## Financial Constraints, Productivity, and Investment: Evidence from Lithuania — Introduction, Methodology, and Age-Size Results

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### Overview and research question
- Research question: Do financial constraints limit firms’ investment and productivity growth in Lithuania, and how could policies improve firm access to finance?
- Data and scope: administrative firm-level data covering the entire population of active firms in Lithuania from 2000–2018 (with exclusions noted below).
- Motivation: Lithuania is a converging economy with a developing financial system; administrative data provide high coverage of micro and small firms enabling analysis across firm ability and desire to invest.

### Measure of financial constraints and empirical approach
- Concept: measure captures gap between existing and desired financing for investment and combines information on both firms’ ability and desire to finance investments.
- Classification and index construction:
  - Firms classified into constrained and unconstrained using balance-sheet information (investment, cash holdings, changes in debt) and asset-side/liability-side rules (Cases I–V mapped to unconstrained "U" and constrained "C"; score 0 for "U" and 1 for "C").
  - Binary classification transformed into continuous index by estimating an ordered probit regression of the constrained dummy on firm characteristics (size, age, cash holdings, debt-to-asset ratios) and taking the predicted probability as FC_it.
  - Ordered probit specification: Pr(I_i,t = j) = X_i,t−1 μ + c_i + u_it, j ∈ {0,1}.
- Validation: interest payment data (available after 2016) used to test validity; median interest rate by sector/year compared to average index (Table 8).

### Key methodological details and thresholds
- Financial gap defined as fixed investment minus cash flow.
- Classification cases (I–V) use thresholds and debt quartiles; sample-based thresholds:
  - 푐̅1 = 0.2
  - 푐̅2 = 1
  - 푐̅3 = 0.5
- Robustness: 푐̅1 varied from 0.05 to 0.3 in 0.05 intervals; 푐̅3 varied from 0.40 to 0.80; 푐̅2 changed to 2 and 3; results remain robust.
- Sample handling:
  - Size dummies based on employment for micro, small, medium, and large firms; main analysis excludes micro firms (firms with less than 10 employees).
  - Data cleaning: drop top and bottom 1 percent of debt ratio, fixed assets, investment, profits, cash holdings, and sales; exclude profit-to-sales ratio outside [-1,1], negative sales, and negative investment ratio.

### Main empirical findings (investment and productivity effects)
- Average relationships:
  - Constrained firms, on average, show lower investment and lower labor productivity; relationships are economically and statistically significant.
- Regression magnitudes (selected reported coefficients):
  - Ordered probit (L.debt ratio): 0.850∗∗∗, 0.853∗∗∗, 0.751∗∗∗, 0.532∗∗∗ across columns (1)–(4).
  - Ordered probit (L.cash/sales): -1.983∗∗∗, -1.976∗∗∗, -1.570∗∗∗, -1.029∗∗∗ across columns (1)–(4).
  - Effect of lagged FC on ln(productivity): -0.0585∗∗∗ (standard error (0.0203)).
  - Effect of lagged FC on ln(investment): -0.821∗∗∗ (standard error (0.0818)).
- Counterfactual and back-of-the-envelope calculations:
  - Average index is 0.15 points higher for the constrained class versus unconstrained class.
  - 59 percent of firms are categorized as constrained.
  - Removing financial constraints (given firm characteristics) increases average firm labor productivity by roughly 0.51 percent (calculation: 0.59 * 0.15 * 0.058).
  - Removing financial constraints increases average firm investment by roughly 7.2 percent.
  - Counterfactual for 2018: removing firm financial constraints that were in place in 2018 would improve average labor productivity and investment by 0.47 percent and 6.7 percent, respectively.

