## _wp1021 ## Source details **Canonical URL:** [_wp1021](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp1021.pdf) ## Other formats - [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp1021.pdf.md) - [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp1021.pdf.json) --- ### 2.1 Household — Preferences, aggregation, and optimization - Preferences and objective: - Households are a continuum of infinitely lived agents maximizing E_0 Σ_{t=0}^∞ β^t U(C_t(j);L_t(j)) with β ∈ (0,1). (equation (1)) - Period utility with habit persistence: U(C_t(j);L_t(j)) = θ_{c,t} (1−b) ln(C_t(j) − b C_{t−1}) − θ_{L,t} L_t(j). (equation (2)) - b ∈ (0,1); θ_{c,t} and θ_{L,t} are preference shocks. In symmetric steady-state where C_t(j) = C_{t−1}, marginal utility of consumption is independent of b. - Consumption aggregation and domestic vs imported goods: - Aggregate consumption: C_t(j) = [ β (C_{H,t}(j))^{(η−1)/η} + (1−β) (C_{F,t}(j))^{(η−1)/η} ]^{η/(η−1)} with β ∈ [0,1], η ∈ [0,1]. (equation (3)) - Domestic consumption index: C_{H,t}(j) = [ ∫_0^1 C_{H,t}(s)^{(ε_t−1)/ε_t} ds ]^{ε_t/(ε_t−1)} with ε_t > 1. (equation (4)) - Budget constraint and financial assets: - Single-period intertemporal budget constraint: - P_t C_t(j) + e_t B_{t+1}(j) + P_t d_t(j) + P_t p_t^d(j) = e_t B_t(j) (1 + i^f_{t−1}) + ∫_0^1 π_t(s) ds + W_t L_t(j) + (1 + i_{t−1}) P_t p_{t−1}^d(j). (equation (5)) - B_t: net holdings of a foreign-currency one-period bond paying i^f_{t−1}; d_t: deposit earning i_t; ∫_0^1 π_t(s) ds: receipts of profits; τ_t: lump-sum tax; W_t: nominal wage; P_t: CPI. - Price indices and import price: - CPI: P_t = [ β (P_{H,t})^{1−η} + (1−β) (P_{F,t})^{1−η} ]^{1/(1−η)}. (equation (6)) - Domestic price index: P_{H,t} = [ ∫_0^1 P_{H,t}(s)^{1−ε_t} ds ]^{1/(1−ε_t)}. (equation (7)) - Import price pass-through (text): P_{F,t} = u^{tot}_t^{ε_t(ε_t−1)} e_t P^*_t; u^{tot}_t is a terms-of-trade shock. - First-order conditions and stochastic discount factor: - FOCs (ruling out Ponzi schemes): - (1−b) θ_{c,t} / (C_t(j) − b C_{t−1}) = λ_t P_t. (equation (9)) - θ_{L,t} L_t(j)^{−1} = λ_t W_t. (equation (10)) - λ_t denotes marginal utility of wealth. - Euler conditions with UIP departures: - 1 = (1 + i_t) E_t [ ζ_{t;t+1} (P_t / P_{t+1}) ]. (equation (11)) - 1 = (1 + i^f_t) E_t [ ζ_{t;t+1} (P_t / P_{t+1}) (e_{t+1}/e_t) ]. (equation (12)) - ζ_{t;t+1} = β_t / β_{t+1} = θ_{c,t} (C_{t+1}(j) − b C_t) / [ θ_{c,t+1} (C_t(j) − b C_{t−1}) ]. - Up to log-linear approximation, (11) and (12) imply E_t ln(e_{t+1}/e_t) ≈ i_t − i^f_t. - Optimal expenditure allocation: - C_{H,t}(j) = β [ P_{H,t} / P_t ]^{−η} C_t(j). (equation (13)) - C_{F,t}(j) = (1−β) [ P_{F,t} / P_t ]^{−η} C_t(j). (equation (14)) - Demand for each domestic variety: C_{H,t}(s) = [ P_{H,t}(s) / P_t ]^{−ε_t} C_{H,t}(j). (equation (15)) ### 2.5 Specification of the Stochastic Processes — shocks, estimation, and key posterior findings - Shocks included (thirteen structural shocks): - three shocks to technology and preferences ( t ;  c;t ;  l;t ) - three foreign shocks: world interest rates (i t ), world inflation ( t ), price elasticity of exports (Q x t ) - two shocks to investment efficiency and firms’ markup ( in;t ;  ;t ) - two financial shocks: cost of borrowing by entrepreneurs and survival rate of entrepreneurs ( n;t ;  v;t ) - a monetary policy shock (assumed white noise) - a government spending shock ( i;t ;  G;t ) - a UIP shock ( uip;t ) - All shocks except the monetary policy shock follow first-order autoregressive processes. Measurement errors are allowed. - Estimation strategy and numerical implementation: - Bayesian estimation in DYNARE; posterior p(|X) from priors and likelihood via Kalman filter; Laplace approximation to find posterior mode; Metropolis-Hastings sampling with 100000 draws in 4 chains, discarding the first 50000 draws. - Data used (India, 1996Q2 to 2007Q4): - Ten variables: GDP, private consumption expenditure, investment, exports, imports (constant prices), real exchange rate, rate of depreciation of the nominal exchange rate, wholesale price inflation, nominal interest rate, Bombay Stock Exchange SENSEX Index. - Proxies/adjustments: 3-month Treasury Bill rate as nominal interest rate; IMF real effective exchange rate; SENSEX deflated by WPI as net worth proxy; variables HP-detrended; seasonally adjusted except for exchange rates, nominal interest rate, and SENSEX. Data source: CEIC database. - Selected calibrated steady-state parameter values: - Substitution elasticity between imported and domestically produced goods: 1.5 - Elasticity of substitution of exports (&): 2.4 - Share of non-tradables in the WPI ( ): 0.8 → steady-state export to GDP ratio of 19 percent and import to GDP ratio