2. A Review of the US Model

2.1 Introduction and History
2.2 Tables of Variables and Equations
2.3 The Structure of the Model
2.4 Properties of the Model
2.5 Alternative Monetary Policy Assumptions
2.6 Important Things to Know About the Program

2.1 Introduction and History
The US model consists of 123 equations---27 stochastic equations and 96 identities. There are 123 endogenous variables, slightly over 100 exogenous variables, and many lagged endogenous variables. The stochastic equations are estimated by two-stage least squares. The data base for the model begins in the first quarter of 1952.

Work began on the theoretical basis of the model in 1972. The theoretical work stressed three ideas: 1) basing macroeconomics on solid microeconomic foundations, 2) allowing for the possibility of disequilibrium in some markets, and 3) accounting for all balance sheet and flow of funds constraints. The stress on microeconomic foundations for macroeconomics has come to dominate macro theory, and this work in the early 1970s is consistent with the current emphasis. The introduction of disequilibrium possibilities in some markets provides an explanation of business cycles that is consistent with maximizing behavior. The model explains disequilibrium on the basis of non rational expectations. Agents must form expectations of the future values of various variables before solving their multiperiod maximization problems. It is assumed that no agent knows the complete model, and so expectations are not rational. Firms, for example, make their price and wage decisions based on expectations that are not rational, which can cause disequilibrium in the goods and labor markets.

The theoretical model was used to guide the specification of the econometric model. This work was done in 1974 and 1975, and by 1976 the model was essentially in the form that it is in today. The explanatory variables in the econometric model were chosen to be consistent with the assumption of maximizing behavior, and an attempt was made to model the effects of disequilibrium. Balance sheet and flow of funds constraints were accounted for: the National Income and Product Accounts (NIPA) data and the Flow of Funds Accounts (FFA) data are completely integrated in the model. This latter feature greatly helps in considering alternative monetary policies, and it allows one to consider carefully "crowding out" questions.

2.2 Tables of Variables and Equations
An attempt has been made in this workbook to have nothing in the model be a "black box," including the collection of the data. This has been done by putting the complete listing of the model and the data collection in The US Model Appendix A: July 31, 2011, which is an update of Appendix A in Estimating How the Macroeconomy Works -- Fair (2004). The hope is that with a careful reading of the tables in Appendix A, you can answer why the model has the particular properties that it has. You should use these tables for reference purposes.

Table A.1 presents the six sectors in the US model: household (h), firm (f), financial (b), foreign (r), federal government (g), and state and local government (s). In order to account for the flow of funds among these sectors and for their balance-sheet constraints, the U.S. Flow of Funds Accounts (FFA) and the U.S. National Income and Product Accounts (NIPA) must be linked. Many of the identities in the US model are concerned with this linkage. Table A.1 shows how the six sectors in the US model are related to the sectors in the FFA. The notation on the right side of this table (H1, FA, etc.) is used in Table A.5 in the description of the FFA data.

Table A.2 lists all the variables in the US model in alphabetical order, and Table A.3 lists all the stochastic equations and identities. The functional forms of the stochastic equations are given in Table A.3, but not the coefficient estimates. The coefficient estimates are presented in Table A.4, where within this table the coefficient estimates and tests for equation 1 are presented in Table A1, for equation 2 in Table A2, and so on. The tests for the equations, which are reported in Table A.4, are explained in Fair (2004), and this discussion is not presented in this workbook.

The remaining tables provide more detailed information about the model. Tables A.5-A.7 show how the variables were constructed from the raw data. Table A.8 shows how the model is solved under various assumptions about monetary policy. Table A.9 lists the first stage regressors per equation that were used for the two-stage least squares estimates. Finally, Table A.10 shows which variables appear in which equations. This table can be useful for tracing through how one variable affects other variables in the model.

2.3 The Structure of the Model
The model is divided into six sectors:
  1. Household sector (h)
  2. Firm sector (f)
  3. Financial sector (b)
  4. Federal government sector (g)
  5. State and local government sector (s)
  6. Foreign sector (r)

Each of these sectors will be discussed in turn.

The Household Sector

In the multiplier model in Chapter 1, consumption is simply a function of current income, but this is obviously much too simple as a description of reality. As noted above, the stress in the model is on microeconomic foundations and possible disequilibrium effects. In the microeconomic story households maximize a multiperiod utility function. Households make two decisions each period. They decide how much to consume and how many hours to work. If households can work as many hours as they wish (no disequilibrium), then income, which is the wage rate times the number of hours worked, is not an appropriate explanatory variable in a consumption equation, because part of it (the number of hours worked) is itself a decision variable. If there is no disequilibrium, decisions about consumption and hours worked are made at the same time. Households do not earn income and then decide how much to consume. Consumption and hours worked are instead determined jointly, and hours worked should not be considered as helping to "explain" consumption if there is no disequilibrium. Both variables are "explained" by other variables.

The main variables that explain consumption and hours worked in the microeconomic story are the wage rate, the price level, the interest rate, tax rates, the initial value of wealth, and nonlabor income. The interest rate affects consumption because of the multiperiod nature of the maximization problem.

This microeconomic story has to be modified if households are not allowed to work as many hours as they would like. If households want to work more hours than firms want to employ and if firms employ only the amount they want (which seems reasonable), then households are "constrained" from working their desired number of hours. These periods correspond to periods of "unemployment." The existence of binding labor constraints is likely to lead households to consume less than they otherwise would. Also, a binding labor constraint on a household means that income is a legitimate explanatory variable for consumption, since the number hours worked is no longer a decision variable. It is imposed from the outside by firms. As discussed below, an attempt has been made in the econometric work to handle possible disequilibrium effects within the context of the microeconomic story.

