Ray C. Fair Specification, Estimation and Analysis of Macroeconometric Models

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Ray C. Fair Specification, Estimation and Analysis of Macroeconometric Models



In his work “Specification, Estimation and Analysis of Macroeconometric Models” Prof. Fair of Harvard (now Yale) developed among other things an econometric model of the US economy. In this paper I will focus on the construction of this model. This stage is a transition from a theoretical to an econometric model. It is of high importance, that the main features of the theoretical model are properly transformed in the econometric system of equations.
The theory underlying this model is based on
§ The assumption of maximizing behaviour,
§ The explicit treatment of disequilibrium effects,
§ And the accounting for balance-sheet constraints.

The first step in the construction of an empirical model is to collect the raw data, create the variables of interest from the raw data, and separate the variables into exogenous variables, endogenous variables explained by identities, and endogenous variables explained by estimated equations.
The data were taken from the Flow of Funds Accounts and National Income and Product Accounts, as published in the Survey of Current Business.
Given the tables in appendix, it should be possible to duplicate the collection of the data with no help from the author. Although one would seldom want to do this, this kind of detail should be presented if at all feasible: it has the obvious scientific merit of allowing for reproducibility of results.
The two main decision variables of a household in the theoretical model are consumption and labour supply. The determinants of these variables include the initial value of wealth and the current and expected future values of the wage rate, the price level, the interest rate, the tax rate, and the level of transfer payments. The labour constraint also affects the decisions if it is binding. The aim of the econometric work is to match the decision variables and the determinants of the variables to observed aggregate variables and then to estimate equations explaining the aggregate variables.
Much searching was done in arriving at the final estimated equations for the household sector.

With respect to functional forms, both the linear and logarithmic forms of the equations were tried, and the decision was made fairly early in the process to use the linear form.
(1, 2, 3, 4, 5, 6, 7, 8) It will be useful in discussing these results to consider the effects of each explanatory variable across the eight equations.
1. The results for the asset variable are good in the sense that this variable is significant in all four of the expenditure equations.
2. The wage rate and price variables are significant in all four expenditure equations with the exceptions of the housing investment equation and the consumption of services equation.
3. With respect to the interest rate variables, the short-term rate is in the first two equations and the long-term rate is in the third and fourth equations. The coefficient estimates are significant except for one coefficient.
4. The results for the non-labour income variables are not very strong.
5. The labour constraint variable appears in three expenditure equations and three labour supply equations. It is significant in all but equation (1).
In general, these results seem fairly supportive of the theory.
In the process of searching for the final equations to be used in the model, one gets a feeling for what the data do and do not support. M
Merely presenting the final set of equations does not always convey this information; it is sometimes helpful to present a few of the intermediate results.
1. The results are not sensitive to the use of the measure of labour market tightness in the construction of the labour constraint variable.
2. The data do not support the use of real interest rates in the expenditure equations.
3. The data do not support the treatment of consumer durable expenditures as investment expenditures.
4. The data provide mild support for the use of the after-tax wage rate rather than the before-tax wage rate in the equations.
5. The data again provide mild support for the use of the after-tax interest rates rather than the before-tax rates.
6. It should also be noted with respect to the treatment of taxes that the non-labour income variable is after-tax non-labour income. This treatment is again in keeping with the theoretical model.
(9) This equation is consistent with the theoretical model, where the optimal level of money holdings of the household is a negative function of the interest rate.
A decrease in tax rates increases expenditures through the wage rate and non-labour income variables. A decrease in tax rates also decreases expenditures through the interest rate variables.

(A decrease in tax rates, other things being equal, raises the after-tax interest rate, which has a negative effect on expenditures.) The net effect of a decrease in tax rates is thus ambiguous.
Transfer payments are part of non-labour income, and thus an increase in transfer payments has a negative effect on labour supply.
An increase in interest rate has a negative effect on expenditures, which, other things being equal, has a positive effect on the household savings rate.

