APPLIED MACROECONOMETRICS TREND-CYCLE BREAKDOWN MACROECONOMETRIC MODELS

1. APPLIEDMACROECONOMETRICSTREND-CYCLE BREAKDOWNMACROECONOMETRIC MODELS pierre-olivier.beffy@polytechnique.org

2. Introduction • For your dissertation, free to use any software. • A good tip to use: writeyourcoding line and comment them; anyeconometricanalysis must bereplicable. • Macroeconometrics software • Econometrics: Stata, SAS, R • Specialised in time series: Eviews, RATS • Matrices : GAUSS, Matlab , Scilab (+Grocer); • Model simulation: DYNARE (with Matlab), Troll • Where to findmacroeconomicseries? • Main sources • France: INSEE, Banque de France • International organisations: OCDE, BCE, FMI • USA: Federal Reserve Saint Louis • Non-free providers: Datastream, Bloomberg

3. Trend-cycle breakdown • Trend vs. cycle: • Statistical description purposes: • - Characterise long-termdevelopments • Syntheticindicator for assessing the position in a cycle • Normative / theoreticalpurposes: • Evaluation of ”cyclicallyadjusted ” quantities: structural public balances • Someempirical/normative relationships (like the Taylor rule) involvecyclical variables • Model estimation: Somemodelsonlyattempt to explain the cyclical part of the data

4. Notations We have representing the logarithm of a variable Typicalexamplewherestands as real GDP Principle: breakdown as with : trend : Cyclical component

5. Why logarithm? • The standards in (macro)econometrics (it reduces heteroscedasticity issues and lead to easy interpretations) • : Growth rate • : deviation from average, in % (Stationary case) • often represents an “equilibrium” or “natural” value • Ex: Equilibrium unemployment rate, Real Interest rates equilibrium • Cyclicalcalled “Output Gap” whenrepresents real GDP

6. Statistical vs. structural methods • Univariate statistical breakdown • 1. Linear trend • 2. Beveridge Nelson breakdown • 3. Statistical filters (Hodrick - Prescott) • Next chapter: Structural approach through VECM • Non exhaustive course: some methods not (or only a little) explained during this course • Kalman filter • Applied example: Forecasts of unobservable variables, eg. The equilibrium unemployment rate (NAIRU) • Markov chained regime - switching models • Applied example: dating of cycles, Hamilton, 1989 • Factor models: extension of the factor analysis to analyse a high number N of time series.

7. Deterministic trends Reference model: : trend growth rate Valid Estimation method : MCO (converges) Cyclical component is equal to the residual of the regression Note: -is very often auto-correlated hence the need to take into account the autocorrelation to perform hypothesis tests (Newey-West) -In practice, the residual is also rarely stationary (no return to average in particular) hence the use of trend disruption or the use of co-integration methods (Next chapters).

8. GDP US (log.) 10 9.5 9 8.5 8 7.5 1940 1950 1960 1970 1980 1990 2000 2010 2020

9. GDP France (log.) 7 6.5 6 5.5 5 4.5 4 1940 1950 1960 1970 1980 1990 2000 2010 2020

10. Deterministic linear trends with break-up • Model takingintoaccount a trend break • yt= α + g1 t+ g2 (t − t1)I (t > t1) + ut whereI (t > t 1) is an indicatorfunctionI (t > t 1) = 0 witht ≤ t1, I (t > t1) = 1 otherwise. • Example: Productivityslowdown in industrial countries from 1974. • Estimate by MCO • Question: how to identify break dates ? • Traditionalapproach: t 1 usuallyknown • Alternative: endogenousdetermination - Estimateof t1 • For each date k ∈ [T min, T max] estimated • yt= α + g1t + g2 (t − k)I (t > k) + ut • Note thatSSR(k) is the sum of the squares of the residuals • Select the date k∗ that minimises the sum of the squares of the residuals.

11. Stochastic trends Hypothesis : non stationarystochastic (unit root) Example: Case of a random walk with trend yt= γ + yt−1 + εt yt= 2γ + yt−2 + εt−1 + εt yt= γt+ y0 + ε1 +... + εt−1 + εt yt= γt+ y0 + yt= y0 + γt+ ut Note: -Deterministic component is identical to the one in the deterministic trend model -No return on average

12. The first difference filter • Stationary variable • Parametersγ : Averagegrowth rate • Note: is a stationary transformation of the serie but is not considered as a variable of output gap • It does not provide an ”equilibrium” level

13. Beveridge and Nelson filter Starting point: ARIMA Model (p,q) of the serie (Wold representation) Trend component Long term forecast of the corrected series of the deterministic trend