In the empirical work the expenditures of the household sector are disaggregated into four types: consumption of services (CS), consumption of nondurable goods (CN), consumption of durable goods (CD), and investment in housing (IHH). Four labor supply variables are used: the labor force of men 25--54 (L1), the labor force of women 25--54 (L2), the labor force of all others 16+ (L3), and the number of people holding more than one job, called "moonlighters" (LM). These eight variables are determined by eight estimated equations.

There are two main empirical approaches that can be taken regarding the use of wage, price, and income variables in the consumption equations. The first is to add the wage, price, nonlabor income, and labor constraint variables separately to the equations. These variables in the model are as follows. The after tax nominal wage rate is WA, the price deflator for total household expenditures is PH, the after tax nonlabor income variable is YNL, and the labor constraint variable is Z. The price deflators for the four expenditure categories are PCS, PCN, PCD, and PIH. Z takes on a value of zero when there is no binding constraint (periods of full employment), and it gets more and more negative as the economy gets further and further from full employment. Consider as an example the CS equation. Under the first approach one might add WA/PH, PCS/PH, YNL/PH, and Z to the equation. The justification for including Z is the following. By construction, Z is zero or nearly zero in tight labor markets. In this case the labor constraint is not binding and Z has no effect or only a small effect in the equation. This is the "classical" case. As labor markets get looser, on the other hand, Z falls and begins to have an effect in the equation. Loose labor markets, where Z is large in absolute value, correspond to the "Keynesian" case. Since Z is highly correlated with hours paid for in loose labor markets, having both WA and Z in the equation is similar to having a labor income variable in the equation in loose labor markets.

The second, more traditional, empirical approach is to replace the above four variables with real disposable personal income, YD/PH. This approach in effect assumes that labor markets are always loose and that the responses to changes in labor and nonlabor income are the same. One can test whether the data support YD/PH over the other variables by including all the variables in the equation and examining their significance. The results of doing this in the four expenditure equations supported the use of YD/PH over the other variables, and so the equations that were chosen for the model use YD/PH. This is a change from the version of the model in Fair (1984), where the first approach was used.

The dominance of YD/PH does not necessarily mean that the classical case never holds in practice. What it does suggest is that trying to capture the classical case through the use of Z does not work. An interesting question for future work is whether the classical case can be captured in some other way.

The first eight equations in Table A.4 in Appendix A are for the household sector. As noted above, there are four expenditure equations and four labor supply equations. These are the first eight equations in Table A.4.

The Firm Sector

There are eleven stochastic equations for the firm sector (equations 10 through 19 and 21 in Table A.4). The firm sector determines production given sales (i.e., inventory investment), nonresidential fixed investment, employment demand, the price level, and the wage rate, among other things.

In the multiplier model in Chapter 1 investment is only a function of the interest rate. There is no labor market, and so employment demand is not determined. Also, no distinction is made between production and sales, and so there is no inventory investment. (Inventory investment in a period is the difference between what firms produce and what they sell.) Finally, no mention is made as to how the price level is determined. A realistic model of the economy must obviously take into account more features of firm behavior.

Production in the model is a function of sales and of the lagged stock of inventories (equation 11). Production is assumed to be "smoothed" relative to sales. The capital stock of the firm sector depends on the amount of excess capital on hand and on current and lagged values of output (equation 12). It also depends on two cost of capital variables: a real interest rate variable and a stock market variable. Nonresidential fixed investment is determined by an identity (equation 92). It is equal to the change in the capital stock plus depreciation. The demand for workers and hours depends on output and the amount of excess labor on hand (equations 13 and 14). (Excess labor is labor that the firm holds (pays for) that is not needed to produce the current level of output.)

The price level of the firm sector is determined by equation 10. It is a function of the lagged price level, the wage rate, the price of imports, the unemployment rate, and a time trend. The lagged price level is meant to pick up expectational effects, the unemployment rate is meant to pick up demand pressure effects, and the wage rate and import price variables are meant to pick up cost effects.

The nominal wage of the firm sector is determined by equation 16. The nominal wage rate is a function of the current and lagged value of the price level and a time trend. The equation is best thought of as a real wage equation, where the nominal wage rate adjusts to the price level with a lag.

Equation 17 determines the demand for money of the firm sector. It is discussed later. Equation 19 explains the level of interest payments of the firm sector.

The other stochastic equations for the firm sector are fairly minor. The level of overtime hours is a nonlinear function of total hours (equation 15). The level of dividends paid is a function of after tax profits (equation 18). Capital consumption is a function of nonresidential investment (equation 21).

The Financial Sector

The multiplier model in Chapter 1 is the IS part of the IS-LM model. The LM part of this model is as follows:

(4) Mtd/Pt = d1 + d2Yt + d3rt + wt

(5) Mts = Mt

(6) Mtd = Mts

where Mtd is the quantity of money demanded, Mts is the quantity of money supplied, and Pt is the price level. In equation (4) the demand for real money balances is a function of income and the interest rate. Equation (5) states that the supply of money is equal to Mt, which is assumed to be the policy variable of the monetary authority. Equation (6) is the equilibrium condition in the money market; the money market is assumed to clear---the quantity of money demanded equals the quantity of money supplied. The three endogenous variables in equations (4)-(6) are Mtd, Mts, and rt. The exogenous variables to this block of equations are Mt, Yt, and Pt.

When equations (4)-(6) are added to equations (1)-(3) in Chapter 1, Yt, which is exogenous in the LM model, becomes endogenous and rt, which is exogenous in the IS model, becomes endogenous. The exogenous variables in this expanded model, the overall IS-LM model, are Gt, Mt, and Pt.

