Nowcasting Norwegian GDP

Transcription

1 Nowcasting Norwegian GDP Knut Are Aastveit and Tørres Trovik May 13, 2007

2 Introduction Motivation The last decades of advances in information technology has made it possible to access a huge amount of data in real time Standard (macro) econometric methods (e.g VARs) are not suitable for exploiting all the potential information in huge data sets Models become hard to identify since number of parameters increases accordingly There is strong co-movements between macroeconomic variables But few sources of common dynamics (3-4 shocks) In VARs the number of variabes = number of (common) shocks Using more information gives more shocks

3 Introduction Factor models Is a method for reducing the parameter space Assumes that there are a few common latent factors that are responsible for the co-movement in the variables Allows for fever shocks than observables Decompose total variance (per variable) in a data set into variance due to Common components (factors) Idiosyncratic components (i.e., noise, measurement error, specification error) The aim is to explain the data with a smaller set of explanatory objects (factors) Ideally the factors should capture most of the total variability in the data The number of factors are exogenously specified

4 Introduction Remaining problem for policy makers Availability and reliability of published data Most data are released with a lag Data are available at different frequencies Most data series are subsequently revised Monetary policy decisions in real time Based on current and future information using incomplete data Important to construct current quarter GDP In practice Construct nowcasts using simple models and qualitative judgement How should they relatively weight the information content in the different data series?

5 Introduction Proposed solution Giannone, Reichlin and Small (2006) Propose a framweork that: Formalizes the updating of the nowcast as data are released Evaluate marginal impact of new data releases on precision of nowcast

6 Introduction Aim of paper Apply the GRS (2006) model on Norwegian data (with modifications) Does a large info set really help to obtain an early and accurate estimate of current Norwegian GDP Aim is to evaluate current quarter nowcasts of GDP on the basis of the flow of information that becomes available during the quarter Extensions: Bayesian estimation Mixed frequency data Bayesian Model Averaging over the number of factors

7 Econometric Methodology Approximate Dynamic Factor Model Developed by Forni, Hallin, Lippi and Reichlin (2000) and (2005) and Stock and Watson (2002) The model combines Exact dynamic factor model introduced by Geweke (1977) and Sargent and Sims (1977) Approximate static factor model introduced by Chamberlain and Rotschild (1983)

8 Econometric Methodology Approximate Dynamic Factor Model We assume there are q common dynamic factors and a finite lag structure: x i,t (1 1) = b i (L) u t (1 q)(q 1) = c i (L) f t (1 q)(q 1) + ξ i,t (1) + ξ i,t (2) u t and f t are observationally equivalent factors, so that c i (L) = b i (L)B 1 a i (L) (3) f t = a i (L) 1 Bu t (4) We assume c i (L) has order s. Let a i (L) = (I a i,1 L a i,p L p ), p s + 1, a is (q q). B is a (q q) rotation matrix

9 Econometric Methodology Approximate Dynamic Factor model From (4) we see that a i (L)f t = Bu t, which is VAR(p) where the innovations, Bu t, is a linear combination of the q common shocks (u t ) in the dynamic factor model. Let F t = (f t, f t 1,..., f t s). We can then write (2) as X it = CF t + ξ it where C = (c i,0, c i,1,..., c i,s ). Hence, the dynamic factor model has the following state-space representation:

10 Econometric Methodology State space representation X it = CF t + ξ it (5) F t (r 1) = AF t 1 + Du t (6) where r = q(s + 1) and A = (r r) a 1 a 2... a p I I I 0, D (r q) = B 0.. 0

11 Econometric Methodology Model Suppose X t follows a generalized dynamic factor model which has the following static factor representation with r common factors X t vj = χ t + ξ t vj = CF t + ξ t vj (7) where v j denotes a specific vintage Our approach is to specify the dynamics of the common factors as follows F t = AF t 1 + Du t (8) u t WN (0, I q ) (9)

12 Econometric Methodology Estimation on Balanced data set We need the following assumptions in order to identify the common and idiosyncratic component Common factor are pervasive lim inf n ( 1 n C C ) > 0 Idiosyncratic factors are non-pervasive lim inf n ( ) max v Ψv = 0 v v=1 Under these assumptions the common factors can be consistently estimated by principal components

13 Econometric Methodology Estimation on Balanced data set Estimate Ĉ, Â, B and Ψ = E(ξξ ) by the following procedure: Project X t on the estimated factors F t from PC and obtain Ĉ and Ψ. Estimate the VAR(p) model in equation (8), using the estimated factors, F t, to obtain  and B. The estimates can be shown to be consistent as n, T

14 Econometric Methodology Unbalanced vs. balanced data set In general, we need a balanced data set in order to extract the factors Assume the following for the idiosyncratic shock E(ξ 2 it v j ) = ψ i = { ψ i if x it vj if x it vj is available is not available (10) Imposing ψ i = when x it vj is not available, filter put no weight on this observation when computing the factors.

