The FR-BDF model and an assessment ofmonetary policy transmission in France1

M. Lemoine, H. Turunen, M. Chahad, A. Lepetit, A. Zhutova,P. Aldama, P. Clerc and J.-P. Laffargue

Banque de France

Forecasting and policy analysis in semi-structural models25 September 2019

1This paper is the outcome of a modelling project, which benefited from theexpertise of many Banque de France economists. Still, the views expressed arethose of the authors and do not necessarily reflect those of Banque de France.

1/28

Motivation and approachWhy a new model for France of Banque de France (FR-BDF)?

I Former model (Mascotte) unsatisfactory for analyzing e.g.transmission of monetary policy and financial shocks

I As the former model lacked important channels, marginalimprovements would have been insufficient

Chosen approach inspired by FRB/US

I Good compromise btw traditional semi-structural models focused ondata fit and DSGEs which have strong theoretical consistency

I Error-correction equations with role for expectations

I Large-scale model estimated under VAR-based expectations andmodel-consistent exp. possible for simulations Estimation

Some specific features of our approach

I France modeled as small open economy (projection process)

I Emphasis on financial block and role of bank lending rates

Comparison with other institutions

2/28

Outline of the presentation

Model specification

Model properties under VAR-based expectations

Short rate shock under different types of expectations

Conclusion

3/28

Simplified scheme of FR-BDF: the widespread role ofexpectations

EXTERNAL TRADE BLOCK: - Imports: internal demand

and price competitiveness - Exports: external demand

and price competitiveness

SUPPLY BLOCK: - Long-run output determined by

production function - Labor demand, employment

and unemployment - Capital accumulation

DEMAND BLOCK: - Consumption: permanent

income and bank lending rate; presence of HtM agents

- Business investment: cost of capital and aggregate demand

- Household investment: cost of capital and permanent income

NOMINAL BLOCK: - Gross wage: expected unemployment (Phillips) - Cost of capital: WACC, expected inflation - Domestic price: cost of production factors - Demand deflators: domestic and import prices

FINANCIAL BLOCK: - Term structure of interest rates - Exch. rate: uncov. int. rate parity condition - Credit to households and firms - Net financial assets of each agent

Expectations VAR-based or

model consistent

In red, variables directly affected by expectations

PUBLIC FINANCE BLOCK: - In simulation: receipts driven

by effective tax rates & tax bases / spending driven by long-run output

4/28

Expectation formation: several possibilities

VAR-based expectations obtained from a small-scalesemi-structural satellite model (E-SAT)

I Agents form their expectations based on few variables: output gapand inflation for FR and EA + EA interest rate

I With a small-scale model: 2 IS curves, 2 Phillips curves and a Taylorrule + rules for long-run anchors of inflation(s) and short rate

I Expectations for other variables can be computed after addingauxiliary equations to the model

Alternative setups of expectations in simulations

I Model-consistent expectations (MCE): come from forecasts of themodel itself under the assumption of perfect foresight

I Hybrid expectations: MCE for some agents (e.g. financial) andVAR-based for others

5/28

Polynomial Adjustment Cost framework: rationalization oferror correction equations

First step: targets obtained from standard theory without frictions

I Long-run targets y∗t derived with static optimization w/o frictions

I E.g. target for investment obtained from a standard firms’ FOC

Second step: adding frictions, we get error-correction equationsextended with a role for expectations

I Given y∗t , minimization of deviations of choice variables yt from y∗tunder polynomial adjustment costs (PAC)

I Solution: change of choice variable related to its former deviationfrom target, its lags and expected present value of target changes

∆yt = a0(y∗t−1−yt−1

)+a1∆yt−1...+PV (∆y∗)t

I PAC applied to headline variables: investment, employment etcExample on investment Construction of PV

6/28

Main blocks

Supply and firm behavior Details

I CES production function (better fit than Cobb-Douglas)

I NK wage Phillips curve with strong role for min. wage

I Bus. investment related to WACC (importance of banks in France)

Demand Details

I Inertial household spending & weak sensitivity of C to interest rate

I Foreign trade: strong sensitivity to price competitiveness

Financial block Details

I Policy rate, key driver of expectations: of long-run rate (termstructure), exchange rate (UIP) and non-fin. variables (PAC)