14. Example: case of AR(1) Model

15. Notes: - is a random walk. We show that - The innovation of the trend and cycle are proportional (not that much economically intuitive) - In practice, is often low: close to - The results are frequently against expectations (See examples): the output gap BN may be negatively correlated to the output growth (despite a possible interpretation related to permanent supply shocks)

16. Statistical filters • Smoother evolution of the trend; less sensitive to trend disruptions. • In general, the filters are written • A ”traditional” indicator the Moving Average (centered) Notes: The last M points in the sample are lost

17. HP (Hodrick - Prescott) filter : Solution of λparameter is the relative weight between the volatility of the cycle and the volatility of the trend λ=0 : λ= +constant (deterministic trend) Value of your parameter λ Usual value : λ = 1600 quarterly data

18. Notes: • The HP filteris the mostused in macroeconometrics • The choice for the parameterλcanmake a genuinestatisticaldifference • The HP filter has the same time range than the sample • But end values of the sample are lessrobust

19. Bandpass filter (Baxter-King) • Spectral density • We have the as the autocorrelation to k of the serie • The spectral density corresponds to Fourier’s transformation of the auto correlated series Period associated to the frequency p Example. 8 years cycle on quarterly data p = 32

20. Filter • Link between spectral density of the rawseries and the filteredseries : • where G (ω)is the gain of the filter at frequencyω • Principle of the Band Passfilter: Select fluctuations at variousfrequencies • An “ideal” BandPassfilter : • G (ω) = 1if ω ∈ [2π/pu , 2π/pl] • G (ω) = 0 otherwise, où puet pl– are the max and min periods. • Example for a procylical cycle : pl= 6, pu= 32 ou 40 quarters.

21. Property: For the Band Pass filter, ideal coefficients are: • for k ≠ 0, where • In practice, we can only calculate a finished moving average • Baxter-King filter: truncate the moving average K and choose the best approximation • Property: Parameters of the BK filter : for k = -K ,…, K • with

22. References (breakdown of trend / cycle methods) Canova F. (1998) ”Detrending and the business cycle facts”, Journal of MonetaryEconomics, 41, 475-512 Canova F. (2007) Methods for AppliedMacroeconomicResearch, Princeton UniversityPress, chapitre 3. De Jong D., Dave C. (2007) Structural Macroeconomics, Princeton UniversityPress, chapitre 3. Doz C. et al. (1995) ”Décomposition tendance/cycle: estimations par des méthodes statistiques univariées” Economie et Prévision, n120.

23. Macroeconometricmodels- Introduction • The economy: a domain without a “life size” experience • Use • In economic policy (quantify the effects of rising health or pension spending on the economy) • In preparation for, or in addition to forecasting • As a synthesis tool (assess impact of a devaluation of the dollar for example)

24. LAYOUT • Overview of macroeconometric models • What is a macroeconometric model? • Critics • Study of main models’ blocks • Accounting framework • Econometrics and forecasting • Main blocks • Use and analysis: • Equilibrium • Presentation of a macroeconometric model (MZE) • Simulations Conclusion

25. 1. Overview of macroeconometricmodels

26. 1.1. What is a macreoconomic model? • A “Model” ! • Simplified representation of the reality • Selection of important characteristics of an economy and "quantification" or "econometric evaluation“ • Non-neutral choice on model results: "A model teaches us only what we have allowed it to teach us! “ • Confronting reality => empirical validation of the relevance of a model • The example to follow? (Normative aspect)

27. What is a macreoconomic model? • “Macroeconomic” • An aggregate analysis (households, enterprises, public administrations ... for a country or a group of countries) => use of the data or even the framework of national accounts • Simultaneity and imbrication of economic behaviours with potentially antagonistic interests => closed macroeconomic framework • The underlying macroeconomic theory: • Importance of "choices" of modelling (which theory of consumption to choose? Is the model adapted to the economic question studied?) • Macroeconomic models are often referred to as "structural”

28. History of macroeconomic models • Jan Tinbergen (first Nobel prize in economics in 1969) • First macroeconomic model in 1936 • Objective: to study the possibility of boosting economic activity in the Netherlands without deteriorating the trade balance, in the context of an international economy in crisis. (study of an expansionary policy) • Four periods : • 1940-1955 : birth of macroeconomic models • 1955-1970 : artisanal and experimental period • 1970-1990 : maturity and complexification (extensive development) • 1990-… : simplification (intensive development)