The demand for money equations in the model are consistent with equation (4) of the LM model. The main demand for money equation is for the firm sector---equation 17. In this equation the demand for money is a function of the interest rate and a transactions variable. There is also a separate demand for currency equation---equation 26---which is similar to equation 17.

An important difference between the present model and the LM model is that the present model accounts for all the flows of funds among the sectors and all balance sheet constraints. This allows the main "tool" of the monetary authority in the model to be open market operations, which is the main tool used in practice.

The other equations of the financial sector consist two term structure equations and an equation explaining the change in stock prices. The bond rate in the first term structure equation is a function of current and lagged values of the bill rate (equation 23). The same is true for the mortgage rate in the second term structure equation (equation 24). In the stock price equation, the change in stock prices is a function of the change in the bond rate and the change in after tax profits (equation 25).

The Foreign Sector

There is one stochastic equation in the foreign sector, which explains the level of imports (equation 27). The level of imports depends on consumption plus fixed investment and on the domestic price level relative to the price of imports. If the price of imports rises relative to the domestic price level, imports are predicted to fall, other things being equal, as people substitute domestic goods for imported goods. Otherwise, the level of imports is just run off of total consumption and fixed investment.

The State and Local Government Sector

There is one stochastic equation in the state and local government sector, an equation explaining unemployment insurance benefits (equation 28). The level of unemployment insurance benefits is a function of the level of unemployment and the nominal wage rate. The inclusion of the nominal wage rate is designed to pick up effects of increases in wages and prices on legislated benefits per unemployed worker.

The Federal Government Sector

There are two stochastic equations in the federal government sector. The first explains the interest payments of the federal government (equation 29), and the second explains the three month Treasury bill rate (equation 30). The federal government sector is meant to include the Federal Reserve as well as the fiscal branch of the government.

Equation 29 for the federal government sector is similar to equation 19 for the firm sector. It explains the level of interest payments of the government sector.

The bill rate is determined by an "interest rate reaction function," where the Fed is assumed to "lean against the wind" in setting its interest rate targets. That is, the Fed is assumed to allow the bill rate to rise in response to increases in inflation and lagged money supply growth and to decreases in the unemployment rate. There is a dummy variable multiplying the money supply variable in the equation. This variable takes on a value of one between 1979:4 and 1982:3 and zero otherwise. It is designed to pick up the change in Fed operating policy between October 1979 and October 1982 when the Fed switched from targeting interest rates to targeting the money supply.

When the interest rate reaction function (equation 30) is included in the model, monetary policy is endogenous. In other words, Fed behavior is explained within the model. How the Fed behaves is determined by what is going on in the economy. There are, however, three other assumptions that can be made about monetary policy. These are 1) the bill rate is exogenous, 2) the money supply is exogenous, and 4) the value of government securities outstanding is exogenous. If one of these three assumptions is made, then monetary policy is exogenous and equation 30 is dropped. This is discussed further below. The program on the site allows you to use equation 30 or to take the bill rate to be exogenous.

2.4 Properties of the Model
As you run the experiments in the following chapters, you will undoubtedly be unsure as to why some of the results came out the way they did. As noted above, however, the model is not a black box, and so with enough digging you should be able to figure out each result. In this section, some examples are given describing the ways in which particular variables affect the economy. The discussion in this section is meant both to get you started thinking about the properties of the model and to serve as a reference once you are into the experiments. You should read this section quickly for the first time and then return to it more carefully when you need help analyzing the experiments.

You may need to use Tables A.2-A.4 in Appendix A when you are puzzled about some aspect of the results. As noted above, these tables provide a complete listing of the variables and equations of the model.

Interest Rate Effects

There are many channels through which interest rates affect the economy. It will first help to consider the various ways that an increase in interest rates affects consumption and housing investment. 1) The short term after tax interest rate RSA is an explanatory variable in equation 1 explaining service consumption (CS), and the long term after tax interest rate RMA is an explanatory variable in equation 2 explaining nondurable consumption (CN), in equation 3 explaining durable consumption (CD), and in equation 4 explaining housing investment (IHH). The interest rate variables have a negative effect in these equations. In addition the long term bond rate is an explanatory variable in the investment equation 12, where a change in the real bond rate has a negative effect on plant and equipment investment.

Interest rates also affect stock prices in the model. The change in the bond rate RB is an explanatory variable in equation 25 determining capital gains or losses on corporate stocks held by the household sector (CG). An increase in RB has a negative effect on CG (i.e., an increase in the bond rate has a negative effect on stock prices). When CG decreases, the net financial assets of the household sector (AH) decrease---equation 66---and thus total net wealth (AA) decreases---equation 89. AA is an explanatory variable in the consumption equations (wealth has a positive effect on spending). Therefore, through the wealth channel, an increase in interest rates has a negative effect on consumption. When RB rises, AA falls and thus spending falls. (It should also be the case that an increase in interest rates lowers wealth in the model through a fall in long term bond prices, but the data are not good enough to pick up this effect.)

It is also the case that an increase in interest rates increases the interest income of the household sector because the household sector is a net creditor, i.e. the household sector lends more than it borrows. Interest income is part of personal income, which has a positive effect on consumption and housing investment, and so on this score an increase in interest rates has a positive effect on consumption and housing investment. This "income effect" of a change in interest rates on household expenditures is now quite large because of the large federal government debt holdings of the household sector. The negative income effect from a fall in interest rates now offsets more of the positive substitution effect than it did earlier.

A change in interest rates thus affects GDP through a number of channels. The size of the net effect on GDP of a change in interest rates is an empirical question, which the model can be used to answer. The final answer obviously depends on the specification of the stochastic equations, and you may want to experiment with alternative specifications to see how the final answer is affected. The size of the net effect is, of course, of critical importance for policy purposes.