I Monetary policy transmission through rich set of interest rates

7/28

Outline of the presentation

Model specification

Model properties under VAR-based expectations

Short rate shock under different types of expectations

Conclusion

8/28

Long-run convergenceI Convergence toward the BGP in ' 40 years, only through price

competitiveness and net exports adjustmentI Phase shift of inflation w.r.t. output gap: convergence of interest rates

toward pre-crisis levelI Slow convergence : (i) no independent monetary policy (ii) price stickiness

and (iii) slow convergence of stock variables Implementation details

-5

-4

-3

-2

-1

0

1

2

3

-5

-4

-3

-2

-1

0

1

2

3

2010 2020 2030 2040 2050 2060 2070 2080 2090 2100

Output gap Inflation gap

9/28

Foreign demand shock: +1% on foreign demand to FranceI Direct effect on exports, imports and real GDP, which transmits

progressively to consumption and investmentI Higher inflation progressively causes a real appreciation in the medium runI Losses of price-competitiveness reduce net exports, employment and real

GDP

-.04

.00

.04

.08

.12

.16

-.04

.00

.04

.08

.12

.16

5 10 15 20 25 30 35 40

Real GDP (in %)

-.02

.00

.02

.04

.06

.08

-.02

.00

.02

.04

.06

.08

5 10 15 20 25 30 35 40

VA Price inflation (y-o-y, in pp)

Consumption price inflation (y-o-y, in pp)

Inflation

-.08

-.06

-.04

-.02

.00

.02

-.08

-.06

-.04

-.02

.00

.02

5 10 15 20 25 30 35 40

Unemployment rate (in pp)

.01

.02

.03

.04

.05

.06

.07

.08

.09

.01

.02

.03

.04

.05

.06

.07

.08

.09

5 10 15 20 25 30 35 40

Real private consumption (in %)

-.10

-.05

.00

.05

.10

.15

.20

-.10

-.05

.00

.05

.10

.15

.20

5 10 15 20 25 30 35 40

Real business investment (in %)

Real household investment (in %)

Investment

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

5 10 15 20 25 30 35 40

Real exports (in %)

Real imports (in %)

Trade

10/28

Short-term interest rate shock: +100bp annualizedI Short rate shock endogenously transmits to long rate through

term-structure equation and to nominal exchange rates through UIPI Hike of cost of capital implies investment fallI Appreciation weights on exports in short run, but price decreases boost

them in medium runI Short rate directly affects all VAR-based expectations, notably expected

unemployment and, hence, wage inflation

Other IRFs

-.15

-.10

-.05

.00

.05

.10

-.15

-.10

-.05

.00

.05

.10

5 10 15 20 25 30 35 40

Real GDP (in %)

-.12

-.10

-.08

-.06

-.04

-.02

.00

.02

.04

-.12

-.10

-.08

-.06

-.04

-.02

.00

.02

.04

5 10 15 20 25 30 35 40

VA Price inflation (y-o-y, in pp)

Consumption price inflation (y-o-y, in pp)

Inflation

-.08

-.04

.00

.04

.08

.12

-.08

-.04

.00

.04

.08

.12

5 10 15 20 25 30 35 40

Unemployment rate (in pp)

-.16

-.12

-.08

-.04

.00

.04

-.16

-.12

-.08

-.04

.00

.04

5 10 15 20 25 30 35 40

Real private consumption (in %)

-.7

-.6

-.5

-.4

-.3-.2

-.1

.0

.1

.2

-.7

-.6

-.5

-.4

-.3-.2

-.1

.0

.1

.2

5 10 15 20 25 30 35 40

Real business investment (in %)

Real household investment (in %)

Investment

-.3

-.2

-.1

.0

.1

.2

.3

.4

-.3

-.2

-.1

.0

.1

.2

.3

.4

5 10 15 20 25 30 35 40

Real exports (in %)

Real imports (in %)

Trade

11/28

Outline of the presentation

Model specification

Model properties under VAR-based expectations

Short rate shock under different types of expectations

Conclusion

12/28

Short rate shock under different types of expectationsImplementation of the experiment

I One-off decrease of short rate by 100bp; EA og and infl. left exo.I Three simulations: VAR-based, MCE and hybrid (MCE for fin. var.)