of 21 percent. - Share of government expenditure in GDP: 11 percent - Steady-state markup factor set to 9 percent so that " = 12 - Technology parameter: 0.33 - Quarterly depreciation rate of capital (): 0.025 - Steady-state annual nominal interest rate: 7 percent - Steady-state inflation: 4.5 percent (annual) - Subjective discount rate ( ): 0.994 - World inflation: 2.5 percent (annual) → implies steady-state depreciation of nominal exchange rate of 2 percent (annual) and a world interest rate of 5 percent per annum - Selected priors and hyperparameters (high-level): - Price adjustment cost parameters (#d ; #x ): gamma, mean 100, s.d. 20 (100 ≈ firms change prices every 3.74 quarters) - Capital cost adjustment parameter (): gamma prior mean 15 - Habit persistence (b): beta prior mean 0.5, s.d. 0.2 - External finance premium elasticity: gamma prior mean 0.07, s.d. 0.02 - Risk premium on foreign-currency borrowing ( d ): gamma prior mean 0.0019, s.e. 0.002 - Autoregressive parameters: beta priors mean 0.8 - Standard errors of structural shocks: inverted gamma with diffuse prior - Selected empirical posterior findings: - Elasticity of the external finance premium with respect to firm leverage (): 0.057. - Investment adjustment cost parameter (): 23.0. - Habit persistence (b): 0.499. - Cost of adjusting import prices: posterior close to prior. - Monetary policy rule estimates: - Reserve Bank of India places relatively high weight on controlling the rate of depreciation of the nominal exchange rate: estimate of e is 3 times higher than the coefficient on inflation (). - Output stabilization coefficient (Y ) insignificantly different from zero. - Interpreted in levels: - Annual nominal interest rate increases by 0.9 percentage points if annual inflation is 1 percentage point above equilibrium. - Annual interest rates increase by 1 percentage point if the nominal exchange rate depreciates by 1 percent more than the equilibrium rate of depreciation. - Comparison: Mohanty and Klau (2004) find 0.13 percentage point increase in annual interest rates for a 1 percentage point rise in annual inflation, and 0.18 percentage point increase for a 1 percent real exchange rate depreciation. - Shock persistence: - Markup and price elasticity of exports shocks are most persistent. - UIP shock persistence indicates pervasive departures from uncovered interest parity. - Standard errors interpretation caveat: depend on variable scaling and normalization. - Model comparison (marginal likelihoods): - Estimated FA model 876:49 - Estimated No-FA model 873:64 - BVAR(1) 1148:54 - BVAR(2) 420:19 - BVAR(3) 673:25 - BVAR(4) 743:61 - Interpretation: - FA improves fit relative to No-FA model. - Estimated FA model does not beat BVAR(1) but outperforms BVARs with more than one lag; marginal likelihood reflects trade-off between model complexity and fit. ### 4.2 Impulse Responses — role of the financial accelerator and policy evaluation - Experimental setup: - Impulse responses to three shocks: a 100 bps increase in the nominal interest rate, a 1 Percent improvement in technology, and a 1 Percent increase in entrepreneurs' borrowing cost. - Responses: percentage deviations from steady state; rate variables in percentage points. - FA model shown in black; No-FA (elasticity of external finance premium set to zero) shown in green. - Response to a 100 bps contractionary monetary policy shock: - Common effects: - Higher nominal interest rate → contraction in consumption; appreciation of domestic currency (real exchange rate appreciation); net worth of entrepreneurs declines via debt-deflation; output contracts; inflation falls. - Additional FA effects: - External finance premium increases → higher real borrowing cost for entrepreneurs → depressed investment and lower capital prices → further net worth decline → second-round amplification and increased persistence of output and inflation effects. - Response to a 1 Percent technology improvement: - Common effects: - Higher return to capital → higher investment and output; lower inflation via reduced marginal costs; monetary policy raises nominal interest rates endogenously reducing deflation. - Additional FA effects: - Rising net worth reduces risk premium → larger investment and capital responses; FA impact on output and inflation is materially smaller than for monetary policy shocks. - Response to a 1 Percent increase in entrepreneurs' borrowing cost: - Common effects: - Higher borrowing cost → lower investment, output, and inflation; decline in absorption → real exchange rate depreciation; depreciation and lower inflation reduce net worth. - Additional FA effects: - Reduced net worth raises risk premium → further depresses