Tax Rate Effects

An increase in personal income tax rates and/or social security tax rates (D1GM, D1SM, D4G) lowers the after tax wage (WA)---equation 126---and disposable income (YD)---equation 115. Disposable income is an explanatory variable in the consumption and housing investment equations---an increase in YD increases spending. Therefore, an increase in tax rates lowers consumption and housing investment by lowering disposable income. An increase in personal income tax rates also lowers the after tax interest rates RSA and RMA, which on this score has a positive effect on consumption and housing investment because the after tax interest rates have a negative effect.

One obvious exercise with the model is to change the corporate profit tax rate D2G and see how this affects the economy. You will find, for example, that an increase in D2G has a fairly small effect on GDP in the model. It appears from an exercise like this that the government can raise a lot of tax revenue (and thus lower the government deficit) by raising D2G with only a small negative effect on the economy. The way an increase in D2G affects the economy is as follows. An increase in D2G increases corporate profits taxes (TFG)---equation 49---which lowers after tax profits . The decrease in after tax profits results in a capital loss on stocks---equation 25---which lowers household wealth, which has a negative effect on consumption and housing investment and thus on sales and production. Also, the decrease in after tax profits results in a decrease in dividends---equation 18---which lowers disposable income, which has a negative effect on consumption and housing investment.

Both of these effects of a change in D2G on GDP are initially quite small. It takes time for households to respond to changes in wealth, and it takes time for dividends to respond to changes in after tax profits. Whether this specification is realistic is not clear. Changes in D2G may affect the behavior of the firm sector in ways that are not captured in the model, and you should thus proceed cautiously in changing D2G (or D2S for the state and local government sector). This may not be as easy a revenue raiser as the model implies.

Labor Supply and the Unemployment Rate

The unemployment rate UR is determined by equation 87. UR is equal to the number of people unemployed divided by the civilian labor force. The number of people unemployed is equal to the labor force minus the number of people employed. The labor force is made up of three groups---prime age men (L1), prime age women (L2), and all others (L3). The three labor force variables along with the number of moonlighters (LM) are the labor supply variables in the model. Three of the four labor supply variables depend positively on the real after tax wage rate (WA/PH), which means that the substitution effect is estimated to dominate the income effect on labor supply.

It is important to note that anything that, say, increases the labor force will, other things being equal, increase the number of people unemployed and the unemployment rate. (Other things equal here includes no change in employment.) For example, suppose the personal income tax rate is lowered, thereby raising the after tax wage rate WA. Then the labor force variables L2 and L3 will rise---equations 6 and 7. This, other things being equal, leads the unemployment rate to rise. Other things are not, of course, equal because the decrease in the tax rate also leads, for example, to a increase in consumption and housing investment, which leads to an increase in production and then to employment. Employment thus rises also. Whether the net effect is an increase or a decrease in the unemployment rate depends on the relative sizes of the increased labor force and the increased employment, which you can see when you run the experiments. The main point to remember is that the labor force responses can be important in determining the final outcome. There is, for example, no simple relationship between the unemployment rate and output (i.e., there is no Okun's "law") because of the many factors that affect the labor force.

L1, L3, and LM depend negatively on the unemployment rate, and for L1 and L3 this is the discouraged worker effect at work. In bad times (i.e., when the unemployment rate is high) some people get discouraged from ever finding a job and drop out of the labor force. (When people drop out of the labor force, they are no longer counted as unemployed, and so this lowers the measured unemployment rate.) When things improve, they reenter the labor force. This "discouraged worker effect" is captured by the unemployment rate in the L1 and L3 equations. Be aware when you run experiments that part of any change in the labor force is due to the discouraged worker effect in operation. This effect can be quantitatively very important in slack periods. The number of people holding two jobs (LM) also decreases in slack periods, and this is captured by the unemployment rate in the LM equation.

Note finally that L2 and L3 depending positively on the after tax wage rate (substitution effect dominating) is consistent with the theory behind the Laffer curve. Labor supply does respond to tax rates in the model. That is, when taxes decrease, the after tax wage rate increases, leading to an increase in the labor force. If you run various experiments, however, you will see that the quantitative responses are fairly small.

"Productivity" Movements

The productivity variable PROD in the model is defined in equation 118. PROD is equal to Y/(JF*HF), where Y is output, JF is the number of jobs, and HF is the number of hours paid for per job. PROD is thus output per paid for worker hour. Although this variable is usually called "productivity," it is important to realize that it is not a good measure of true productivity. In slack periods firms appear to pay for more worker hours than they actually need to produce the output; they hold what is called in the model "excess labor." This means that JF*HF is not a good measure of actual hours worked, and so Y/(JF*HF) is an imperfect measure of the true ability of the economy to produce per hour worked.

PROD is a procyclical variable. It falls in output contractions as excess labor is built up (output falls faster than hours paid for), and it rises in output expansions as excess labor is eliminated (output rises faster than hours paid for). The amount of excess labor on hand appears as an explanatory variable in the employment and hours equations---equations 13 and 14.

Output and the Unemployment Rate

It was mentioned above that there is no simple relationship between output and the unemployment rate in the model (no Okun's law) because of the many factors that affect the labor force. Even though the relationship is not stable, one can say that changes in output are likely to correspond to less than proportional changes in the unemployment rate. That is, when output increases (decreases), the unemployment rate will decrease (increase) but by proportionally less than output. There are three main reasons for this in the model. First, when output decreases by a certain percentage, the number of jobs falls by less than this percentage because firms cut hours worked per job as well as jobs and also build up some excess labor. Second, the number of people employed falls by less than the number of jobs because some of the jobs that are cut are held by people holding two jobs. These people are still employed; they just hold one job now rather than two. Third, as the economy contracts, the discouraged worker effect leads some people to drop out of the measured labor force and thus the measured labor force falls, which ceteris paribus decreases the unemployment rate. These three effects show why the unemployment rate tends to change by proportionately less than output does. You should examine these effects when you do the various experiments with the model.