### Firm age, size, and nonlinear interactions (Section 4.4)
- Core patterns:
  - Firm size and firm age are negatively related to the measure of financial constraints: smaller and younger firms have more difficulty accessing liquidity for investment.
  - For each size class, age and financial constraints are negatively related: younger firms of a given size group are more likely to be financially constrained.
  - Non-linear relationship: among young firms (age group 0-5), large firms are more likely to be financially constrained; among older firms (particularly ages above 10), smaller firms become more likely to be financially constrained.
- Interaction effects reported:
  - Interaction of debt ratio with size: higher debt leads to higher probability of being constrained for smaller firms; old firms with higher debt ratio have higher probability of being constrained.
  - Interaction of cash with age and size has limited explanatory power.
- Table 6 — Effect of Age and Size on the Likelihood of Being Constrained (cell values are sums of relevant coefficients):
  - Columns: 0-5 | 6-10 | 11-15 | 15+
  - Small (10-49): 0-5: - (reference group); 6-10: 0.031*; 11-15: -0.005; 15+: -0.057*
  - Med (50-249): 0-5: 0.108***; 6-10: 0.102; 11-15: 0.028***; 15+: -0.082**
  - Large (250+): 0-5: 0.091; 6-10: 0.070; 11-15: -0.038*; 15+: -0.223***
  - Significance notation: * p < .10, ** p < .05, *** p < .01.
- Transition dynamics (Table 7):
  - Unconstrained → Unconstrained: 52.90
  - Unconstrained → Constrained: 47.10
  - Constrained → Unconstrained: 28.65
  - Constrained → Constrained: 71.35
  - Total row: Unconstrained 37.10 | Constrained 62.90 | Total 100

### Data coverage, sample construction, and descriptive statistics
- Universe and exclusions:
  - Dataset covers the entire population of active firms in Lithuania from 2000 to 2018.
  - Exclusions: sole proprietorships or associations (unlimited liability business forms), public firms, firms in the financial sector, insurance services and public administration, and observations that may violate data confidentiality requirements.
  - Coverage reported: close to 95 percent of active firms in the Lithuanian economy (Constantinescu and Proskute, 2019).
- Sample cleaning rules:
  - Drop firms with negative sales, assets below five thousand euros, and firms whose maximum employment never exceeds two over their lifetime.
  - Final sample after filtering: 669,820 unique observations and 86,209 unique firms.
- Firm population features:
  - Firms’ average age during the period is slightly over nine years.
  - Firm average age increases from 4.6 to 12.6 years during the study period.
  - For firms where Register Date is missing, firm age is calculated using the first year the firm appears in the data.
- Selected 2018 sector and size summaries (Table 1 excerpts):
  - Observations by sector: 88,859; 23,826; 67,163; 213,418; 88,592; 60,513; 90,030.
  - Firms by sector: 12,486; 3,634; 9,991; 30,256; 13,434; 11,074; 14,796.
  - Employees (Mean) by sector: 44.1; 18.2; 25.4; 16.3; 11.4; 22.6; 27.5.
  - Employees (Median) by sector: 13; 6; 7; 6; 5; 8; 9.
  - Assets (Mean, log of total real assets) by sector: 7.6; 7.0; 7.4; 7.4; 6.6; 6.7; 7.5.
  - Assets (Median, log) by sector: 7.4; 6.8; 7.3; 7.3; 6.4; 6.4; 7.3.
  - Firm size counts by sector (Small / Medium / Large): 35,632 / 13,799 / 2,669; 5,905 / 1,281 / 168; 19,646 / 4,278 / 720; 55,953 / 8,479 / 885; 19,939 / 2,570 / 217; 20,792 / 3,834 / 688; 31,103 / 9,816 / 1,142.
  - Age (Mean) by sector: 9.7; 8.6; 8.5; 9.1; 8.5; 8.3; 8.4.
- Sector notes:
  - High skilled service sectors include education, entertainment, health, and professional services.
  - Low skilled services include hotels, restaurants, support services and other services.
  - The final column “Other” contains agriculture, mining, electricity, construction, and utilities.
  - SME definition: all firms below 250 employees; includes micro-firms.
  - Assets are presented as log of total real assets of firms.

### Policy implications and recommendations
- Targeting: in a converging economy with rapid financial deepening like Lithuania, improving access to finance for a select group of firms could further boost productivity and investment growth.
- Priority group identified: young and large firms with high potential for further growth are expected to show the greatest return to alleviating access to finance.
- Practical targeting variables: firm size and age are easy to observe and, when combined, effectively predict financial constraints—useful to minimize administrative burdens and improve targeting of capital-deepening policies.
- Potential sources of constraints to address:
  - Due diligence processes of creditors.
  - Lack of financial instruments for firms’ financing needs.
  - Firms’ awareness and knowledge of financing options.
  - Firms’ reporting practices.
- Recommendation: prioritize efforts to identify constrained firms and to understand the sources of constraints to enhance capital allocation and support sustained economic convergence over the medium- and long-run.