15 Econometric Methodology Unbalanced vs. balanced data set Use Kalman filter to estimate common factors assuming Gaussian errors. F t vj = Proj [ ] F t Ω vj ; Ĉ, Â, B, Ψ (11) Evaluate degree of precision of the factor estimates given the consistent parameter estimates [ ( = E F t F ) ( t F t s F ) ] t s ; Ĉ, Â, B, Ψ (12) V s vj

16 Econometric Methodology Unbalanced vs. balanced data set We use monthly variables ((x t )to perform forecast for quarterly GDP growth ((y t ) Construct monthly variables that correspond to quarterly growth changes by applying the following filter (x t + x t 1 + x t 2 ) (x t 3 + x t 4 + x t 5 ) = (1 + 2L + 3L 2 + 2L 3 + L 4 ) x t Nowcast will then be performed by using the factors obtained from the transformed monthly variables by running the OLS regression y t = α + βf t + ɛ t (13) Method disregard the idiosyncratic component of each variable Idiosyncratic captures what is unforecastable

17 Algorithm Operational procedure Step 1: Transform variables to be stationary and standardize. Transform monthly variables to monthly observations of quarterly change. Step 2: Estimate the common factors, F t in equation (5) by computing the principal components of the balanced part of data set X t. Step 3: Estimate Ĉ, Â, B and Ψ = E(ξξ ) by the following procedure: Project Xt on the estimated factors F t from step 1 and obtain Ĉ and Ψ. Estimate the VAR(p) model in equation (6), using the estimated factors, F t, to obtain  and B.

18 Algorithm Operational procedure Step 4: Update the estimates of the common factors, F t, using the Kalman filter Can now also account for unbalanced part of the data set Step 5: Transform monthly estimated factors to quarterly frequency and project the quarterly GDP growth.

19 Data Application Objective Data set To Nowcast Norwegian GDP using monthly information Update the nowcast as new information is released 97 monthly variables for Norway Period: 1990 to 2007 Unbalanced data set Balanced up to Last observation

20 Data Application We most available seasonal adjusted monthly macroeconomic variables Industrial production, financial markets data and interest rates are over-represented Monthly averages for financial variables and interest rates are used Potential relevant series that are not included are surveys, money aggregates, housing prices and produce price index at goods Potential problem: Seasonal adjusted variables

21 Data Structure of the panel Category # series Industrial production 24 Labor markets 7 Construction 8 Credit 4 Financial markets 17 Interest rates 5 Prices 13 Import and exports 5 Retail and consumption 2 Raw materials 3 Foreign variables 6 Others 3

22 Data Spectral density of noise Percent of total variance Frequency

23 Data Spectral density of data 0.6 Percent of total variance Frequency

24 Empirical results Determine the number of common factors No clear framework Look at SPC (determine r) and DPC (determine q)(forni et. al (2000)) Formal test or Information Criterion IC for determine r (Bai and Ng (2002)) IC for determine q (Bai and Ng (2007)) IC for determine q (Hallin and Liska (2005)) Look at forecasting performance

25 Empirical results Determine the number of common factors Percentage of total variance explained by the first q (dynamic) and r (static) principal components (q) (r)

26 Empirical results Forecast comparison Forecast comparison: Means Square Forecast Errors (MSFE) Beginning of estimation sample: 1991m1 Out-of-sample evaluation sample: 2003q1 2005q4 Quarters ahead r = 6, q = r = 8, q = r = 10, q = r = 12, q = Naive model

27 Empirical results Forecast comparison Nowcasts and Forecasts for quarterly GDP growth, r = 10, q = 5 Performed with data available up to 14/02/07 Year Actual Model KF uncertainty Total uncertainty 2005Q Q Q Q Q Q Q Q Q

28 Empirical results Forecast comparison Forecast comparison: Means Square Forecast Errors (MSFE) Beginning of estimation sample: 1991m1 Out-of-sample evaluation sample: 2003q1 2005q4 Data available Quarters ahead Start December Mid January Mid February

29 Empirical results Forecast comparison Uncertainty in Nowcasts and Forecasts for quarterly GDP growth at different time Year Start Dec Mid Jan Mid Feb 2006Q Q Q Q Q Q

30 Further work Extensions Incorporate both monthly and quarterly information, i.e. use mixed frequencies (Bayesian) Model Averaging Different forecast specifications Compare with more sophisticated forecasts

31 Further work Mixed Frequencies Few monthly (heterogenous) series No survey data Survey data most important for US How adjust GRS model to exploit information from data with mixed frequencies? Interpolate quarterly variables? Use Kalman filter. Treat quarterly variables as missing information on monthly basis?

32 Further work Bayesian Model Averaging There is no clear framework for choosing number of factors It is not obvious that one should choose sequential factors for forecasting Use posterior weights to guide selection and BMA Obtain a predictive distribution for the variable of interest Model uncertainty (seen across factor choices) is integrated out Develop a Bayesian estimator for factor models with unbalanced data set and mixed frequencies