problem;

- Demonstrate its impact;

- Show potential solutions and policy alternatives.

It can be developed at three different levels corresponding to the policy levels. They are:

- Microeconomic level, which is focused on policies aimed at individual parts of the economy, such as, industries, businesses and households;

- Sector level, which is targeted to interventions directed to a specific sector of the economy, for example, the maize sector;

- Macroeconomic level, which is centred on policies aimed at the aggregate economy.

In order to investigate the policy impact, quantitative policy analysis adopts a four-step approach illustrated in Figure 1.

Figure 1 - Steps in quantitative policy analysis

The roots of the process are represented by the economic theory that, implemented with information provided by historical trends and experience, provides guidelines to help conceptualise and design policy interventions (De Janvry, Saudolet, ….). For this reason, quantitative policy analysis can be define as a process aimed at quantifying the various mechanisms analysed by theory.

On the basis of a theory, quantitative modelling designs a model and estimate parameters and calibrate the model itself in order to provide the framework for policy simulation.

Modelling and policy simulation are the two core elements of quantitative policy analysis.

Modelling includes the construction of a model and the computation of the base run.

1.3. Construction of a model

Constructing a model consists on the definition of a theoretical construct that represents the investigated economic process. It is made of equations which represent logical and/or quantitative relationships (equalities or inequalities) between a set of four components. They are:

- Exogenous variables;

- Endogenous variables;

- Parameters;

- Indices.

The exogenous or independent variables are factors that affect a model without being affected by the model. They are fixed in the sense that they cannot be manipulated within the economic model.

The endogenous or dependent variables are those whose values are determined within the model.

Parameters or coefficients are fixed values that describe the effect of one exogenous variable on the endogenous variable.

Let us consider a linear model for the estimate of the quantity of meat demanded by a group of consumers (D) given a certain level of price (P), income (Y), the related price and income coefficients (b, g) and technical efficiency (a). Its mathematical notation and the typology of components is represented in Figure 2.

Figure 2 - Linear demand model

The exogenous variables and parameters can be further distinguished in uncontrollable and policy instruments. They are both observable variables and coefficients, but the latter are the objective of the policy intervention.

In addition, in the model the endogenous variable is selected to enter into the definition of criteria for policy evaluation.

In our previous example, let us assume that the government controls meat price (policy instrument) and wants to change it in order to achieve a certain level of meat consumption (criteria for policy evaluation). The other exogenous variables and the parameters are uncontrollable to the purpose of the policy intervention (Figure 3).

Figure 3 - Linear demand model with uncontrolled variables and parameters and a policy instrument

The indices are used to specify the elements of an array of numbers (variables and parameters). Turning to the above described example, let us assume that the same model structure allows estimating demand of the same group of consumers for not only meat but also maize. The model in Figure 2 or 3 can be rewritten as:

In a model, equations describe a system, namely a set of two or more simultaneous equations with the same set of unknowns.

Let us consider a linear model for the analysis of the market equilibrium for two commodities, meat and fish, with demand (D), supply (S) and prices (P) the endogenous variables. The index i is

i=meat, fish

while the equations are

Di=ai+bi*Pi (1. Demand function)

Si=fi+zi*Pi (2. Supply function)

Di=Si (3. Equilibrium condition)

where a and f are the technical coefficients of the demand and supply equations, respectively, and b and z the price coefficients of demand and supply.

The definition of system of equations provide an important rule in modelling design: in order to be solved, a system of equations must be characterised by a number of equations equals to the number of endogenous variables. The model, in our example, is consistent in the sense that it has three unknown variables (D, S and P) and three equations and, thus, it has a solution.

When the number of equations is greater than the number of endogenous variables, the model is inconsistent, that is it provides no solution while if the number of equations is less than the number of endogenous variables, the model has an infinite number of solutions.

1.4. Computation of the base run

Once the model is constructed, its solution for the observed values yields the base run.

Let us consider the linear market equilibrium model specified for meat and fish in the previous paragraph. Given the observed values for the known components, the endogenous variables can be estimated as illustrated in the following.

The liner market equilibrium model components are

- Two commodities
i=meat, fish
- The system of equations
Di=ai+bi*Pi
Si=fi+zi*Pi
Di=Si
- the observed variables
a technical coefficient of the demand equation
f technical coefficient of the supply equation
b price coefficient of demand
z price coefficient of supply
- the value of the observed variables
ameat=1.07 afish=1.012
bmeat=-0.804 bfish=-3.09
fmeat=1.03 ffish=0.47
zmeat=1.08 z(fish)=4.87

For the computation of the base run for meat:

- First, substitute the observed values in the model

D(meat)=1.07-0.804*P(meat) (a)

S(meat)=1.03+1.08*P(meat) (b)

D(meat)=S(meat) (c)

- Second, solve the model as follows.

Substitute in equation c, equation a and b

1.07-0.804*Pmeat=1.03+1.08*Pmeat

Calculate meat equilibrium price

1.07-1.03=1.08+0.804*P(meat)

0.04=1.884*P(meat)

Pmeat=0.041.884=0.021

Substitute meat price in equation a and b and calculate demand and supply that mast be equal because this quantity is the meat equilibrium quantity

D(meat)=1.07-0.804*0.021=1.053

S(meat)=1.03+1.08*0.021=1.053

For the computation of the base run for fish:

- First, substitute the observed values in the model

D(fish)=1.012-3.09*P(fish) (A)

S(fish)=0.47+4.87*P(fish) (B)

D(fish)=S(fish) (C)

- Second, solve the model as follows.

