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1. cover Introduction toMacroeconometric Models Gennaro Zezza Department of Economics, Cassino, Italy Levy Institute of Economics at Bard College

2. 0.1 Classes of models • Macroeconomic events are the result of innumerable decisions, often inter-related, taken under given constraints. • What we measure are aggregates obtained through samples (consumption, income, etc.) • A model is an attempt to isolate the (hopefully) most important links among aggregates, in order to • Gain insights on complex relationships • Project or forecast future events

3. 0.2 Classes of models Linear models take the form (in matrix notation) B(L)Y = C(L)X + u Where, in each equation, Y is a vector of variables explained by the model, X is a vector of exogenous variables, and B, C are vectors of parameters in the lag operator L. Finally, u is a random shock, usually with some well defined properties

4. 0.3 Classes of models Abandoning matrix notation, the i-th equation of our model should be expressed as bi11·Y1t + bi12·Y1t-1 + … +bi21·Y2t +bi21·Y2t-1 + … + … = ci11·X1t + ci12·X1t-1 + … ci21·X2t + ci22·X2t-1 + … + … + ut

5. 0.4 Classes of models There are several problems to solve to have an operational model: • How to distinguish between endogenous variables (Y) and exogenous (X) • (provided we solve 1) How to identify parameters in B, C. If we have r endogenous variables Y and s exogenous variables X, and a maximum of l lags is important, each equation of our model will have (r-1+s)*l parameters.

6. 0.5 Classes of models A now popular class of models chooses not to address the exogeneity problem. If all variables are potentially endogenous, our i-th equation can be rewritten as And the equations form a VAR

7. 0.6 Classes of models In this course we will explore how to develop a structural model. This implies to distinguish (somewhat arbitrarily) between variables endogenous or exogenous to the model. Such hypothesis can be usually tested. A priori information on the relationship among some variables let us distinguish between identities (where parameters are known, and there is no random shock component) and equations where parameters need to be estimated.

8. 1.1 SAM When creating a model, we are guided by our ultimate goals in defining the level of detail we want to achieve, bearing in mind that as the level of detail increases, the cost of producing and mantaining the model will increase more than proportionally.

9. 1.2 SAM A Social Accounting Matrix records payments in the columns, and receipts in the rows.

10. 1.3 SAM • From row 1 (and column 1) we get the usual GDP identity at both current and constant prices: • 1] p·GDP = p·Y - p·IG - p·M = p·C + p·ΔK + p·G + p·E - p·M • 2] GDP = Y - IG - M = C + ΔK + G + E - M • where ΔK is inclusive of the change in inventories. • From column (1) and equation [1] above we get the distribution of income • 3] p·GDP = WB + FT + TI • Using row and column (2) we can define households' disposable income Yhd: • 4] Yhd = Yh - Td - TRhh = WB +FD +Fb +iM + iBh + TRwh - Td • and households savings: • 5] Sh = Yhd - p·C • From row and column (3) we get the definition of firms' savings, i.e. undistributed profits Fu: • 6] Fu = FT + (TRwf - TRfw) - FD - iL - Tf • and so on. Notice that in Table 1.1 we assume that banks distribute all of their profits to households, while the Central bank transfers all of its "profits" to the government. • Notice also the defition of government deficit GD from row and column 6: • 7] GD = -Sg = p·G + (iB* -Fc) + (TRgw - TRwg) - (Td + Ti + Tf) • and the balance of payments on current account: • 8] BP = -Sw = (p·E - p·M) + (TRw* -TR*w)

11. 1.4 SAM Table 1 above implies at least the following stocks: • A stock of capital (with inventories) • Financial assets issued by the government • Financial assets issued by firms • Financial assets issued by banks • Financial assets issued by the Central Bank (currency) • Financial assets issued by the Rest of the World • It must be the case that, for any sector, savings equals the net change in its stock of real and financial assets. We can therefore build Table 1.2 below

12. 1.5 SAM

13. 1.6 SAM • From each column in Table 1.2 we can get an identity which distributes savings into real and financial assets or, in other words, specifies the budget constraint of the sector. For instance, firms can acquire real capital according to: 1] p·ΔKf + ΔFR = Fu + ΔLf + ΔE·pe • which clarifies that to invest in the U.S. or abroad firms have to get funds either from undistributed profits Fu, or from issuing new equities ΔE, or by getting new bank loans L. • Similar identities must be constructed for all sectors in our economy.

14. 1.7 SAM • It is now easy to move from changes in stocks to the (end of period) level of a stock, at least theoretically. Generally speaking, for any stock Xt Xt = Xt-1 + ΔXt • The problem arises when X is measured in nominal terms, and its market price varies between t-1 and t. Consider the stock of equities E: pet·Et = petEt-1 + pet·ΔEt • or, in other words, the closing value of the stock of equities is given by the opening stock, valued at current prices, plus the net acquisition of equities within the period (assumed here to occur at the closing price pe). Adding and subtracting pet-1Et-1 we get pet·Et = pet-1Et-1 + pet·ΔEt + Δpet·Et-1 • where the last term gives the net capital gains on equities during the period. • Care should be given to the impact of capital gains at the macro level: for instance, within the household sector, capital gains should not matter unless they are realized, and they should not matter when an individual holding equities sells them to another member of the household sector (unless the two parts have very different propensity to save). • In practice, capital gains seem to matter...