The maximization problem for a firm in the theoretical model is fairly complicated, which is partly a result of the large number of decision variables. The five main variables are the firm’s price, production, investment, demand for employment, and wage rate.
The theoretical model of firm behaviour is more difficult to handle empirically than is the theoretical model of household behaviour, and the links from the theory to the econometric specifications are weaker for firms. One of key approximations that were made was to assume that the five decisions of a firm are made sequentially rather than jointly. The sequence starts from the price decision and then goes to the production decision, to the investment and employment decisions, and finally to the wage rate decision.
(10) The price level is a function of the lagged price level, the wage rate inclusive of employer social security costs, the import price deflator, and the demand pressure variable.
(16) The wage rate is a function of the lagged wage rate, the current and lagged values of the price level, the time trend, and the unemployment rate.
Movements of the real wage in the model affect the division of income between profits and wages. A lot of searching was done for both equations, but the results are rather technical.
(11) The specification of the production equation is the point at which the assumption that a firm’s decisions are made sequentially begins to be used. The equation is based on the assumption that the firm sector first sets its price, and then knows what its sales for the current period will be.
No searching was done for the production equation other than to try a few strike dummy variables.
(12) The investment equation is based on the assumption that the production decision has already been made. In the theoretical model, because of costs of changing the capital stock, it may sometimes be optimal for a firm to hold excess capital. If there were no such costs, investment each period would merely be the amount needed to have enough capital to produce the output of the period. In the theoretical model there was no need to postulate explicitly how investment deviates from this amount, but for empirical work this must be done.
The employment and hours equations (13, 14, 15) are similar in spirit to the investment equation. They are also based on assumption that the production decision has already been made. Because of adjustment costs, it may sometimes be optimal in the theoretical model for firms to h old excess labour.

Were it not for the costs of changing employment, the optimal level of employment would merely be the amount needed to produce the output of the period. In the theoretical model there was no need to postulate explicitly how employment deviates from this amount, but this must be done for the empirical work.
(17) The demand for real money balances is a function of sales and the after-tax short-term interest rate. THE DIVIDEND EQUATION (18)
The current level of interest payments of the firm sector is a function of its outstanding debt and of the interest rates that were in effect at the times of the relevant debt issues.
The capital consumption of the firm sector is assumed to be a function of the current and past values of nominal investment expenditures, where the lag structure is geometrically declining.
1. Production is smoothed relative to sales. Investment, employment, and hours are smoothed relative to production. The buffer for production is the stock of inventories. The buffer for employment and hours is the amount of excess labour on hand.
2. Although the bond rate is not an explanatory variable in the investment equation, interest rate have indirect negative effects on investment. Interest rates are explanatory variables in the consumer expenditure equations with negative coefficients, and thus an increase in interest rates directly lowers expenditures. This in turn lowers sales, which lowers production and then investment and employment. The main channel by which interest rates affect the economy is through their effects on consumer expenditures.
3. Although interest rates affect investment in the manner just discussed, there is no means in the model by which interest rates affect capital-labour substitution. Any changes in the substitution of capital for labour (or vice versa) brought about by changes in the cost of capital relative to the cost of labour are not explained.

The effects of long-run changes in the relationship of capital to labour are not explained.
The stochastic equations for the financial sector consist of an equation explaining member bank borrowing from the Federal Reserve (22), two term structure equations (23, 24), an equation explaining the change in stock prices (25), and a demand for currency equation (26).
The ratio of borrowed reserves to total reserves is assumed to be a function of the difference between the three-month Treasury bill rate and the discount rate. This equation does not fit very well, and the estimate of the serial correlation coefficient is fairly high. There is, however, at least some slight evidence that bank borrowing responds to the interest rate differential.
The expectations theory of the term structure of interest rates states that long-term rates are a function of the current and expected future short-term rates. The two long-term interest rates in the model are the bond rate and the mortgage rate. These rates are assumed to be determined according to the expectations theory, where current and past values of the short-term interest rate are used as proxies for expected future values.
The capital gains variable is the change in the market values of stocks held by the household sector. In the theoretical model the aggregate value of stocks is determined as the present discounted value of expected future after-tax cash flow, the discount rates being the current and expected future short-term interest rates. The theoretical model thus implies that capital gains should be a function of changes in expected future after-tax cash flow and of changes in current and expected future interest rates. In the empirical work the change in the bond rate was used as a proxy for changes in expected future interest rates, and the current and one-quarter-lagged values of the change in after-tax cash flow were used as proxies for changes in expected future after-tax cash flow.
This equation states that the real per-capita demand for currency is a function of the real per-capita level of sales and of the after-tax short-term interest rate. A time trend is also included in the equation, although it is not significant.