Despite common features, some differences among simulationsI Hyb. vs MCE: smaller output response under MCE (dampening

effect) as non-fin. agents aware of future undershootI Hyb. vs VAR-based: bigger output response under Hyb.

(amplification effect) because of large response of financial variablesExtra hints

-.2

-.1

.0

.1

.2

.3

-.2

-.1

.0

.1

.2

.3

1 21 41 61 81

VAR_based Hyb.E. MCE

Quarters

Output

-.10

-.05

.00

.05

.10

.15

.20

-.10

-.05

.00

.05

.10

.15

.20

1 11 21 31 41 51 61 71 81

VAR_based Hyb.E. MCE

Quarters

VA price inflation (annualized)

13/28

Outline of the presentation

Model specification

Model properties under VAR-based expectations

Short rate shock under different types of expectations

Conclusion

14/28

Conclusions and further researchSome general conclusions

I Compared to our former model, goal fulfilled of having reinforcedrole of financial variables and expectations

I The last application also shows the interest of analyzing monetarypolicy transmission under different types of expectations

Other results not shown here about non-standard monetary policyI Forward guidance: linear increase of output and inflation responses

with duration of interest rate shocks (no puzzle)

I Asset purchase programmes: large inflation response comes morefrom depreciation than from compression of term premia

Further researchI To connect FR-BDF to a euro area model, in order to capture trade

spillovers and EA monetary policy response

I To improve modeling of leverage dynamics, in order to study thepossibility of financial accelerator at least in stressed times

15/28

Appendix

16/28

Comparison with other institutions Back

Similar approach in some other large central banks

I An approach applied at FRB (e.g. in Bernanke et al. 2019), in BoCsince 2014 and currently developed at ECB

I Some other large central banks, like BuBa and BoI, improved theirtraditional models with an emphasis on macro-financial linkages

French institutions improved their traditional models along otherdimensions

I The Mésange model (INSEE and Treasury) was extended in 2017with differentiated qualifications in the labor market for improvingthe analysis of targeted cuts of labor costs

I The e-mod model of OFCE was extended in 2011 with non-linearhysteresis effect in the labor market, which leads to largergovernment spending multipliers in recessions

17/28

Example: equations for firms’ investment Back

I Long run equation:

log It = logY SMt −0.52 logRk

t +

(I ∗

K ∗

)+ ν

I Where

Rkt = (WACCt + δt −VPt−1 [π])

Pinvest,t

Poutput,t

I Short run equation:

D log It =

0.08 log(

It−1It−1

)+0.3D log It−1 +0.2D log It−2

+VPt−1[∆I

]+0.5

(D logY SM

t−1 −∆ logY POTt−1

)(1−0.3−0.2)

(∆Y POT

t−1 −0.52∆HTRkt−1

)18/28

Constructing PV variables under different assumptions Back

Example of the expected component of long-run interest rateI Approximation of the long-run bond by console with exponentially

decaying payments

I In such a case, simplified term structure: expected component =present value of future discounted short-run rates

PV (i)t = (1−κ) ∑j≥0

κj it+j

Alternative constructions of the PV variable within the modelI VAR-based expectations: using iterated VAR-based forecasts, this

present value appears to be a weighted sum of VAR variables

PV (i)t = c0 +c1(it−1− i)+c2(it−1− i)+c3yEA,t−1 +c4(πEA,t−1− πEA,t−1)

I Model-consistent expectations (MCE): written in a recursive waywith a single lead

PV (i)t = (1−κ)it + κPV (i)t+1

19/28

Main blocks I: Supply and firm behavior Back

Long run output determined by a CES production functionI Long run behavior of VA price also derived from CES price frontier

augmented by a markupI Deviation from FRB/US (Cobb-Douglas) because of low elasticity

of substitution estimated on French data (0.5)

Labor market strongly influenced by minimum wageI Labor supply: wages related to expected wages and unemployment

(NK Phillips curve), with a strong role for min. wage (SR elasticityat 0.35)

