Advanced Macroeconomics Lecture 14 Financial Accelerator

Advanced Macroeconomics Lecture 14 Financial Accelerator Marcin Bielecki June 6, 2016

To motivate interest in a paper on financial factors in business fluctuations it used to be necessary to appeal either to the Great Depression or to the experiences of many emerging market economies. This is no longer necessary. Gertler and Kiyotaki (2009)

Financial frictions Crisis detected important channels of the monetary/credit transmission mechanism Matter for our understanding of driving forces in the economy Place discussion of financial variables within a consistent framework Paramount when dealing with issues related to financial stability Interactions between macroprudential and monetary policy Brunnermeier, Eisenbach and Sannikov (2012) Macroeconomics with Financial Frictions: A Survey

Cetral banks DSGE models General equilibrium models with financial frictions before the financial crisis Kiyotaki and Moore (1997), Bernanke, Gertler and Gilchrist (1999), Iacoviello (2005) Financial frictions were absent from DSGE models at central banks at the time of the financial crisis Usual simplifications of financial mechanisms Modigliani-Miller theorem holds balance sheet positions do not affect real decisions Financial markets state summarized by one interest rate No heterogeneity (in terms of discounting) no borrowing and lending in equilibrium Feedback from financial markets to real economy hard to analyze Many central banks have now implemented financial frictions/spillovers in core DSGE models

Shortcomings of standard DSGE models Linear framework (Taylor expansions around steady state) Abstracts from nonlinearities, higher order effects of risk/uncertainty Not suitable for analyzing precautionary saving/hoarding Or movements in asset prices, where risk is an important factor Rational expectations Make the existence of bubbles unlikely Analyzing non-fundamental developments is hard

Financial market frictions Due to asymmetric information (combined with moral hazard and/or costly state verification), lenders will generally require that borrowers post collateral and/or pay a credit premium to obtain funding. Starting with Akerlof (1970), there is a large literature on optimal financial contracts that link the net worth (balance sheet) of borrowers to their access to credit Since net worth is determined by assets in place, movements in asset prices will determine agents access to credit When asset values increase, the borrower s stake in the project increases, implying that the incentives to default decreases, leading in turn the lender to reduce the finance premium Establishes direct link between asset prices and credit Hence, financing costs become countercyclical, which will strengthen the effects of a given shock

Costly state verification Townsend (1979), Bernanke and Gertler (1989), Carlstrom and Fuerst (1997), Bernanke, Gertler and Gilchrist (1999), Christiano, Motto and Rostagno (2003, 2005, 2014) Entrepreneurs borrow funds to finance risky projects Project outcome is known ex post to the entrepreneur only information assymetry If the project outcome is low entrepreneur defaults on the loan But successful entrepreneurs are temped to default as well moral hazard Verification of the project success by outsiders is costly Optimal contract: fixed rate loan, verification in case of default Endogenous premium on loans

Bernanke, Gertler and Gilchrist (1999) model New Keynesian model with entrepreneurial sector which requires external funding to invest in new projects Entrepreneurs identical up to an idiosyncratic productivity shock a E Funds provided by intermediary sector financed from household deposits Asymmetric information, costly state verication (Townsend, 1979) External finance premium (credit premium) is a decreasing function of the share of project financed by net worth (equity) Net worth equals retained profits by surviving entrepreneurs Gives rise to a financial accelerator mechanism

Households Utility maximization problem ( ) max E 0 β t ct 1 σ 1 σ φ h1+η t 1 + η subject to t=0 P t c t + D t + P t g t = W t h t + R t 1 D t 1 + Div t Lagrangian L = E 0 FOCs t=0 β t [ c 1 σ t 1 σ φ h1+η t 1+η +λ t [w t n t + (R t 1 /Π t ) d t 1 + div t c t d t g t ] c t : ct σ = λ t h t : φht η = λ t w t d t : λ t = βe t [λ t+1 (R t /Π t+1 )] ] Define Λ t,t+j = λ t+j /λ t

Final goods producers Profit maximization problem under perfect competition Resulting in max P t y t ˆ 1 0 P t (i) y t (i) di (ˆ 1 subject to y t = y t (i) 1 µ di 0 )µ y t (i) = P t = ( Pt (i) P t (ˆ 1 0 ) µ 1 µ yt P t (i) 1 1 µ di )1 µ

Intermediate goods producers I Cost minimization problem min subject to w t h t (i) + r k,t k t 1 (i) y t (i) = z t k t 1 (i) α h t (i) 1 α Resulting in w t = mc t (1 α) z t kt 1h α t α r k,t = mc t αz t k α 1 t 1 h1 α t

Intermediate goods producers II Profit maximization problem Resulting in [( ) ] max E 0 (βθ) t p0 (i) Λ 0,t mc t y t (i) t=0 ( p0 (i) subject to y t (i) = Π 0,t Π 0,t ) µ 1 µ yt p 0 (i) = µ E 0 t=0 (βθ)t λ t mc t y t Π p t = µ Num t Den t µ µ 1 0,t E 0 t=0 (βθ)t λ t y t Π 1 µ 1 0,t Num t = λ t mc t y t + βθe t Π µ µ 1 t+1 Num t+1 Den t = λ t y t + βθe t Π 1 µ 1 t+1 Den t+1

