The establishment of appropriate liabilities for losses and loss expenses is an inherently uncertain process, and we can provide no assurance that our insurance subsidiaries’ ultimate liabilities for losses and loss expenses will not exceed their loss and loss expense reserves and have an adverse effect on our results of operations and financial condition. Furthermore, we cannot predict the timing, frequency and extent of adjustments to our insurance subsidiaries’ estimated future liabilities, because the historical conditions and events that serve as a basis for our insurance subsidiaries’ estimates of ultimate claim costs may change. As is the case for substantially all property and casualty insurance companies, our insurance subsidiaries have found it necessary in the past to increase their estimated future liabilities for losses and loss expenses in certain periods, and, in other periods, their estimated future liabilities for losses and loss expenses have exceeded their actual liabilities for losses and loss expenses. Changes in our insurance subsidiaries’ estimate of their liabilities for losses and loss expenses generally reflect actual payments and their evaluation of information received subsequent to the prior reporting period.

We summarize activity in our insurance subsidiaries’ liabilities for losses and loss expenses as follows:


	Nine Months Ended September 30,
	2021			2020

	(in thousands)
Balance at January 1	$	962,007		$	869,674
Less reinsurance recoverable		(404,818	)		(362,768	)

Net balance at January 1		557,189			506,906

Incurred related to:
Current year		407,193			353,798
Prior years		(25,874	)		(10,321	)

Total incurred		381,319			343,477

Paid related to:
Current year		183,165			169,610
Prior years		149,910			139,024

Total paid		333,075			308,634

Net balance at end of period		605,433			541,749
Plus reinsurance recoverable		444,730			400,181

Balance at end of period	$	1,050,163		$	941,930

Our insurance subsidiaries

recognized a decrease in their liabilities for losses and loss expenses of prior years of $

25.9

million

and $10.3 million for the nine months ended September 30, 2021 and 2020, respectively. Our insurance sub

idiaries made no significant changes in their reserving philosophy or claims management personnel, and they have made no significant offsetting changes in estimates that increased or decreased their loss and loss expense reserves in those years. The 2021 development represented

4.6

% of the December 31, 2020 net carried reserves and resulted primarily from lower-than-expected loss emergence or severity in nearly all lines of business. The majority of the 2021 development related to decreases in the liabilities for losses and loss expenses of prior years for Atlantic States and MICO. The 2020 development represented 2.0% of the December 31, 2019 net carried reserves and resulted primarily from lower-than-expected severity in nearly all lines of business, with the exception of modest higher-than-expected severity in commercial automobile. The majority of the 2020 development related to decreases in the liabilities for losses and loss expenses of prior years for Atlantic States and MICO.

Short-duration contracts are contracts for which our insurance subsidiaries receive premiums that they recognize as revenue over the period of the contract in proportion to the amount of insurance protection our insurance subsidiaries provide. Our insurance subsidiaries consider the policies they issue to be short-duration contracts. We consider the material lines of business of our insurance subsidiaries to be personal automobile, homeowners, commercial automobile, commercial multi-peril and workers’ compensation.

Our insurance subsidiaries determine incurred but not reported (“IBNR”) reserves by subtracting the cumulative loss and loss expense amounts our insurance subsidiaries have paid and the case reserves our insurance subsidiaries have established at the balance sheet date from their actuaries’ estimate of the ultimate cost of losses and loss expenses. Accordingly, the IBNR reserves of our insurance subsidiaries include their actuaries’ projections of the cost of unreported claims as well as their actuaries’ projected development of case reserves on known claims and reopened claims. Our insurance subsidiaries’ methodology for estimating IBNR reserves has been in place for many years, and their actuaries made no significant changes to that methodology during the nine months ended September 30, 2021.

The actuaries for our insurance subsidiaries generally prepare an initial estimate for ultimate losses and loss expenses for the current accident year by multiplying earned premium by an expected loss ratio for each line of business our insurance subsidiaries write. Expected loss ratios represent the actuaries’ expectation of losses at the time our insurance subsidiaries price and write their policies and before the emergence of any actual claims experience. The actuaries determine an expected loss ratio by analyzing historical experience and adjusting for loss cost trends, loss frequency and severity trends, premium rate level changes, reported and paid loss emergence patterns and other known or observed factors.

The actuaries use a variety of actuarial methods to estimate the ultimate cost of losses and loss e

penses. These methods include paid loss development, incurred loss development and the Bornhuetter-Ferguson method. The actuaries base their selection of a point estimate on a judgmental weighting of the estimates each of these methods produce.

The actuaries consider loss frequency and severity trends when they develop expected loss ratios and point estimates. Loss frequency is a measure of the number of claims per unit of insured exposure, and loss severity is a measure of the average size of claims. Factors that affect loss frequency include changes in weather patterns and economic activity. Factors that affect loss severity include changes in policy limits, reinsurance retentions, inflation rates and judicial interpretations.

Our insurance subsidiaries create a claim file when they receive notice of an actual demand for payment, an event that may lead to a demand for payment or when they otherwise determine that a demand for payment could potentially lead to a future demand for payment on another coverage under the same policy or another policy they have issued. In recent years, our insurance subsidiaries have noted an increase in the period of time between the occurrence of a casualty loss event and the date at which they receive notice of a liability claim. Changes in the length of time between the loss occurrence date and the claim reporting date affect the actuaries’ ability to predict loss frequency accurately and the amount of IBNR reserves our insurance subsidiaries require.

Our insurance subsidiaries generally create a claim file for a policy at the claimant level by type of coverage and generally recognize one count for each claim event. In certain lines of business where it is common for multiple parties to claim damages arising from a single claim event, our insurance subsidiaries recognize one count for each claimant involved in the event. Atlantic States recognizes one count for each claim event, or claimant involved in a multiple-party claim event, related to losses Atlantic States assumes through its participation in its pooling agreement with Donegal Mutual. Our insurance subsidiaries accumulate the claim counts and report them by line of business.