capital demand → much larger declines in investment and output with FA present. - Comparative impacts: - FA amplifies and propagates shocks mainly via investment channels. - FA increases output and inflation volatility for contractionary monetary policy and borrowing-cost shocks; FA has much less impact for technology shocks. - Results consistent with Christensen and Dib (2006). - Policy rule parameter summaries (Table 3): - Estimated Policy Rule: 0:83 0:89 0:02 2:44 - Optimal Policy Rule: 0:995 5:75 0:00 1:05 - Key policy findings: - Welfare-maximizing optimal rule differs significantly from estimated rule: - Estimated rule places too little weight on inflation stabilization and too much weight on stabilizing the rate of depreciation of the nominal exchange rate. - Consequence: under the estimated rule inflation volatility is higher and exchange rate volatility is lower compared to the optimal rule. - Both rules show significant interest-rate inertia (interest-rate smoothing); authorities react more aggressively to inflation in the long run than in the short run. - Higher-than-optimal weight on exchange rate depreciation under the estimated rule increases volatility in the real economy and financial-sector variables (borrowing costs and net worth). - Welfare cost of estimated rule: - Welfare loss of the estimated policy rule relative to the optimal rule is equivalent to a 0.4 percent of permanent consumption (consumption in every period would be 0.4 percent lower under the estimated rule). - Standard deviations of key macro variables (Table 4; Header order: GDP | Cons. | Inv. | Nom . ER | Real ER | Nom . IR | WPI Iná. | Net Worth | Premium | Welfare | Cons. Cost): - Estimated Policy Rule: - GDP: 0.1100 - Cons.: 0.0547 - Inv.: 0.0520 - Nom . ER: 0.0020 - Real ER: 0.0126 - Nom . IR: 0.0025 - WPI Iná.: 0.0036 - Net Worth: 1.6081 - Premium: 0.0059 - Welfare: -120.0098 - Cons. Cost: 0.004 - Optimal Policy Rule: - GDP: 0.0971 - Cons.: 0.0537 - Inv.: 0.0485 - Nom . ER: 0.0064 - Real ER: 0.0134 - Nom . IR: 0.0029 - WPI Iná.: 0.0013 - Net Worth: 1.4621 - Premium: 0.0053 - Welfare: -119.6640 - Cons. Cost: ... - Simulation evidence: - Simulated paths using estimated shocks indicate inflation volatility would have been lower under the optimal rule, notably toward the end of 2004 (WPI inflation increased to 8.1 percent y.o.y. in the third quarter of 2004) and in 2006/07. - Rate of depreciation of the nominal exchange rate is more volatile under the optimal rule over the sample period. - Nominal interest rates would have been higher toward the end of the sample under the optimal rule, reflecting relatively high inflation. - Concluding summary: - A DSGE model with macrofinancial linkages for India (BGG-style financial accelerator added to Saxegaard (2006b)) was estimated; Bayesian estimation produced plausible parameter estimates though some parameters are weakly identified. - Financial accelerator improves the model’s fit relative to a No-FA variant and outperforms BVARs with more than one lag. - Policy implication: the Reserve Bank of India appears to weigh exchange rate depreciation stabilization more heavily and inflation stabilization less heavily than is welfare-optimal, generating higher inflation and real/financial volatility; switching to the optimal policy rule yields welfare gains equivalent to 0.4 percent of permanent consumption. ### Selected estimated priors and posterior table highlights (Table 5) - Policy and structural parameter posterior highlights (selected entries): - Interest Rate Smoothing (i): Prior Beta mean 0.7 s.d. 0.2 → Posterior mean 0.829, 90% interval [0.647, 0.999]. - Inflation Stabilization (): Prior Uniform(0,3) → Posterior mean 0.890, 90% interval [0.002, 1.737]. - Output Stabilization (Y ): Prior Uniform(-1,1) → Posterior mean -0.017, 90% interval [-0.049, 0.014]. - Exchange Rate Stabilization (e): Prior Uniform(0,3) → Posterior mean 2.438, 90% interval [1.852, 3.000]. - Habit Persistence (b): Prior Beta mean 0.5 s.d. 0.2 → Posterior mean 0.499, 90% interval [0.150, 0.885]. - Cost of Non-tradable Goods Price Adjustment (#d): Prior Gamma mean 100 s.d. 200 → Posterior mean 118.220, 90% interval [84.184, 151.489]. - Cost of Imported Goods Price Adjustment (#m): Posterior mean 100.043, 90% interval [67.992, 151.489]. - Capital Stock Adjustment Costs (1): Posterior mean 23.008, 90% interval [19.430, 26.462]. - Elasticity of External Finance Premium: Prior Beta mean 0.07 s.d. 0.02 → Posterior mean 0.057, 90% interval [0.038, 0.074]. - Selected shock persistence posteriors (posterior means shown): - Technology shock persistence ( ): 0.808 - Foreign interest rate shock persistence ( i): 0.831 - Foreign inflation shock