*IMF Working Paper — “Financial Constraints, Productivity, and Investment: Evidence from Lithuania” — Introduction, Methodology, and chapter section 4.4.*

### 1.  Introduction .......................................................................................................

### 1.  Introduction

### Overview
- Research question: Do financial constraints limit firms’ investment and productivity growth in Lithuania, and how could policies improve firm access to finance?
- Data and scope: administrative firm-level data covering the entire population of active firms in Lithuania from 2000–2018 (with exclusions noted below).
- Motivation: Lithuania is a converging economy with a developing financial system; administrative data provide high coverage of micro and small firms enabling analysis across firm ability and desire to invest.

### Measure of financial constraints and empirical approach
- Concept: A good measure of financial constraint should capture the gap between existing and desired financing for investment and combine information on both firms’ ability and desire to finance investments.
- Method summary:
  - Classify firms into constrained and unconstrained using information from both liability and asset sides of balance sheets, combining multiple financial variables (investment, cash holdings, changes in debt).
  - Transform binary classification into a continuous index by estimating an ordered probit regression of the constrained dummy on firm characteristics including size, age, cash holdings, and debt-to-asset ratios.
  - Take the predicted probability from the ordered probit as the index of financial constraints.
- Empirical models: regressions of investment and firm-level labor productivity (value added per employee) on the continuous index, controlling for firm characteristics and firm and time-sector fixed effects.

### Main findings
- Constrained firms, on average, show lower investment and lower labor productivity; relationships are economically and statistically significant.
- Estimated impacts (back-of-the-envelope calculations):
  - Removing financial constraints (given firm characteristics) increases average firm labor productivity by roughly 0.51 percent.
  - Removing financial constraints increases average firm investment by roughly 7.2 percent.
- Counterfactual for 2018: removing firm financial constraints that were in place in 2018 would improve average labor productivity and investment by 0.47 percent and 6.7 percent, respectively.
- Age and size are important predictors of financing constraints with non-linear interactions:
  - Among young firms, large firms have a higher predicted probability of being constrained.
  - Among older firms, smaller firms are more likely to be constrained.
  - Interpretation: the measure captures both desire and ability to borrow; large young firms may have high growth potential but limited access to external financing.

### Policy implications and recommendations
- Targeting: In a converging economy with rapid financial deepening like Lithuania, improving access to finance for a select group of firms could further boost productivity and investment growth.
- Priority group identified: young and large firms with high potential for further growth.
- Practical targeting variables: firm size and age are easy to observe and, when combined, effectively predict financial constraints—useful to minimize administrative burdens and improve targeting of capital-deepening policies.

### Data coverage and sample characteristics
- Universe and exclusions:
  - Dataset covers the entire population of active firms in Lithuania from 2000 to 2018.
  - Exclusions: sole proprietorships or associations (unlimited liability business forms), public firms, firms in the financial sector, insurance services and public administration, and observations that may violate data confidentiality requirements.
  - Coverage reported: close to 95 percent of active firms in the Lithuanian economy (Constantinescu and Proskute, 2019).
- Sample cleaning: drop firms with negative sales, assets below five thousand euros, and firms whose maximum employment never exceeds two over their lifetime.
- Final sample after filtering: 669,820 unique observations and 86,209 unique firms.
- Firm population features:
  - Lithuania is a transition economy with a young firm population; firms’ average age during the period is slightly over nine years.
  - Firm average age increases from 4.6 to 12.6 years during the study period.
  - For firms where Register Date is missing, firm age is calculated using the first year the firm appears in the data.
- Table 1 (selected sector and size statistics, year 2018 sample counts and summaries):
  - Observations by sector: 88,859; 23,826; 67,163; 213,418; 88,592; 60,513; 90,030.
  - Firms by sector: 12,486; 3,634; 9,991; 30,256; 13,434; 11,074; 14,796.
  - Employees (Mean) by sector: 44.1; 18.2; 25.4; 16.3; 11.4; 22.6; 27.5.
  - Employees (Median) by sector: 13; 6; 7; 6; 5; 8; 9.
  - Assets (Mean, log of total real assets) by sector: 7.6; 7.0; 7.4; 7.4; 6.6; 6.7; 7.5.
  - Assets (Median, log) by sector: 7.4; 6.8; 7.3; 7.3; 6.4; 6.4; 7.3.
  - Firm size counts by sector (Small / Medium / Large): 35,632 / 13,799 / 2,669; 5,905 / 1,281 / 168; 19,646 / 4,278 / 720; 55,953 / 8,479 / 885; 19,939 / 2,570 / 217; 20,792 / 3,834 / 688; 31,103 / 9,816 / 1,142.
  - Age (Mean) by sector: 9.7; 8.6; 8.5; 9.1; 8.5; 8.3; 8.4.
- Sector notes:
  - High skilled service sectors include education, entertainment, health, and professional services.
  - Low skilled services include hotels, restaurants, support services and other services.
  - The final column “Other” contains agriculture, mining, electricity, construction, and utilities.
  - SME definition: all firms below 250 employees; includes micro-firms.
  - Assets are presented as log of total real assets of firms.