29. 1940-1955 : birth of models • 3 major innovations • IS/LM model (Hicks 1937) • Improvement of econometrics, which provides techniques for quantifying models’ parameters • Introduction of the first electronic computers necessary for the numerical resolution of the models • The Klein-Goldberger macroeconomic model of 1955 drives away the then-scepticism for models (lack of means, data poverty ...) • Small model of 17 nonlinear equations (essentially the demand-side GDP approach and a price determination block): Keynesian inspiration • 1955-1970 : artisanal and experimental period • Expansion of macroeconomic modelling primarily in the United States • Innovation on investment (accelerator-profit), on the price-wage loop (generalization of the Phillips curve) • Brookings Institution failure: consistency over juxtaposition of equations

30. 1970-1990 : maturity and extensive development • Increasingly ambitious models (> 1000 equations) thanks to the progress of the computer and strong diffusion outside the USA, notably in France • For instance, Propage, DMS, Metric, Copain in French public administrations first • Then more general development (Mogli in Nanterre, Hermes in Centrale, Bank of France, OFCE and CEPII) • First international models (OECD, IMF, World Bank) • First criticisms with Sims and Lucas • Competition between models concomitant with their abundance • 1990-… : towards a simplification… • Simplification of the accounting framework often too time-consuming to update (data update, maintenance of models ...) for a result not significantly improved => Models of average size • At the international models level, zone-based reasoning is needed (USA, Eurozone, Japan, China and ... the others!) • Use of wealth effects

31. 1.2. Limits and critics • Lucas critique • 1976 : Econometric policy evaluation : a critique • Are econometric evaluations of behavior invariant in the face of changes in economic policy? • "If you see my car on Clark Street heading north, you're unlikely to be mistaken in assuming that in a few minutes I'll still be driving Clark Street heading north. But if you want to know what would I do in the event that Clark Street is closed to traffic, you must have an idea of ​​my destination as well as the different ways to reach it. In other words, you must know the nature of my decision-making problem."

32. Lucas critique (ctd) • Macroeconomic models record economic regularities, which is insufficient for Lucas: the behaviour of agents must be deducted from their objectives and the constraints they face => shed light on the decision-making problem of agents. • It is not empirically proven that the parameters of the behavioural equations of macroeconometric models change when economic policy changes: macro models are generally a good approximation of reality • In addition, macroeconometric models provide a structural framework for interpreting shocks

33. The theoretical foundations • Treatments of anticipations… • Anticipations approximated by past achievements • Backward-looking models • Hard for these models to analyse a sudden change of agents’ anticipation • Study of the underlying microeconomic behaviours in order to calibrate the coefficients’ changes in the macro equations • However… • These two critiques do not prevent the widespread use of models: is there a better compromise between theory and facts? • DSGE models close to macro models introduce expectations and foundations of utility ...

34. 2. Study of main models blocks

35. 2.1. The accounting framework • Accounting/behavioural equations • Definition by sectors • Merchant/non merchant • Manufacturing/non manufacturing • Definition of agents • Operations of distribution of wealth produced and relations between sectors • Equilibrium uses/resources • Generally close to national accounts

36. 2.2. Econometrics and forecasting • Structural models => High theoretical content • “Neo-Keynesian” • Keynesian ST: determination of the equilibrium by the components of demand • Classical LT: determination of the equilibrium by the components of supply • ST/LT => ECM • Disadvantage: we do not distinguish in the ST between the form of expectations and short-term adjustment costs • Econometrics • Stock and Watson on individual equation, two-stage estimate • Idea: orthogonalize the residue with the history of the regressors • Truncated projection polynomial • Simple to implement • Cointegration of the panels (generalised DOLS) to establish groups of countries on certain coefficients (foreign trade for example)

37. Economic forecasting/projection • Difference forecasting/projection • Horizon • Goal: anticipate and analyse LT trends • How to forecast? • Forecast horizon: usually several quarters => quarterly model • Extending exogenous variables • Exogenous variables: independent of the functioning of the modelled economy (small country for example etc.…) • Impact of fiscal policies • Residuals • Interest rates, oil prices, world trade if “country” model ... • Necessary coherence between assumptions made on exogenous variables (eg oil prices and world demand) • Initial forecast ... published forecast: a process of analysis on the results

38. Difficulty is to assess the reliability of forecasts for a model • Multivariate tool (usually many univariate indicators as an average squared error) • GDP and household consumption are expected to be better predicted than private investment and foreign trade • Prices are generally hard to predict, the best results being on consumer prices • Turning point hardly predictable • The farthest we forecast, the more we are wrong • Too much structural a priori? => Other more descriptive tools are used • For instance VAR models: generally more efficient but less explanatory