persistence ( ): 0.785 - Markup shock persistence ( ): 0.860 - UIP shock persistence ( uip): 0.794 - Labour supply shock persistence ( l): 0.806 - Marginal utility shock persistence ( c): 0.810 - Investment efficiency shock persistence ( in): 0.785 - Export elasticity shock persistence ( Q x): 0.857 - Government spending shock persistence ( G): 0.640 - Borrowing cost shock persistence ( n): 0.809 - Survival rate shock persistence ( v): 0.805 *Italic: Source PDF: _wp1021* ### 2.1 Household ### 2.1 Household ### Preferences and objective - Households are a continuum of infinitely lived agents with preferences over consumption, C_t(j), and labor effort, L_t(j). - Objective: maximize expected discounted sum of period utility: - E_0 Σ_{t=0}^∞ β^t U(C_t(j);L_t(j)) (equation (1)) - β ∈ (0,1) is the consumer subjective discount factor. - Period utility with habit persistence: - U(C_t(j);L_t(j)) = θ_{c,t} (1−b) ln(C_t(j) − b C_{t−1}) − θ_{L,t} L_t(j) (equation (2)) - b ∈ (0,1). θ_{c,t} and θ_{L,t} are preference shocks to marginal utility of consumption and supply of labour. - In symmetric steady-state where C_t(j) = C_{t−1}, marginal utility of consumption is independent of b. ### Consumption aggregation and preferences over domestic vs imported goods - Aggregate consumption bundle C_t(j) is a CES composite of domestically produced goods C_{H,t}(j) and imported foreign good C_{F,t}(j): - C_t(j) = [ β (C_{H,t}(j))^{(η−1)/η} + (1−β) (C_{F,t}(j))^{(η−1)/η} ]^{η/(η−1)} (equation (3)) - β ∈ [0,1] measures home-bias; η ∈ [0,1] is elasticity of substitution between domestic and foreign goods. - Domestic consumption index C_{H,t}(j): - C_{H,t}(j) = [ ∫_0^1 C_{H,t}(s)^{(ε_t−1)/ε_t} ds ]^{ε_t/(ε_t−1)} (equation (4)) - s ∈ [0,1] denotes variety; ε_t > 1 is elasticity of substitution between domestic varieties. ### Budget constraint and financial assets - Households have access to foreign financial markets/nominal contingent claims that span all relevant uncertainty. - Single intertemporal budget constraint: - P_t C_t(j) + e_t B_{t+1}(j) + P_t d_t(j) + P_t p_t^d(j) = e_t B_t(j) (1 + i^f_{t−1}) + ∫_0^1 π_t(s) ds + W_t L_t(j) + (1 + i_{t−1}) P_t p_{t−1}^d(j) (equation (5)) - B_t: net holdings of a foreign-currency one-period bond maturing in t paying i^f_{t−1}. - d_t: deposit with financial intermediary earning interest i_t. - ∫_0^1 π_t(s) ds: receipts of profits from domestic retailers owned by household. - τ_t: lump-sum tax. W_t: nominal wage per unit of labor. P_t: CPI price index. ### Price indices and import price - CPI price index: - P_t = [ β (P_{H,t})^{1−η} + (1−β) (P_{F,t})^{1−η} ]^{1/(1−η)} (equation (6)) - Domestic price index: - P_{H,t} = [ ∫_0^1 P_{H,t}(s)^{1−ε_t} ds ]^{1/(1−ε_t)} (equation (7)) - For simplicity, changes in the exchange rate are passed through immediately to import price: - P_{F,t} = u^{tot}_t^{ε_t(ε_t−1)} e_t P^*_t (textual specification describing pass-through; u^{tot}_t is a terms-of-trade shock) ### Consumer optimization and first-order conditions - Consumer chooses {C_t(j), L_t(j), d_t(j), B_{t+1}(j)}_{t=0}^∞ subject to budget constraint and initial B_0. - First-order conditions (ruling out Ponzi schemes): - (1−b) θ_{c,t} / (C_t(j) − b C_{t−1}) = λ_t P_t (equation (9)) - θ_{L,t} L_t(j)^{−1} = λ_t W_t (equation (10)) - λ_t denotes Lagrange multiplier (marginal utility of wealth). ### Asset returns, UIP departures, and stochastic discount factor - Due to documented departures from uncovered interest parity (UIP), an exogenous shock is introduced into the first-order condition for foreign-currency bond holdings (following Kollmann (2002)). - Euler conditions for deposits and foreign bond holdings: - 1 = (1 + i_t) E_t [ ζ_{t;t+1} (P_t / P_{t+1}) ] (equation (11)) - 1 = (1 + i^f_t) E_t [ ζ_{t;t+1} (P_t / P_{t+1}) (e_{t+1}/e_t) ] (equation (12)) - ζ_{t;t+1} = β_t / β_{t+1} = θ_{c,t} (C_{t+1}(j) − b C_t) / [ θ_{c,t+1} (C_t(j) − b C_{t−1}) ] is the stochastic discount factor. - Up to log-linear approximation, (11) and (12) imply E_t ln(e_{t+1}/e_t) ≈ i_t − i^f_t. ### Optimal expenditure allocation between domestic and imported goods - Optimal shares: - C_{H,t}(j) = β [ P_{H,t} / P_t ]^{−η} C_t(j) (equation (13)) - C_{F,t}(j) = (1−β) [ P_{F,t} / P_t ]^{−η} C_t(j) (equation (14)) - Demand for each domestic variety: - C_{H,t}(s) = [ P_{H,t}(s) / P_t ]^{−ε_t} C_{H,t}(j) (equation (15)) *Source: _wp1021 - 2.1 Household* ### 2.5 SpeciÖcation of the Stochastic Processes ### 2.5 SpeciÖcation of the Stochastic Processes ### Shocks included in the model - The model includes thirteen structural shocks: - three shocks to technology and preferences ( t ;  c;t ;  l;t ) - three foreign shocks to world interest rates, world ináation, and