### Literature connections
- Builds on cross-country and firm-level literature linking financial development and access to external financing to growth (Rajan and Zingales, 1996; Chen and Guariglia, 2013; Ferrando and Ruggieri, 2018, among others).
- Methodological approach follows Pal and Ferrando (2010) and Ferrando and Ruggieri (2018) in combining multiple balance-sheet variables to construct measures of financial constraint.
- Aligns with Hadlock and Pierce (2010) on the predictive power of firm age and size for financial constraints, and extends by documenting nonlinear age-size interactions in a transition-economy context.

*IMF Working Paper — “Financial Constraints, Productivity, and Investment: Evidence from Lithuania” — Introduction chapter (pages 3–8).*

### 3. Methodology

### 3. Methodology

### 3.1 Measure of Financial Constraints
- Objective: create a clean measure of financial constraints from firms’ balance sheet data using asset-side and liability-side information; classify firms into groups with various degrees of financial constraint following Ferrando and Ruggieri (2018) and Pal and Ferrando (2010).
- Rationale: avoids endogeneity of firm financial decisions and high data requirements of exogenous measures; trade-off is that not all firms can be categorized, reducing sample size.
- Financial gap definition: fixed investment minus cash flow.
- Classification scheme (Table 2): five cases (I–V) grouped into unconstrained "U" and constrained "C"; score 0 assigned to "U" and 1 to "C".
  - Case I: investing (investment > 0), cash ≥ investment, ∆Debt > 0, and asset liquidation limited by threshold 푐̅1.
  - Case II: disinvesting (investment < 0), cash ≥ investment, ∆Debt > 0.
  - Case III: investing (investment > 0), cash < investment, ∆Debt > 0.
  - Case IV: disinvesting (investment < 0), cash < investment, ∆Debt < 0, and debt quartile > 푐̅2.
  - Case V: investing condition and asset liquidation below threshold 푐̅3 (as presented in Table 2).
- Time-series patterns and persistence:
  - Share of constrained firms rose to highest value after 2009 and stabilized at roughly 55 percent in subsequent years.
  - Transition matrix (Table 7): roughly 53 percent of unconstrained firms remain unconstrained next period; about 47 percent become constrained. About 71 percent of constrained firms remain constrained; roughly 29 percent become unconstrained.

- Note on sample coverage: to mitigate uncategorized firms, classification outcomes are used to estimate an ordered probit model and predict constraint probabilities for firms out of sample; results robust to excluding predicted firms.

### 3.2 Empirical Strategy
- Goal: convert classification into a continuous index of financial constraint and estimate effects on productivity and investment.
- Index construction:
  - Estimate an ordered probit regression with the classification as dependent variable (I_i,t ∈ {0,1}, j = 0 unconstrained, j = 1 constrained).
  - Regressors X_i,t−1 include firm characteristics (age, size, industry, year dummies) and financial outcomes (leverage, cash holdings) and interactions with firm size and age. All regressors lagged one period.
  - Firm-specific time-invariant terms c_i included following Chamberlain (1979) to account for correlation between unobserved and observed firm characteristics.
  - Predicted conditional probability from the ordered probit is denoted FC_it and used as the continuous financial-constraint index.
- Validation:
  - Use interest payment data (available only after 2016) to test validity: higher interest rates expected to be associated with higher likelihood of being constrained; median interest rate calculated by sector and year and compared to average index.
- Ordered probit specification (text form):
  - Pr(I_i,t = j) = X_i,t−1 μ + c_i + u_it, j ∈ {0,1}.
- Sample note:
  - Size dummies based on employment for micro, small, medium, and large firms; main analysis excludes micro firms (firms with less than 10 employees).