39. 2.3.1 The supply block 2.3. The different blocks of macroeconometric models • Neo-classical structural approach: determining the long term • In the short term, adjustment costs • Symmetric equilibrium of firms in perfect competition or monopolistic competition • Production function like Cobb-Douglas or CES • Kmenta development around unit-elasticity (1976) • Very often, the Cobb-Douglas function is selected • Long-term factor demand equations (first order conditions) • Note: • LT strongly constrained; in particular capital demand is hard to estimate: high volatility of the real cost of capital, approximated by Jorgensen’s formula (intertemporal arbitrage between investing in physical capital or financing capital) • The capital accumulation equation sometimes makes it possible to directly estimate an investment equation rather than a capital equation

40. Short-term investment/capital equation: • financial variables (profit variable as return on capital, debt ratio - very rare because difficult to put in the models), • production constraint (Utilization capacity rate), • GDP => accelerating effect • Short-term labour demand equation: • GDP adjustment time of at least one year (productivity cycle) • Split between manufacturing and non-manufacturing sectors • Public employment usually exogenous • Changes in inventories • One of the worst equations: very difficult to model • Anticipation of production (supply shock) => pro-cyclic accelerating effect (generally dominant effect) • Buffer effect if changes in demand are unanticipated (demand shock) => contra-cyclic

41. 2.3.2 The demand block • Demand approach of GDP: • Households consumption expenditures: • In the LT, life cycle theory: wealth effect, unit elasticity of consumption to permanent income • In the ST : • Effect of real cash balances (inflation): not significant since 1980 • Precautionary savings (unemployment rate as a proxy of the probability of being unemployed and hence of reducing future income, or a change in the unemployment rate for income volatility) • Effect of debt constraint (real interest rate) • Generally very robust equation

42. Public administrations’ consumption expenditure • Generally, indexation of receipts on the taxable base, constant expenditure as a share of GDP or even adjusted on the cycle if the potential is well defined • Strong non-linearity of public administrations’ account items => generally succinct • Business investment and inventory changes from the supply block • Foreign trade • “Country” model: • exogenous exchange rate, • exogenous world demand • exogenous foreign prices • “Multi-country” model: • endogenous exchange rate (Uncovered Interest Rate Parity: generally induces instability in simulations) • foreign prices of a country endogenous to the model: anchoring on the prices of basic materials (oil and agriculture) • endogenous global demand: same growth in the LT as global potential GDP, • Balancing volumes and values ​​(or prices) of imports and exports: a boost by domestic demand

43. Export equation • World demand: unit indexing • Price-competitiveness: relative price of foreign exporters relative to domestic exporters • Openness • Differentiation of energy for exporting countries • Import equation • Differentiation of energy (very rigid because substitution for other slow energies: for example nuclear energy against oil) • Domestic demand: unit indexing • Price-competitiveness: relative price of imports relative to domestic production prices for the domestic market • Openness • Price-taker/price-maker countries • USA: price-maker => no J-curve • Others: generally price-taker

44. The price-wage loop • Lots of prices: • Consumption, investment prices • Import prices • Export prices • Stocks, demand demand prices • However, the two main prices are: • VA or production prices • Wages • Other price equations define relative prices • ST rigidity and reaction to labour market tensions, in the LT: determination of the NAIRU as well as the potential of the economy • VA or production price equation: Factor Price Frontier in the LT • Note: efficience in Cobb-Douglas = TFP/α • In the ST, tension on import and energy prices, on firms margins

45. World prices Export prices Import prices Investment prices Cost of capital (interest rate) Production prices VA prices Consumption prices Unit labour costs Wages (unemployment, productivity, etc…)

46. Wage equation • Two types of specification: • Phillips • WS (LT) • Definition of equilibrium unemployment rate with dynamic homogeneity in the ST for WS and PS • Phillips • WS (LT) • Definition of potential • First order labour constraint: • Active population: • Factor Price Frontier:

47. 3. Use and analysis

48. P-P* Aggregate supply Aggegate demand GDP 3.1. Equilibriumsynthesis • In the LT, it is assumed that prices and quantities have adjusted to balance the market for goods and services: GDP = C + I + G + X – M + ΔS Supply = Demand • Simplified:

49. In the ST, the supply curve is genrally vertical • The supply and demand curves depend on the parameters of the model • Supply curve: • Technologic characteristics • Demographic characteristics • Determinants of the equilibrium unemployment rate • Generally quite steep • Demand cruve: • Components of the demand side • No homogeneity with respect to prices (only relative prices matter: anchoring on foreign prices) • Illustration of supply shocks (increase in productivity) and pure demand shocks (increase in public consumption or global demand spending) • Generally, shocks move both the demand curve and the supply curve: • Real interest rate shock • Oil prices

50. 3.2. MZE presentation • Quarterly model (Eurostat data) with one country (exogenous external variables) • Neo-classical in the LT • Keynesian in the ST • Small size (150 equations, around 20 of which are econometric) • Cobb-Douglas