the price elasticity of exports (i t ; t ;Q x t ) - two shocks to investment e¢ ciency and Örmsímarkup ( in;t ; ;t ) - two Önancial shocks to the cost of borrowing by entrepreneurs and the survival rate of entrepreneurs ( n;t ; v;t ) - a monetary policy shock (assumed to be white noise) - a government spending shock ( i;t ; G;t ) - a UIP shock ( uip;t ) - With the exception of the monetary policy shock (white noise), all shocks are assumed to follow a Örst-order autoregressive process. - In addition to the thirteen structural shocks, the approach allows for measurement errors in the data. ### Estimation strategy and Bayesian implementation - Estimation framework: - Bayesian estimation module in DYNARE (Juillard (2001)). - Posterior density p(jX) constructed from prior p() and likelihood f(Xj) using Bayes law: p(jX) = p()f(Xj) / f(X). - Likelihood calculated from state-space representation of the model using the Kalman Ölter. - Numerical procedure: - Posterior mode approximated using a Laplace approximation; the posterior mode is used as starting value for Metropolis-Hastings. - Metropolis-Hastings sampling: generate draws using a normal proposal with mean equal to previously accepted draw. - Sampling details: 100000 draws in 4 chains, discarding the Örst 50000 draws. ### Data used - Ten key macroeconomic variables for India, 1996Q2 to 2007Q4: - GDP, private consumption expenditure, investment, exports, imports (all expressed in constant prices), the real exchange rate, the rate of depreciation of the nominal exchange rate, wholesale price ináation, the nominal interest rate, and the Bombay Stock Exchange SENSEX Index. - Proxies and adjustments: - 3-month Treasury Bill rate used as proxy for the nominal interest rate. - IMF real e§ective exchange rate used as proxy for the real exchange rate. - SENSEX (deáated using the wholesale price index) used to proxy the net worth of entrepreneurs. - Variables expressed as deviations from a Hodrick-Prescott trend; except for real and nominal exchange rates, nominal interest rate, and SENSEX, seasonally adjusted using the X12 Ölter. - Data source: CEIC database. ### Calibration of steady-state parameters (selected calibrated values) - Substitution elasticity between imported and domestically produced goods: 1.5 - Elasticity of substitution of exports (&): 2.4 - Share of non-tradables in the WPI ( ): 0.8 - Corresponds to steady-state export to GDP ratio of 19 percent and steady-state import to GDP ratio of 21 percent. - Share of government expenditure in GDP: 11 percent - Steady-state markup factor set to 9 percent so that " = 12 - Technology parameter: 0.33 - Quarterly depreciation rate of capital (): 0.025 - Steady-state annual nominal interest rate: 7 percent - Steady-state ináation: 4.5 percent (annual) - Subjective discount rate ( ): 0.994 - World ináation: 2.5 percent (annual) — implies steady-state depreciation of nominal exchange rate of 2 percent (annual) and a world interest rate of 5 percent per annum ### Prior distributions and chosen hyperparameters (selected) - Structural parameters: gamma or beta distributions when restricted to [0,1]; uniform distributions for monetary policy rule parameters; inverted gamma for standard errors of shock processes. - Price adjustment cost parameters (# d ; # x ): gamma distribution, mean 100, standard deviation 20 (an adjustment cost of 100 ≈ firms change prices every 3.74 quarters). - Capital cost adjustment parameter (): gamma distribution, prior mean 15. - Monetary policy rule parameters: - Feedback on WPI ináation (  ) and rate of exchange rate depreciation ( q ): uniform(0,3). - Feedback on output gap ( y ): uniform(-1,1). - Lagged interest rate prior ( i ): beta distribution with mean 0.7 and standard deviation 0.2. - Habit persistence (b): beta distribution, mean 0.5, standard deviation 0.2. - External Önance premium elasticity: gamma prior, mean 0.07, standard deviation 0.02. - Risk premium on foreign-currency borrowing ( d ): gamma prior, mean 0.0019, standard error 0.002. - Autoregressive parameters: beta priors with mean 0.8. - Standard errors of structural shocks: inverted gamma with di§use prior; means informed by variance decomposition experiments to achieve reasonable contributions of each structural shock. ### Empirical results (selected posterior findings) - Estimated posterior model yields plausible parameter estimates broadly in line with previous studies. - Key posterior estimates: - Elasticity of the external Önance premium with respect to Örm leverage (): 0.057. - Investment adjustment cost parameter (): 23.0 (signiÖcantly higher than the prior mean). - Habit persistence parameter (b): 0.499. - Cost of adjusting import prices: posterior close to prior (data less informative on this parameter). - Monetary policy rule implications: - Reserve Bank of India places a relatively high weight on controlling the rate of depreciation of the nominal exchange rate: estimate of e is 3 times higher than the coe¢ cient on ináation (). - Output stabilization coefficient (Y ) insigniÖcantly di§erent from zero. - Interpreted in levels: - Annual nominal interest rate increases by 0.9 percentage points if annual ináation is 1 percentage point above equilibrium. - Annual interest rates increase by 1 percentage point if the nominal exchange rate depreciates by 1 percent more than the equilibrium rate of depreciation. - Comparison to Mohanty and Klau (2004): they find 0.13 percentage point increase in annual interest rates for a 1 percentage point rise in annual ináation, and 0.18 percentage point increase for a 1 percent real exchange rate depreciation. - Shock process persistence: - Shock to the markup and the price elasticity of exports are the most persistent stochastic processes. - Persistence of the UIP shock indicates departures from uncovered interest parity are pervasive in the data. - Interpretation caveat: standard errors of structural shocks depend on variable scaling and normalization. ### Model comparison and marginal likelihoods - Models compared: - Estimated FA model (financial accelerator) - Estimated No-FA model (identical except elasticity of external Önance premium constrained to zero) - BVARs with lags 1 to 4 (Litterman prior) - Marginal likelihoods (Table 2): - Estimated FA model 876:49 - Estimated No-FA model 873:64 - BVAR(1) 1148:54 - BVAR(2) 420:19 - BVAR(3) 673:25 - BVAR(4) 743:61 - Interpretation: - Estimated FA model has higher marginal likelihood than Estimated No-FA model → introduction of a Önancial accelerator improves the modelís ability to capture the data. - Estimated FA model does not compare favorably to BVAR(1) but outperforms BVARs with more than one lag. - Trade-off: marginal likelihood falls with increasing model complexity and increases with model Öt; Estimated FA model's improved Öt relative to BVARs with more lags provides some support for its usefulness in policy analysis. *Source: _wp1021 - 2.5 SpeciÖcation of the Stochastic Processes* ### 4.2 Impulse Responses ### _wp1021 - 4.2 Impulse Responses ### Role of the financial accelerator (FA) in dynamics - Impulse responses are generated for three shocks: a 100 bps increase in the nominal interest rate, a 1 Percent improvement in technology, and a 1 Percent increase in entrepreneurs' borrowing cost. - Responses are expressed as percentage deviations from steady state; rate variables are in percentage points. - The FA model impulse responses are shown in black; responses with the financial accelerator turned off are shown in green (implemented by setting the elasticity of the external finance premium with respect to firm leverage equal to zero while keeping other parameter estimates). - The difference between black and green lines indicates the impact of the financial accelerator on each variable after a given shock. ### Response to a 100 bps contractionary monetary policy shock (Figure 3) - Common effects in both models: - Increase in the nominal interest rate raises the cost of domestic borrowing for consumers → contraction in consumption. - Raises demand for domestic bonds → appreciation of the domestic currency (real exchange rate appreciation). - Net worth of entrepreneurs declines due to declining return to capital and higher real interest costs on existing debt (the debt-deflation effect). - Output contracts due to decreased domestic demand and decreased competitiveness following the real exchange rate appreciation. - Contraction in demand leads to a fall in inflation. - Additional effects when the financial accelerator is present: - External finance premium increases due to declining net worth and rising leverage → higher real borrowing cost for entrepreneurs. - Higher borrowing cost depresses investment and the price of capital → further reduction in net worth. - Second-round effects: further increases in the premium reduce capital, investment and output more. - Net effect: the FA amplifies and increases the persistence of the impacts of a contractionary monetary policy shock. ### Response to a 1 Percent improvement in technology (Figure 4) - Common effects in both models: - Technology shock increases the return to capital → increase in investment and output. - Improvement in technology reduces firms’ marginal costs → reduces inflation. - Higher return to capital and lower inflation have opposite effects on net worth; in the model the positive impact of higher return to