Price Responses to Output Changes

One of the most difficult issues in macroeconomics is trying to determine how fast inflation increases as the economy approaches full capacity. The data are not good at discriminating among alternative specifications because there are so few observations at very high levels of capacity or low unemployment rates. The demand pressure variable used in the price equation (equation 10) is simply the level of the unemployment rate. No nonlinear transformation of the unemployment rate or output gap measure has been used. When other functional forms were tried, the fit of the equation was not quite as good as the fit using the level of the unemployment rate.

Because of the uncertainty of how the aggregate price level behaves as unemployment approaches very low levels, you should be cautious about pushing the model to extremely low unemployment rates. The price response that the model predicts for very low unemployment rates may be much less than would actually exist in practice. Again, the data are not good in telling us what this response is. You should probably not push the economy much below an unemployment rate of about 3.5 percent if you want to trust the estimated price responses.

You will notice if you run an experiment that increases output that the estimated size of the price response is modest, especially in the short run. This is a common feature of econometric models of price behavior. The estimated effects of demand pressure variables on prices are usually modest. This is simply what the data show, although many people are of the view that the effects should be larger. If you would like a larger response in the model, simply make the coefficient of the unemployment rate in equation 10 larger in absolute value (i.e., make it more negative). Advanced users may want to reestimate the equation using various nonlinear transformations of the unemployment rate. Be warned, however, that this is unlikely to make much difference to the fit of the price equation.

The key price variable in the model is PF, which is determined by equation 10, and this is the variable you should focus on. For most experiments PF and the GDP price deflator GDPD, respond almost identically. If, however, you, say, increase government purchases of goods, COG, which is a common experiment to perform, this will initially have a negative effect on the GDP price deflator even though it has a positive effect on PF. One would expect a positive effect because the increase in COG increases Y, which lowers the gap. The problem is that the GDP price deflator is a weighted average of other price deflators, and when you change COG you are changing the weights. It so happens that the weights change in such a way when you increase COG as to have a negative effect on the GDP price deflator. This is not an interesting result, and in these cases you should focus on PF, which is not affected by the change in weights.

Although demand pressure effects on prices are modest in the model, the effects of changing the price of imports (PIM) on domestic prices are fairly large, as you can see if you change PIM. In fact, much of the inflation of the 1970s is attributed by the model to the increases in PIM in this period. The model also attributes much of the drop in output in the 1970s to the rise in import prices. The reason for this is as follows. When PIM rises, domestic prices initially rise faster than nominal wages (because wages lag prices in the model). Higher prices relative to wages have a negative effect on real disposable income (YD/PH) and thus on consumption and housing investment, which leads to a drop in sales and production. In addition, if the money supply is held unchanged, the rise in prices leads to an increase in interest rates (through the standard LM story), which has a negative effect on consumption and housing investment. Interest rates also rise if the Fed instead behaves according to the interest rate reaction function---equation 30---because the Fed is estimated in this equation to let interest rates rise when inflation increases. One of the experiments in Chapter 8 is to examine what the 1970s might have been like had PIM not risen in this period.

Response Lags and Magnitudes

You will soon see as you begin the experiments that the effects of any change on the economy take time. There are significant response lags estimated in the model; it is by no means the case that firms and households respond quickly to policy changes.

You should also be aware regarding the magnitudes of the responses that they depend on the sizes of the estimated coefficients in the stochastic equations. If, say, one category of consumption responds more to a particular change than does another category, this reflects the different coefficient estimates in the two relevant stochastic equations. Also, some potentially relevant explanatory variables have been dropped from one equation and not from another (variables are generally dropped if their coefficient estimates have the wrong sign), which can account for the differences in responses. Another way of putting this is that no prior constraints on, say, the consumption equations have been imposed in order to have the responses of the different categories of consumption be the same. The data are allowed to determine these differences.

2.5 Alternative Monetary Policy Assumptions
One of the key uses of the model is to examine the links between monetary policy and fiscal policy. This can be done carefully because the model has accounted for all balance sheet and flow of funds constraints. This section discusses some of the key features of the monetary policy/fiscal policy links. The material is somewhat difficult, but if you take the time to work through the discussion and the equations, you should have a good understanding of how monetary policy works. You can consider the equations discussed in this section to be the LM part of the model---they replace equations (4)-(6) above. The following are four of the equations in the model. (The symbol <> means "change in." For example, <>AG = AG - AG-1, where AG-1 is the value of AG of the previous period.)

17. MF = f(RS,...)

26. CUR = f(RS,...)

77. 0 = SG - <>AG - <>MG + <>CUR + <>(BR - BO) - <>Q - DISG - CTGB

81. M1 = M1-1 + <>MH + <>MF + <>MR + <>MS + MDIF

There is also the interest rate reaction function, equation 30:

30. RS = f(...)

The notation f( ) means that the equation is stochastic. The variables inside the parentheses are explanatory variables. For the sake of the present discussion, only the explanatory variables that are needed for the analysis are listed in the parentheses.

The relevant notation is:

AG     net financial assets of the federal government
BO     bank borrowing from the Fed
BR     total bank reserves
CTGB   capital transfers from the federal government to finanical business
CUR    currency held outside banks
DISG   discrepancy for the federal government
M1     M1 money supply
MDIF   discrepancy between M1 and other variables
MF     demand deposits and currency of firms
MG     demand deposits and currency of the federal government
MH     demand deposits and currency of households
MR     demand deposits and currency of the foreign sector
MS     demand deposits and currency of the state and local governments
Q      gold and foreign exchange of the federal government
RS     three month Treasury bill rate
SG     saving of the federal government

Equations 17 and 26 are the demand for money equations.