I Labor demand target derived from production function; depends onvalue added, labor efficiency and real wage (PAC in the short run)

Business investment related to WACC, taking into accountimportance of banks in France

I Investment target derived from production function; depends onvalue added and user cost (PAC in the short run)

I User cost mainly driven by WACC, with large share for BLR (30%)20/28

Main blocks II: Demand Back

Inertial household spending

I Despite of a role for current demand in SR, important consumptionsmoothing of income shocks due to permanent income in LR

I Weak sensitivity of C to interest rate: no direct role for financialwealth & implicit intertemporal elasticity around 0.1

I Investment target driven by perm. income, house prices and BLR

Foreign trade: strong sensitivity to price competitiveness

I Export market shares and import penetration related to pricecompetitiveness with strong LR elasticities (-1.3 and -1.1)

I Large import content of exports (around 33%)

Public finances: determined by satellite model in forecasts / by fiscalrule, effective tax rates and shares in simulations

Demand deflators driven by VA price and import price

21/28

Main blocks III: Financial block Back

Policy rate: a key driver of expectations

I In simulations, follows a Taylor rule based on EA output gap andinflation

I Still, EA variables generally exogenized because foreign demand andprices are exogenous

I In forecasts, from Eurosystem assumptions

I As it belongs to the core of the VAR, it influences all expectations

Monetary policy transmission through a rich set of interest rates

I 10 year public rate related to policy rate through term structureequation (in simulations)

I Bank lending rates, CoE and BBB determined from 10 year rate

Financial asset incomes explicitly modeled, rate of returndetermined by 10 year rate

22/28

Estimation strategy: a three-step approach Back

1st step: Calibration of the production functionI Elasticity of substitution of the CES: from free estimation of LR

equation of investmentI Markup and other parameters of the CES: recovered from estimated

intercepts of LR equations of employment, investment and pricesI This ensures equality btw output and LR output on balanced growth

path

2nd step: Estimation of the satellite model of expectationsI Joint Bayesian estimation of the core block of equationsI Least squares for auxiliary equations

3rd step: Estimation of PAC equations with iterative least squaresI Given expected present values of target changes, estimation with

least squares of each equationI Given coefficient estimates of each equation, computation of

expected present values of target changes

23/28

Implementation details Back

Model versionII VAR-based expectations

I Exogenous og and inflation of euro area

Baseline and shocksI Baseline constructed by setting residuals at zero and extrapolating other

exogenous variables with their steady state growth rate

I Shocks hit in 2150Q1, i.e. at an horizon where the baseline is close to itsbalanced growth path

I Historical persistence (when estimated) or calibrated at 0.9 (for shocks onexo. variables)

24/28

Cost-push shock: +1% on value added price Back

I Markup shock of +1% on VA price: transmits to all PAC equationsthrough expectations

I Direct negative impact on exports of the loss of competitivenessI Households consumption and investment strongly decrease through

expected permanent income. Business investment decreases with VA ofmarket branches

-.5

-.4

-.3

-.2

-.1

.0

.1

-.5

-.4

-.3

-.2

-.1

.0

.1

5 10 15 20 25 30 35 40

Real GDP (in %)

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

5 10 15 20 25 30 35 40

VA Price inflation (y-o-y, in pp)

Consumption price inflation (y-o-y, in pp)

Inflation

-.10

-.05

.00

.05

.10

.15

.20

-.10

-.05

.00

.05

.10

.15

.20

5 10 15 20 25 30 35 40

Unemployment rate (in pp)

-.28

-.24

-.20

-.16

-.12

-.08

-.04

.00

.04

-.28

-.24

-.20

-.16

-.12

-.08

-.04

.00

.04

5 10 15 20 25 30 35 40

Real private consumption (in %)

-.8

-.7-.6

-.5-.4

-.3-.2

-.1.0.1

-.8

-.7-.6

-.5-.4

-.3-.2

-.1.0.1

5 10 15 20 25 30 35 40

Real business investment (in %)

Real household investment (in %)

Investment

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

5 10 15 20 25 30 35 40

Real exports (in %)

Real imports (in %)