Inflation, price dispersion, policies and shocks Π 1 1 µ t = θ + (1 θ) ( p t Π t ) 1 1 µ t = θ t 1 Π µ µ 1 t + (1 θ) p µ 1 µ t y t = z t kt α ht 1 α / t ln g t = (1 ρ g ) ln (ḡ/ȳ) + ρ g ln g t 1 + ε g,t R t = R γ R t 1 ( R ( Πt Π ln z t = ρ z ln z t 1 + ε z,t ) γπ ( yt ȳ ) γy ) 1 γr exp (ε R,t)

Capital goods producers Profit maximization problem max E 0 β t Λ 0,t [q t (k t (1 δ) k t 1 ) i t ] t=0 subject to k t = (1 δ) k t 1 + ( 1 κ 2 ( ) ) 2 it 1 i t i t 1 where q t = Q t /P t is the real price of capital goods and κ measures cost of adjusting investment [ ( L = E 0 β t Λ 0,t q t 1 κ ( ) ) ] 2 it 1 i t i t 2 i t 1 t=0 Resulting in ( 1 =q t 1 κ ( ) 2 ( ) it it it 1 κ 1 2 i t 1 i t 1 [ ( ) ( ) ] 2 λ t+1 it+1 it+1 + βe t q t+1 κ 1 λ t i t i t i t 1 )

Capital goods producers Profit maximization problem max E 0 β t Λ 0,t [q t (k t (1 δ) k t 1 ) i t ] t=0 subject to k t = (1 δ) k t 1 + ( 1 κ 2 ( ) ) 2 it 1 i t i t 1 where q t = Q t /P t is the real price of capital goods and κ measures cost of adjusting investment [ ( L = E 0 β t Λ 0,t q t 1 κ ( ) ) ] 2 it 1 i t i t 2 i t 1 t=0 Resulting in ( 1 =q t 1 κ ( ) 2 ( ) it it it 1 κ 1 2 i t 1 i t 1 [ ( ) ( ) ] 2 λ t+1 it+1 it+1 + βe t q t+1 κ 1 λ t i t i t i t 1 )

Entrepreneurs I Take loans to finance purchases of raw capital L t (j) = Q t k t (j) V t (j) 0 where L t (j) denotes loan and V t (j) net worth of j-th entrepreneur Entrepreneurs transform raw capital k t (j) into productive capital a E,t+1 (j) k t (j) Assume E [a E ] = 1 Gross return on capital R E,t+1 (j) = R k,t+1a E,t+1 (j) k t (j) + Q t+1 (1 δ) a E,t+1 (j) k t (j) Q t k t (j) R E,t+1 = R k,t+1 + Q t+1 (1 δ) R E,t+1 (j) = a E,t+1 (j) R E,t+1 Q t

Entrepreneurs II Optimal contract: loan size L t (j) and gross non-default interest rate R L,t+1 ã E,t+1 R E,t+1 Q t k t (j) = R L,t+1 L t (j) Entrepreneurs with a E below the threshold level go bankrupt All their resources are taken over by the banks, after they pay proportional monitoring costs ψ.

Banks Perfect competition in banking generates zero profits where (1 F t+1 ) R L,t+1 L t + (1 ψ) G t+1 R E,t+1 Q t k t = R t L t Equivalently F t+1 = G t+1 = ˆ ãe,t+1 0 ˆ ãe,t+1 0 df t+1 (a E ) a E df t+1 (a E ) R E,t+1 Q t k t [ã E,t+1 (1 F t+1 ) + (1 ψ) G t+1 ] = R t L t

Optimal contract Entrepreneur return on equity maximization max [ ] ã E E,t+1 [R E,t+1 Q t k t (j) a E R L,t+1 L t (j)] df t+1 (a E ) t R t V t (j) subject to constraint on banks zero profits Resulting in (derivation skipped) [ R E,t+1 R E t [1 ã E,t+1 (1 F t+1 ) G t+1 ] + t 1 F t+1 1 F t+1 ψã E,t+1 F t+1 [ RE,t+1 R t (ã E,t+1 (1 F t+1 ) + (1 ψ) G t+1 ) 1 ] ] = 0 where if ψ = 0 then E t [R E,t+1 ] = R t frictionless financial markets Optimal contract is summarized by leverage ratio ϱ t = (Q t k t ) /V t and threshold value ã E,t+1 Resulting gross interest rate on loan is R L,t+1 = ãe,t+1r E,t+1 ϱ t ϱ t 1

Closing the model Net worth evolution V t = v Output acounting [ R E,t Q t 1 k t 1 ( R t 1 + ψg ) ] tr E,t Q t 1 k t 1 L t 1 + T E L t 1 c t + i t + g t + ψg t R E,t Q t 1 k t 1 = y t

Monetary policy shock

Technology shock

Government spending shock

Net worth shock

Core message Due to asymmetric information lenders will generally require that borrowers post collateral and/or pay a credit premium to obtain funding BGG use a simple optimal contracting framework to highlight the interaction between financial strength (net worth) and the credit premium In particular, the credit premium will vary inversely with net worth Hence, to the extent that net worth is procyclical, movements in credit premia will amplify business cycle fluctuations This is the financial accelerator Hints at the role of asset prices in the transmission mechanism

Limitations Rudimentary treatment of banking sector, mainly passive supplier. However, the recent credit freeze can be traced back to financial intermediation Assuming risk neutral agents. Aggregate risk does not really matter Ignores alternative sources of risk spread (risk aversion, liquidity) Rational expectations. Rules out fluctuations due to non-fundamental movements Many firms have alternative means of financing. The share of firms dependent on bank finance might not be that significant Household credit affecting consumption might be more important.