There is one estimated equation (27) for the foreign sector, an equation explaining the demand for imports. Since this demand is demand by domestic sectors, the position of the equation is somewhat arbitrary. It was put here to highlight the fact that the demand for imports has an important effect on the savings of the foreign sector.

There is only one stochastic equation (28) for the state and local government sector. It explains unemployment insurance benefits as a function of the level of unemployment and of the nominal wage rate.

The inclusion of the nominal wage rate is designed to try to pick up the effects of increases in wages and prices on legislated benefits per unemployed worker.

There are two estimated equations (29, 30) for the federal government sector: the first is an equation explaining the interest payments of the federal government, and the second is an equation explaining the short-term interest rate. The second equation is interpreted as an interest rate reaction function of the Federal Reserve.
The current level of interest payments of the federal government is a function of current and past government security issues and of the values of the interest rates at the time of the issues.
In at least one respect, trying to explain Fed behavior is more difficult than, say, trying to explain the behavior of the household or firm sectors. Since the Fed is run by a relatively small number of people, there can be fairly abrupt changes in behavior if the people with influence change their minds or are replaced by others with different views.

In the exogenous monetary policy case, the main way in which monetary policy affects the economy is by changing interest rates. The main effects of the interest rates on the economy are the direct effects on the consumer expenditures. What this means is that the three instruments of monetary policy – all do the same thing, namely, they affect the economy by affecting interest rates. Using all three different instruments is essentially no different from using one with respect to trying to achieve, say, some real output target.
As to fiscal policy variables, it should be obvious that fiscal policy effects are not independent of what one assumes about monetary policy. For a given change in fiscal policy, there are a variety of assumptions that can be made about monetary policy. Fiscal policy effects are in fact quite sensitive to what is assumed about monetary policy. The reason for this is that the different assumptions have quite different implications for interest rates, and the latter have large effects on the real side of the economy.

The links between the theoretical model and the econometric specifications are closer for the household sector than they are for the firm sector, although the specifications of the main equations for the firm sector are in the spirit of theoretical model.
There is heavy use of lagged dependent variables in the model, and they are very important explanatory variables.
A number of the stochastic equations are not tied very closely (if at all) to decision variables in the theoretical model.

These equations tend to be less important with respect to their effects on the main variables in the model. Some of these equations are simply approximations to definitions that would hold if sufficient data were available.
Since the theoretical model was used to guide the specification of the econometric model, it is likely that the two models have similar qualitative policy effects.

The objective of this paper was achieved in presenting an abstract of the most exciting parts of the specification done by Prof. Fair. Preparation of data was shown and chosen parts of the system of stochastic equations were described. Only the interesting, technically unusual or by other means attracting parts were discussed in detail.
The summaries provide implications for both economic policy and theory. The parts that present results are of high interest for reader, as they provide a view of what the data support and not support. Finally, reading Prof. Fair’s books gives one an edge in every classroom or cafeteria discussion on the economic policy.
An appendix is provided for quick reference of equations discussed.

Copyright (C) 2003, Ivan Rybar Jr. All rights reserved. Academic use wellcome. German law applies.

Ivan Rybar Jr.
Faculty of Economic Sciences
Martin-Luther-University Halle-Wittenberg.

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