Equation 77 is the budget constraint of the federal government. SG is the saving of the federal government. SG is almost always negative because the federal government almost always runs a deficit. If the government runs a deficit, it can finance it in a number of ways. Two minor ways are that it can decrease its holdings of demand deposits in banks (MG) and it can decrease its holdings of gold and foreign exchange (Q). More importantly, it can increase the amount of high powered money (currency plus non borrowed reserves) in the system, which is CUR + (BR - BO). Finally, it can increase the value of government securities in the hands of the public, meaning the government borrows from the public. -AG in the model is the value of government securities outstanding. (AG is negative because government securities are a liability of the government, and so -AG is the (positive) value of government securities outstanding). The variable The variable CTGB in equation 77 is the value of capital transfers from the federal government to finanical business---this reflects the bailout spending. DISG in equation 77 is a discrepancy term that is needed to make the NIPA data and the FFA data match. It reflects errors of measurement in the data. Ignoring MG, Q, CTGB, and DISG in equation 77, the equation simply says that when, say, SG is negative, either government securities outstanding must increase or the amount of high powered money must increase. This is the budget constraint that the government faces, the government being defined here to be the federal government inclusive of the monetary authority.

Equation 81 is the definition of M1. The change in M1 is equal to the change in MH + MF + MR + MS plus some minor terms that are included in the MDIF variable.

The importance of the above equations for understanding how monetary policy works and the relationship between monetary policy and fiscal policy cannot be overstated. We are now ready to consider various cases. First, it is important to consider what is exogenous in the above equations, what is determined elsewhere in the model, and what is endogenous. The following variables are taken to be exogenous in the model: BO, BR, MH, MR, MG, MS, Q, CTGB, DISG, and MDIF. In addition, there is a monetary policy tool, namely AG, which for now can be assumed to be exogenous. AG is the variable that is changed when the Fed is engaging in open market operations. The variable SG is determined elsewhere in the model (by equation 76 in Table A.3 in Appendix A). This leaves four endogenous variables for the four equations (we are not using equation 30 yet): MF, CUR, RS, and M1. Given the other values, the four equations can be used to solve for the four unknowns. (It is usually the case in macroeconometric models that counting equations and unknowns is sufficient for solution purposes.)

If AG is exogenous and if fiscal policy is changed in such a way that the deficit is made larger (SG larger in absolute value), then the increase in the deficit must be financed by an increase currency (CUR). With AG exogenous, there is nothing else endogenous in equation 77 (except SG, which is determined elsewhere). If government spending is increased with AG exogenous, this will lead to a fall in the interest rate (RS). Here is where the insights from the IS-LM model might help (although be careful of oversimplification). In order for CUR to increase, households and firms must be induced to hold it, which is done through a lower interest rate.

Although AG is the main tool used by the Fed in its conduct of monetary policy, it is actually not realistic to take AG to be exogenous. The Fed is much more concerned about RS or M1 than it is about AG. A better way to think about this setup is that the Fed uses AG to achieve a target value of RS or M1.

Consider an M1 target first. If the Fed picks a target value for M1, then M1 is now exogenous (set by the Fed). This means that we now have an extra equation above---81---with no unknown matched to it. The obvious choice for the unknown is AG. In other words, AG is now endogenous; its value is whatever is needed to have the target value of M1 be met. A similar argument holds for an RS target. If the Fed picks a target value for RS, then RS is exogenous and AG is endogenous. AG is whatever is needed to have the RS target be met. This is also where equation 30 can come in. Instead of setting a target value of RS exogenously, the Fed can use an equation like 30 to set the value. If this is done, then RS is endogenous---it is determined by equation 30. AG, of course, is also endogenous, because its value must be whatever is needed to have the value of RS determined by equation 30 be met.

As a final point about the above equations, note the relationship between fiscal policy and monetary policy. Fiscal policy changes SG, which from equation 77 must be financed in some way. If the Fed keeps AG unchanged, an unrealistic assumption, the financing will all be through a change in currency. If the Fed keeps M1 unchanged, then AG will adjust to offset any effects of the fiscal policy change that would have otherwise changed M1. If the Fed keeps RS unchanged, then AG will adjust to offset any fiscal policy effects on RS. It should be clear from this that the size of fiscal policy effects on the economy are likely to be sensitive to what is assumed about monetary policy.

In terms of solving the model by the Gauss-Seidel technique, which needs one left hand side variable per equation, the four equations above have to be rearranged depending on what is assumed about monetary policy. The details are listed in Table A.8 in Appendix A. If equation 30 is used or if RS is taken to be exogenous, then the matching is MF to equation 17, CUR to equation 26, AG to equation 77, and M1 to equation 81. If M1 is taken to be exogenous (no equation 30), the matching is RS to equation 17, CUR to equation 26, AG to equation 77, and MF to equation 81. If AG is taken to be exogenous (also no equation 30), the matching is MF to equation 17, RS to equation 26, CUR to equation 77, and M1 to equation 81.

It is difficult to solve the model when M1 or AG is taken to be exogenous, and the site does not allow this to be done. The two options are to use equation 30 or take RS to be exogenous. If RS is taken to be exogenous, the user can enter values for RS.