capital dominates. - Monetary policy responds endogenously by pushing up nominal interest rates, thereby reducing the amount of deflation. - Additional effects when the financial accelerator is present: - Rise in net worth pushes down the risk premium faced by entrepreneurs → larger response of investment and capital. - Output is somewhat more volatile when the FA is present, but the FA impact is significantly less than after a monetary policy shock. ### Response to a 1 Percent increase in entrepreneurs' borrowing cost (Figure 5) - Common effects in both models: - Higher borrowing costs depress demand for new capital → lower investment, output, and inflation. - Decline in absorption reduces demand for non-tradables → real exchange rate depreciation. - Exchange rate depreciation (raising external borrowing cost) together with lower inflation reduces entrepreneurs’ net worth. - Additional effects when the financial accelerator is present: - Reduced net worth raises entrepreneurs’ risk premium → further reduces demand for capital. - Result: much larger decline in investment and output when the FA is present. - Conclusion: the FA amplifies and propagates the effects of financial shocks on investment and the broader economy. ### Comparative impacts across shock types - The financial accelerator amplifies and propagates shocks mainly via investment channels. - Impact on output and inflation depends on shock type: - Contractionary monetary policy shock and entrepreneurs' borrowing cost shock → output and inflation volatility increase when FA is present. - Technology shock → FA has much less impact on output and inflation. - These results are consistent with previous studies including Christensen and Dib (2006). ### Parameters of policy rules (Table 3) - Estimated Policy Rule0:83 0:89 0:02 2:44 - Optimal Policy Rule0:995 5:75 0:00 1:05 ### Optimal policy vs. estimated (empirical) policy rule — key findings - The welfare-maximizing policy rule differs significantly from the estimated rule: - Estimated rule places too little emphasis on inflation stabilization and too much emphasis on stabilizing the rate of depreciation of the nominal exchange rate. - Consequence: inflation volatility is higher under the estimated rule than under the optimal rule; exchange rate volatility is lower under the estimated rule. - Both rules feature significant interest-rate inertia (interest-rate smoothing), implying authorities react more aggressively to inflation in the long run than in the short run. - The higher-than-optimal weight on exchange rate depreciation in the estimated rule comes at the expense of: - Higher volatility in the real economy (despite similar weights on output stabilization). - Higher volatility in financial sector variables, particularly borrowing costs and net worth. ### Welfare cost of the estimated policy rule - A second-order accurate measure of consumer welfare is calculated following Schmitt-Grohe and Uribe (2004). - The welfare loss of the estimated policy rule relative to the optimal rule is equivalent to a 0.4 percent of permanent consumption. - Interpretation (from text): consumption in every period over the lifetime of a consumer would be 0.4 percent lower under the estimated rule than under the optimal rule. ### Standard deviations of key macroeconomic variables (Table 4) - Header order: GDP | Cons. | Inv. | Nom . ER | Real ER | Nom . IR | WPI Iná. | Net Worth | Prem ium | Welfare | Cons. Cost - Estimated Policy Rule: - GDP: 0.1100 - Cons.: 0.0547 - Inv.: 0.0520 - Nom . ER: 0.0020 - Real ER: 0.0126 - Nom . IR: 0.0025 - WPI Iná.: 0.0036 - Net Worth: 1.6081 - Prem ium: 0.0059 - Welfare: -120.0098 - Cons. Cost: 0.004 - Optimal Policy Rule: - GDP: 0.0971 - Cons.: 0.0537 - Inv.: 0.0485 - Nom . ER: 0.0064 - Real ER: 0.0134 - Nom . IR: 0.0029 - WPI Iná.: 0.0013 - Net Worth: 1.4621 - Prem ium: 0.0053 - Welfare: -119.6640 - Cons. Cost: ... ### Simulation evidence (Figure 6) - Simulated paths using estimated shocks confirm: - Inflation volatility would have been lower under the optimal policy rule, notably toward the end of 2004 (WPI inflation increased to 8.1 percent y.o.y. in the third quarter of 2004) and in 2006/07. - The rate of depreciation of the nominal exchange rate displays significantly higher volatility under the optimal rule over the sample period. - Nominal interest rates would have been higher toward the end of the sample under the optimal rule, reflecting relatively high inflation. ### Summary conclusions (Section 6 concluding remarks) - A DSGE model with macrofinancial linkages for India was estimated (extension of Saxegaard (2006b) with a BGG-style financial accelerator). - Bayesian estimation produced plausible