### 3.3 Financial Constraints, Labor Productivity, and Investment
- Labor productivity measure:
  - Value added of a firm, deflated, divided by number of employees.
  - Natural log of firm-specific labor productivity ln(prod_i,t) used as dependent variable.
  - Regression specification:
    - ln(prod_i,t) = δ_i + δ_st + β0 + β1 FC_i,t−1 + β2 ln(prod_i,t−1) + β_ch X_i,t−1^ch + β_FC W_i,t−1^FC + ε_i,t
    - δ_i: firm fixed effects; δ_st: sector-year fixed effects; standard errors clustered at the fixed-effect level; all explanatory variables lagged one period.
  - W_i,t−1^FC includes debt ratio and cash-to-sales ratio.
  - X_ch contains firm size, firm age, and interactions with FC index.
- Investment specification:
  - Investment at time t defined as change in fixed assets from time t−1 to time t plus depreciation; zero values handled by adding one before log transformation.
  - Regression specification:
    - ln(investment_i,t) = δ_i + δ_st + β0 + β1 FC_i,t−1 + β2 ln(prod_i,t−1) + β_ch X_i,t−1^ch + β_FC W_i,t−1^FC + ν_i,t
  - Rationale: include ln(prod_i,t−1) instead of ln(investment_i,t−1) to mitigate attenuation bias due to investment volatility.
  - W^FC includes debt and cash; X_ch contains firm size, firm age, and interactions with FC index.
- Robustness checks:
  - Results robust to ordered logit specification.
  - Multicollinearity checks performed because some regressors used in FC construction also appear in outcome specifications.
  - Data cleaning: drop top and bottom 1 percent of debt ratio, fixed assets, investment, profits, cash holdings, and sales; exclude profit-to-sales ratio outside [-1,1], negative sales, and negative investment ratio.

### 4. Sample construction and classification cutoffs (from Methodology into Results)
- Threshold choices used to categorize firms (Section 4, based on Table 2):
  - 푐̅1 = 0.2 (limit on extent of asset liquidation for unconstrained classification).
  - 푐̅2 = 1 (firms above the first debt quartile in the data).
  - 푐̅3 = 0.5 (cutoff for liquidation that categorizes firms as constrained).
  - Debt quartiles defined on four-digit NACE sectors for each year.
- Robustness: 푐̅1 varied from 0.05 to 0.3 in 0.05 intervals; 푐̅3 varied from 0.40 to 0.80; 푐̅2 changed to 2 and 3; results remain robust.

### Key empirical results (methodology-linked estimates reported in Section 4)
- Ordered probit index estimation (Table 4):
  - L.debt ratio coefficients: 0.850∗∗∗, 0.853∗∗∗, 0.751∗∗∗, 0.532∗∗∗ across columns (1)–(4).
  - L.cash/sales coefficients: -1.983∗∗∗, -1.976∗∗∗, -1.570∗∗∗, -1.029∗∗∗ across columns (1)–(4).
  - Observations: 77,636 for columns (1)–(3); 107,917 for column (4).
  - Age groups: 0–5, 6–10, 11–15, 15+ years. Size groups: 10–49, 50–249, 250+ employees.
- Effects of financial constraints on productivity and investment (Table 5):
  - Coefficient on lagged FC (L.FC) in ln(productivity): -0.0585∗∗∗ (standard error (0.0203)).
  - Coefficient on L.FC in ln(investment): -0.821∗∗∗ (standard error (0.0818)).
  - Interpretation and counterfactual:
    - Average index is 0.15 points higher for the constrained class versus unconstrained class.
    - 59 percent of firms are categorized as constrained.
    - Removing financial constraints counterfactual: 0.59 * 0.15 * 0.058 ~ 0.51% (implied increase in labor productivity).
    - Under the scenario in which firms are not financially constrained, average firm-level investment is expected to increase by roughly 7.2 percent.