2.6 Important Things to Know About the Program
The Datasets

The datasets are discussed in About US User Datasets, and you should read this now if you have not already done so. It is important to note that the data in BASE up to the beginning of the forecast period are actual data. From the beginning of the forecast period on, the data are forecasted data. Each quarter the model is used to make a forecast of the future, and the new forecast is added to the Web site as soon as it is done. The exogenous variable values for the forecasted quarters are the values chosen before the model is solved. The endogenous variable values for the forecasted quarters are the solution values (given the exogenous variable values).

BASE also contains the coefficient estimates that existed at the time of the forecast (the model is reestimated quarterly). All the other information that is needed to solve the model is also in BASE, and this is also true of the datasets that you create.

It is important that you understand the following. If you ask the program to solve the model for the forecast period (or any subperiod within the forecast period) and you make no changes to the coefficients and exogenous variables, the solution values for the endogenous variables will simply be the values that are already in BASE. If, on the other hand, you ask the program to solve the model for a period prior to the forecast period, where actual data exist, the solution values will not be the same as the values in BASE because the model does not predict perfectly (the solution values of the endogenous variables are not in general equal to the actual values). It is thus very important to realize that the only time the solution values will be the same as the values in BASE when you make no changes to the exogenous variables and coefficients is when you are solving within the forecast period.

Using the Forecast Period to Examine the Model's Properties

The easiest thing to do when running experiments with the model is to run them over the forecast period. Say that you want to examine what happens to the economy when government purchases of goods (COG) is decreased by $10 billion. You make this change in the program and ask for the model to be solved, creating, say, dataset NEW. If you do this over the forecast period, the solution values in NEW can be compared directly to the values in BASE. If you had not changed COG, the solution values NEW would have been the same as those in BASE, and so any differences between the solution values in NEW and BASE can be attributed solely to the change in COG.

Many of the experiments in this workbook are thus concerned with making changes in the exogenous variables, solving the model over the forecast period, and comparing the new solution values to the solution values in BASE. The difference between the two solution values for a particular endogenous variable each quarter is the estimated effect of the changes on that variable.

You should be aware that most of the time one is comparing the solution value in one dataset with the solution value in another dataset. One is not generally examining solution values over time in a single dataset. Students often confuse changes over time in a given dataset with changes between two datasets. It is critical that you understand this distinction, and so make sure that you do before going on.

You should also be clear on what is meant when a variable is said to be "held constant" for an experiment, such as the money supply or the interest rate being held constant. This means that the values of the variable for the experiment are the same as the values in the base dataset. They are not changed from the base values during the experiment. Being held constant does not mean that the variable is necessarily unchanged over time. If the values of the variable in the base dataset change over time (which most values do), then the variable values in the new data set will change over time; they just won't be changed from the values in the base dataset.

Using Non Forecast Periods to Examine the Model's Properties

In some cases one must use non forecast periods to carry out the experiment. If, for example, you are concerned with examining how the economy would have behaved in the 1970s had the price of imports (PIM) not increased so dramatically, you must deal with the period of the 1970s. Say you are interested in the 1973:1-1979:4 period, and you want to know what would have happened in this period had PIM not changed at all. The first thing you must do is solve the model for this period making no changes to PIM (or any other exogenous variable). Call the dataset of these solution values BASEA. At this point you can compare the solution values in BASEA with the values in BASE, which are the actual values. The differences in these values are the prediction errors, and you can examine these errors to see how well the model predicted the period. Remember that this prediction uses the actual values of all the exogenous variables---it is an ex post prediction.

Once you have created BASEA, this dataset is your "base" dataset for v any further experiments. Using BASEA as your base, you can then change PIM for the 1973:1-1979:4 period, where the new values of PIM are unchanged over time, and solve the model again, creating, say, NEWA. You can then compare the values in NEWA with those in BASEA to examine the effects of the PIM change. You do not compare the values in NEWA with those in BASE. The differences between these values are a combination of the prediction errors of the model and the effects of the changes in PIM, and you cannot separate the differences into the two parts. Again, it is extremely important that you understand what is going on here.

Changing Coefficients

Some of the experiments call for changing one or more coefficients in the model. Even if you are dealing with the forecast period, once you make a change in a coefficient, the solution values are not the same as the values in BASE even if no exogenous variables have been changed. When you change one or more coefficients, you must first solve the model with only these coefficients changed. The dataset created by this solution, say BASEA, is your base dataset. You can then make changes in the exogenous variables and solve the model for these changes. The dataset created from this solution, say NEWA, can then be compared to BASEA. It is not correct to compare NEWA to BASE, because the differences between these two datasets are due both to the coefficient changes and to the exogenous variable changes.

Selecting Variables to Display

There are 123 endogenous and slightly over 100 exogenous variables in the model. It is clear that you do not want to display results for each of these variables, or even for each of the endogenous variables, for each experiment. The program allows you to display a subset of these variables, and you should in general use this option. A few key variables should always be displayed, and other variables should be displayed as the experiment warrants.

The following list includes most of the variables that you will ever want to examine. You can select from this group as the experiment warrants. The variables are in alphabetical order.