Trade

25/28

Oil price shock: +10% on oil priceI No direct effect of energy price on VA price and no effect on competitor

prices (i.e asymmetric shock)I Increase in consumption price inflation through energy import price

reduces HH real income and consumptionI Net exports decreases in the short run due to import content of exportsI VA price inflation decreases and progressively restores price

competitiveness of exports

-.20

-.16

-.12

-.08

-.04

.00

.04

-.20

-.16

-.12

-.08

-.04

.00

.04

5 10 15 20 25 30 35 40

Real GDP (in %)

-.2

-.1

.0

.1

.2

.3

-.2

-.1

.0

.1

.2

.3

5 10 15 20 25 30 35 40

VA Price inflation (y-o-y, in pp)

Consumption price inflation (y-o-y, in pp)

Inflation

-.02

.00

.02

.04

.06

.08

.10

.12

-.02

.00

.02

.04

.06

.08

.10

.12

5 10 15 20 25 30 35 40

Unemployment rate (in pp)

-.24

-.20

-.16

-.12

-.08

-.04

.00

-.24

-.20

-.16

-.12

-.08

-.04

.00

5 10 15 20 25 30 35 40

Real private consumption (in %)

-.35

-.30

-.25

-.20

-.15

-.10

-.05

.00

.05

-.35

-.30

-.25

-.20

-.15

-.10

-.05

.00

.05

5 10 15 20 25 30 35 40

Real business investment (in %)

Real household investment (in %)

Investment

-.3

-.2

-.1

.0

.1

.2

.3

-.3

-.2

-.1

.0

.1

.2

.3

5 10 15 20 25 30 35 40

Real exports (in %)

Real imports (in %)

Trade

26/28

Term premium shock: +100bp annualized on the long rateI Endogenous transmission to bank lending rates and user cost of K (no

impact on short rate and nominal ER)I Negative impact on the real side through investment sub-componentsI Disinflation causes a real depreciation on the nominal sideI Stabilization through net exports in the short run and consumption

reaction in the medium run

-.06

-.04

-.02

.00

.02

.04

-.06

-.04

-.02

.00

.02

.04

5 10 15 20 25 30 35 40

Real GDP (in %)

-.03

-.02

-.01

.00

.01

.02

-.03

-.02

-.01

.00

.01

.02

5 10 15 20 25 30 35 40

VA Price inflation (y-o-y, in pp)

Consumption price inflation (y-o-y, in pp)

Inflation

-.03

-.02

-.01

.00

.01

.02

.03

-.03

-.02

-.01

.00

.01

.02

.03

5 10 15 20 25 30 35 40

Unemployment rate (in pp)

-.12

-.08

-.04

.00

.04

.08

.12

-.12

-.08

-.04

.00

.04

.08

.12

5 10 15 20 25 30 35 40

Real private consumption (in %)

-.5

-.4

-.3

-.2

-.1

.0

.1

-.5

-.4

-.3

-.2

-.1

.0

.1

5 10 15 20 25 30 35 40

Real business investment (in %)

Real household investment (in %)

Investment

-.12

-.08

-.04

.00

.04

.08

-.12

-.08

-.04

.00

.04

.08

5 10 15 20 25 30 35 40

Real exports (in %)

Real imports (in %)

Trade

27/28

Some hints about differences related to expectations Back

Differences among simulationsI Hyb. vs MCE: expected unemployment responses illustrate the

awareness of non-fin. agents of future undershoot under MCEcompared to Hyb. (lhs figure)

I Hyb. vs VAR-based: long-term rate responses illustrate largeresponses of financial variables under Hyb. compared to VAR-based(rhs figure, related to exo. EA)

-.08

-.06

-.04

-.02

.00

.02

.04

-.08

-.06

-.04

-.02

.00

.02

.04

1 21 41 61 81 101 121

Hyb.E. MCE

Quarters

Expected sum of future unemployment gaps

-.28

-.24

-.20

-.16

-.12

-.08

-.04

.00

-.28

-.24

-.20

-.16

-.12

-.08

-.04

.00

1 21 41 61 81 101 121

Hyb.E. VAR-based

Quarters

Long-run interest rate (annualized)

28/28