Substitute in equation C, equation A and B

1.012-3.09*P(fish)=0.47+4.87*P(fish)

Calculate fish equilibrium price

1.012-0.47=(3.09+4.87)*P(fish)

0.542=7.96*P(fish)

P(fish)=0.5427.96=0.068

Substitute fish price in equation A and B and calculate demand and supply that mast be equal because this quantity is the fish equilibrium quantity

D(fish)=1.012-3.09*0.068=0.801

S(fish)=0.47+4.87*0.068=0.801

Table 1 summarizes the base run.

Table 1 - Base run for meat and fish

Equilibrium value / Meat / Fish
Price / 0.021 / 0.068
Quantity / 1.053 / 0.801

1.4.1. Importance of the base run

Calculating the base run has different purposes. Two of them have a specific importance. The solution of a model for the observed values can be adopted:

- for the validation of the model;

- as a benchmark against which to measure the impact of counterfactual policy scenarios.

The objective of the validation of a model is to seek to minimize the difference between the observed values of the endogenous variable and its estimated value. The validation techniques can be classified in:

- Econometric approaches, with which the accuracy of the model is verified by statistical criteria of goodness of fit;

- Calibration procedures, adopted when the number of available observed values is not enough to apply econometric techniques.

GAMS adopt the latter technique for CGE models…….

The second purpose of the base run is to represent the benchmark against which to measure the impact of alternative simulated policies or shocks. This is a very important point. It means that in order to understand the effect of a simulation on an endogenous variable, the value of the impact variable after the simulation must be compare with its base run value and not with its observed value. An example allows clarifying the issue.

Figure 4 illustrates the historical trend in production of maize in a hypothetical country where two drought periods brake the normal production years.

Figure 4 - Data on production of maize in a

hypothetical country (1990-2012)

Let us model this trend with a linear model where production of maize (y) is a function of labor (x) that is

y=a+b*x

where a is equal to 7.055 and b to 0.825.

Figure 5 compare the base run with the observed historical data

Figure 5 - Data on production of maize in a

hypothetical country and base run (1990-2012)

Let us introduce a policy aimed at increasing production as described by the “policy impact” line in Figure 6.

Figure 6 - Data on production of maize in a hypothetical

country, base run and policy impact line (1990-2012)

If we compare the 2007 observed value with its value in the same year after the policy intervention we make a mistake because the shock is calculated with a model that predict a level of production, in that year, represented by the base run. In other words, the effect of a policy must be assessed against the state predicted by the model that describe how the observed economic process evolves without the implementation of any shock. In our example, the comparison must be between the base run and the policy impact lines.

1.5. Taxonomy of models

Models can be classified into four typologies, namely conceptual, analytical, stylized and applied models (Figure 7).

Figure 7 - Taxonomy of models and policy evaluation options

A model is a simplified framework designed to illustrate a complex observed economic process. Theoretical framework and mathematical methods allow to filter out its inessential details and to represent the investigated real complex process in terms of stylized facts, that is to design a conceptual model. This latter allows describing the observed economic process.

Focusing on few important assumptions and casual mechanisms, casting economic relationships into a form susceptible to mathematical analysis leads to analytical models. They are suitable for the investigation of the implications of various sets of postulates with a few assumptions as possible about the magnitudes of parameters.

Attaching numbers to an analytical model and relating them to the economic performance allows designing a stylized model. This typology of framework can be adopted not only to investigate the size of various effects but also to analyse problems that are too difficult to solve analytically or that have ambiguous analytical answers and hence depend on particular parameter values (Dervarajan, Lewis, Robinson (1994) Getting the Model Right: The General Equilibrium Approach to Adjustment Policy).

Including in stylized model more details and important features of a particular economy or situation lead to an applied model. An example can better clarify the distinction between a stylized and applied model: the former may refer to a group of countries, for instance the Oil-importing countries, while the applied model is related to a specific country in a group, such as Saudi Arabia.

The specific features of the above mentioned models made them suitable for different purposes. A conceptualise model allows describing the observed economic process, an analytical model is useful for strategic planning that is for the definition and analysis of strategies (general, undetailed plan of action over the long time period in order to achieve the overall organization’s goals), while stylized and applied models are indicated for policy analysis, that is for the investigation of particular interventions aimed at specific targets.

2

Introduction to GAMS

2.1. Introduction

GAMS stands for General Algebraic Modeling System. It is a software package for:

- Designing and

- Solving

various types of models.

Originally developed by a group of economists at the World Bank for economic models, GAMS is today suitable to solve systems of equations in any field of study.

Designing and solving represents the two parts of GAMS (Figure 8).

Figure 8 – The two parts of GAMS

The former is the core of the software that allows creating the model through a specific language. The latter consists on a set of solvers for running the model.

2.2. Downloading GAMS and the user interface

A free version of the software can be downloaded at the GAMS Home Page (www.gams.com) clicking on “Download the current GAMS system”.

The free version of GAMS has some model limitations. They are:

- The number of constraints and variables, which must be lower than 300;

- The number of nonzero elements, which must be not more than 2,000 (of which 1,000 nonlinear);

- The number of discrete variables, for a maximum of 50 (including semi continuous, semi integer and member of SOS-Sets).

Once installed, clicking on the GAMS icon the software opens showing the user interface (Figure 9).

Figure 9 - GAMS’ user interface

At the top of the user interface there are the Menu headings and the Buttons, which in most cases are just an alternative way of carrying out functions of the menu options, (Figure 10) whose meaning is explained in Figure 11.

Figure 10 – Components of the user interface