AA      Total net wealth of the household sector
AG      Net financial assets of the federal government
        (-AG is roughly the federal government debt)
BO      Bank borrowing from the Fed
BR      Total bank reserves
CD      Consumer expenditures for durables
CG      Capital gains (+) or losses (-) on stocks held by households
CN      Consumer expenditures for nondurables
COG     Federal government purchases of goods
COS     State and Local government purchases of goods
CS      Consumer expenditures for services
CUR     Currency held outside banks
D1G     Personal income tax parameter for federal taxes
E       Total employment
EX      Exports
GDPD    GDP price deflator
GDPR    Real GDP
IHH     Residential investment, household sector
IKF     Nonresidential fixed investment of the firm sector
IM      Imports
INTF    Interest payments of the firm sector
INTG    Interest payments of the federal government
IVF     Inventory investment of the firm sector
JF      Number of jobs in the firm sector
KK      Capital stock of the firm sector
L1      Labor force, men 25-54
L2      Labor force, women 25-54
L3      Labor force, all others 16+
LM      Number of moonlighters
MB      Net demand deposits and currency of banks
MF      Demand deposits and currency of the firm sector
MH      Demand deposits and currency of the household sector
M1      Money supply
PCGDPD  Percentage change in the GDP price deflator (annual rate)
PCGDPR  Percentage change in real GDP (annual rate)
PCM1    Percentage change in the money supply (annual rate)
PF      Price deflator for the firm sector
PG      Price deflator for COG
PIEF    Before tax profits of the firm sector
PIM     Import price deflator
POP     Population, 16+
POP1    Population, men 25-54
POP2    Population, women 25-54
POP3    Population, all others 16+
PROD    Output per paid for worker hour ("productivity")
RB      Bond rate
RM      Mortgage rate
RS      Three month Treasury bill rate
SG      Savings of the federal government
SGP     Federal government surplus (+) or deficit (-)
SHRPIE  Ratio of after tax profits to the wage bill
SRZ     Household saving rate
SR      Savings of the foreign sector (-SR is the U.S. current account)
THG     Personal income taxes to the federal government
TRGH    Transfer payments from the federal government to households
U       Total number of people unemployed
UR      Unemployment rate
WA      After tax nominal wage rate
WF      Nominal wage rate of the firm sector
WR      Real wage rate
X       Total sales of the firm sector
Y       Total production of the firm sector

The Possible Transformations for Modifying the Stochastic Equations

The program allows you to modify the stochastic equations in the US model subject to two restrictions. The first restriction is that the left hand side variables of the stochastic equations cannot be changed. The second restriction is that only certain variables can be used as right hand side variables. The right hand side variables can be any endogenous or exogenous variable in the model, that is, any variable listed in Table A.2 in Appendix A. In addition, certain transformations of the endogenous and exogenous variables are allowed. These are as follows:

Name     Transformation
LCSZ      log(CS/POP)
LCNZ      log(CN/POP)
CDZ       CD/POP
L1Z       log(L1/POP1)
L2Z       log(L2/POP2)
L3Z       log(L3/POP3)
LMZ       log(LM/POP)
LMHZ      log[MH/(POP*PH)]
LPF       logPF
IKF1      <>IKF
LJF1      <>logJF
LHF1      <>logHF
LHO       logHO
LWF       logWF
LMFZ      log(MF/PF)
LY1       <>logY
LHF       logHF
PCPD      100*[(PD/PD-1)4-1]
LPX       logPX
LXMFAZ    log[(X-FA)/POP]
RB1       <>RB
LCURZ     log[CUR/(POP*PF)]
LIMZ      log(IM/POP)
LUB       logUB
LDF1      <>logDF
CFM1      <>(CF-TFG-TFS)
LCCF      logCCF
LXMFA     log(X-FA)
LU        logU
LWFD5     log[WF*(1+D5G)]
PCM1L1A   D794823*PCM1-1
LMHL1Q    log[MH-1/(POP-1*PH)]
LMFL1Q    log(MF-1/PF)
LCURL1Q   log[CUR-1/(POP-1*PF)]
KDZ       KD/POP
LGAPA     log[(YS-Y)/YS + .04]
LEXL      log(JF/JHMIN)
LY        logY
YDZ       YD/(POP*PH)
LWAZPH    log(WA/PH)
LYNLZ     log[YNL/(POP*PH)]
LAAZ      log(AA/POP)
AAZ       AA/POP
PX1VL     (PX-PX-1)*V-1
LEXLL1D   DD772*log(JF/JHMIN)-1
LL1Z      log(L1/POP1)
LJF1L1D   DD772*Ch logJF-1
RS1       <>RS
KHZ       KH/POP
LL2Z      log(L2/POP2)
LL3Z      log(L3/POP3)
TDD       DD772*T
LCNZ1     <>log(CN/POP)
LPIM      logPIM
LYDZ      log[YD/(POP*PH)]
RSB       RS*(1-D2G-D2S)
LLMZ      log(LM/POP)
RBA4L3A   IKFA*(real, after tax RB-3)
Y1        <>Y

If you study Table A.3 carefully, you will see that many of the above transformations are used in the 27 stochastic equations. To give an example of how these transformations can be used, say that one wanted to add the log of the lagged value of assets to the housing investment equation, equation 4. This addition could be made using LAAZ above. When you are modifying the equations, different lag lengths can be used for any variable. Likewise, different values of the order of the autoregressive process for the error term can be used.

Annual Rates versus Quarterly Rates

As noted in About US User Datasets, the flow variables are displayed at annual rates even though the variables are at quarterly rates in the model. This generally poses no problem in performing the experiments in this workbook except for examining a budget constraint equation like 77. (See the discussion of equation 77 in Section 2.5.) Equation 77 is:

77 0 = SG - <>AG - <>MG + <>CUR + <>(BR - BO) - <>Q - DISG - CTGB

SG is a flow variable, and so it is displayed in at an annual rate. A variable like AG, on the other hand, is a stock variable, where the quarterly rate/annual rate distinction is not relevant. The change in AG (<>AG), however, is a flow variable. (<>AG is the value of AG this quarter minus the value of AG last quarter.) Say that you display all the variables in equation 77 and want to see if equation 77 is met in the data (which it will be). When you compute a change like <>AG, it will be at a quarterly rate unless you multiply it by four. If you don't multiply all computed changes by four, equation 77 will not be met because SG and DISG are at annual rates. Therefore, remember to multiply all computed changes by four when examining an equation like 77.