*Source: 3. Methodology (Content unit: wpiea2022249-print-pdf - 3. Methodology)*

### 4.4 Financial Constraints, Firm Age, and Size

### 4.4 Financial Constraints, Firm Age, and Size

### Key findings
- Firm size and firm age are negatively related to the measure of financial constraints: smaller and younger firms have more difficulty accessing liquidity for investment.
- For each size class, age and financial constraints are negatively related: younger firms of a given size group are more likely to be financially constrained.
- Size, age, and financial constraints display a non-linear relationship:
  - Among young firms (age group 0-5), large firms are more likely to be financially constrained.
  - As firms grow older (particularly ages above 10), smaller firms become more likely to be financially constrained.
- Interaction effects:
  - The interaction of debt ratio with size suggests that higher debt leads to a higher probability of being constrained for smaller firms, while old firms having higher debt ratio have a higher probability of being constrained.
  - The interaction of cash with age and size does not have high explanatory power.

### Table 6 — Effect of Age and Size on the Likelihood of Being Constrained (cell values are sums of relevant coefficients)
- Columns: 0-5 | 6-10 | 11-15 | 15+
- Small (10-49):
  - 0-5: - (reference group; no value reported)
  - 6-10: 0.031*
  - 11-15: -0.005
  - 15+: -0.057*
- Med (50-249):
  - 0-5: 0.108***
  - 6-10: 0.102
  - 11-15: 0.028***
  - 15+: -0.082**
- Large (250+):
  - 0-5: 0.091
  - 6-10: 0.070
  - 11-15: -0.038*
  - 15+: -0.223***

- Significance notation reproduced from source:
  - * p < .10, ** p < .05, *** p < .01.
- Note: The reference group is small and young firms. Size is based on number of employees; definitions in parentheses.

### Implications and policy recommendations
- Removing financial constraints can yield measurable gains:
  - Improvement in average labor productivity by .51 percent.
  - Improvement in investment by 7.2 percent.
- In the context of Lithuania, young and large firms are expected to show the greatest return to alleviating access to finance.
- Policy approaches should be targeted to the nature of constraints faced by specific firms. Potential sources of constraints include:
  - Due diligence processes of creditors.
  - Lack of financial instruments for firms’ financing needs.
  - Firms’ awareness and knowledge of financing options.
  - Firms’ reporting practices.
- Prioritizing efforts to identify constrained firms and to understand the sources of constraints will help policymakers enhance capital allocation and support sustained economic convergence over the medium- and long-run.

### Additional empirical statistics reported in the chapter
- Transition matrix (Table 7: probability of staying or switching class in subsequent period; rows sum to 100):
  - Category row: Unconstrained | Constrained | Total
  - Unconstrained: 52.90 | 47.10 | 100
  - Constrained: 28.65 | 71.35 | 100
  - Total: 37.10 | 62.90 | 100
- Table 8: Probability of Being Constrained Based on Interest Rate (i ≤ median | i > median)
  - 2016: 0.49 | 0.54
  - 2017: 0.48 | 0.54
  - 2018: 0.49 | 0.55

### Regression evidence linking constraints to productivity and investment (selected reported magnitudes)
- Removing constraints associated with:
  - Average labor productivity improvement: .51 percent
  - Investment improvement: 7.2 percent
- Regression table highlights (selected coefficients and significance as reported):
  - L.ln((productivity)): 0.255*** (in multiple specifications)
  - L.debt ratio: 0.175***; 0.177***; 0.176***; 0.157*** (across specifications)
  - L.cash to sales: -0.0230; -0.0226; 0.00207; 0.0343 (across specifications)
  - L.constrained: -0.0585***; -0.0616**; -0.135**; -0.120* (across specifications)
  - Interaction L.med×L.constrained: -0.0671***; -0.0789*** (specifications reported)
  - Interaction L.large×L.constrained: -0.0478; -0.125 (specifications reported)
- Model fit and sample sizes (as reported):
  - R-squared: 0.755; 0.755; 0.755; 0.762
  - Obs: 95977; 95977; 95977; 110770

*Source: IMF Working Paper — chapter section 4.4 Financial Constraints, Firm Age, and Size.*

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_Source: https://www.imf.org/-/media/files/publications/wp/2022/english/wpiea2022249-print-pdf.pdf_