15. 1.8 SAM

16. 2.1 US model structure • Our simple model for the U.S. economy has the objective of analyzing the three major financial balances, i.e. Government Deficit, the Balance of Payments and the Private Sector Balance. We will therefore need a simpler structure than the one presented above. • More specifically, we will consolidate the households and the (non financial) business sector. • Assuming that the financial sector distributes all of its profits, we don’t need to model it explicitly as a first approximation • The Central Bank can be consolidated with the Government (altough we will make some simplifying assumptions when dealing with the data)

17. 2.2 US model structure

18. 2.3 US model structure

19. 2.4 US model structure GDP identity • GDP identity can be derived as usual from row and colum 1 of Table 2.1 1] GDP = Y - MGS = PREXT + G + XGS - MGS • but note now that, in the "real" world, there is more than a single good, and so all components of demand will require their own deflator. Adding _k to names to denote constant-price values we have: 2] GDP = pgdp·GDP_K3] PREXT = pprext·PREXT_K4] G = pg·G_K5] XGS = pxgs·XGS_K6] MGS = pmgs·MGS_K • Using chain price indexes, GDP identity at constant prices does not hold. We have to ways out: change equation [2], using it to derive pgdp, or use a residual variable in 7] GDP_K = PREXT_K + G_K + XGS_K - MGS_K + GDPRES_K • Since the former solution will imply using model variables which differ from published data, the latter option is preferrable.

20. 2.5 US model structure Data sources • National Accounts • Source: Bureau of Economic Analysis (www.bea.gov) (BEA), National Income and Product Accounts (NIPA). We will use: • GDP Accounts • Government Accounts • Balance of Payments Accounts • Flow of Funds • Source: Federal Reserve (www.federalreserve.gov) (FED). • We will use: • Debt outstanding for all sectors • Assets and liabilities of the Rest of the World • Other data. • Interest rate on Treasury Bills. Source: FED. • Interest rate data • World GDP; U.S. exchange rate index. Source: Levy Institute. See Levy Institute Working Paper n.387, September, 2003. Projections updated Sep. 2006. • World GDP and Exchange rates data and projections • S&P 500 Index. Source: Standards & Poors. • S&P 500 Index

21. 3.1 Introduction to Eviews • Eviews can be run interactively, or trough programs, which are sequences of Eviews commands • We will use programs, so to keep memory of what we are doing! This will require some knowledge of Eviews language, which is readily available in Eviews Command Reference guide • The first step is to create (or load) a workfile, specifying the type of data to be used: wfcreate(wf=usmodel, page=quarterly)q 1947q1 2015q4

22. 3.2 Introduction to Eviews • In a program we can use string variables, preceeded by a % character %lastq = "2007q4" • The following instruction sets the working sample from the first available data to the quarter specified in our string variable smpl @first %lastq • We can specify the location of our data through a string variable %path="D:\usdata\" %file="Section1All_xls.xls“ • The following instruction will read the file from the right path: read(D10, s=gdp, t) %path%file GDP CONS • Inspect the first program 01_load_data.prg to see how to load data into Eviews from original sources

23. 3.3 Introduction to Eviews • Eviews stores objects in the workfile • Each object has specific views and procedures. • It is a good practice to document your data! gdp.label(d) Gross domestic product gdp.label(s) NIPA Table 1.1.5 Row 1 gdp.label(u) Billions of US dollars • See the second program 02_doc_data.prg for more

24. 3.4 Introduction to Eviews • We already identified 7 equations for our model: let's start constructing a model in Eviews. We can do it with the following program: ' delete eventual previous model objects delete usmod* ' defines an object model named usmodel model usmodel 'append identities to the model usmodel.append @identity gdp = prext + g + xgs – mgs usmodel.append @identity gdp_k = prext_k + g_k + xgs_k - mgs_k + gdpk_res usmodel.append @identity prext = prext_k*pprext usmodel.append @identity g = g_k*pg usmodel.append @identity xgs = xgs_k*pxgs usmodel.append @identity mgs = mgs_k*pmgs usmodel.append @identity pgdp = gdp/gdp_k • Starting only from the GDP identity at constant and current prices, we already have 7 equations in 16 variables, between endogenous and exogenous.

25. 3.5 Introduction to Eviews Starting only from the GDP identity at constant and current prices, we already have 7 equations in 16 variables, between endogenous and exogenous. Eviews provides convenient ways of exploring model properties. Double click on the wgmodel object, and then on View/Variables to obtain the ordered list of variables in the model below.