parameter estimates, though data were not informative about several parameters. - Cross-validation tests indicate the FA mechanism improves the model’s ability to capture observed dynamics; the FA model outperforms a BVAR at more than one lag. - Policy implication: the Reserve Bank of India (RBI) appears to place a higher-than-optimal weight on stabilizing the rate of depreciation of the nominal exchange rate and a lower-than-optimal weight on inflation stabilization, even accounting for financial accelerator effects. This tradeoff yields higher inflation volatility and higher volatility in real and financial-sector variables, but lower exchange rate volatility under the empirical rule. - Welfare implication: switching from the estimated empirical policy rule to the welfare-maximizing optimal policy rule yields a welfare gain equivalent to 0.4 percent of permanent consumption. *Source: _wp1021 - 4.2 Impulse Responses* ### References ### References ### Bibliographic entries - Aghion, P., P. Bacchetta, and A. Banerjee (2001). Currency crises and monetary policy in an economy with credit constraints. European Economic Review 47, 1121ñ1150. - Ambler, S., A. Dib, and N. Rebei (2004). Optimal taylor rules in an estimated model of a small open economy. Technical report. - Batini, N., P. Levine, and J. Pearlman (2009). Monetary and Öscal rules in an emerging small open economy. Working paper WP/09/22, International Monetary Fund. - Bauwens, L., M. Lubrano, and J.-F. Richard (1999). 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Journal of Applied Econometrics 20(2), 161ñ183. ### Table 5: Parameter Priors and Posterior Estimates - Table heading columns: Prior Posterior - Parameter | Description | Density | Mean/Min | S.D./Max | Mean | 90% Interval - i Interest Rate Smoothing | Beta | 0.7 | 0.2 | 0.829 | 0.647 | 0.999 -  Ináation Stabilization | Uniform | 0 | 3 | 0.890 | 0.002 | 1.737 - Y O utput Stabilization | Uniform | -1 | 1 | -0.017 | -0.049 | 0.014 - e Exchange Rate Stabilization | Uniform | 0 | 3 | 2.438 | 1.852 | 3.000 - b Habit Persistence | Beta | 0.5 | 0.2 | 0.499 | 0.150 | 0.885 - # d Cost of Non-tradable G oods Price Adjustm ent | G am m a | 100 | 200 | 118.220 | 84.184 | 151.489 - # m Cost of Im p orted G oods Price Adjustm ent | G am m a | 100 | 200 | 100.043 | 67.992 | 151.489 -  1 Capital Stock Adjustm ent Costs | G am m a | 122 | 23.008 | 19.430 | 26.462 - Elasticity of External Finance Prem ium | Beta | 0.07 | 0.02 | 0.057 | 0.038 | 0.074 -   Technology Shock Persistence | Beta | 0.8 | 0.1 | 0.808 | 0.658 | 0.959 -  i  Foreign Interest Rate Shock Persistence | Beta | 0.8 | 0.1 | 0.831 | 0.718 | 0.945 -    Foreign Ináation Shock Persistence | Beta | 0.8 | 0.1 | 0.785 | 0.643 | 0.948 -   Markup Shock Persistence | Beta | 0.8 | 0.1 | 0.860 | 0.731 | 0.978 -  uip UIP Shock Persistence | Beta | 0.8 | 0.1 | 0.794 | 0.654 | 0.931 -  l Labour Supply Shock Persistence | Beta | 0.8 | 0.1 | 0.806 | 0.650 | 0.966 -  c Marginal Utility Shock Persistence | Beta | 0.8 | 0.1 | 0.810 | 0.658 | 0.959 -  in Investm ent E¢ ciency Shock Persistence | Beta | 0.8 | 0.1 | 0.785 | 0.640 | 0.947 -  Q x Exp ort Elasticity Shock Persistence | Beta | 0.8 | 0.1 | 0.857 | 0.759 | 0.961 -  G G overnm ent Sp ending Shock Persistence | Beta | 0.8 | 0.1 | 0.640 | 0.465 | 0.821 -  n Borrowing Cost Shock Persistence | Beta | 0.8 | 0.1 | 0.809 | 0.675 | 0.958 -  v Survival Rate Shock Persistence | Beta | 0.8 | 0.1 | 0.805 | 0.656 | 0.958 - "  Size of Technology Shock | InvG am m a | 0.005 | Inf | 0.005 | 0.001 | 0.009 - " i  Size of Foreign Interest Rate Shock | InvG am m a | 0.001 | Inf | 0.001 | 0.000 | 0.002 - "   Size of Foreign Ináation Shock | InvG am m a | 0.001 | Inf | 0.001 | 0.000 | 0.002 - "  Size of Markup Shock | InvG am m a | 1 | Inf | 1.198 | 0.270 | 2.219 - " uip Size of UIP Shock | InvG am m a | 0.001 | Inf | 0.001 | 0.000 | 0.002 - " l Size of Labour Supply Shock | InvG am m a | 0.01 | Inf | 0.010 | 0.002 | 0.021 - " c Size of Marginal Utility Shock | InvG am m a | 0.01 | Inf | 0.016 | 0.003 | 0.028 - " i Size of M onetary Policy Shock | InvG am m a | 0.005 | Inf | 0.004 | 0.002 | 0.007 - " in Size of Investm ent E¢ ciency Shock | InvG am m a | 0.05 | Inf | 0.048 | 0.012 | 0.092 - " Q x Size of Exp ort Elasticity Shock | InvG am m a | 0.1 | Inf | 0.320 | 0.190 | 0.454 - " G Size of G overnm ent Sp ending Shock | InvG am m a | 0.01 | Inf | 0.068 | 0.052 | 0.083 - " n Size of Borrowing Cost Shock | InvG am m a | 0.001 | Inf | 0.002 | 0.000 | 0.004 - " v Size of Survival Rate Shock | InvG am m a | 0.001 | Inf | 0.002 | 0.000 | 0.004 *Italic: Source PDF: _wp1021 - References* --- _Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp1021.pdf_